Sunday, June 29, 2008

Creating A New Planck’s Formula of Spectral Density of Black-body Radiation by Means of AF(A) Diagram

This 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 the mean of energy of black-body cavity in 2nd order of Bernoulli equation. The new Planck’s formula is created by means AF(A) diagram of solving arctangent differential equation after transformin the Bernoulli equation into the arctangent differential equation The New Planck’s formula not only contains the terms of the photon energy and the energy difference between two states of the motion of harmonic oscillator (), but also contains both terms of the minimum energy of harmonics oscillator () and the phase differences () as representing the intermodes-orthogonality, hence it can answer why the explanation of black-body radiation has been associated with the harmonic oscillators.

I. Introduction


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 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 he also created a new constant h called as Planck’s constant that not known previously in classical physics [1]. Based on his constant, Planck postulated the discretitation of electromagnetic energy in packet of energy called as photon, where for every angular frequency (), the energy per photon is , 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].

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Monday, June 23, 2008

How to upgrade the running time of Computer

One 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

Sample Image

where,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

Sample Image

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 10321 x1635of 1635nd coefficient of infinite series of tangent function calculated using matlab needs2.744 s, while Maple 9.5 soft needs 36.35 s


Sample Image

Sample Image


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Discussion and Conclusion

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.

References :

  1. Abranowitz,M., and Stegun, I.A., “Handbook of Mathematical Functions”, New-York, 1972
  2. Spiegel,M.R.,”Mathematical Handbook of Formulas and Tables”, Schaum’s Outline Series,McGRAW-Hill Book Company, page 104, 1968.
  3. 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.
  4. 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.
  5. Shortcut Solution for Bernoulli Equation in AF(A) Formula Based on Stable Modulation Technique (will be submitted for publication
This paper will be submitted for publication.

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Tuesday, June 17, 2008

Profile of Ali Yunus Rohedi


Ali Yunus Rohedi

Head of ROHEDI Laboratory, Surabaya

E-mail:afasmt@yahoo.com

I was born in Bangkalan Madura, East Java, Indonesia on May 14, 1967. I received the B.E from Department of Physics, Sepuluh Nopember Institute of Technology (ITS) Surabaya in 1991, and M.E degrees from Optoelectronics and Laser Applications (OEAL) Indonesia University in 1997 respectively. Since 1992, I have been working at Department of Physics, Sepuluh Nopember Institute of Technology (ITS) in Surabaya. My current research of interest include optical and microwave communications, nonlinear optical phenomena, and developing “smart technique” for solving Problems of Mathematics.




Paper Publications :

  1. Ali Yunus Rohedi, “A Novel : Solving of Homogeneous Bernoulli Differential Equation using Stable Modulation Technique”, 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.
  2. Ali Yunus Rohedi, “Analytic Solution of the Ricatti Differential Equation for High Frequency Derived by Using Stable Modulation Technique”, Presented on Internartional Conference of Mathematics and Natural Sciences, Poster Edition, Faculty of Natural Sciences, ITB, Bandung, Indonesia, 29-30 Nopember 2006.
  3. Ali Yunus Rohedi, ”Smart Solution of Bernoulli and Arctangent Differential Equations in AF(A) Diagram Based on Anti Einstein Technique”, Presented on Workshop of Theoretical Physics (WTP2K), LafTiFA, Department of Physics, Faculty of Natural Sciences, Sepuluh Nopember Institute of Technology, Surabaya, Indonesia, 13 May 2007.
  4. Ali Yunus Rohedi, ”Introducing Bernoulli Integral for Solving Some Physical Problems”, Proceeding Symposium of Physics and` Applications, Department of Physics, Faculty of Natural Sciences, Sepuluh Nopember Institute of Technology, pp:A6.1-5, Surabaya, Department of Physics, Faculty of Natural Sciences, Sepuluh Nopember Institute of Technology, Surabaya, Indonesia, 14 May 2007.
  5. Ali Yunus Rohedi, “Applying Stable Modulation Scheme for Solving Bernoulli Differential Equation”, Journal of Physics and its Applications, Vol.3 pp:1-5, Surabaya, Indonesia, January 2007.
  6. Ali Yunus Rohedi, ”Analytic solution of Nonlinear Schrödinger Equation by Means of A New Approach” Presented on International Symposium of Modern Optics and Its Applications, Physics Department ITB, Bandung, Indonesia, 6-10 August 2007.
  7. Ali Yunus Rohedi, ”Introducing A Stable Modulation Technique for Solving An Inhomogeneous Bernoulli Differential Equation”, Presented on International Colaboration Laser applications (ICOLA), Indonesia of University, Yogjakarta, Indonesia, 5-7 September 2007.
  8. Ali Yunus Rohedi,”Creating A New Planck’s Formula of Spectral Density of Black-body Radiation by Means of AF(A) Diagram”, will be presented on 2nd JIPC, Gadjah Mada University, Yogjakarta, Indonesia, 6-8 September 2007.
  9. Sekartedjo and A.Y. Rohedi,Generalized Linear Dispersion Relation for Symmetrical Directional-coupler of Five-layer Waveguide”, Presented on International Colaboration Laser applications (ICOLA), Indonesia University, Yogjakarta, Indonesia, 5-7 September, 2007
  10. A.M. Hatta1, Sekartedjo1, D. Sawitri1, A. Rubiyanto2, A. Y. Rohedi2, G. Yudhoyono2, ”Design of all-optical logic gates based on multimode interference structure”, Presented on International Colaboration Laser applications (ICOLA), Indonesia University, Yogjakarta, Indonesia, 5-7 September, 2007.

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Monday, June 16, 2008

Letter from Rohedi Laboratory (Laboratory of New Science)

Dear All,

I interest to investigate the validity of output symbolic software especially for calculating the roots of polynomials . Now, I have been developing a new method for the purpose. The method can create analytical formulation for n order polynomials,


To show the performance of the method, firstly, I present the comparison the first root of the following polynomial to the matlab result.


From ROHEDI Laboratory Surabaya

>>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,

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,

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,

800,81,82,83,84,85,86,87,88,89,900,91,92,93,94,95,96,97,98,99,1000,101,102,103,

104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,

124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,

144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,

164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,

184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,

204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,

224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,

244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,

264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,

284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,

304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,

324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,

344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,

364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,

384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,

404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,

424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,

444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,

464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,

484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,

504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,

524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,

544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,

564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,

584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,

604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,

624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,

644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,

664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,

684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,

704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,

724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,

744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,

764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,

784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,

804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,

824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,

844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,

864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,

884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,

904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,

924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,

944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,

964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,

984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,

1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,

1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,

1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,

1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061])


The first root of 1060 order polynomial above is


The root of matlab = 0.90967612057974 + 0.65233483663790i

with remainder = -5.386242315198940e+040 +3.112117014950832e+040i

matlab time consuming = 28.711 s.


myroot= -0.99461160642852 + 0.10321236597345i

with remainder = 9.436007530894131e-010 -5.946915848653589e-009i

my time consuming = 3.725 s.


My formula not only very accurate but also requires least of time consuming.

Here, I need your information what is the appropriate journal for publication the method. Or, if any one or company who interest to buy the formula, you can contact me via email :afasmt@yahoo.com

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Simplified Calculation of Guided Nonlinear Boundary-Wave Parameters Using Optimization Procedure. Download -- View

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Generalized Linear Dispersion Relation for Symmetrical Directional-coupler of Five-layer Waveguide. Download -- View

Formulasi Analitis Tetapan Propagasi Efektif Modus TE untuk Directional Coupler Linier Diturunkan dengan Metode Matrik Karakteristik Lapis Jamak. Download -- View