tag:blogger.com,1999:blog-86562088937011721332024-03-05T06:22:11.661-08:00New Science FutureThe equation likes relativity, scrodinger, bernouli, plank, pythagoras, ricatti, newton, etc are wrong. The SMT (Stable modulation technique) is the best only one equation on the world and Ali Yunus Rohedi is the man.CGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.comBlogger19125tag:blogger.com,1999:blog-8656208893701172133.post-29693540947199749882008-10-15T03:03:00.000-07:002008-10-15T03:12:11.132-07:00Introducing Bernoulli Integral For Solving Some Physical Problems<p style="text-align: justify;"> <span class="awal">S</span>ome of both modeling and problems in physics have been commonly presented in a first-order nonlinear differential equations (DE) of constant coefficients. Because the DE are integrable, therefore one must have an integral formulation for solving the physical problems. This paper introduces Bernoulli integral to complete the Tables of Integral for all of the Mathematical Handbooks. </p><div style="text-align: justify;"> Basically, the Bernoulli integral is integral form of the homogeneous Bernoulli differential equation (BDE) of constant coefficients. Under proper transformation, the Bernoulli integral can be used to generate another integral formulation especially for integrals that can be transformed into arctangent DE. By using the Bernoulli integral, one can create its self the integral formulation of solving the physical problems, and hence reduces utilization the tables of integral. A special application in generating Euler formula also presented. </div><p style="text-align: justify;"> </p><div style="text-align: justify;"> </div><p style="text-align: justify;"> <b>Introduction</b> </p><div style="text-align: justify;"> </div><p style="text-align: justify;"> Some of both modeling and problems in physics have been commonly presented in a first-order nonlinear differential equations (DE) of constant coefficients For instance, in designing electromagnetic apparatus [Markus,1979], the logistic growth process [Welner,2004], chaotic behavior [Barger et al,1995], the generation and propagation of soliton [Wu et al 2005],[Morales,2005], the transport of fluxon [Gonzile et al,2006], the generation of squeezed laser [Friberg,1996 ],etc. One requires Table of Integral to solve a specific integral for solving such differential equation [Spiegel,MR,1968]. To complete the Table of integral, we introduce Bernoulli integral that until now not including in both of the Table integral and mathematical Handbook. By using the Bernoulli integral, one can create the integral formulation required in solving the physical problems, and hence reduces utilization the Tables of integral.<br /></p><p style="text-align: justify;"><span style="color: rgb(255, 0, 0);font-size:85%;" >Key-words : Arctangent, tangent, arctangent differential equation, Bernoulli equation, Bernoulli differential equation, integral, Bernoulli integral, Schrödinger equation, modulation instability, Euler formula, Argand diagram, electromagnetic, logistic growth, chaotic, soliton, fluxon, squeezed laser</span></p><p style="text-align: justify;">For Detail<br /></p><p style="text-align: justify;">Visit <a href="http://rohedi.com/">http://rohedi.com</a> or<br />Download <a href="http://rohedi.com/component/option,com_docman/task,doc_download/gid,28/Itemid,99999999/">Here</a></p>CGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com1tag:blogger.com,1999:blog-8656208893701172133.post-90501129762434987102008-09-23T23:43:00.000-07:002008-10-16T18:10:05.812-07:00Fighting of the Cause of Allah by Governing a Smart Mathematics Based on Islamic Teology<span class="awal">E</span>xistence of the universe is reality evidence of supremacy and science fame of God Allah SWT. Inking seven of times water in all ocean world (even more) not enough to write down it. According to writer, mathematical model which representatively as stepping in developing the Islamic Scientific is arctangent differential equation <p style="text-align: justify;"> </p><div style="text-align: justify;"> </div><p style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOoK-PIZBCP9azxkkpwyCW3Jc3NI-ARWoB-KeZFZa2LJGyWnwa2KXDgDn5IRLVUuc7HZdaU4WuPXEaBDXc4Kv1ZBG5l-PxFTP3WjzyQfqy8j4yDtaA_QWID3qm8RdgbMcINojE5ETW6V2Y/s1600-h/revisiprs1.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgOoK-PIZBCP9azxkkpwyCW3Jc3NI-ARWoB-KeZFZa2LJGyWnwa2KXDgDn5IRLVUuc7HZdaU4WuPXEaBDXc4Kv1ZBG5l-PxFTP3WjzyQfqy8j4yDtaA_QWID3qm8RdgbMcINojE5ETW6V2Y/s200/revisiprs1.JPG" alt="" id="BLOGGER_PHOTO_ID_5257923755476967922" border="0" /></a>Eqs.(1)<br /></p><p style="text-align: justify;"><br /></p><div style="text-align: justify;"> which its exact solution is of the form:</div><p style="text-align: justify;"> <img src="http://rohedi.com/images/stories/jihat_image2.gif" alt="jihat_image2.gif" title="jihat_image2.gif" style="margin: 5px; float: left; width: 294px; height: 50px;" height="50" width="294" /> </p><div style="text-align: justify;"> </div><p style="text-align: justify;"><br /></p><p style="text-align: justify;">Eqs.(2)<br /></p><p style="text-align: justify;"><br /></p><div style="text-align: justify;"> Because of writer looks into this arctangent differential equation is having the religion character<br />(according to writer that for a=1, b=1, and both of initial values <i>t</i><sub>0 </sub>= 0 dan <i>y</i><sub>0</sub> = 0 the value <img src="http://rohedi.com/images/stories/-.gif" alt="-.gif" title="-.gif" style="width: 31px; height: 12px;" height="12" width="31" /> of the tangent function at <img src="http://rohedi.com/images/stories/fungsi_tan.gif" alt="fungsi_tan.gif" title="fungsi_tan.gif" style="width: 69px; height: 11px;" height="11" width="69" /> correspond to the Qidam and Baqa properties), hence solution yielded a solver technique entering religion factors must still appropriate to the exact solution</div><p style="text-align: justify;"> This paper introduces a new technique of solving a nonlinear first order ordinary differential equation so-called as SMT (stands for Stable Modulation Technique) which its solution is in the form of AF(A), that is a formula of modulation function which its amplitude term is also including in the phase function. The transfromation function applied for solving eq.(1) by using SMT is <img src="http://rohedi.com/images/stories/jihat_image4.gif" alt="jihat_image4.gif" title="jihat_image4.gif" style="width: 163px; height: 16px;" height="16" width="163" /> what gives its final solution in the form :</p><div style="text-align: justify;"> </div><p style="text-align: justify;"> <img src="http://rohedi.com/images/stories/jihat_image3.gif" alt="jihat_image3.gif" title="jihat_image3.gif" style="margin: 5px; float: left; width: 371px; height: 65px;" height="65" width="371" /> </p><div style="text-align: justify;"> </div><p style="text-align: justify;"> </p><div style="text-align: justify;"> </div><p style="text-align: justify;"><br /></p><p style="text-align: justify;"><br /></p><p style="text-align: justify;"> Eqs.(3)</p><div style="text-align: justify;"> </div><p style="text-align: justify;"> The idea of developing this stable modulation technique based on the event of Isra' and Mi’raj of prophet Muhammad, which alongside its journey towards Sidhratulmuntaha guided by angel Jibril. Eqs.(3) assures writer that when mi’raj the energy of prophet Muhammad is transferred into the energy form of modulated wave. The fundamental aspect for developing of modern mathematics and computing is obtained when to = 0, yo = 0, a = 0 dan b = 0 where eq.(3) then reduces to the form :</p><p style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjS42ipPKHnWMY9QNFNWm4R_wopuo8evN5wMEt8vnBdbu839PB5UmM3wWD0szvLXta6nDD-YaIRv1d1C0eVkq_ur1mQqzmKtEfYsn7s8Am_sBhgITK1cTE5-3XiBqLaVEJInnCMAbT7hsnk/s1600-h/berjihadpers4.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjS42ipPKHnWMY9QNFNWm4R_wopuo8evN5wMEt8vnBdbu839PB5UmM3wWD0szvLXta6nDD-YaIRv1d1C0eVkq_ur1mQqzmKtEfYsn7s8Am_sBhgITK1cTE5-3XiBqLaVEJInnCMAbT7hsnk/s200/berjihadpers4.JPG" alt="" id="BLOGGER_PHOTO_ID_5254645437943152946" border="0" /></a> Eqs .(4)</p><p style="text-align: justify;">Eqs.(4) as a representative form of tangent function up to now has not been met in Mathematics Handbook, because the only</p><p style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6s3tKN2z_jSl0zzXGX6YEXt3V2FVft6ppDwjua6NRiRcuFMyWuSe9sjDk7wZGSrM-xi5DXhVsIAUFRraZ4pvl2t65lRBwuP1j5UadWCheM7qr1-B0M7zzZ4kFL04eqoTY0wUmpfeOpbQv/s1600-h/berjihadpers5.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6s3tKN2z_jSl0zzXGX6YEXt3V2FVft6ppDwjua6NRiRcuFMyWuSe9sjDk7wZGSrM-xi5DXhVsIAUFRraZ4pvl2t65lRBwuP1j5UadWCheM7qr1-B0M7zzZ4kFL04eqoTY0wUmpfeOpbQv/s200/berjihadpers5.JPG" alt="" id="BLOGGER_PHOTO_ID_5254648415764716834" border="0" /></a> Eqs .(5)</p><p style="text-align: justify;">But both of eq.(4) and eq.(5) are still giving the same value with the value of tan(t) for all values of t except at t = pi / 2 in eq.(4) and at t = pi in eq.(5) which both giving value of 0/0, though value of tan(pi/2) = ~. In mathematics the value of 0/0 is unknown as commonly called as NaN (stands for Not a Number). The value of ~ is still not obtaining from eq.(4) and eq.(5), even if has been performed the limit operation because it is only giving devide by zero:</p><p style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIXfD7XFzlyEweFu_jqPt7_wPdhjJ2HShTAjLWe-SNubHCgyZqVBCS_XrmE2E-CuLcXxbvvJk1dhnfRWO2PHzC8qv6MAIb9vqxEnWcYrBZZl6a-JRLeQAX2LUD7LkEKpzXa_39OABF21JN/s1600-h/berjihadpers6.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIXfD7XFzlyEweFu_jqPt7_wPdhjJ2HShTAjLWe-SNubHCgyZqVBCS_XrmE2E-CuLcXxbvvJk1dhnfRWO2PHzC8qv6MAIb9vqxEnWcYrBZZl6a-JRLeQAX2LUD7LkEKpzXa_39OABF21JN/s200/berjihadpers6.JPG" alt="" id="BLOGGER_PHOTO_ID_5254649111340789234" border="0" /></a> Eqs .(6)</p><p style="text-align: justify;">At presentation of the exact solution of arctangent differential equation brightens the confidence of writer that during journey Isra', angel Jibril telling the exact properties of God, while during journey Mi’raj of prophet Muhammad is supplied by a stabilization of believe that God doesn't spell out members as apparently at 0/0, and man will never can reach God will desire, as apparently at 1/0. The primary message is that mathematics applied as "approach" properly in the effort of explaining the Sunnatullah, and don't make mathematics as a justification tool.</p><p style="text-align: justify;"><span style="color: rgb(255, 0, 0);font-size:85%;" >Keywords : Jihad, Isra’ Mi’raj, Prophet Muhammad, Angel Jibril, mathematics, arctangent, arctangent differential equation, tangent function, NaN (0/0), devide by zero (1/0), sunnatullah</span><br /></p><p style="text-align: justify;">For Detail<br /></p><p style="text-align: justify;">Visit <a href="http://rohedi.com/">http://rohedi.com</a> or<br />Download <a href="http://rohedi.com/component/option,com_docman/task,doc_download/gid,27/Itemid,99999999/">Here</a></p>CGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com0tag:blogger.com,1999:blog-8656208893701172133.post-21745775476052679182008-09-23T23:30:00.001-07:002008-10-07T23:03:46.439-07:00Berjihad Di Jalan Allah Dengan Membangun Matematika Cerdas Berbasis Teologi Islam<span class="awal">K</span>eberadaan alam semesta merupakan bukti nyata keagungan dan kemasyhuran ilmu Allah S.W.T. Tinta sebanyak tujuh kali air di seluruh lautan duniapun (bahkan lebih) tidaklah cukup untuk menuliskannya. Menurut penulis, model matematik yang representatif sebagai pijakan dalam mengembangkan Sains Islam adalah persamaan diferensial (PD) arctangent:<img src="http://rohedi.com/images/stories/jihat_image1.gif" alt="jihat_image1.gif" title="jihat_image1.gif" style="margin: 5px; float: left; width: 274px; height: 49px;" height="49" width="274" /> <p> </p> <p><br /></p><p style="text-align: center;">pers (1)</p><br />yang solusi eksaknya berbentuk: <p style="text-align: left;"> <img src="http://rohedi.com/images/stories/jihat_image2.gif" alt="jihat_image2.gif" title="jihat_image2.gif" style="margin: 5px; float: left; width: 294px; height: 50px;" height="50" width="294" /> </p><div> </div><p style="text-align: right;"><br /></p><p style="text-align: center;">pers. (2)</p><div style="text-align: justify;"><br /><br />Oleh karena penulis memandang PD arctangent ini merupakan persamaan diferensial yang bersifat religi (menurut penulis bahwa untuk a=1, b=1, serta nilai awal <i>t</i><sub>0 </sub>= 0 dan <i>y</i><sub>0</sub> = 0 nilai <img src="http://rohedi.com/images/stories/-.gif" alt="-.gif" title="-.gif" style="width: 31px; height: 12px;" height="12" width="31" /> fungsi tangent pada <img src="http://rohedi.com/images/stories/fungsi_tan.gif" alt="fungsi_tan.gif" title="fungsi_tan.gif" style="width: 69px; height: 11px;" height="11" width="69" />mensyiratkan sifat Qidam dan Baqa), maka solusi yang dihasilkan suatu teknik pemecah persamaan diferensial yang memasukkan faktor-faktor religipun semestinya tetap sesuai dengan solusi eksaknya. </div><p style="text-align: justify;"> Pada makalah ini diperkenalkan Teknik Modulasi Stabil (SMT=Stable Modulation Technique) sebuah teknik baru pemecah persamaan diferensial nonlinear berderajad satu yang solusinya berbentuk AF(A), yaitu suatu formula gelombang termodulasi yang suku amplitudonya juga terlingkup dalam fungsi fasanya. Fungsi transformasi untuk pemecahan Pers.(1) dengan SMT adalah <img src="http://rohedi.com/images/stories/jihat_image4.gif" alt="jihat_image4.gif" title="jihat_image4.gif" style="width: 163px; height: 16px;" height="16" width="163" /> yang memberikan bentuk solusi akhir: </p> <p style="text-align: center;"> <img src="http://rohedi.com/images/stories/jihat_image3.gif" alt="jihat_image3.gif" title="jihat_image3.gif" style="margin: 5px; float: left; width: 371px; height: 65px;" height="65" width="371" /> </p><div> </div><p style="text-align: center;"> </p><div style="text-align: center;"> </div><p style="text-align: center;"><br /></p><p style="text-align: center;">pers.(3)</p><p><br /></p> <p style="text-align: justify;"><br /></p><p style="text-align: justify;">Ide pengembangan teknik modulasi stabil ini didasarkan pada peristiwa Isra’ dan Mi’raj nabi Muhammad, yang di sepanjang perjalanannya menuju Sidhratulmuntaha dibimbing oleh malaikat Jibril. Pers.(3) meyakinkan penulis bahwa saat bermi’raj energi nabi Muhammad ditransfer ke dalam bentuk energi gelombang termodulasi. Hal fundamental bagi pengembangan matematika dan komputasi modern diperoleh ketika to = 0, yo = 0, a = 0 dan b = 0 Pers.(3) tereduksi ke dalam bentuk:</p><p style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjS42ipPKHnWMY9QNFNWm4R_wopuo8evN5wMEt8vnBdbu839PB5UmM3wWD0szvLXta6nDD-YaIRv1d1C0eVkq_ur1mQqzmKtEfYsn7s8Am_sBhgITK1cTE5-3XiBqLaVEJInnCMAbT7hsnk/s1600-h/berjihadpers4.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjS42ipPKHnWMY9QNFNWm4R_wopuo8evN5wMEt8vnBdbu839PB5UmM3wWD0szvLXta6nDD-YaIRv1d1C0eVkq_ur1mQqzmKtEfYsn7s8Am_sBhgITK1cTE5-3XiBqLaVEJInnCMAbT7hsnk/s200/berjihadpers4.JPG" alt="" id="BLOGGER_PHOTO_ID_5254645437943152946" border="0" /></a> pers.(4)</p><br />Pers.(4) sebagai bentuk representatif dari fungsi tan(t) hingga kini belum dijumpai dalam Handbook Matematika manapun, karena yang ada hanyalah <p style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6s3tKN2z_jSl0zzXGX6YEXt3V2FVft6ppDwjua6NRiRcuFMyWuSe9sjDk7wZGSrM-xi5DXhVsIAUFRraZ4pvl2t65lRBwuP1j5UadWCheM7qr1-B0M7zzZ4kFL04eqoTY0wUmpfeOpbQv/s1600-h/berjihadpers5.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj6s3tKN2z_jSl0zzXGX6YEXt3V2FVft6ppDwjua6NRiRcuFMyWuSe9sjDk7wZGSrM-xi5DXhVsIAUFRraZ4pvl2t65lRBwuP1j5UadWCheM7qr1-B0M7zzZ4kFL04eqoTY0wUmpfeOpbQv/s200/berjihadpers5.JPG" alt="" id="BLOGGER_PHOTO_ID_5254648415764716834" border="0" /></a> pers.(5)<br /></p><p><br /></p><p>Namun kedua Pers.(4) dan Pers.(5) tepat </p> <p style="text-align: justify;">memberikan nilai yang sama dengan nilai fungsi tan(t) untuk semua nilai t kecuali di t = pi / 2 untuk Pers.(4) dan di t = pi untuk Pers.(5) yang keduanya memberi nilai 0/0, padahal nilai tan(pi/2) = tak hingga. Dalam matematika nilai tersebut tidak dikenal, karena itu lazim disebut NaN (Not a Number) alias bukan bilangan. Nilai tak hingga untuk tan(pi/2) tetap tidak diperoleh dari Pers.(4) dan Pers.(5) sekalipun telah dikenakan operasi limit, karena hanya memberikan nilai devide by zero:</p><p style="text-align: center;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIXfD7XFzlyEweFu_jqPt7_wPdhjJ2HShTAjLWe-SNubHCgyZqVBCS_XrmE2E-CuLcXxbvvJk1dhnfRWO2PHzC8qv6MAIb9vqxEnWcYrBZZl6a-JRLeQAX2LUD7LkEKpzXa_39OABF21JN/s1600-h/berjihadpers6.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiIXfD7XFzlyEweFu_jqPt7_wPdhjJ2HShTAjLWe-SNubHCgyZqVBCS_XrmE2E-CuLcXxbvvJk1dhnfRWO2PHzC8qv6MAIb9vqxEnWcYrBZZl6a-JRLeQAX2LUD7LkEKpzXa_39OABF21JN/s200/berjihadpers6.JPG" alt="" id="BLOGGER_PHOTO_ID_5254649111340789234" border="0" /></a> pers.(6)</p><p style="text-align: justify;"><br /></p><p style="text-align: justify;">Paparan solusi eksak PD arctangent di atas mencerahkan keyakinan penulis bahwa selama perjalanan Isra’ malaikat Jibril mengumandangkan sifat haq (sifat exact) Allah, sedangkan selama perjalanan bermi’raj nabi Muhammad dibekali pemantapan iman bahwa Allah tidak berbilang yang terepresentasi pada 0/0, dan manusia tidak akan pernah dapat menjangkau kehendak Allah sebagaimana terepresentasi pada 1/0. Pesan utamanya adalah bahwa matematika seyogyanya digunakan sebagai “pendekatan” secara benar dalam upaya menerangkan Sunnatullah, dan jangan jadikan pula matematika sebagai alat penjustifikasi.<br /></p><p style="text-align: justify;"><o:smarttagtype namespaceuri="urn:schemas-microsoft-com:office:smarttags" name="date"></o:smarttagtype><!--[if gte mso 9]><xml> <w:worddocument> <w:view>Normal</w:View> <w:zoom>0</w:Zoom> <w:donotshowrevisions/> <w:donotprintrevisions/> <w:donotshowmarkup/> <w:compatibility> <w:breakwrappedtables/> <w:snaptogridincell/> <w:wraptextwithpunct/> <w:useasianbreakrules/> </w:Compatibility> <w:browserlevel>MicrosoftInternetExplorer4</w:BrowserLevel> </w:WordDocument> </xml><![endif]--><!--[if !mso]><object classid="clsid:38481807-CA0E-42D2-BF39-B33AF135CC4D" id="ieooui"></object> <style> st1\:*{behavior:url(#ieooui) } </style> <![endif]--><style> <!-- /* Style Definitions */ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-parent:""; margin:0cm; margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman";} p.MsoFooter, li.MsoFooter, div.MsoFooter {mso-style-link:" Char"; margin:0cm; margin-bottom:.0001pt; mso-pagination:widow-orphan; tab-stops:center 216.0pt right 432.0pt; font-size:12.0pt; font-family:"Times New Roman"; mso-fareast-font-family:"Times New Roman";} span.Char {mso-style-name:" Char"; mso-style-noshow:yes; mso-style-link:Footer; mso-ansi-font-size:12.0pt; mso-bidi-font-size:12.0pt; mso-ansi-language:EN-US; mso-fareast-language:EN-US; mso-bidi-language:AR-SA;} @page Section1 {size:595.45pt 841.7pt; margin:72.0pt 72.0pt 72.0pt 72.0pt; mso-header-margin:36.0pt; mso-footer-margin:36.0pt; mso-paper-source:0;} div.Section1 {page:Section1;} --> </style><span style="color: rgb(255, 0, 0);font-size:85%;" >Kata Kunci : Jihad, Isra’ Mi’raj, Nabi Muhammad, Malaikat Jibril, matematika, arctangent, PD arctangent, fungsi tangent, NaN (0/0), devide by zero (1/0), Tuhan takberbilang, sunnatullah</span><br /></p><p>For Detail :<br /></p><p>Visit <a href="http://rohedi.com/">http://rohedi.com</a> or<br />Download <a href="http://rohedi.com/component/option,com_docman/task,doc_download/gid,26/Itemid,99999999/">Here</a></p>CGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com1tag:blogger.com,1999:blog-8656208893701172133.post-80597877090242524522008-09-23T23:11:00.000-07:002008-09-23T23:26:02.643-07:00Anti Einstein Technique : Analytic Solution of Nonlinear Schrödinger Equation by Means of A New Approach<div style="text-align: justify;"><i><b></b></i><span class="awal">T</span>he nonlinear Schrödinger equation (NSE) has served as the governing equation of optical soliton in the study of its applications to optical communication and optical switching. Various schemes have been employed for the solution of this nonlinear equation as well as its variants. We report in this paper a relatively simpler new approach for the analytic solution of NSE. In this scheme the equation was first transformed into an arctangent differential equation, which was then separated into the linear and nonlinear parts, with the linear part solved in a straight forward manner. The solution of the nonlinear equation was written in the form of modulation function characterized by its amplitude function A and phase function F(A). Substituting the linear solution for A, the arctangent differential equation was solved for a certain initial value of A. It is shown that this method is applicable to other first-order nonlinear differential equation such as the Korteweg de Vries equation (KdV), which can be transformed into an arctangent differential equation.<br /><br /><i><b>I. Introduction</b></i><br /><br />The phenomenon of the solitary wave propagation was observed for the first time by the Scottish scientist John Scott Russell in 1844, when one day he was watching water waves of a certain shape kept on traveling without changing their shape for a distance as far as his eye could see. To explain the behavior of such unusual wave, Korteweg and de Vries governed a model for the wave propagation in shallow water in form a partial differential equation called as KdV differential equation, which its solution appropriates to the features of the solitary wave called as soliton[1]. The existence of solitons in optical fiber was predicted by Zakarov and Zabat (1972) after they derived a differential equation for the light propagating in an optical fiber, that demonstrated later by Hazagawa in 1973 at Bell Laboratory. Next, Mollenauer and Stolen employed the solitons in optical fiber for generating subpicosecond pulses.<br /><br />Keywords : nonlinear Schrödinger equation, KdV, arctangent, Anti Einstein Technique<br /><br />For Detail :<br /><br />Visit <a href="http://rohedi.com/">http://rohedi.com</a> or<br />Download <a href="http://rohedi.com/component/option,com_docman/task,doc_download/gid,9/Itemid,99999999/">Here</a><br /></div>CGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com0tag:blogger.com,1999:blog-8656208893701172133.post-46423207062232919402008-09-23T22:28:00.000-07:002008-09-23T23:17:40.229-07:00Anti Einstein Technique : Analytic Solution of Nonlinear Schrödinger Equation by Means of A New Approach (Indonesia)<i><b></b></i><span class="awal">P</span>ersamaan Schrödinger Nonlinear (NSE) bertindak sebagai solusi optik dalam studi aplikasi komunikasi optik dan switch optik. Berbagai usaha telah dilakukan untuk mencari penyelesaian dari persamaan non linier ini seperti halnya terhadap variannya. Pada tulisan ini kita berikan suatu pendekatan yang relatif lebih sederhana mudah dan baru mengenai penyelesaian persamaananalitik dari NSE. Di rencana ini persamaan yang pertama diubah ke dalam suatu persamaan arctangent yang diferensial, yang kemudian dipisahkan ke dalam linier dan nonlinear , dengan bagian yang linier memecahkan suatu cara lurus kedepan. Solusi dari persamaan nonlinear ditulis dalam format dari fungsi modulasi ditandai oleh F(A fungsi fase dan A fungsi amplitudo nya). menggantikan solusi yang linier untuk A, persamaan arctangent yang diferensial dipecahkan untuk suatu nilai awal yang tertentu dari A. Ditunjukkan bahwa metoda ini sesuai persamaan nonlinear orde 1 seperti persamaan Korteweg de Vries equation ( Kdv), yang dapat diubah ke dalam suatu penyamaan arctangent yang diferensial.<br /><br /><i><b>I. Introduction (pengenalan)</b></i><br /><br />Peristiwa dari perambatan gelombang yang tunggal diamati untuk pertama kali oleh Scott Russell Yohanes ilmuwan Scottish di 1844, ketika suatu hari ia sedang menyaksikan ombak air dari suatu bentuk yang tertentu yang disimpan ketika bepergian tanpa mengubah bentuknya untuk suatu jarak sejauh mata melihat. Untuk menjelaskan perilaku dari gelombang yang tidak biasa seperti itu, Korteweg de Vries membuat suatu model untuk perambatan gelombang di air yang dangkal seperti persamaan diferensial KdV, solusi nya seperti pada persamaan [1].<br /><br />Keberadaan dari solitons di serabut yang berhubung dengan mata diramalkan oleh Zabat dan Zakarov ( 1972) setelah mereka memperoleh suatu persamaan diferensial untuk cahaya menyebarkan di suatu serabut optik, yang ditunjukkan kemudian oleh Hazagawa di 1973 pada Bell Laboratory. yang berikutnya, Stolen dan Mollenauer yang dipekerjakan solitons di serabut optik untuk membangkitkan denyut nadi subpicosecond.<br /><br />Kata Kunci: nonlinear Schrödinger equation, KdV, arctangent, Anti Einstein TechniqueCGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com0tag:blogger.com,1999:blog-8656208893701172133.post-65530017613366989742008-09-03T20:51:00.000-07:002008-09-03T21:06:46.217-07:00Introducing Stable Modulation Technique for Solving an Inhomogeneous Bernoulli Differential Equation<span class="awal">T</span>he Bernoulli differential equation that has been used as primary modeling in many application branches commonly contains harmonic force function in the inhomogeneous term. The nhomogeneous Bernoulli differential equation (IBDE) is specified by nonlinearity of nth order. For instance, 3rd order IBDE is called a stochastic differential equation that has been commonly applied for describing the corrosion mechanism, the transport of fluxon, the generation of squeezed laser, etc. Due to the difficulty of applying a linearization procedure for IBDE, it has commonly been solved numerically. In this paper we introduced a so-called Stable Modulation Technique (SMT) which is able to solve a first order nonlinear differential equation that transformable into the homogeneous Bernoulli differential equation (BDE). SMT is employed by splitting BDE into linear and nonlinear parts. The solution of its nonlinear part has been found to be AF(A) where A is the initial value of nonlinear solution part and F is the modulation function whose phase is a function of A. The general solution of BDE obtained by substituting the linear solution part into initial value of the nonlinear solution part. Although IBDE can not be transformed into BDE completely, SMT gives nevertheless an approximation solution in AF(A) form, where the homogeneous solution part becomes its amplitude term. The AF(A) formula for stochastic differential equation with cosine function as inhomogeneous term can be decomposed as well into transient and steady state solutions. In addition, a special example of solving 2 ogeneous Bernoulli differential equation (BDE) has en used as a primary modeling scheme in many ation branches. A nonlinear BDE is specified by a nonlinearity of n. Although the stochastic differential equation is the first order differential equation, nevertheless the procedure of obtaining its analytical solution is very complicated as shown in utilizing of BWK (Brillouin, Wenzel, Kramer) and Reversion methods nd order BDE in creating a new Planck’s formula of black-body radiation is also presented.<br /><br />Keywords–Stable modulation technique, modulation function, stochastic differential equation.<br /><br />For Detail :<br /><br />Visit <a href="http://rohedi.com/">http://rohedi.com</a> or<br />Download <a href="http://www.snapdrive.net/files/568161/Paper/AF%28A%29%20InhoBernoulli_ICOLA07.pdf">Here</a>CGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com0tag:blogger.com,1999:blog-8656208893701172133.post-19754324746688432742008-09-01T22:20:00.000-07:002008-09-02T18:55:05.999-07:00Analytical Solution Of The Ricatti Differential Equation For High Frequency Derived By Using The Stable Modulation Technique<div style="text-align: justify;"><div style="text-align: justify;"><span class="awal">T</span>he Ricatti differential equation dy/dt = P(t)y2+Q(t)y+R(t) is a nonlinear differential equation which is of contemporary interest in various fields, including particle dynamics, optics, and petroleum exploration. The Ricatti differential equation is easily solved by numerical methods. But in order to obtain the exact solution in analytical form, the first order of nonlinear inhomogeneous differential equation is commonly convert into a second order linear differential equation by use of a change of the dependent variable. In this paper we introduce the stable modulation technique (SMT) to solve the Ricatti differential equation without of the use linearization procedure. The main principle of the SMT in solving a first order nonlinear differential equation is modulate the solution of the linear part into the initial value of the nonlinear part solution. Important to be stressed here that the solution of nonlinear part must be written in the modulation function, where the initial value acts as amplitude and also including in the total phase shift. For a special case, dy/dt = -by2+ay+Acos(2πft) where a and b of both are constants, while t is variable of the time (in s), frequency f in Herzt (Hz) we find that the analytical solution of the SMT is appropriate with numerical solution espescially for high frequency f≥10 Hz, amplitude value A≤1, and initial value of the y in the range 0.1≤y0≤1. The analytical solution above can be used as trial function when the Ricatti differential equation will be solved by using combination of the modulational instability technique and variational approximation.<br /><br />Keywords : Nonlinear inhomogeneous differential equation, linearization procedure, stable modulation technique, modulational instability<br /><br />I. Introduction<br /><br />The general form of the Ricatti differential equation (DE) is of the form :<br />dy/dt = P(t)y2+Q(t)y+R(t), .......................................(1)<br />where y and t are respectively dependent and independent variables, both of P(t) and Q(t) are homogeneous coefficients, where R(t) is the inhomogeneous term[1]. The Ricatti DE is mother of all ordinary differential equations (ODE’s) second order generating special functions like Airy, Bessel and etc,[2] even the Helmholtz equation[3] which has broad applications including optics and geophysics. Common procedure in solving the Ricatti DE is by transforming into a linear ODE second order[1],[2],[4]. For special case, the analytical exact solution of the Ricatti DE can not be obtained, because the analytical solution of the corresponding linear ODE second order is not available.<br /><br />For Detail :<br /><br />Visit <a href="http://rohedi.com/">http://rohedi.com</a> or<br />Download <a href="http://www.snapdrive.net/files/568161/Paper/prociding_ricatti.pdf">Here</a><br /></div><br /></div>CGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com0tag:blogger.com,1999:blog-8656208893701172133.post-15799019544429521382008-08-31T18:55:00.000-07:002008-09-02T18:56:14.314-07:00How can prove that zero equal zero (0=0) or (1=1)<span class="awal">W</span>ho want to know and solve this equation?<br />if anybody can solve this problem and explain this equation, maybe you the best on matematic<br /><br /> 1 = 1<br /> a = a<br />(a**2 - a**2) = (a**2 - a**2)<br /><br /> ..........................................<br /> ..........................................<br /> ..........................................<br />the result must be 1 = 1 ,but<br />the result is 1 = 2<br /><br />you can answer on comment at the sidebarCGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com1tag:blogger.com,1999:blog-8656208893701172133.post-25535562222923138892008-08-28T20:32:00.000-07:002008-08-28T21:59:12.739-07:00Komparasi Matematikanya Einstein Vs AF(A) Rohedi (Arabic Version)omerrassikh14@hotmail.com: برید الكتروني<br /><div style="text-align: right;">یعتبر ألبرت آینشتاین من أعظم العلماءفي ھذا القرن. بسببتلكالعظمة التي نالھا ھذا العالم فقدمجدهبعض<br />أتباعھبل و اعتبروهكنبي للعلوم. إن ھذا التمجیدلا یفُاجئَأحدا،فإذانظرنا إلىمسیرةجمیع العلماء الذین جاءوا من بعده<br />نجد أن شغلھم الشاغل كان في تفسیر و تبریرنظریتھَ. ذلكجدیر باحترامھذا العالم. لمِاذا ؟ لأنھ على نحو المستوى الرفیع<br />للعلِمِْ الحقیقي،ِفإنآینشتاینفي مسیرتھ الطویلة في مجال العلمنجدهقدخطىخْطُى واسعةبل نستطیع القول بأنھ ركض<br />( سعي كما في التعبیرِ العربيِ) ، ثمركب عربة تجرھا الأحصنةوبعد ذلك استقلھحافلةً.ھذا البیانِ لیَسَ بدون سبب، لأن في<br />سیاقِ الریاضیات،ِ مشكلة النسبیةِ الخاصةِّ لكِي تكَوُنَ شكلَ الاستغلالمِنْ نظریةِ فیثاغورس.ھنا تتجلى عظمة آینشتاین<br />الجدیر بالثناء بزیادتھُ في استغلالالنظریة بالتقریبذيالحدینِ التي لم یفكر بھا عالم من قبلھ. في الحقیقة، نسبیتھ الخاصةّ<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZySZNb_9oHL5k_BJKUgnuuVgfRrnR9fay2FWa0_M9A6LxIEjScEunZSmc_eQzmAyyQuS_B6QUmk7SCezzj8fuNEfVvYR1YgIsp3uHPTBq4dC3SWWEGR6DQbYDRUSkz5jA9cxR3uO_qzEB/s1600-h/1.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgZySZNb_9oHL5k_BJKUgnuuVgfRrnR9fay2FWa0_M9A6LxIEjScEunZSmc_eQzmAyyQuS_B6QUmk7SCezzj8fuNEfVvYR1YgIsp3uHPTBq4dC3SWWEGR6DQbYDRUSkz5jA9cxR3uO_qzEB/s400/1.JPG" alt="" id="BLOGGER_PHOTO_ID_5239783002061822386" border="0" /></a>(c) و التيتقتربمن سرعةَ الضوء (ν) طبقّتْ فقط على حركةِ الأجسام التي سرعت<br />طبقاً للمعادلة التفاضلیةِ اللاخطیّة،ِ نظریة التقریب ذاتالحدین التي طبقتْ مِن قبِل آینشتاین<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdNE2q2Ow_6TcbEIUwSdti6ZwpruCyoFDp7M0m0uUoq39PvY2B1G4Mx8SO1-vCzqxGMs4zQlRJNNWxqft8Npk-S-W2v15T1Ksudq2rnUEVKiZUh9CKkkrsRPIH5kEKyJmiX7fUCGehefMA/s1600-h/2.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjdNE2q2Ow_6TcbEIUwSdti6ZwpruCyoFDp7M0m0uUoq39PvY2B1G4Mx8SO1-vCzqxGMs4zQlRJNNWxqft8Npk-S-W2v15T1Ksudq2rnUEVKiZUh9CKkkrsRPIH5kEKyJmiX7fUCGehefMA/s200/2.JPG" alt="" id="BLOGGER_PHOTO_ID_5239783760774832370" border="0" /></a><br />والتي منھاتم التوصل للعلاقة<br />0التيأتاحةالمجال لبعض التقریبات و E = m c**2<br />،(Perturbation method) النظریات في حل المعادلة التفاضلیةِ اللاخطیّةِ. على سبیل المثال،نظریة الاضطراب<br />Floquent ،(Krylof and Bogoligof theorem) نظریة ،( Pocker-Planck approximation) تقریب<br />الخ. تلك النظریات استطاعتإلى حد ما في حلالمعادلة التفاضلیة المتجانسة اللاخطیّة.بینما في حالة .. method<br />المعادلة التفاضلیةاللامتجانسة اللاخطیّة فإنحلھا ما زالَ مَنْ الضَّروُري أَنْ یُختبَرَ.على سبیل المثال،حلمعادلة<br />على نحو عام فإنھا ملائمة فقط للحالة الثابتة. ،(stochastic resonances)<br />والرنین العشوائي (duffing oscillator)<br />نجد أن حلھا یقتصر فقط حتى الحد الثاني،كما یبدو فإن (Perturbation method) إذانظرنا إلى نظریة الاضطراب<br />الطریقة تكَوُنَ مستندة على الخطیةّ،ِ تليذلك خطوة قام بھاآینشتاین في حصر تعبیر الدالة إلى حدین فقط. لذلك یجب إعادة<br />النظر مرة أخرى في طرق ( نظریات)التقریب (مسألة الصندوق الأسود )التي تطرق إلیھا آینشتاین في نظریة النسبیة<br />العامة بعد فشلھفي الوصول لحل المعادلة التفاضلیة غیر التكاملیة خارج نطاق نظریة فیثاغورس.<br /><br />في القریب العاجل سیتم التغلب على العقبات التي تواجھنا في إیجاد حل للمعادلات التفاضلیة اللاخطیّة بواسطة<br />.ROHEDI یدعى “maduresse physicist” ( تقنیة متطورة قد توصل إلیھا فیزیائي من أصل إندونیسي(مادوري<br />.(Stable Modulation Technique) اختصارا من SMT( أطلق على ھذه التقنیة الجدیدة أسم ( تقنیة التحویر المستقرةّ<br />التفاضلیة، ویعطى arc-tangent و معادلات ( Bernoulli ) تستند ھذه التقنیة الجدیدة على كل من معادلات برنو لي<br />لكي نكون صورة لكیفیة أداء ھذه الطریقة الجدیدة، على القارئ أن یتأمل في .AF(A) الحل لھذه التقنیة الجدیدة في صیغة<br />التفاضلیة في الأسفل.ستتضح لك إلي أي مدى stochastic و معادلات Ricatti الرسوم البیانیة لبع ض من معادلات<br />للرتبة Runge Kutha التي تمثل الحل الریاضي لآینشتاین ( ھنا (numerical method) استقرار الطریقة العددیة<br />.step-size الرابعة) الذي یعتمد بدرجة كبیرة على استعما<br /><span id="fullpost"><br />كموضوعأطروحةالدكتوراهبمشیئة و تحت إشرافاللهسبحانھ و SMT سیجعل كاتبھذهالتقنیة الجدیدة<br />. DIKTI تعالى برغم من المضایقات التي یواجھھا الكاتب من قبل إدارة التعلیم الأكادیمي<br />أملأن تكَوُن ھذهالمقالةمفیدة،<br />Rohedi الكاتب<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5FSIY-o3cmJNwZjOtli19eoPGYn33MgNfCvp49oeW4EsjQ6mlZWfxutOrzB4LRdSP5mOmLv4GW8h9Od9FhM9auKcP8yktu3tGUfzJhdEmikbXpEDQ-7GguhTXRJEQKgh59rOukQJcC3dv/s1600-h/3.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi5FSIY-o3cmJNwZjOtli19eoPGYn33MgNfCvp49oeW4EsjQ6mlZWfxutOrzB4LRdSP5mOmLv4GW8h9Od9FhM9auKcP8yktu3tGUfzJhdEmikbXpEDQ-7GguhTXRJEQKgh59rOukQJcC3dv/s200/3.JPG" alt="" id="BLOGGER_PHOTO_ID_5239785704266284914" border="0" /></a> التفاضلیة Ricatti حَلّمعاد<br />f =20 Hz وعند تردد منخفض y0 = بقیمة ابتدائیة 0.1<br />step-size h = حل المعادلة باستخدام 0.1<br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqWBIb_YpbLVGIVDdtFbUYSo8f0u3irl-0IUiPEKi5Ue2AsNKpAPAQAoRpIzO-Lhw4bICm8kithrOv_2JPtrZIc5ibN_vFeVibRVm9M3M0FOUwo8ONyNGxOVKCdHhWNnFL5fjfnsqgjCbj/s1600-h/4.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqWBIb_YpbLVGIVDdtFbUYSo8f0u3irl-0IUiPEKi5Ue2AsNKpAPAQAoRpIzO-Lhw4bICm8kithrOv_2JPtrZIc5ibN_vFeVibRVm9M3M0FOUwo8ONyNGxOVKCdHhWNnFL5fjfnsqgjCbj/s200/4.JPG" alt="" id="BLOGGER_PHOTO_ID_5239786852450613394" border="0" /></a><br /><br />step-size h = حل المعادلة باستخدام 0.05<br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVDA7jELzfCMAo982MVX47HwrvLsVIlTUV-KnlhI64hwB4nWCUVEAhsxpclfCI_Eany-G7Q1qYgt73Axz08_ERh1SdFFTa-bm-JH_0Jg7ygIpaWSxkKDO9qKvrcxV54ofR2wp3ixfwCQQ0/s1600-h/5.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjVDA7jELzfCMAo982MVX47HwrvLsVIlTUV-KnlhI64hwB4nWCUVEAhsxpclfCI_Eany-G7Q1qYgt73Axz08_ERh1SdFFTa-bm-JH_0Jg7ygIpaWSxkKDO9qKvrcxV54ofR2wp3ixfwCQQ0/s200/5.JPG" alt="" id="BLOGGER_PHOTO_ID_5239787796405308754" border="0" /></a><br /><br />step-size h = حل المعادلة باستخدام 0.01<br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-f_DNGC9d4TxAgZn_-5UkMGKT9u62H2AmDQyCReLzE5JMhiA_KNlqtTf_672y4jcwcspbJhfzSoL6ki51yg_eA0yOaKMgXwP0tWuIwMjlBTGYGPoEvBSjoH2rvo2lsASccO7P0mmjehO8/s1600-h/6.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-f_DNGC9d4TxAgZn_-5UkMGKT9u62H2AmDQyCReLzE5JMhiA_KNlqtTf_672y4jcwcspbJhfzSoL6ki51yg_eA0yOaKMgXwP0tWuIwMjlBTGYGPoEvBSjoH2rvo2lsASccO7P0mmjehO8/s200/6.JPG" alt="" id="BLOGGER_PHOTO_ID_5239788291554756050" border="0" /></a><br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLWKh0RSUVx7UM7ZcQ6oYertd6IVFLnw2luE0ANSd81FbBDm6or0R1aZ5MKvzCxM2GJ7Wts-IPm-NhZllas5q-laS6uGFGho9r5KJmCEOH92bJeAfROqxmOe8gNKUbP5FRi6mq74ESBPPd/s1600-h/77.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhLWKh0RSUVx7UM7ZcQ6oYertd6IVFLnw2luE0ANSd81FbBDm6or0R1aZ5MKvzCxM2GJ7Wts-IPm-NhZllas5q-laS6uGFGho9r5KJmCEOH92bJeAfROqxmOe8gNKUbP5FRi6mq74ESBPPd/s200/77.JPG" alt="" id="BLOGGER_PHOTO_ID_5239791052600994530" border="0" /></a> التفاضلیة Stochastic حَلّمعاد<br />a<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyWO7GcQX6e9ic4tiN-dHlIn9KNoaizjGQ5cLxIjIFquAWmKOdiqJ0_BdTZz8dSTcAchJFxNYsf5BxMORm9DGq_FU3bPdi3u9XCvcW4lb5qPgivQn4YmPlQcha3c9FMj79azx3EKn9j2Bw/s1600-h/9.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyWO7GcQX6e9ic4tiN-dHlIn9KNoaizjGQ5cLxIjIFquAWmKOdiqJ0_BdTZz8dSTcAchJFxNYsf5BxMORm9DGq_FU3bPdi3u9XCvcW4lb5qPgivQn4YmPlQcha3c9FMj79azx3EKn9j2Bw/s200/9.JPG" alt="" id="BLOGGER_PHOTO_ID_5239792460989341762" border="0" /></a>وعند تردد عالي<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjstWHLuiXPnI8nNa04B5uoozTUseK6JMNhMRufIEePUONZ5MEBxREa6ccFVSx2F01O4SlHx4hORgdLVpMR31aPQDZy6fFwvt4jAAsoff0_SeRxT1yrwzRlM_9FXeR79J8bVgoNbXJi3o1C/s1600-h/8.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjstWHLuiXPnI8nNa04B5uoozTUseK6JMNhMRufIEePUONZ5MEBxREa6ccFVSx2F01O4SlHx4hORgdLVpMR31aPQDZy6fFwvt4jAAsoff0_SeRxT1yrwzRlM_9FXeR79J8bVgoNbXJi3o1C/s200/8.JPG" alt="" id="BLOGGER_PHOTO_ID_5239791718853835282" border="0" /></a>بقیمة ابتدائیة<br /><br />step-size h =حل المعادلة باستخدام 0.01<br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8jHF6uxVI46_6175r7vg9y0pcGtjbl5RRvBwVdC4ftmWdSpEqd5RrHcto3MwJrfEJwFogpaWxgcBXIG8kGMoo5LlbxlWYPYQo3zLRBdD2IMSs7vuFvabkw6W78td31lCFn0haDBQV2W8w/s1600-h/10.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj8jHF6uxVI46_6175r7vg9y0pcGtjbl5RRvBwVdC4ftmWdSpEqd5RrHcto3MwJrfEJwFogpaWxgcBXIG8kGMoo5LlbxlWYPYQo3zLRBdD2IMSs7vuFvabkw6W78td31lCFn0haDBQV2W8w/s200/10.JPG" alt="" id="BLOGGER_PHOTO_ID_5239793355501148402" border="0" /></a><br /><br />step-size h =حل المعادلة باستخدام 0.001<br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPH17D7LLHtnNibG7RAqanxmaRF57FH7wpzbjKOjKHTBacQLkqs6QxO0MvkCUM2Ca9ouCH9iwh3HUNFkB-MzylKETySrpB4WpS8C7ePSEmfePeHO9Yvx4wgZ8hdiTfOq1Sz5H37ctwjuPI/s1600-h/11.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjPH17D7LLHtnNibG7RAqanxmaRF57FH7wpzbjKOjKHTBacQLkqs6QxO0MvkCUM2Ca9ouCH9iwh3HUNFkB-MzylKETySrpB4WpS8C7ePSEmfePeHO9Yvx4wgZ8hdiTfOq1Sz5H37ctwjuPI/s200/11.JPG" alt="" id="BLOGGER_PHOTO_ID_5239793960296209090" border="0" /></a><br /><br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkBY-3K2cwCV7thNsZQG8JzDnQIrEMnEEpflKkFri0fZTrLZ7FQuoJsAnprJPZOyFobNLnUgtE1eU1MQXfU9pnJagAEXIuiuMdkc55C95MTwq8B7z1uWLr8Z4q3AYFnVmXlG3_3tk_8Nyb/s1600-h/12.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjkBY-3K2cwCV7thNsZQG8JzDnQIrEMnEEpflKkFri0fZTrLZ7FQuoJsAnprJPZOyFobNLnUgtE1eU1MQXfU9pnJagAEXIuiuMdkc55C95MTwq8B7z1uWLr8Z4q3AYFnVmXlG3_3tk_8Nyb/s200/12.JPG" alt="" id="BLOGGER_PHOTO_ID_5239794724018010050" border="0" /></a> التفاضلیة Stochastic حَلّمعاد<br />وعند تردد عالي<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjstWHLuiXPnI8nNa04B5uoozTUseK6JMNhMRufIEePUONZ5MEBxREa6ccFVSx2F01O4SlHx4hORgdLVpMR31aPQDZy6fFwvt4jAAsoff0_SeRxT1yrwzRlM_9FXeR79J8bVgoNbXJi3o1C/s1600-h/8.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjstWHLuiXPnI8nNa04B5uoozTUseK6JMNhMRufIEePUONZ5MEBxREa6ccFVSx2F01O4SlHx4hORgdLVpMR31aPQDZy6fFwvt4jAAsoff0_SeRxT1yrwzRlM_9FXeR79J8bVgoNbXJi3o1C/s200/8.JPG" alt="" id="BLOGGER_PHOTO_ID_5239791718853835282" border="0" /></a>بقیمة ابتدائیةa<br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyWO7GcQX6e9ic4tiN-dHlIn9KNoaizjGQ5cLxIjIFquAWmKOdiqJ0_BdTZz8dSTcAchJFxNYsf5BxMORm9DGq_FU3bPdi3u9XCvcW4lb5qPgivQn4YmPlQcha3c9FMj79azx3EKn9j2Bw/s1600-h/9.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyWO7GcQX6e9ic4tiN-dHlIn9KNoaizjGQ5cLxIjIFquAWmKOdiqJ0_BdTZz8dSTcAchJFxNYsf5BxMORm9DGq_FU3bPdi3u9XCvcW4lb5qPgivQn4YmPlQcha3c9FMj79azx3EKn9j2Bw/s200/9.JPG" alt="" id="BLOGGER_PHOTO_ID_5239792460989341762" border="0" /></a><br />step-size h =1 حل المعادلة باستخدا<br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcGNKhr8UjtZjs3eW_F4XKctFV9ya_ZriIwOfuJ2-52RORKqUjUEXksLWHw5RxJJD74ZwV55xxcuvoxS1rA0P0Vnjq7_2CMJlxiH3RDdRAzuzXqlb-zTs6L3x8UKQre8Mc7b81GpIv6jz_/s1600-h/13.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcGNKhr8UjtZjs3eW_F4XKctFV9ya_ZriIwOfuJ2-52RORKqUjUEXksLWHw5RxJJD74ZwV55xxcuvoxS1rA0P0Vnjq7_2CMJlxiH3RDdRAzuzXqlb-zTs6L3x8UKQre8Mc7b81GpIv6jz_/s200/13.JPG" alt="" id="BLOGGER_PHOTO_ID_5239796696105212402" border="0" /></a><br /><br />step-size h = حل المعادلة باستخدام 0.1<br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDyaLipPTN86uXUFB0FD850hqowYqU1azS_-LMMEKPByz9mRnTDXlVRfSZLEKT57zOulQ0SVU_ASQzRcmAqRRUlrdSjlRt3TC9ITIpn9QQR4cotYGuA8tsobt6lN4p_kAbq5b55cObPKv8/s1600-h/14.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDyaLipPTN86uXUFB0FD850hqowYqU1azS_-LMMEKPByz9mRnTDXlVRfSZLEKT57zOulQ0SVU_ASQzRcmAqRRUlrdSjlRt3TC9ITIpn9QQR4cotYGuA8tsobt6lN4p_kAbq5b55cObPKv8/s200/14.JPG" alt="" id="BLOGGER_PHOTO_ID_5239797532064803586" border="0" /></a><br /><br /></div></span>CGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com0tag:blogger.com,1999:blog-8656208893701172133.post-32393525893314223332008-08-28T20:23:00.000-07:002008-09-02T18:57:27.613-07:00Kunci Sains Dan Teknologi Ada Di Angka Kelahiran Republik Indonesia<span class="awal">P</span>ara visitor tentu ingat bahwa saat saya meluncurkan website rohedi.com kepada khalayak, artikel pertama yang saya tampilkan adalah info tentang formula analitik untuk polinomial orde positif sembarang versi saya. Pada artikel tersebut saya contohkan pula komparasi nilai sisa polinomial (remainder) antara rohedi’s formula dengan hasil hitungan perangkat lunak Matlab untuk polinomial orde 1060.<br /><br />Remainder hitungan rohedi’s formula tetap konsisten dengan teori matematika yakni mendekati nol, sedangkan remainder hitungan Matlab sangat payah karena nilainya mendekati takberhingga. Walaupun demikian saya tidak terburu-buru mengklaim formula analitik yang saya miliki tersebut sebagai penemuan, karena disamping paper tentang formula digdaya itu belum saya publikasikan ke manca negara, juga karena saya masih ingin berbagi tip dengan sesama anak bangsa, siapa tahu ada diantara visitor yang brillian mendapatkannya, sehingga saya turut berbangga mengantarkan sang penemu meraih field medal yaitu gelar prestisius di bidang matamatika. Tak ayal lagi kelak Indonesia akan menjadi sentra New Science sebagaimana saya ilustrasikan pada rohedi.blogspot. Mengapa? karena saya akan sependapat dengan semua visitor, bahwa karya Profesor PTN dan PTS produk DIKTI tentu jauh lebih hebat dari karya ROHEDI yang hanya tamatan S2 dalam negeri.<br /><p>Sebagaimana inspirasi untuk mendapatkan rohedi’s reversion sebagai teknik reversi baru dalam menyelesaikan persamaan diferensial biasa nonlinear dalam bentuk Maclaurin series (silahkan baca kembali artikel How to upgrade the running time of computer), untuk mendapatkan formula analitik polinomial orde sembarang dimaksud, sayapun terinspirasi akan ketajaman hati nurani para Pendiri Bangsa dalam menetapkan kelahiran RI (Republik Indonesia) tercinta ini pada 17–8–1945. Pada penyelesaian persamaan diferensial arctanget, ternyata angka-angka tanggal, bulan, dan tahun kelahiran RI tersebut termaktub dalam koefisien deret tangent function pada suku ke 8 (delapan) yakni Perlu visitor ketahui bahwa tangent function dan arctangent merupakan fungsi trigonometri yang perannya amat vital dalam pemecahan problem integral dan persamaan diferensial secara analitik sebagaimana saya jelaskan dalam artikel surat ke KAMINDO (Komisi Ahli Matematika Analisis Indonesia). Semoga pernyataan saya tidak salah kalau Angka Kelahiran RI tersebut merupakan representasi visi akademis para Pendiri Bangsa yang harus diwujudkan oleh siapapun yang memimpin bangsa ini melalui misi-misi pencerdasan bangsa yang harus ditargetkan selama masa kepemimpinannya. Namun sayang, baru 45 tahun pasca kemerdekaan bangsa kita, sistem pendidikan di Indonesia berjalan tanpa arah yang jelas, itupun dengan punguatan biaya pendidikan yang sangat mencekik. Semoga pula surat tersebut sampai ke KAMINDO setelah saya berpulang ke rahmatullah, demikian pula jumlah suku deret tangent function hasil hitung tangan saya dalam isi surat tersebut tidak tercium oleh pengelola musium rekor Indonesia (MURI) sebagai rekor jumlah suku terbanyak yang dapat dicapai anak bangsa Indonesia (bahkan mungkin di dunia). Mengapa? karena mempertanggungjawabkan langkah perumusannya di depan mereka, berarti membuka rahasia teknik reversi baru tersebut, yang tentu saja akan menghilangkan kesempatan saya untuk mematenkan teknik smart tersebut di lembaga PATEN USA sebagai lembaga Paten terpercaya hingga saat ini. Begitu nomor PATEN itu keluar, copy right dari teknik smart pemecah persamaan diferensial nonlinear tersebut akan saya lego dengan harga yang sangat fantantis, yaitu Rp. 100 T. Semoga jerih payah rumus sakti yang saya niatkan untuk mengentaskan kaum Duafa (Fakir miskin dan orang terlantar) serta membahagiakan Anak Yatim Piatu itu segera terwujud<br /></p><p>Keterangan lebih lanjut kunjungi <a href="http://rohedi.com/">http://rohedi.com</a></p>CGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com0tag:blogger.com,1999:blog-8656208893701172133.post-60938803875418624642008-08-28T20:21:00.000-07:002008-09-02T18:57:50.242-07:00Komparasi Matematikanya Einstein Vs AF(A) Rohedi<span class="awal">A</span>lbert Einstein adalah ilmuwan terbesar sepanjang sejarah. Saking hebatnya sampai-sampai beliau ditasbihkan oleh para pemujanya sebagai prophet of siences. Karena itu tidak mengherankan kalau kiprah seluruh ilmuwan lainnya dianggap hanya sebagai penjustifikasi terhadap teori-teori yang telah ditelorkannya. Masya Allah, sungguh penobatan ini sangat berlebihan. Mengapa? <p> ya karena dalam menuju singgasana sains yang sangat prestisius tersebut, Pak Einstein tidak berjalan kaki sembari ber“sai“ atau berlari-lari kecil, melainkan terlebih dahulu naik delman segitiga Phytagoras kemudian menumpang bus binomial. Pernyataan ini bukannya tanpa alasan, karena dalam kontek matematika, persoalan relativitas khusus merupakan bentuk ekploitasi hukum Phytagoras. Kehebatan Pak Einstein yang patut diacungkan jempol adalah terletak pada kejelian beliau memanfaatkan pendekatan binomial yang sama sekali tak terfikirkan oleh ilmuwan lain sebayanya. Faktanya relativitas khusus tersebut berlaku hanya untuk pergerakan partikel yang kecepatannya (v) mendekati kecepatan cahaya (c)<br /></p><p>Keterangan lebih lanjut kunjungi <a href="http://rohedi.com">http://rohedi.com</a><br /></p>CGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com0tag:blogger.com,1999:blog-8656208893701172133.post-22962294073367447962008-08-28T20:13:00.000-07:002008-09-02T18:58:18.482-07:00Fenomenal Invention in End the Year 2006<span class="awal">P</span>enemuan yang dimaksudkan pada judul tulisan ini tidak berhubungan dengan tengara polisi akan keterlibatan sindikat narkoba dibalik kematian selebritis Alda Risma. Juga tidak berhubungan dengan pengakuan YZ mantan anggota DPR pusat tentang motif dibalik penyebaran gambar ”mesum hubungan intimnya” dengan penyanyi dangdut ME, apalagi berhubungan dengan nuasa kepuasan mendalam yang tersirat dari wajah beberapa pegawai di salah satu PEMDA di Jawa Barat, manakala mereka beramai-ramai melihat komputer yang memuat gambar ”harta karun” rekan wanita sekantornya. <p style="text-align: justify;" class="MsoNormal"> <span>Esensi penemuan ini justru berkaitan erat dengan upaya mendapatkan formula racikan beberapa bahan kimia kelompok G yang aman dikonsumsi masyarakat, serta teknologi pembuatan chip optik-elektronik yang menjadi pengendali proses penyaluran informasi pada handpone dan pemerosesan data di dalam komputer. Andai mereka sempat merenungkan betapa mulianya tujuan para periset dan pengembang chip yang menjadi otak dari <i>handpone</i> dan komputer itu, barangkali para sindikat narkoba dan penyebar gambar porno akan berpikir dua kali untuk menyalahgunakan kedua produk teknologi tinggi tersebut. Lantas mengapa penyalahgunaan ini sedemikian mudah dilakukan?, para pembaca harap bersabar sejenak, karena penulis akan memaparkan salah satu penyebabnya di akhir tulisan ini. </span> </p> <p style="text-align: justify; text-indent: 36pt;" class="MsoNormal"> <span>Penemuan fenomenal yang penulis maksudkan berupa <u>teknik baru pemecahan persamaan diferensial nonlinear</u>. Masyarakat umum tentu awam terhadap istilah persamaan diferensial ini, tetapi penulis juga meyakini bahwa tidak semua mahasiswa dan dosen<span> </span>di perguruan tinggi yang mengenal betul bentuk persamaan diferensial nonlinear tersebut. <span> </span>Hal ini karena materi kuliah di perguruan tinggi umumnya di seputaran persamaan diferensial linear. Karena itu para pembaca pastilah mengira kalau penulispun kebingungan tentang bagaimana cara menyampaikan berita baik ini kepada khalayak, agar penemuan yang menurut keyakinan penulis Insya Allah bakal<span> </span>”mengibarkan merah putih” di manca negara itu dapat membanggakan siapa saja yang membaca tulisan ini Ibu ibu di rumah tentu lumrah mempraktekkan resep adonan kue yang dibacanya dari sebuah majalah. Menurut resep itu untuk membuat sepotong kue diperlukan sekian gram tepung terigu, sekian gram gula, sekian miligram panili, dan sekian gram kuning telur (ibu-ibu sekalian, di buku pelajaran fisika jumlah gram ini dinamakan massa bukanlah berat seperti yang biasa kita sebut). Kalau jumlah gram<span> </span>tepung terigu, gula, panili dan kuning telur masing-masing dilambangkan dengan <i>u</i>,<i>v</i>,<i>w</i>,<i>x</i> , maka resep kue itu dapat dituliskan dalam sebuah persamaan sederhana </span><span><i>y= u + v + w + x</i> </span><span><span style="overflow: auto; position: relative; top: 5pt;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" spt="75" preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum @10 21600 0"> </v:formulas> <v:path extrusionok="f" gradientshapeok="t" connecttype="rect"> <o:lock ext="edit" aspectratio="t"> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style="'width:81pt;" ole=""> <v:imagedata src="file:///C:\DOCUME~1\NYAMBU~1\LOCALS~1\Temp\msohtml1\04\clip_image001.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1025" drawaspect="Content" objectid="_1276061396"> </o:OLEObject> </xml><![endif]-->. Tetapi kalau ibu-ibu hendak membuka usaha katering kue, maka rumus atau formula resep itu disamping harus memasukkan upah produksi, juga perlu mengoptimalkan komposisi bahan-bahannya, guna meraup keuntungan yang maksimal. Resep kue tersebut sekarang berubah menjadi y = au + bv + cw + dx + e<span style="position: relative; top: 5pt; width: 0px; height: 0px;"><!--[if gte vml 1]><v:shape id="_x0000_i1026" type="#_x0000_t75" style="'width:122.25pt;height:15.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\NYAMBU~1\LOCALS~1\Temp\msohtml1\04\clip_image003.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1026" drawaspect="Content" objectid="_1276061397"> </o:OLEObject> </xml><![endif]-->, yang oleh mahasiswa ekonomi dikenal dengan persamaan linear yang mengandung 4 perubah bebas u,v,w, dan x. Tentu formula resep kue yang terakhir ini sudah diluar jangkauan ibu-ibu, karenanya ibu-ibu perlu menyekolahkan salah seorang putra-putrinya ke fakultas ekonomi, untuk mengetahui bagaimana cara mendapatkan angka a,b,c,d, dan e optimal yang akan membuat usaha katering kue tersebut sukses menyedot banyak pelanggan. Lantas dalam bentuk apa persamaan yang notabene menjadi basis sains dan teknologi tinggi itu?</span> </p> <span id="fullpost"> <p style="text-align: justify;" class="MsoNormal"> <span>Menurut penulis berkembangnya ilmu pengetahuan modern merupakan perwujudan cara memandang alam sekitar yang ditindaklanjuti dengan upaya menjelaskan keteraturan dan ketidakteraturan peristiwa yang terjadi di dalamnya (ini oleh para fisikawan disebut hukum alam). Dulu ketika di sekolah dasar kita sama-sama pernah diajarkan cara menghitung panjang garis miring segitiga siku-siku dengan dalil phitagoras. Ternyata dalil Phitagoras itu tidak sekedar untuk menghitung panjang ”garing” segitiga siku-siku, melainkan merupakan pembangun tiga fungsi trigonometri fundamental yaitu fungsi sin</span><span style="font-family:Symbol;"><span>a</span></span><span>, cos</span><span style="font-family:Symbol;"><span>a</span></span><span>, dan tan</span><span style="font-family:Symbol;"><span>a</span></span><span>. Mungkin tidak banyak yang tahu bahwa sesungguhnya hampir semua persoalan kehidupan di dunia ini pada dasarnya dapat ditangani dengan ketiga fungsi penting tersebut, asalkan mereka tahu bagaimana cara menggunakannya. Mengingat demikian pentingnya maka penulis mensketsakan gambar segitiga ”keramat” tersebut di bawah ini lengkap dengan definisi ketiga fungsi fundamental sin</span><span style="font-family:Symbol;"><span>a</span></span><span>, cos</span><span style="font-family:Symbol;"><span>a</span></span><span>, dan tan</span><span style="font-family:Symbol;"><span>a</span></span> </p> <p style="text-align: justify;" class="MsoNormal"> </p> <p style="text-align: justify; text-indent: 36pt;" class="MsoNormal" align="center"> <img src="http://rohedi.com/images/stories/penemuan2006-1.gif" alt="Image" title="Image" width="473" border="0" height="242" hspace="6" /> </p> <p style="text-align: justify; text-indent: 36pt;" class="MsoNormal"> <span><br />Menurut segitiga di atas, sekecil apapun bertambahnya ti</span>nggi <i>y</i> selalu diikuti oleh bertambahuya sudut <i><span style="font-family:Symbol;"><span>a</span></span></i><span> </span>(perubahan kecil dari nilai <i>y</i> dan <i><span style="font-family:Symbol;"><span>a</span></span></i> ini masing-masing dilambangkan dengan <i>dy</i> dan <i>d</i><i><span style="font-family:Symbol;"><span>a</span></span></i> yang lazim dinamakan panjang diferensial). Menurut ilmu matematika hubungan laju atau kecepatan perubahan nilai y terhadap perubahan sudut <i><span style="font-family:Symbol;"><span>a</span></span></i> tersebut mematuhi persamaan : </p> <p style="text-align: justify;" class="MsoNormal"> <img src="http://rohedi.com/images/stories/penemuan2006-2.gif" alt="Image" title="Image" width="132" border="0" height="64" hspace="6" /><img src="" alt=" " align="middle" /><img src="" alt=" " align="middle" /><img src="" alt=" " align="middle" />............ (1) </p> <p style="text-align: justify;" class="MsoNormal"> Pangkat 2 di atas y menunjukkan bahwa ternyata hubungan perubahan tinggi benda terhadap perubahan sudut pandang tidak berbanding secara linear, sehingga sifatnya sama sekali berbeda dengan model persamaan linear pada pembuatan kue di atas. Pemecahan Pers.(1) yang dinamakan persamaan diferensial arctan ini menjadi salah satu topik bahasan mata kuliah kalkulus yang diberikan kepada mahasiswa eksakta dan teknik pada semester kedua. Tujuannya adalah menentukan nilai y untuk setiap nilai yang divariasi. Karena nilai bebas untuk diubah maka dinamakan perubah atau variabel bebas, sedangkan nilai y sangat tergantung pada nilai karenanya dinamakan variabel tak bebas yang bertindak sebagai suatu fungsi. Fungsi y yang cocok untuk semua nilai adalah y() = tan. Kalau hubungan y dan ini diplotkan dalam sebuah kuva dimulai dari sudut dari 0o hingga hampir 900 , kurvanya membentuk kurva lengkung transedental mengarah ke nilai y tak berhingga. Hingga saat ini tidak ada komputer canggih manapun yang mampu mengeplotkan kurva y=tan untuk nilai dari 0o hingga tepat 900, hal ini karena nilai tan(900) = alias takberhingga. Bila dikaitkan dengan cara pandang mata, maka wajarlah kalau tidak ada satupun manusia di muka bumi ini yang dapat melihat vertikal ke atas sembari wajahnya lurus ke depan, sekalipun dengan mata terbelalak. Sungguh sangat ajaib, ketika angka 1 digantikan dengan , atau 2, apalagi diganti dengan cos, Insya Allah tidak banyak mahasiswa yang bisa mendapatkan bentuk fungsi pemecahannya tanpa bantuan perangkat lunak simbolik, seperti MapleV, Matlab, dan Matematica yang umum beredar di kalangan akademisi. Mengapa? karena pemecahan bentuk persamaan diferensial yang baru ini memang tidak diajarkan pada perkulihaan tingkat sarjana.<br /> Kemudian penulis memperumum bentuk Pers.(1) ke dalam bentuk yang common atau lazim dikenal para matematikiawan sedunia, yakni ke dalam bentuk : </p> <p style="text-align: justify;" class="MsoNormal"> <img src="http://rohedi.com/images/stories/penemuan2006-3.gif" alt="Image" title="Image" width="296" border="0" height="63" hspace="6" /><img src="" alt=" " align="middle" /> ............(2)<br /><span>dengan variabel bebasnya dilambangkan dengan <i>x</i>, dan mengandung tiga koefisien bebas (nilainya bergantung pada <i>x</i>) yakni P(<i>x</i>), Q(<i>x</i>), dan R(<i>x</i>). Kalau suku pertama pada ruas kanannya dihilangkan maka Pers.(2) berubah ke bentuk persamaan diferensial linear, yang pemecahannya diajarkan pada perkulihan matematika semester ketiga. Tetapi <u>bila Pers.(2) ditulis utuh, maka ia dinamakan persamaan diferensial nonlinear Ricatti</u>. Kalau ketiga koefisien P,Q, dan R bernilai tetap (konstan) atau tidak bergantung pada nilai <i>x</i>, maka pemecahan untuk mendapatkan fungsi <i>y(x)</i> sangat mudah dilakukan, karena setelah dilakukan pemisahan variabel <i>y</i> dan <i>x</i>, maka pemecahan masing masing dapat dilakukan dengan integral. Karena itu persamaan diferensial Ricatti yang berkoefisien konstan termasuk kelompok <i>integrable</i> <i>differential equations</i>, yaitu persamaan diferensial yang bisa diintegralkan. Tetapi begitu koefisiennya tidak konstan seperti bentuk berikut :</span><br /><img src="http://rohedi.com/images/stories/penemuan2006-4.gif" alt="Image" title="Image" width="391" border="0" height="62" hspace="6" /> ..................... (3) </p> <p style="text-align: justify;" class="MsoNormal"> <span>lagi-lagi Insya Allah tidak banyak yang mampu mengeluarkan solusi eksaknya dalam bentuk fornula analitik. Padahal Pers.(3) merupakan persamaan kunci dalam perancangan peralatan elektronik yang biasa dipraktekkan oleh mahasiswa Teknik Elektro. Mahasiswa dan dosen umumnya termanjakan oleh pemakaian program simbolik, lagi pula tanpa rumus analitikpun perancangan alat elektronik tetap berjalan karena solusi Pers.(3) dapat diperoleh secara mudah dengan metode numerik, ibarat pepatah tidak ada rotan akarpun jadi. Disini mereka lupa bahwa kalau formula eksak analitik itu ada ditangan, maka akurasi kinerja peralatan yang dibuatnya dijamin tidak diragukan lagi.<span> </span>Lantas apa hubungannya persamaan diferensial Ricatti ini dengan pengembangan sains dan teknologi tinggi. Menurut literatur matematika terapan,<span> </span>persamaan diferensial Ricatti dalam Pers.(2) merupakan ”ibu” dari persamaan Helmholtz, yang untuk kasus dimensi 1 yaitu mengandung satu variabel bebas x bentuknya adalah :</span> </p> <p style="text-align: justify;" class="MsoNormal"> <img src="http://rohedi.com/images/stories/penemuan2006-5.gif" alt="Image" title="Image" width="251" border="0" height="62" hspace="6" /> ........................(4)<br /><span>disini </span><span style="position: relative; top: 5pt; width: 0px; height: 0px;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" spt="75" preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum @10 21600 0"> </v:formulas> <v:path extrusionok="f" gradientshapeok="t" connecttype="rect"> <o:lock ext="edit" aspectratio="t"> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style="'width:9.75pt;" ole=""> <v:imagedata src="file:///C:\DOCUME~1\NYAMBU~1\LOCALS~1\Temp\msohtml1\02\clip_image001.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1025" drawaspect="Content" objectid="_1276372101"> </o:OLEObject> </xml><![endif]--><span>beta </span>adalah tetapan yang nilainya khas atau tertentu untuk setiap fungsi <i>k(x)</i>. Perlu pembaca ketahui, Persamaan Helmholtz ini merupakan perangkat matematika atau ”model utama” dalam eksplorasi minyak bumi dan pengembangan chip optik (digunakan baik dalam sistem komunikasi menggunakan serat optik, salah satu komponen penting dalam CCD kamera, dan <i>Handpone</i> multi warna, serta komputer masa depan yang dirancang bakal mampu memproses data secepat kilatan cahaya). Perlu diinformasikan pula, bahwa hingga saat ini persamaan Helmholtz untuk sembarang fungsi <i>k(x)</i> terutama yang berupa fungsi Gaussian <img src="http://rohedi.com/images/stories/penemuan2006-6.gif" alt="Image" title="Image" width="44" border="0" height="27" hspace="6" /><span style="position: relative; top: 3pt; width: 0px; height: 0px;"><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1026" drawaspect="Content" objectid="_1276372102"> </o:OLEObject> </xml><![endif]-->belum berhasil dipecahkan secara eksak dalam bentuk formula analitik. Namun demikian metode numerik yang diprogram dengan komputer dapat menyelesaikannya secara mudah, walaupun hasil perhitungannya masih dalam taraf pendekatan alias belum akurat. Penulis menengarahi kemudahan pemecahan persamaan Helmholtz dengan metode numerik ini turut menjadi penyebab mengapa orang begitu mudah menyalahgunaan produk teknologi tinggi sebagaimana marak terjadi belakangn ini. Penulis menganggap perburuan terhadap metode yang bisa mengeluarkan solusi persamaan Helmholtz secara eksak dalam bentuk analitik tetap belum berhenti, mungkin para ahlinya masih beristirahat sejenak sambil berfikir mau diapakan lagi persamaan diferensial Helmholtz itu. Ini baru untuk kasus satu dimensi apalagi yang mengandung variabel bebas multidimensi, tentu dapat dibayangkan betapa rumitnya bentuk solusi eksak analitiknya.</span><br /> </p> <p style="text-align: justify;" class="MsoNormal"> <span>Sesungguhnya teknologi tinggi saat ini tidak hanya berkutat di sekitar ekplorasi minyak bumi dan cara berkomunikasi yang mudah, efisisen, dan murah. Teknologi tinggi lainnya adalah teknologi pembuatan pesawat terbang dan kapal selam, bahkan teknologi yang berkembang beberapa tahun terahkir mengarah pada perekayasaan material sehingga peralatan elektronik di masa mendatang dapat dibuat berskala atom (berukuran nano meter), sebagaimana yang didengungkan dengan istilah <i>nano technology</i>. Menurut berbagai literatur yang penulis baca, bentuk persamaan diferensial yang secara umum mewakili atau menjadi basis model teknologi yang berkembang saat ini adalah persamaan diferensial nonlinear Bernoulli inhomogen, yang bentuknya adalah :</span><br /> <img src="http://rohedi.com/images/stories/penemuan2006-7.gif" alt="Image" title="Image" width="284" border="0" height="59" hspace="6" /> ................(5) </p> Coba pembaca bandingkan Pers.(2) dengan Pers,(5), ternyata persamaan umum Ricatti merupakan salah satu kelompok dari persamaan Bernoulli inhomogen, tepatnya untuk n=2. Para pembaca sekalian, hal-hal yang tidakpastipun (undeterministic) atau yang lebih dikenal dengan fenomena stokastik juga terwakili oleh persamaan Bernoulli inhomogen, yaitu oleh n=3. Kelihatannya sampai baris ini para pembaca mulai ragu terhadap pernyataan penulis. Apa sulitnya memecahkan Pers.(5) itu, terlebih lagi ia merupakan basis teknologi tinggi. Apakah tidak satu orangpun di Indonesia yang mampu memecahkan persamaan tersebut. Setelah penulis membaca literatur bahwa persamaan Bernoulli untuk n =3 terutama yang f(x) nya berupa fungsi sinusoida seperti susah dipecahkan secara eksak, penulis terlebih dahulu mencoba memecahkannya untuk kasus kedua koefisien p dan Q konstan dengan semua program simbolik yang penulis miliki. Perangkat lunak Matematica yang dibuat Wolfram manusia terjenius saat ini mengeluarkan jawaban : soal anda bukan proses aljabar biasa, MapleV mengeluarkan jawaban no library, sedangkan Matlab tanpa meninggalkan pesan alias langsung heng. Penulis merasa tertantang untuk berupaya mencari tahu apa penyebabnya. Mengapa demikian? karena Pers.(5) terkatagori dalam non-integrable differential equations, yang konon katanya hingga kini masih diburu. Anehnya ketika f(x) dibuang, walaupun kedua koefisien p dan Q tidak konstan serta untuk berapapun nilai n, kecuali <img src="http://rohedi.com/images/stories/penemuan2006-8.gif" alt="Image" title="Image" width="376" border="0" height="61" hspace="6" />persamaan diferensial ini tetap dapat diintegralkan, yang bentuk solusi eksaknya banyak dijumpai dalam banyak pustaka matematika. <br /> Para pembaca sekalian, penulis terperangkap dalam jebakan persamaan diferensial Bernoulli inhomogen ini sejak bulan mei 2006, hingga merasuk ke dalam lamunan. Namun persamaan Bernoulli ini tidak sampai merasuk ke dalam mimpi, karena sejak saat itu dalam sehari semalam penulis dapat tidur rata-rata hanya dua jam. Barangkali karena upaya ini dilandasi oleh niat tulus untuk mencerdaskan anak bangsa dengan tanpa dukungan dana riset dari manapun, suatu hari penulis mendapat hidayah tentang cara menyelesaikan persamaan diferensial nonlinear tersebut, yang integrable dipecahkan dengan teknik modulasi stabil, sedangkan yang non-integrable dipecahkan dengan metode reversif baru yang sama sekali berbeda dengan metode reversif yang berkembang hingga saat ini. Teknik modulasi stabil pada dasarnya menerapkan proses penumpangan (modulasi) informasi ke dalam penyelesaian persamaan diferensial nonlinear yang terintegrable dalam bentuk formula AF(A), dengan A dan F masing-masing mewakili solusi bagian linear dan solusi bagian nonliner dari persamaan diferensial nonlinear berderajad satu yang hendak diselesaikan. Sedangkan maksud A dalam kurung adalah solusi bagian linear tersebut ditumpangkan ke solusi bagian nonlinear yang sebelumnya telah dituliskan dalam bentuk fungsi gelombang, dengan F adalah fungsi fasanya. Istilah A dan F penulis gunakan untuk menganalogikan bentuk sampul gelombang termodulasi (A=amplitudo dan F=fungsi fasa) dengan solusi persamaan diferensial nonlinear yang terintegrable.<br />Penemuan kedua metode ini untuk sementara penulis klaim sebagai penemuan yang fenomenal di akhir tahun 2006. Dua buah paper tentang performansi teknik modulasi stabil sudah disampaikan pada even nasional dan internasional (Paper I disampaikan pada simposium nasional Matematika Analisis dan Aplikasinya yang diselenggarakan Jurusan Matematika ITS Surabaya, 10 Agustus 2006, sedangkan Paper ke II disampaikan pada International Conference of Mathematics and Natural Sciences ITB, Bandung, 29-30 Nopember 2006). Saat ini penulis sedang mempersiapkan beberapa paper untuk disubmit langsung ke jurnal matematika (domestik dan manca negara) dan beberapa lagi dipersiapkan untuk koferensi Matematika Terapan di luar negri, salah satunya akan disampaikan pada konferensi ahli matematika untuk Geofisika Universitas Kalsure di Jerman pada bulan Pebruari 2007 mendatang. Kedua metode ini siap untuk diuji oleh para ahli matematika manapun untuk dipertanggung-jawabkan kebenaran ilmiahnya, agar segera bisa digunakan secara resmi oleh mahasiwa-mahasiswa di Indonesia.<br />Hal lain yang berkenaan dengan kedua metode ini diantaranya :<br /><ul><li>formula AF(A) teknik modulasi stabil (SMT=Stable Modulation Technique) dapat diberikan dalam bentuk diagram yang menjadikannya sebagai teknik pemecah persamaan diferensial nonlinear supercepat </li><li>dapat menderet takhinggakan fungsi (infinite series of function) tanpa menggunakan deret Maclaurin</li><li>dapat digunakan untuk membuktikan seluruh integral rumit yang terdaftar di Tabel Mathematical Handbooks of America, Ed. Stegun Abronowics</li><li>dapat digunakan untuk memecahkan persamaan diferensial khusus orde 2 seperti Fungsi khusus Bessel, Hermite, Airy, dan teman-temannya tanpa menggunakan deret pangkat (power series) dan atau deret Frobenius</li><li>salah satu aplikasi penting dari kedua metode ini adalah dapat meningkatkan akurasi perhitungan waktu tiba sinyal gelombang pembawa gempa dan mendeteksi gejala anomali di bawah permukaan bumi</li><li>solusi analitik Digaram AF(A) SMT ini bisa digunakan oleh para pengguna metode numerik untuk menguji kestabilan solusinya.</li></ul> Sebagai bukti dari pernyataan point terakhir, penulis tampilkan komparasi hasil perhitungan solusi analitik formula AF(A) terhadap Pers.(3) dengan perhitungan metode Runge-kutha orde 4 yang dilakukan dengan sofware test Matlab versi 6.5. Komparasi hasil perhitungan tersebut ditunjukkan dalam Gambar 2 dan Gambar 3 berikut.<br /> <p style="text-align: justify;" class="MsoNormal"> <img src="http://rohedi.com/images/stories/penemuan2006-9.gif" alt="Image" title="Image" width="363" border="0" height="308" hspace="6" /> </p> <p style="text-align: justify;" class="MsoNormal"> <img src="http://rohedi.com/images/stories/penemuan2006-10.gif" alt="Image" title="Image" width="400" border="0" height="308" hspace="6" /> </p> <p style="text-align: justify;" class="MsoNormal"> Gambar 2 Komparasi solusi Pers.(3) untuk nilai a=1, b=-0,5, A=5, f=1Hz, dan stepsize </p> <p style="text-align: justify;" class="MsoNormal"> <img src="http://rohedi.com/images/stories/penemuan2006-11.gif" alt="Image" title="Image" width="363" align="middle" border="0" height="359" hspace="6" /> </p> <p style="text-align: justify;" class="MsoNormal"> <img src="http://rohedi.com/images/stories/penemuan2006-12.gif" alt="Image" title="Image" width="348" border="0" height="377" hspace="6" /> </p> <p style="text-align: justify;" class="MsoNormal"> Gambar 3 Komparasi solusi Pers.(3) untuk nilai a=1, b=-1, A=1, f=60 Hz </p> <p style="text-align: justify;" class="MsoNormal"> Para pembaca sekalian, tampak dari Gambar 2 dan Gambar 3 di atas, ternyata solusi metode numerik sangat tergantung pada pemakaian stepsize h. Karena itu para pengguna metode numerik seyogyanya terlebih dahulu melakukan uji kestabilan terhadap metode numerik yang akan digunakan. Jika tidak, maka akurasi solusi numerik tersebut perlu dipertanyakan. Bagaimana para ahli numerik mempertanggungjawabkan solusinya untuk persamaan-persamaan diferensial nonlinear yang solusi eksak analitiknya belum diketahui, Wallahu a’lam.<br /><br />Semoga tulisan ini bermanfaat bagi perkembangan ilmu pengetahuan di Indonesia terutama untuk meningkatkan kecerdasan anak bangsa.<br /><br /><br />Salam ....<br /><br />Rohedi </p></span>CGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com0tag:blogger.com,1999:blog-8656208893701172133.post-9806337931383166472008-08-26T19:53:00.000-07:002008-09-02T18:59:19.421-07:00Analytical Formulation of Normal Modes in Symmetrical Directional-coupler<span class="awal">T</span>he analysis of the optical power transfer in the linear step index directional-coupler based on the couple-mode theory is inaccurate for a small gap. This problem has been previously overcome by using the normal-modes approximation. Commonly, <p>this approximation has been solved by numerical methods such as Fourier transform or finite difference. In this paper, the Helmholtz equation is, instead, analytically solved by using a characteristic matrix of multiplayer waveguides in order to find the electric field and its propagation constant of the normal-modes. The importance of these analytical formulas, is that a phase shift of the normal modes along the propagation can be easily analyzed. </p> <p> </p> <h4><b> 1. Introduction</b></h4> <p>In integrated optics areas, the directional-couplers are the major interest with potential applications to optical communications, i.e, used to fabricate low-loss optical switches[1], high speed modulators[2], polarization splitter[3] and wavelength demultiplexer/multiplexer[4]. Due to coupling effect, optical power can be transferred from one waveguide to another adjacent waveguide as a result of the overlap in the evanescent fields of the two guides. The amount of power transferred between the waveguides depends upon the waveguide parameters, i.e, the guided wavelength, the confinement of the individual waveguides, the separation between them, the length over which they interact, and the phase mismatch between the individual waveguides[5]. </p> <p> The power transfer of two waveguides in the directional-couplers has been treated extensively utilizing the coupled-mode method, but as shown in [6] this method becomes less accurate when the waveguides get too close. An alternative choice is the normal-modes approximation. This approximation taken full account of the entire structure and solves for modal indices and guided fields of the supermodes. In the normal-modes approach, the characteristic of the directional-couplers are then represented by interferences between the guided fields of the supermodes[7], i.e symmetrical and asymmetrical modes. In practical, the directional-couplers are made in 3-D structure, consist of waveguides with finite lateral dimensions. In order to obtain the exact solutions of normal modes, the 3-D is usually reduced to 2-D guides structure[7],[8]. Hence in the 2-D guides, the two parallel waveguides with their surrounding medium can be considered as a single structure, so that the normal-modes of the such structure can be solved by method of multilayer waveguides. In this paper we use the multilayer waveguides to formulate the optical electric fields in the symmetrical directional-couplers. The expression of such the guided fields derived by method of multilayer waveguides given by Kogelnik[9], and Rohedi[10].<br /></p><p>For Detail Visit <a href="http://rohedi.com/">http://rohedi.com</a></p>CGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com0tag:blogger.com,1999:blog-8656208893701172133.post-88060383924363788902008-08-26T19:51:00.000-07:002008-09-02T18:59:51.191-07:00Application of Stable Modulation Scheme for Solving Bernoulli Differential Equation<span class="awal">S</span>olving of Bernoulli differential equation traditionally always is done applies linearization procedure by using Bernoulli transformation function. This paper introduces a new technique of solving the Bernoulli differential equation without using linearization by application of stable modulation scheme. <p> Application of the method named Stable Modulation Technique (called as SMT) is started by splitting the Bernoulli differential equation to parts of linear and nonlinear, then writes down the solution of nonlinear part in the form of modulation function which its initial value besides played the part of as amplitude A and also is modulated into a phase function F(A). The exact solution of Bernoulli differential equation given in AF(A) formula obtained after replacing the linear solution part into initial value of its nonlinear part solution. In this paper presented the usage of SMT for solving the storage model of magnetic energy into inductor. </p> <p> </p> <p> <b> I. Introduction</b><br />The homogeneous Bernoulli differential equation that commonly called Bernoulli differential equation (BDE) to become as primary model in so many application branches. The BDE is distinguished to the degree of its nonlinearity (n). For instance, the BDE having degree of two commonly applied to model growth of logistic in Biology[1] and the behavior of chaos[2], while for the degree of three (n=3)<br />the BDE forms Gizbun or quartic equation commonly used to analyze corrosion process[3]. The BDEalso is nonlinear part of Klein Gordon partial differential equation which is the usage widely, among these are in studying the dynamics of elementary particles and stochastic resonances4], the transportation of fluxon[5], the excitation of squeezed laser[6], etc. </p> <p><br />As commonly explained in mathematical handbook[7],[8], solving of BDE always is done through linearization procedure as in recommending by Jacob Bernoulli. The transformation from the form of nonlinear to the linear differential equation is performed by using Bernoulli transformation function, and hereinafter solved by using the common method of solving a linear differential equation. Recently, Rohedi[9] has reported verification of the Bernoulli transfomation function, and justify the general solution of Bernoulli differential equation which written in mathematical handbook. At the paper was introduced stable modulation technique (called as SMT) focused to solve BDE of constant coefficients, especially which its solution is started from ordinary point. Rohedi[10] has also reported application of SMT for solving a Ricatti differential equation of constant coefficients which its inhomogeneous term in form of sinusoidal function that also was started from ordinary point. In this paper, applying the SMT is developed to solve BDE for arbitrary value of its linear and nonlinear coefficients, either and also constant valuable and varying as function of its dependent variable. In mathematics, this differential equation is known as the general homogeneous Bernoulli differential<br />equation.<br /></p><p>For Detail Visit <a href="http://rohedi.com/">http://rohedi.com</a></p>CGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com0tag:blogger.com,1999:blog-8656208893701172133.post-31517578768209429432008-08-26T19:47:00.001-07:002008-09-02T19:00:27.945-07:00Simplified Calculation of Guided Nonlinear Boundary-Wave Parameters Using Optimization Procedure<span class="awal">A</span> guided wave excited along the boundary between linear and nonlinear media known as initial inspiration for developing devices based on Kerr nonlinear optics, such as the nonlinear directional coupler, etc. Two important parameters for such structure are respectively the minimum amplitude of light required for the excitation, and the location of the peak of guided nonlinear boundary wave. Analytical procedure of derivation the two parameters commonly involved the Jacobi’s elliptic functions based on the numerical integration. In order to simplify the calculation procedure, in this paper we introduce optimization procedure based on applying the solitary wave solution for guided field inside the nonlinear media. The simulation of guided wave excitation at the interface between linear and nonlinear media is also presented<br /><h4>1. Introduction</h4> <p> In integrated optics, all of optical devices have been made in waveguide structures, based on both linear and nonlinear optics materials. The simpliest structure of optical waveguides made of linear materials whose all of refractive indices independently to the propagating light intensity requires three layers that known as slab optical guide or slab waveguide [1]. Hence, an advanced devices such as directional-coupler that commonly applicable for optical power transfer and/or optical switching, beside in complicated structure, but also it requires applying of external treatments, because all devices made of linear materials only can operate as passive components [2]. On the other hand, due to the dependency to the propagating light intensity, recently the nonlinear materials especially for the Kerr optics materials much be applied for fabricating active-optical waveguides, that have been commonly used in many application branches, for examples, all devices of X-junction, Mach-zender interferometer, feedback grating, optical bistability, etc [3]. In addition, because of self focusing of the nonlinear Kerr optics materials, the number layer of slab waveguide reduces from three into two layers, while optical wave that propagates over the waveguide is commonly called as the boundary wave. Important to be stressed here, that the two-layer slab waveguide consists of a nonlinear Kerr optics material as the guiding layer is deposited on top a substrate of linear optics material [4].<br />The main problem in designing the two layers slab waveguide that are determination of the minimum amplitude of light required for the excitation, and the location of the peak of guided nonlinear boundary wave. The two parameters are depend on the effective refractive index of the slab waveguide. This paper introduces optimization procedure for obtaining all parameters of the two layer slab waveguide. The procedure of optimization was primarly applied to maximize the peak of electric field guided boundary wave in the nonlinear guiding layer.<br /></p><p>For Detail Visit <a href="http://rohedi.com/">http://rohedi.com</a><br /></p>CGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com0tag:blogger.com,1999:blog-8656208893701172133.post-21271879414929780612008-06-29T20:14:00.000-07:002008-12-14T00:07:09.011-08:00Creating A New Planck’s Formula of Spectral Density of Black-body Radiation by Means of AF(A) Diagram<span class="awal">T</span>his paper reports derivation of a new Planck’s formula of spectral density of black-body radiation, that was originated by modeling the interpolation formula of Planck’s law of obtaining<span style="font-size:100%;"> </span><span style="font-size:100%;">the mean of energy of black-body cavity in 2<sup>nd</sup> order of Bernoulli equation. The new Planck’s formula is created by means AF(A) diagram of solving arctangent differential equation after transformin</span><span style="font-size:100%;"> </span><span style="font-size:100%;">the Bernoulli equation into the arctangent differential equation The New Planck’s formula not only contains the terms</span><span style=";font-size:100%;color:black;" > of the photon energy and the energy difference between two states of the motion of harmonic oscillator (<span style="position: relative; top: 3pt;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" spt="75" preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum @10 21600 0"> </v:formulas> <v:path extrusionok="f" gradientshapeok="t" connecttype="rect"> <o:lock ext="edit" aspectratio="t"> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style="'width:17.25pt;" ole=""> <v:imagedata src="file:///C:\DOCUME~1\lala\LOCALS~1\Temp\msohtml1\03\clip_image001.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1025" drawaspect="Content" objectid="_1276326181"> </o:OLEObject> </xml><![endif]--></span><span style="font-size:100%;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIaS8c34j3w0-UKdHTdKEGfgEqEodypRgBZZLZDvt6WuCNSpEaLEAs27YP9_6OuKA2wbVHJJGZV2PF8zG8m4dg3OSQMj6mcW95mEY02pehJSk56t-4ApIkeMDYrC7q-i0X74_yIW6w5xrO/s1600-h/hw.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhIaS8c34j3w0-UKdHTdKEGfgEqEodypRgBZZLZDvt6WuCNSpEaLEAs27YP9_6OuKA2wbVHJJGZV2PF8zG8m4dg3OSQMj6mcW95mEY02pehJSk56t-4ApIkeMDYrC7q-i0X74_yIW6w5xrO/s400/hw.JPG" alt="" id="BLOGGER_PHOTO_ID_5217510261826713282" border="0" /></a></span><span style=";font-size:100%;color:black;" >), but also </span><span style="font-size:100%;">contains both terms of the minimum energy of harmonics oscillator (</span><span style="position: relative; top: 3pt;font-size:100%;" ><!--[if gte vml 1]><v:shape id="_x0000_i1026" type="#_x0000_t75" style="'width:27pt;height:12.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\lala\LOCALS~1\Temp\msohtml1\03\clip_image003.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1026" drawaspect="Content" objectid="_1276326182"> </o:OLEObject> </xml><![endif]--><span style="font-size:100%;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjYarTIzC9OPO87C4wivjF5DNpk6dlA-5LJrEGLp3SkiDUT-q97-JsbX95qHbKFaNwbYWozuWwm2cYoCLREfTuCc_BZ8EZxzNBsBpq2au4XXeLuGUZd1qjyTC_lKyJzQYS65yCLtG4lXFZ/s1600-h/hw2.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjjYarTIzC9OPO87C4wivjF5DNpk6dlA-5LJrEGLp3SkiDUT-q97-JsbX95qHbKFaNwbYWozuWwm2cYoCLREfTuCc_BZ8EZxzNBsBpq2au4XXeLuGUZd1qjyTC_lKyJzQYS65yCLtG4lXFZ/s400/hw2.JPG" alt="" id="BLOGGER_PHOTO_ID_5217510270012091698" border="0" /></a>) and the phase differences (</span><span style="position: relative; top: 3pt;font-size:100%;" ><!--[if gte vml 1]><v:shape id="_x0000_i1027" type="#_x0000_t75" style="'width:19.5pt;height:12pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\lala\LOCALS~1\Temp\msohtml1\03\clip_image005.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1027" drawaspect="Content" objectid="_1276326183"> </o:OLEObject> </xml><![endif]--><span style="font-size:100%;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjF4cECjOM9zYmx__C85f6XJDTNaKHtGkMIhEpHfwAIgjuUmKj-ZUDm7lskIKiFJbhWLhYv_GsAZjjySHQ_WYPIOnQuwGQnQoKsGlOKw9ZGPkk0s_y6S-jwAJQGblY8HkYhw_IHnzYrNoUj/s1600-h/phi2.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjF4cECjOM9zYmx__C85f6XJDTNaKHtGkMIhEpHfwAIgjuUmKj-ZUDm7lskIKiFJbhWLhYv_GsAZjjySHQ_WYPIOnQuwGQnQoKsGlOKw9ZGPkk0s_y6S-jwAJQGblY8HkYhw_IHnzYrNoUj/s400/phi2.JPG" alt="" id="BLOGGER_PHOTO_ID_5217510271115818050" border="0" /></a>) as representing the intermodes-orthogonality, hence </span><span style="font-size:100%;">it can answer why the explanation of black-body radiation has been associated with </span><span style="font-size:100%;">the harmonic oscillators.</span><p></p><p class="Abstract" style="margin-bottom: 0.0001pt; text-align: justify;"> </p><p class="SectionTitle" style="margin: 0cm 0cm 0.0001pt; line-height: normal;"><span style="font-size:100%;"><span style="font-weight: bold;">I. Introduction</span></span></p><p class="SectionTitle" style="margin: 0cm 0cm 0.0001pt; line-height: normal;"><br /><span style="font-size:100%;"><span style=""> </span><span style="font-size:10;"><o:p></o:p></span></span></p> <div style="text-align: justify;"><span style="font-size:100%;"><span style="">The era of developing the modern scientific was originated by presence the Planck’s law of black-body radiation as representation of the light sources in a thermal equilibrium. Planck not only could complete<span style=""> </span>the Rayleigh-Jeans and Wien’s laws, both of radiation laws previously that of each only appropriates to the experimental for the range of long wavelength and short wavelength respectively, but </span></span><span style="font-size:100%;"><span style="">he also created a new constant h called as Planck’s constant that not known previously in classical physic</span></span><span style="font-size:100%;"><span style="">s [1]. Based on his constant, Planck postulated the discretitation of electromagnetic energy in packet of energy called as photon, where for every angular frequency (<span style="position: relative; top: 3pt;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" spt="75" preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum @10 21600 0"> </v:formulas> <v:path extrusionok="f" gradientshapeok="t" connecttype="rect"> <o:lock ext="edit" aspectratio="t"> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style="'width:9.75pt;" ole=""> <v:imagedata src="file:///C:\DOCUME~1\lala\LOCALS~1\Temp\msohtml1\06\clip_image001.wmz" title=""> </v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1025" drawaspect="Content" objectid="_1276327016"> </o:OLEObject> </xml><![endif]--></span></span><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhY1XqSMdUmPGLRT1uS4kWAdC48qaEOtW0fiuffTdvf3oZGb4zqHHZ6IESeLbXtVw2FIi21CYsHJIxA_JjMbEnBUtdZlwmnZgqcxypgYJbiuIcDRbkbO3V40VEbDMaOgHrbb1_7rO3ssWVz/s1600-h/ohm.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhY1XqSMdUmPGLRT1uS4kWAdC48qaEOtW0fiuffTdvf3oZGb4zqHHZ6IESeLbXtVw2FIi21CYsHJIxA_JjMbEnBUtdZlwmnZgqcxypgYJbiuIcDRbkbO3V40VEbDMaOgHrbb1_7rO3ssWVz/s400/ohm.JPG" alt="" id="BLOGGER_PHOTO_ID_5217517627432837458" border="0" /></a><span style="font-size:100%;"><span style="">), the energy per photon is </span></span><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLM5mL-rPJxfN-3fhuaBpu_pqNgbMT6QQH1Bms4G_a6PuWEmT_8bt5M2DncE2jMna6_opll3TU_pzG8hlP9R7Ie5ILAzDfuChq_0lNLnKC-6XwQbqxnDn8ahjQDxzAXzChr57JNKk5MS0Q/s1600-h/ehw.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgLM5mL-rPJxfN-3fhuaBpu_pqNgbMT6QQH1Bms4G_a6PuWEmT_8bt5M2DncE2jMna6_opll3TU_pzG8hlP9R7Ie5ILAzDfuChq_0lNLnKC-6XwQbqxnDn8ahjQDxzAXzChr57JNKk5MS0Q/s400/ehw.JPG" alt="" id="BLOGGER_PHOTO_ID_5217517629496665378" border="0" /></a><span style="font-size:100%;"><span style=""><span style="position: relative; top: 3pt;"><!--[endif]--></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1026" drawaspect="Content" objectid="_1276327017"> </o:OLEObject> </xml><![endif]-->, which was justified later by Einstein through fotoelectric effect [2]. Planck’s law for black-body radiation also became the primary base of derivation Einstein coefficients of spontaneous and stimulated of emission rates for generating the light sources such as maser and laser [3].</span></span></div><p class="Abstract" style="margin-bottom: 0.0001pt; text-align: justify;"><span style="font-size:100%;">For Detail:<span style="text-decoration: underline;"><br /></span></span></p><p class="Abstract" style="margin-bottom: 0.0001pt; text-align: justify;">visit: <a href="http://rohedi.com/">http://rohedi.com</a> OR</p><p class="Abstract" style="margin-bottom: 0.0001pt; text-align: justify;">Download <a href="http://www.snapdrive.net/files/568161/Paper/9_AF%28A%29_Planck_JIPC.pdf">Here</a><br /><span style="font-size:100%;"><span style="text-decoration: underline;"></span></span></p><p class="Abstract" style="margin-bottom: 0.0001pt; text-align: justify;"><br /><span style="font-size:100%;"><o:p></o:p></span> </p>CGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com0tag:blogger.com,1999:blog-8656208893701172133.post-17132572581655736832008-06-23T19:25:00.000-07:002008-12-14T00:07:09.177-08:00How to upgrade the running time of Computer<p><strong></strong><span class="awal">O</span>ne of built-in function required in building micro-processor of computer is infinite series of tangent function. Until now, there is one general formula for the infinite series of tangent function that available in mathematical handbook, and also used in all symbolic software-package. The general formula was created by Sir. Bernoulli that is of form</p><p align="center"><img src="http://rohedi.com/images/stories/bernauly-tan.gif" alt="Sample Image" width="443" height="69" /> </p> <p>where,<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxfF9niPf2JGEUF6znQkjl9iiPhnogZFC-DfvqQNgBDNEBanHxz5WQ-lkVvBqSSbpwyIxf9r5UOugkisWkS5o7U7c_3uXMY73MzvmBjoQGsJ_A2OrmC1umvqE1he0oNay9VyxCr19JBFS3/s1600-h/b2n.JPG"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhxfF9niPf2JGEUF6znQkjl9iiPhnogZFC-DfvqQNgBDNEBanHxz5WQ-lkVvBqSSbpwyIxf9r5UOugkisWkS5o7U7c_3uXMY73MzvmBjoQGsJ_A2OrmC1umvqE1he0oNay9VyxCr19JBFS3/s400/b2n.JPG" alt="" id="BLOGGER_PHOTO_ID_5217488669089863890" border="0" /></a>is Bernoulli numbers, and n 1,2,3,. Unfortunately, the general formula is not consistent with Maclaurin series that always contains n ! in denominator of each terms. In this paper, we present Rohedi’s reversion for obtaining the infinite series of tangent function without of use the Maclaurin series, but its result is still consistent with the Maclaurin series. Derivation of RohediSmart reversion formula based on solution of the arctangent differential equation</p><div style="text-align: center;"><img src="http://rohedi.com/images/stories/arctan.gif" alt="Sample Image" width="186" height="55" /></div><p>solved ecursively by using short stable modulation technique (S-SMT). Comparison the infinite series of tangent function of Rohedi’s reversion with the result of both Matematica 5.1, Maple 9.5 shows thattime consuming of Rohedi’s reversion is shortest, hence need smallest of computational memory.Finally, we give comparison the time consuming of Rohedi’s reversion for 4.0365 10321 x1635of 1635nd coefficient of infinite series of tangent function calculated using matlab needs2.744 s, while Maple 9.5 soft needs 36.35 s </p><br /><p><img src="http://rohedi.com/images/stories/deret_tan.gif" alt="Sample Image" width="502" height="331" /></p><span id="fullpost"><p> <img src="http://rohedi.com/images/stories/rohedi_rever.gif" alt="Sample Image" width="459" height="155" /></p><br /><p> <img src="http://rohedi.com/images/stories/byhand.gif" alt="Sample Image" width="505" height="469" /></p><h4>Discussion and Conclusion</h4><p>We show that output of Rohedi’s reversion for infinite series of tangent function is still consistent with Maclaurin series. According to the equality of output both of Matematica and Maple software-package, we resume that both software-package have been used equal general formula, that is Bernoulli’s formula. Hence, we take a conclusion that Rohedi’s reversion formula as a new general formula of infinite series of the tangent function that can be used to upgrade the running time of computer.<br /></p><p>References :<br /></p><ol><li>Abranowitz,M., and Stegun, I.A., “Handbook of Mathematical Functions”, New-York, 1972</li><li>Spiegel,M.R.,”Mathematical Handbook of Formulas and Tables”, Schaum’s Outline Series,McGRAW-Hill Book Company, page 104, 1968.</li><li>Rohedi,A.Y., “Solving of the homogeneous nonlinear differential equation by using Stable Modulation Technique”, Presented on Conference of Mathematical Analysis and its Applications”, Department of Mathematics, Natural Sciences, ITS, Surabaya, Indonesia, 10-11 August 2006.</li><li>Rohedi,A.Y., “Analytical Solution Of The Ricatti Differential Equation For High Frequency Derived By Using The Stable Modulation Technique”, Presented on International Conference of Mathematics and Natural Sciences, Poster Edition, Faculty of Natural Sciences, ITB, Bandung, Indonesia, 29-30 Nopember 2006.</li><li>Shortcut Solution for Bernoulli Equation in AF(A) Formula Based on Stable Modulation Technique (will be submitted for publication</li></ol>This paper will be submitted for publication.</span>CGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com0tag:blogger.com,1999:blog-8656208893701172133.post-11191356308477300062008-06-17T22:43:00.000-07:002008-12-14T00:07:09.449-08:00Profile of Ali Yunus Rohedi<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNx_RuQVm2dOA3R622DlBAcq9bJDuWxa9lsPFSwDK20Bpy3k0DcwCG-Tztj6ZEM0ESk4xrJ5phJfKIUT6ODIeXVqAZecaeZkAJ-eLdu3_yRnBcUV_WiHtn6nqA7E5c0fROjo5h97HI9wnG/s1600-h/Prof+Ali+Yunus+Rohedi,+MT.gif"><img style="margin: 0pt 10px 10px 0pt; float: left; cursor: pointer; width: 265px; height: 309px;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNx_RuQVm2dOA3R622DlBAcq9bJDuWxa9lsPFSwDK20Bpy3k0DcwCG-Tztj6ZEM0ESk4xrJ5phJfKIUT6ODIeXVqAZecaeZkAJ-eLdu3_yRnBcUV_WiHtn6nqA7E5c0fROjo5h97HI9wnG/s400/Prof+Ali+Yunus+Rohedi,+MT.gif" alt="" id="BLOGGER_PHOTO_ID_5213093631300742226" border="0" /></a><span style="color: rgb(51, 51, 255);font-size:180%;" ><span lang="EN-US"><span style="font-weight: bold;"><br />Ali Yunus Rohedi</span> </span></span> <p style="font-weight: bold;" class="MsoNormal"><span lang="EN-US">Head of ROHEDI Laboratory, </span><st1:city><st1:place><span lang="EN-US">Surabaya</span></st1:place></st1:city><span lang="EN-US"><o:p></o:p></span></p> <p class="MsoNormal"><span lang="EN-US"><span style="font-weight: bold;">E-mail:</span><span style="color: rgb(0, 32, 96); font-weight: bold;">afasmt@yahoo.com</span><o:p></o:p></span></p> <span style=";font-family:arial;font-size:85%;" lang="EN-US" >I was born in Bangkalan Madura, East Java, Indonesia on </span><span style=";font-family:georgia;font-size:85%;" ><st1:date year="1967" day="14" month="5" style="font-family:arial;"><span style="" lang="EN-US">May 14, 1967</span></st1:date></span><span style=";font-family:arial;font-size:85%;" lang="EN-US" >. I received the B.E from Department of Physics, Sepuluh Nopember Institute of Technology (ITS) </span><span style=";font-family:georgia;font-size:85%;" ><st1:city style="font-family:arial;"><st1:place><span style="" lang="EN-US">Surabaya</span></st1:place></st1:city></span><span style=";font-family:arial;font-size:85%;" lang="EN-US" > in 1991, and M.E degrees from Optoelectronics and Laser Applications (OEAL) </span><span style=";font-family:georgia;font-size:85%;" ><st1:place style="font-family:arial;"><st1:placename><span style="" lang="EN-US">Indonesia</span></st1:placename><span style="" lang="EN-US"> </span><st1:placetype><span style="" lang="EN-US">University</span></st1:placetype></st1:place></span><span style=";font-family:arial;font-size:85%;" lang="EN-US" > in 1997 respectively. Since 1992, I have been working at Department of Physics, Sepuluh Nopember Institute of Technology (ITS) in </span><span style=";font-family:georgia;font-size:85%;" ><st1:city style="font-family:arial;"><st1:place><span style="" lang="EN-US">Surabaya</span></st1:place></st1:city></span><span style="" lang="EN-US"><span style=";font-family:georgia;font-size:85%;" >. My current research of interest include optical and microwave communications, nonlinear optical phenomena, and developing “smart technique” for solving Problems of Mathematics.</span><br /></span><span lang="SV" style="font-size:12;"><span style="font-weight: bold;font-size:130%;" ><br /><br /><br /><br />Paper Publications :<br /><br /></span><o:p></o:p></span> <span id="fullpost"> <ol style="margin-top: 0cm;" start="1" type="1"><li class="MsoNormal" style="text-align: justify;"><span style="" lang="EN-US">Ali Yunus Rohedi, “<i style="">A Novel : Solving of Homogeneous Bernoulli Differential Equation using Stable Modulation Technique</i>”, Presented on Conference of Mathematical Analysis and its Applications, Department of Mathematics, Faculty of Natural Sciences, Sepuluh Nopember Institute of Technology, Surabaya, Indonesia, 11-12 August 2006.<o:p></o:p></span></li><li class="MsoNormal" style="text-align: justify;"><span style="" lang="EN-US">Ali Yunus Rohedi, <i style="">“Analytic Solution of the Ricatti Differential Equation for High Frequency Derived by Using Stable Modulation Technique”</i>, Presented on Internartional Conference of Mathematics and Natural Sciences, Poster Edition, Faculty of Natural Sciences, ITB, </span><st1:place><st1:city><span style="" lang="EN-US">Bandung</span></st1:city><span style="" lang="EN-US">, </span><st1:country-region><span style="" lang="EN-US">Indonesia</span></st1:country-region></st1:place><span style="" lang="EN-US">, 29-30 Nopember 2006. <o:p></o:p></span></li><li class="MsoNormal" style="text-align: justify;"><span style="" lang="EN-US">Ali Yunus Rohedi</span><span lang="EN-US">, ”<i style="">Smart Solution of Bernoulli and Arctangent Differential Equations in AF(A) Diagram Based on Anti Einstein Technique</i>”, Presented on Workshop of Theoretical Physics (WTP2K), LafTiFA, Department of Physics<span style="">, Faculty of Natural Sciences, Sepuluh Nopember Institute of Technology,</span> </span><st1:place><st1:city><span lang="EN-US">Surabaya</span></st1:city><span lang="EN-US">, </span><st1:country-region><span lang="EN-US">Indonesia</span></st1:country-region></st1:place><span lang="EN-US">, </span><st1:date year="2007" day="13" month="5"><span lang="EN-US">13 May 2007</span></st1:date><span lang="EN-US">. <o:p></o:p></span></li><li class="MsoNormal" style="text-align: justify;"><span style="" lang="EN-US">Ali Yunus</span><span lang="EN-US"> Rohedi, ”<i style="">Introducing Bernoulli Integral for Solving Some Physical Problems</i>”, Proceeding <span style=""> </span>Symposium of<span style=""> </span>Physics and` Applications, Department of Physics<span style="">, Faculty of Natural Sciences, Sepuluh Nopember Institute of Technology</span>, pp:A6.1-5, Surabaya, Department of Physics<span style="">, Faculty of Natural Sciences, Sepuluh Nopember Institute of Technology,</span> Surabaya, Indonesia, 14 May 2007.<o:p></o:p></span></li><li class="MsoNormal" style="text-align: justify;"><span style="" lang="EN-US">Ali Yunus<span style=""> </span></span><span lang="EN-US">Rohedi, “Applying Stable Modulation Scheme for Solving <i style="">Bernoulli Differential Equation</i>”, Journal of Physics and its Applications, Vol.3 pp:1-5, <span style=""> </span></span><st1:place><st1:city><span lang="EN-US">Surabaya</span></st1:city><span lang="EN-US">, </span><st1:country-region><span lang="EN-US">Indonesia</span></st1:country-region></st1:place><span lang="EN-US">, January 2007.<o:p></o:p></span></li><li class="MsoNormal" style="text-align: justify;"><span style="" lang="EN-US">Ali Yunus</span><span lang="EN-US"> Rohedi, ”<i style="">Analytic solution of Nonlinear Schrödinger Equation by Means of A New </i><span style=""> </span><i style="">Approach”</i> Presented on International Symposium of Modern Optics and Its Applications, Physics Department ITB, Bandung, Indonesia, 6-10 August 2007.<span style=""><o:p></o:p></span></span></li><li class="MsoNormal" style="text-align: justify;"><span style="" lang="EN-US">Ali Yunus</span><span lang="EN-US"> Rohedi, ”<i style="">Introducing A Stable Modulation Technique for Solving An Inhomogeneous Bernoulli Differential Equation</i>”, Presented on <span style="">International Colaboration Laser applications (ICOLA), Indonesia of University, </span></span><st1:place><st1:city><span style="" lang="EN-US">Yogjakarta</span></st1:city><span style="" lang="EN-US">, </span><st1:country-region><span style="" lang="EN-US">Indonesia</span></st1:country-region></st1:place><span style="" lang="EN-US">, 5-7 September 2007. <o:p></o:p></span></li><li class="MsoNormal" style="text-align: justify;"><span style="" lang="EN-US">Ali Yunus</span><span lang="EN-US"> Rohedi,”<i style="">Creating A New Planck’s Formula of Spectral Density of Black-body Radiation by Means of AF(A) Diagram</i>”, will be presented on 2<sup>nd</sup> JIPC<span style="">, </span></span><st1:place><st1:placename><span style="" lang="EN-US">Gadjah</span></st1:placename><span style="" lang="EN-US"> </span><st1:placename><span style="" lang="EN-US">Mada</span></st1:placename><span style="" lang="EN-US"> </span><st1:placetype><span style="" lang="EN-US">University</span></st1:placetype></st1:place><span style="" lang="EN-US">, </span><st1:place><st1:city><span style="" lang="EN-US">Yogjakarta</span></st1:city><span style="" lang="EN-US">,<span style=""> </span></span><st1:country-region><span style="" lang="EN-US">Indonesia</span></st1:country-region></st1:place><span style="" lang="EN-US">, 6-8 September 2007.</span></li><li class="MsoNormal" style="text-align: justify;"><span style="" lang="EN-US"></span><span style="" lang="EN-US"><span style=""></span></span><span style="" lang="FI">Sekartedjo and A.Y. Rohedi,<i style="">”</i></span><i style=""><span lang="EN-US">Generalized Linear Dispersion Relation for Symmetrical Directional-coupler of Five-layer Waveguide”</span></i><span lang="EN-US">, Presented on <span style="">International Colaboration Laser applications (ICOLA), Indonesia University, Yogjakarta, Indonesia, 5-7 September, 2007</span></span><span style="" lang="EN-GB"></span></li><li class="MsoNormal" style="text-align: justify;"><span style="" lang="EN-GB">A.M. Hatta<sup>1</sup>, Sekartedjo<sup>1</sup>, D. Sawitri<sup>1</sup>, A. Rubiyanto<sup>2</sup>, A. Y. Rohedi<sup>2</sup>, G. Yudhoyono<sup>2</sup></span><span lang="EN-US">, ”<i style=""><span style="">Design of all-optical logic gates based on multimode interference structure</span></i><span style="">”, </span>Presented on <span style="">International Colaboration Laser applications (ICOLA), </span></span><st1:place><st1:placename><span style="" lang="EN-US">Indonesia</span></st1:placename><span style="" lang="EN-US"> </span><st1:placetype><span style="" lang="EN-US">University</span></st1:placetype></st1:place><span style="" lang="EN-US">, </span><st1:place><st1:city><span style="" lang="EN-US">Yogjakarta</span></st1:city><span style="" lang="EN-US">, </span><st1:country-region><span style="" lang="EN-US">Indonesia</span></st1:country-region></st1:place><span style="" lang="EN-US">,<span style=""> </span>5-7 September, 2007.<o:p></o:p></span></li></ol></span>CGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com0tag:blogger.com,1999:blog-8656208893701172133.post-86777546125348197942008-06-16T19:59:00.000-07:002008-12-14T00:07:09.953-08:00Letter from Rohedi Laboratory (Laboratory of New Science)<span style="line-height: 115%;font-family:arial;font-size:100%;" lang="EN-US">Dear All, <o:p></o:p></span> <p class="MsoNormal" style="text-align: justify;font-family:arial;"><span style="line-height: 115%;font-size:100%;" lang="EN-US">I interest to investigate the validity of out</span><span style="line-height: 115%;font-size:100%;" lang="EN-US">put symbolic software especially for calculating the roots of polynomials .</span><span style="line-height: 115%;font-size:100%;" lang="EN-US"> Now, I have been developing a new method for the purpose. The method c</span><span style="line-height: 115%;font-size:100%;" lang="EN-US">an create analytical formulation for n order polyn</span><span style="line-height: 115%;font-size:100%;" lang="EN-US">omials,<o:p></o:p></span></p> <p class="MsoNormal" style="text-indent: 36pt;font-family:arial;"><span style="font-size:100%;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyEksJ_Ptx_Ia7GgMCFiLfUJ-xzu9YDljh10xUqRm0IC-i1DvDdoBX8PTptHlpnN7sG-ipcvv9wuz1AWHNSw_lklq55fLHFOEXJ0h0l7a3DHIF8K0XeKyG484-WQo9HNpPxZ2yNl7lk4vT/s1600-h/letterfromrohedilaboratorygambar1.bmp"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjyEksJ_Ptx_Ia7GgMCFiLfUJ-xzu9YDljh10xUqRm0IC-i1DvDdoBX8PTptHlpnN7sG-ipcvv9wuz1AWHNSw_lklq55fLHFOEXJ0h0l7a3DHIF8K0XeKyG484-WQo9HNpPxZ2yNl7lk4vT/s320/letterfromrohedilaboratorygambar1.bmp" alt="" id="BLOGGER_PHOTO_ID_5212681261081524306" border="0" /></a><br /></span><span style="line-height: 115%;font-size:100%;" lang="EN-US"><o:p></o:p></span></p> <p class="MsoNormal" style="font-family:arial;"><span style="line-height: 115%;font-size:100%;" lang="EN-US">To show the performance of the met</span><span style="line-height: 115%;font-size:100%;" lang="EN-US">hod, firstly, I present the comparison the first root of the following polynomial to the matlab result.<o:p></o:p></span></p> <p class="MsoNormal" style="text-indent: 36pt; font-family: arial;"><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4IWOf4zWDQxs0Kjmyo9MupZJ0SJ51Zi1E4XC8YSpgPS3uTZ5btudfJGHrRcQCrhMd7CdYTZtJd7QWn6UGWhyiViiTvjEaIK46um0JLIOV5_nu8G4LSGiAsY4AFyb57QyC-YK4RYPeIiuc/s1600-h/letterfromrohedilaboratorygambar2.bmp"><img style="cursor: pointer;" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi4IWOf4zWDQxs0Kjmyo9MupZJ0SJ51Zi1E4XC8YSpgPS3uTZ5btudfJGHrRcQCrhMd7CdYTZtJd7QWn6UGWhyiViiTvjEaIK46um0JLIOV5_nu8G4LSGiAsY4AFyb57QyC-YK4RYPeIiuc/s320/letterfromrohedilaboratorygambar2.bmp" alt="" id="BLOGGER_PHOTO_ID_5212681904972664338" border="0" /></a><br /><span style="line-height: 115%;font-size:100%;" lang="EN-US"><o:p></o:p></span></p> <p class="MsoNormal" style="font-family:arial;"><span style="line-height: 115%;font-size:100%;" lang="EN-US">From ROHEDI Laboratory </span><span style="font-size:100%;"><st1:city><st1:place><span style="line-height: 115%;" lang="EN-US">Surabaya</span></st1:place></st1:city></span><span style="line-height: 115%;font-size:100%;" lang="EN-US"> <o:p></o:p></span></p><span id="fullpost"> <p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">>>polinomn([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,500,51,52,53,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">54,55,56,57,58,59,600,61,62,63,64,65,66,67,68,69,700,71,72,73,74,75,76,77,78,79,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">800,81,82,83,84,85,86,87,88,89,900,91,92,93,94,95,96,97,98,99,1000,101,102,103,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;">1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061])</span></p><p class="MsoNormal" style="font-family:arial;"><span lang="EN-US" style="font-size:100%;"><br /></span></p> <p class="MsoNormal" style="line-height: normal;font-family:arial;"><span lang="EN-US" style="font-size:100%;">The first root of 1060<span style=""> </span>order polynomial above is</span></p><p class="MsoNormal" style="line-height: normal;font-family:arial;"><br /><span lang="EN-US" style="font-size:100%;"> <o:p></o:p></span></p> <p class="MsoNormal" style="line-height: normal;font-family:arial;"><span lang="EN-US" style="font-size:100%;"><span style="color: rgb(255, 0, 0); font-weight: bold;">The root of matlab = </span><span style="color: rgb(255, 0, 0); font-weight: bold;"> </span><span style="color: rgb(255, 0, 0); font-weight: bold;">0.90967612057974 + 0.65233483663790i</span><o:p></o:p></span></p> <p class="MsoNormal" style="line-height: normal; font-weight: bold; color: rgb(255, 0, 0);font-family:arial;"><span lang="EN-US" style="font-size:100%;">with remainder<span style=""> </span>= -5.386242315198940e+040 +3.112117014950832e+040i<o:p></o:p></span></p> <p class="MsoNormal" style="line-height: normal;font-family:arial;"><span lang="EN-US" style="font-size:100%;"><span style="font-weight: bold; color: rgb(255, 0, 0);">matlab time consuming</span><span style="font-weight: bold; color: rgb(255, 0, 0);"> </span><span style="font-weight: bold; color: rgb(255, 0, 0);">= 28.711 s.</span></span></p><p class="MsoNormal" style="line-height: normal;font-family:arial;"><br /><span lang="EN-US" style="font-size:100%;"><span style="font-weight: bold; color: rgb(255, 0, 0);"></span><o:p></o:p></span></p> <p class="MsoNormal" style="line-height: normal; font-weight: bold; color: rgb(51, 51, 255);font-family:arial;"><span lang="EN-US" style="font-size:100%;">myroot= -0.99461160642852 + 0.10321236597345i<o:p></o:p></span></p> <p class="MsoNormal" style="line-height: normal; font-weight: bold; color: rgb(51, 51, 255);font-family:arial;"><span lang="EN-US" style="font-size:100%;">with remainder<span style=""> </span>= <span style=""> </span>9.436007530894131e-010 -5.946915848653589e-009i<o:p></o:p></span></p> <p class="MsoNormal" style="line-height: normal;font-family:arial;"><span lang="EN-US" style="font-size:100%;"><span style="font-weight: bold; color: rgb(51, 51, 255);">my time consuming</span><span style="font-weight: bold; color: rgb(51, 51, 255);"> </span><span style="font-weight: bold; color: rgb(51, 51, 255);">= 3.725 s.</span><o:p></o:p></span></p> <p class="MsoNormal" style="line-height: normal;font-family:arial;"><span lang="EN-US" style="font-size:100%;"><br /></span></p><p class="MsoNormal" style="line-height: normal;font-family:arial;"><span lang="EN-US" style="font-size:100%;">My formula not only very accurate but also requires least of time consuming.<o:p></o:p></span></p> <span style="line-height: 115%;font-family:Calibri;font-size:100%;" lang="EN-US"><span style="font-family:arial;">Here, I need your information what is the appropriate journal </span><span style="font-family:arial;"> </span><span style="font-family:arial;">for publication the method. Or, if any one or company who interest to buy the formula, you can contact me via email</span> :</span><a href="mailto:afasmt@yahoo.com"><span style="line-height: 115%;font-family:Calibri;font-size:11;" lang="EN-US"><span style="line-height: 115%;font-size:14;" >afasmt@yahoo.com</span></span></a></span>CGyphttp://www.blogger.com/profile/03083920129653642192noreply@blogger.com0