Welcome to Applied Mathematics and Physics

Applied Mathematics and Physics is a peer-reviewed, open access journal that publishes original research articles and review articles in all areas of mathematics and physics. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote, share, and discuss various new issues and developments in different areas of mathematics and physics.

ISSN (Print): 2333-4878

ISSN (Online): 2333-4886

Editor-in-Chief: Vishwa Nath Maurya

Website: http://www.sciepub.com/journal/AMP

   

Article

Chaos and Order in the Integers Primes

1Doctor of Engineering Science, Academician of RANS, member of EANS, Volga State University of Technology, Russia


Applied Mathematics and Physics. 2014, 2(4), 146-156
doi: 10.12691/amp-2-4-4
Copyright © 2014 Science and Education Publishing

Cite this paper:
P.M. Mazurkin. Chaos and Order in the Integers Primes. Applied Mathematics and Physics. 2014; 2(4):146-156. doi: 10.12691/amp-2-4-4.

Correspondence to: P.M.  Mazurkin, Doctor of Engineering Science, Academician of RANS, member of EANS, Volga State University of Technology, Russia. Email: kaf_po@mail.ru

Abstract

Statistical modeling by asymmetric waves, with variables amplitude and a half-cycle of fluctuation, dynamics of a scatter of block structure of positive part of a number of the integers prime which located in a row of 10 million natural numbers, proved emergence of three stages of growth of the left and right reference points in blocks of binary decomposition of prime numbers. These a reference point settle down on each side from the dividing line in the form of the two in the degree equal to number of the category of a binary numeral system, without unit. The first stage of critical chaos is formed by critical prime numbers 0, 1 and 2. The second stage of an accruing order begins with number 3 and comes to the end with a margin error in 1% at the 1135th category of binary notation for the left reference point. At blocks increasing on length among the integers prime by calculations after the 1135th category there comes the third stage with high definiteness of the beginning and the end of blocks of binary decomposition of positive prime numbers.

Keywords

References

[1]  I.N. Beckman, “Informatics. Course of lectures.” URL: http://profbeckman.narod.ru/InformLekc.htm
 
[2]  P.M. Mazurkin. “Patterns of primes”. Germany: Palmarium Academic Publishing, 2012. 280 p.
 
[3]  P.M. Mazurkin, “Series Primes in Binary.” American Journal of Applied Mathematics and Statistics, vol. 2, no. 2 (2014): 60-65.
 
[4]  P.M. Mazurkin, “Proof the Riemann Hypothesis.” American Journal of Applied Mathematics and Statistics, vol. 2, no. 1 (2014): 53-59.
 
[5]  P.M. Mazurkin, “Increment Primes.” American Journal of Applied Mathematics and Statistics, vol. 2, no. 2 (2014): 66-72.
 

Article

Spherical Harmonic on a Four Sphere

1Department of Physics, National Institute of Technology, Srinagar, Kashmir, India

2Department of Applied Sciences, College of Engineering and Technology, BGSB University, Rajouri, India

3Department of Physics, Aligarh Muslim University, U.P, India


Applied Mathematics and Physics. 2014, 2(5), 157-160
doi: 10.12691/amp-2-5-1
Copyright © 2014 Science and Education Publishing

Cite this paper:
Shabir Ahmad Akhoon, Ashaq Hussain Sofi, Anil Maini, Asloob Ahmad Rather. Spherical Harmonic on a Four Sphere. Applied Mathematics and Physics. 2014; 2(5):157-160. doi: 10.12691/amp-2-5-1.

Correspondence to: Ashaq  Hussain Sofi, Department of Physics, National Institute of Technology, Srinagar, Kashmir, India. Email: shifs237@gmail.com

Abstract

In this paper, we will analyse the scalar harmonics on a four sphere using a associated Legendre function. Then, we will use these modes to construct two types of vector harmonics on a four sphere. Finally, we will also construct three types of tensor harmonics on a four sphere. As there is a relation between de Sitter spacetime and four sphere, these modes are related to the modes on de Sitter spacetime.

Keywords

References

[1]  K. Bamba, G. Cognola, S. D. Odintsov, and S. Zerbini, Phys. Rev. D 90, 023525 (2014).
 
[2]  D. Seery, JCAP 0905, 021 (2009).
 
[3]  S. Dubovsky, L. Senatore and G. Villadoro, JHEP. 0904, 118 (2009).
 
[4]  A. del Rio and J. Navarro-Salas, Phys. Rev. D89, 084037 (2014).
 
[5]  A. Higuchi, J. Math. Phys. 43, 6385 (2002).
 
Show More References
[6]  C. de Rham and G. Gabadadze, Phys. Rev. D 82, 4 (2010).
 
[7]  F. Melia, arXiv:1202.0775.
 
[8]  I. Ya. Aref'eva, N. V. Bulatov and R. V. Gorbachev, arXiv:1112.5951.
 
[9]  K.L. Mahanta, Astrophys. Space Sci. 353, 683 (2014).
 
[10]  H. Hossienkhani, A. Najafi and N. Azimi, Astrophys. Space Sci. 353, 311 (2014).
 
[11]  J. Rekier, I. Cordero-Carrion and A. Fuzfa, arXiv:1409.3476.
 
[12]  I. A. Meitei, T. I. Singh and K. Y. Singh, Int. J. Mod. Phys. D23, 1450077 (2014).
 
[13]  P. Helbig, Springer Proc. Phys. 157, 355 (2014).
 
[14]  D. S. Gorbunov, Phys. Usp. 57, 503 (2014).
 
[15]  L. Fabbri, Int. J. Theor. Phys. 50, 3616, 2011.
 
[16]  T. Kugo and I. Ojima, Nucl. Phys. B144, 234, 1978.
 
[17]  K. Nishijima and M. Okawa, Prog. Theor. Phys. 60, 272, 1978.
 
[18]  N. Nakanishi and I. Ojima, Covariant operator formalism of gauge theories and quantum gravity - World Sci. Lect. Notes. Phys -, 1990.
 
[19]  A. Lesov, arXiv:0911.0058,
 
[20]  M. Faizal and S. Upadhyay, Phys. Lett. B 736 (2014) 288.
 
[21]  M. Faizal and T. S. Tsun, arXiv:1407.3119.
 
[22]  M. Faizal and S. I. Kruglov, arXiv:1406.2653.
 
[23]  Mohammad Vahid Takook.
 
[24]  A. F. Ali, M. Faizal, B. Majumder, arXiv:1406.1980.
 
[25]  R. R. Metsaev, arXiv:1407.2601.
 
[26]  P. Yu. Moshin and A. A. Reshetnyak, arXiv:1406.5086.
 
[27]  M. Faizal, arXiv:1406.0273 J. MacDonald and D. J. Mullan, Phys. Rev. D80, 043507, 2009.
 
[28]  A. M. Sinev, arXiv:0806.3212.
 
[29]  C. Pagliarone, arXiv:hep-ex/0612037.
 
[30]  M. Faizal, Class. Quant. Grav. 29, 035007, 2012.
 
[31]  A. Pakman, JHEP 0306, 053, 2003.
 
[32]  S. I. Kruglov and M. Faizal, arXiv:1408.3794.
 
[33]  K. Izumi and T. Tanaka, Prog. Theor. Phys. 121, 427, 2009.
 
[34]  M. Faizal and B. Majumder, arXiv:1408.3795.
 
[35]  M. Faizal, J. Phys. A 44, 402001, 2011.
 
[36]  I. A. Batalin and G. A. Vilkovisky, Phys. Lett. B 102, 27, 1981.
 
[37]  I. A. Batalin and G. A. Vilkovisky, Phys. Rev. D 28, 2567, 1983.
 
[38]  C. Bizdadea and S. O. Saliu, J. Phys. A 31, 8805, 1998.
 
[39]  C. Bizdadea, I. Negru and S. O. Saliu, Int. J. Mod. Phys. A 14, 359, 1999.
 
[40]  M. Faizal, Found. Phys. 41, 270, 2011.
 
[41]  M. Faizal, Phys. Lett. B 705, 120, 2011.
 
[42]  J. W. Mo_at, Phys. Lett. B 506, 193, 2001.
 
[43]  J. W. Mo_at, Phys. Lett. B 491, 345, 2000.
 
[44]  M. Faizal, Mod. Phys. Lett. A27: 1250075, 2012.
 
[45]  S. Ahmad, Comm. in Theo.l Phys, 59, 439, 2013.
 
[46]  M. Faizal, Phys. Rev. D 84, 106011, 2011.
 
[47]  M. Faizal and D. J. Smith, Phys. Rev. D85: 105007, 2012.
 
[48]  V. Mader. M. Schaden, D. Zwanziger and R. Alkofer, arXiv:1309.0497.
 
[49]  M. Faizal, JHEP 1204: 017, 2012.
 
[50]  A. Gustavsson, arXiv:1203.5883.
 
[51]  M. Faizal, Comm. Theor. Phys. 57, 637, 2012
 
[52]  M. S. Bianchi, M. Leoni and S. Penati, arXiv:1112.3649.
 
[53]  M. Faizal, Europhys. Lett. 98: 31003, 2012.
 
[54]  M. Marino and P. Putrov, arXiv:1110.4066.
 
[55]  K. Okuyama, arXiv:1110.3555.
 
[56]  M. Faizal, JHEP. 1204, 017, 2012.
 
[57]  A. Belhaj, arXiv:1107.2295.
 
[58]  M. Faizal, arXiv:1303.5477.
 
[59]  D. Zwanziger, AIPConf.Proc.892:121-127, 2007.
 
[60]  M. Faizal, Mod. Phys. Lett. A28: 1350034, 2013.
 
[61]  D. Zwanziger, Phys. Rev. D76: 125014, 2007.
 
[62]  M. Faizal, Int. J. Mod. Phys. A28: 1350012, 2013.
 
[63]  M. Golterman, L. Zimmerman, Phys.Rev. D71, 117502, 2005.
 
[64]  M. Faizal, JHEP. 1301: 156, 2013.
 
[65]  D. Polyakov, Phys.Lett. B611, 173, 2005.
 
[66]  M. Faizal, Europhys. Lett. 103: 21003, 2013.
 
[67]  A. Imaanpur, JHEP 0503, 030, 2005.
 
[68]  M. Faizal, Nucl. Phys. B. 869: 598, 2013.
 
[69]  Jen-Chi Lee, Eur.Phys.J.C1:739-741, 1998.
 
[70]  M. Faizal, Phys. Rev. D87: 025019, 2013.
 
[71]  A. Kapustin, Y. Li, Anton Kapustin, Adv.Theor.Math.Phys. 9, 559, 2005.
 
[72]  M. Faizal, Int. J. Theor. Phys. 52: 392, 2013.
 
[73]  Chuan-Tsung Chan, Jen-Chi Lee, Yi Yang, Phys.Rev. D71 086005, 2005.
 
[74]  M. Faizal,Class. Quant. Grav. 29: 215009, 2012.
 
[75]  R. P. Malik, arXiv:hep-th/0412333.
 
[76]  M. Faizal, Comm. Theor. Phys. 58: 704, 2012.
 
[77]  N. Boulanger, J.Math.Phys. 46, 053508, 2005.
 
[78]  M. Faizal, Mod. Phys. Lett. A27: 1250147, 2012.
 
[79]  W. H. Huang, arXiv:1107.2030.
 
[80]  M. Faizal and M. Khan, Eur. Phys. J. C 71, 1603, 2011.
 
[81]  J. T. Liu and Z. Zhao, arXiv:1108.5179.
 
[82]  M. Fontanini and M. Trodden, Phys. Rev. D 83, 103518, 2011.
 
[83]  V. O. Rivelles, Phys. Lett. B 577, 137, 2003.
 
[84]  B. S. DeWitt, Phys. Rev. 160, 1113, 1967.
 
[85]  M. Faizal, J.Exp.Theor.Phys. 114, 400, 2012, arXiv:gr-qc/0602094.
 
[86]  Y. Ohkuwa, Int. J. Mod. Phys. A 13, 4091, 1998.
 
[87]  M. Faizal, Mod. Phys. Lett. A 27, 1250007, 2012.
 
[88]  I. T. Durham, arXiv:1307.3691.
 
[89]  M. Faizal, Phys. Lett. B727: 536, 2013.
 
[90]  V. Bonzom, Phys.Rev.D84:024009, 2011.
 
[91]  M. Faizal, arXiv:1303.5478.
 
[92]  D. Chowdhury, S. Raju, S. Sachdev, A. Singh and P. Strack, Phys. Rev. B87, 085138 (2013).
 
[93]  S. Singh, C. Ganguly and T. Padmanabhan, Phys. Rev. D 87, 104004 (2013).
 
[94]  M. Faizal, A. F. Ali and A. Nassar, arXiv:1405.4519.
 
[95]  M. Faizal, arXiv:1404.5024.
 
[96]  M. V. Takook, arXiv:1403.1204.
 
[97]  M. Faizal, arXiv:1407.3118.
 
[98]  M. Faizal and T. S. Tsun, arXiv:1402.6802.
 
[99]  Ru-Nan Huang, arXiv:1304.5309.
 
[100]  S. I. Kruglov and M. Faizal, arXiv:1408.3794.
 
[101]  R. Garattini and B. Majumder, Nucl. Phys. B 884, 125 (2014).
 
[102]  A. Awad, A. F. Ali and B. Majumder, JCAP 10,052 (2013).
 
[103]  A. Awad and A. F. Ali, JHEP 1406, 093 (2014).
 
[104]  M. Faizal, arXiv:1301.0224.
 
[105]  M. Faizal and B. Majumder, arXiv:1408.3795.
 
[106]  R. M. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics- University of Chicago Press- (1994) 10.
 
Show Less References

Article

Attenuation in Left-handed Waveguide Structure by Equivalent Current Theory Method

1Physics Department, Al Azhar University, Gaza Strip, Palestinian Authority

2Physics Department, Islamic University, Gaza Strip, Palestinian Authority


Applied Mathematics and Physics. 2015, 3(1), 1-5
doi: 10.12691/amp-3-1-1
Copyright © 2015 Science and Education Publishing

Cite this paper:
Hana M. Mousa, Mohammed M. Shabat. Attenuation in Left-handed Waveguide Structure by Equivalent Current Theory Method. Applied Mathematics and Physics. 2015; 3(1):1-5. doi: 10.12691/amp-3-1-1.

Correspondence to: Hana  M. Mousa, Physics Department, Al Azhar University, Gaza Strip, Palestinian Authority. Email: H.mousa @ alazhar.edu.ps

Abstract

In this work, the propagation and attenuation characteristics of both TE and TM waves in a waveguide structure consisting of left handed material (LHM) film by using the equivalent current theory of optical waveguide coupling method have been derived and obtained. The dispersion relations and the attenuation coefficient were numerically solved for a given set of parameters: allowed phase angles; core’s thicknesses; and propagation constants. We found that lower attenuation is realized for higher propagation constants. Moreover, attenuation coefficient has same small positive values for all thickness in phase angles range of values (00-570). Besides that, the attenuation decreases to negative values with thickness increase in phase angles range of values (570-590) which means a gain of the wave is achieved for wider buffer layer and at larger phase angles. We also found that, TE waves have lower attenuation than that of TM waves.

Keywords

References

[1]  Wu, Y., “Introduction to equivalent current theory of optical waveguide coupling,” J. Chin. Inst. Commun. 3, 1-8, 1982.
 
[2]  Wu, Y. “Derivation of general coupling equation of coupler and its verification,” Sci. Sin. 26, 894-900, 1983.
 
[3]  Harris, J.H., Shubert R., and Polky, J.N. “Beam coupling to films,” J. Opt. Soc. Am. 60, 1007-1016, 1970.
 
[4]  Gruchmann, D. Petermann, K., Satudige,L. l, and Weidel, E. “Optic polarizers with high extinction ratio,” in Proc.9th European Conf.Opt. Commun., 305-308, 1983.
 
[5]  Wu, Y., “Equivalent current theory of optical waveguide coupling,” J. Opt. Soc. Am. A, 4 (10) 1902-1910, 1987.
 
Show More References
[6]  Yu,T. and Wu,Y. “Theoretical study of metal –clad optical waveguide polarizer,” IEEE, J. of Qun.Elec. 25, (6) 1209-1213-1989.
 
[7]  Boifot A. M., Lier E., Schaug T., Petersen T., “Simple and broadband orthomode transducer,: Proc. of IEEE, 137, 396-400, 1990.
 
[8]  Yeap, K. H., Tham C.Y., Yassin, G., Yeong, K.C., “Attenuation in rectangular waveguides with finite conductivity walls,” Radioengineering, 20, (2), 472-478, 2011.
 
[9]  Mousa, H.M. and Shabat, M.M., “TM waves in cylindrical Superlattices (LANS) bounded by left handed materials,” App. Phys A 111, 1057-1063, 2013.
 
[10]  Mousa, H. M., and Shabat, M. M. 'Electromagnetic Guided Waves in a Metamaterial-Magnetic Waveguide structure,' Int. J. Modern Physics B, 25 (32) 2011.
 
[11]  Mousa, H. M., and Shabat, M. M.,” TM waves in cylindrical superlattices (LANS) bounded by left-handed material (LHM),” Appl. Phys.A, 111, 1057-1063, 2012.
 
[12]  Tang, T. T.,. Liu, W. L, He X. J. and Gao, X. Y., Optik- International Journal for Light and Electron Optics, Vol. 123, 2012.
 
[13]  Caloz, C. and Itoh, T., “Electromagnetic Metamaterials Transmission Line Theory and Microwave Applications,” IEEE Press and Wiley, New York, 2005.
 
[14]  Zhang S., Fan, W., Mallo, K. J. y and Brueck, S. R. J., “Near-infrared double negative metamaterials', Optics Express, 13, (13), pp.4922-4930(2005).
 
Show Less References