Applied Mathematics and Physics»Articles

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

Block Structure of a Number of the Integers Prime

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


Applied Mathematics and Physics. 2014, 2(4), 135-145
DOI: 10.12691/amp-2-4-3
Copyright © 2014 Science and Education Publishing

Cite this paper:
P.M. Mazurkin. Block Structure of a Number of the Integers Prime. Applied Mathematics and Physics. 2014; 2(4):135-145. doi: 10.12691/amp-2-4-3.

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

Abstract

Binary decomposition of numbers forms geometrical blocks. They depend on approach of a prime or whole prime number to values of the two in the degree equal to number from a natural row. As a result there is a strict geometry among prime or whole prime numbers in the form of block structure. This structure receives distinctive signs and harmonicas in positive part of a number of the whole prime numbers are shown. Statistically from a natural numbers regularities of growth of power of the left and right reference points, as borders previous and the subsequent from values of the two in degree, at blocks increasing on length among the whole prime numbers are proved.

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References

[[[
[[1]  P.M. Mazurkin, “Wavelet Analysis of a Number of Prime Numbers.” American Journal of Numerical Analysis, vol. 2, no. 2 (2014): 29-34.
 
[[2]  P.M. Mazurkin. Patterns of primes. Germany : Palmarium Academic Publishing, 2012. 280 p.
 
[[3]  P.M. Mazurkin, “Stable Laws and the Number of Ordinary.” Applied Mathematics and Physics, vol. 2, no. 2 (2014): 27-32.
 
[[4]  P.M. Mazurkin, “Series Primes in Binary.” American Journal of Applied Mathematics and Statistics, vol. 2, no. 2 (2014): 60-65.
 
[[5]  P.M. Mazurkin, “Proof the Riemann Hypothesis.” American Journal of Applied Mathematics and Statistics, vol. 2, no. 1 (2014): 53-59.
 
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[6]  P.M. Mazurkin, “Increment Primes.” American Journal of Applied Mathematics and Statistics, vol. 2, no. 2 (2014): 66-72.
 
[7]  P.M. Mazurkin, “Identification of statistical stable patterns.” SCIENCE AND WORLD. International scientific journal, № 3 (3), 2013. p. 28-33.
 
[8]  P.M. Mazurkin, A.S. Filonov, “Mathematical modeling. Identification univariate statistical regularities: tutorial.” Yoshkar-Ola, Mari State Technical University, 2006. 292 p.
 
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Article

Asymmetric Wavelet Signal of Gravitational Waves

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


Applied Mathematics and Physics. 2014, 2(4), 128-134
DOI: 10.12691/amp-2-4-2
Copyright © 2014 Science and Education Publishing

Cite this paper:
P.M. Mazurkin. Asymmetric Wavelet Signal of Gravitational Waves. Applied Mathematics and Physics. 2014; 2(4):128-134. doi: 10.12691/amp-2-4-2.

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

Abstract

On the example of a complex of 10 pulsars shows a method to identify the statistical models and the analysis of the model amplitude of gravitational waves, depending on the rotation periods of pulsars. Hilbert applied invariants. Shows the levels of adequacy asymmetric wavelet signals detected by statistical data. Proved insufficient deterministic models for the Laplace-Mandelbrot law. For 10 pulsars obtained statistical model pulsating universe. The model contains two modified 's law and two asymmetric wavelets oscillatory perturbation of gravitational waves in overcoming the energy crisis. Interpretation of the resulting statistical model is given based on the relativistic theory of gravitation. To do this, four components of the statistical model are divided into two cones of causality.

Keywords

References

[
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[[2]  S.F. Levin Statistical methods of the solution of measuring problems of cosmology and gravitation // International session conference of Section of nuclear physics of Office of physical sciences of the Russian Academy of Sciences "Physics of fundamental interactions": 12-16.11.2012. Moscow: National Research Nuclear University “MEPhI”, 2012. 75 pages.
 
[[3]  P.M. Mazurkin, “Wavelet Analysis of a Number of Prime Numbers.” American Journal of Numerical Analysis, vol. 2, no. 2 (2014): 29-34.
 
[[4]  P.M. Mazurkin. Patterns of primes. Germany: Palmarium Academic Publishing, 2012. 280 p.
 
[[5]  P.M. Mazurkin, “Stable Laws and the Number of Ordinary.” Applied Mathematics and Physics, vol. 2, no. 2 (2014): 27-32.
 
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[6]  P.M. Mazurkin, A.S. Filonov, Mathematical modeling. Identification univariate statistical regularities: tutorial. Yoshkar-Ola, Mari State Technical University, 2006. 292 pages.
 
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Article

Two Numerical Methods to Solve the Second Order Multi-pantograph Equation with Boundary Conditions

1Department Mathematics, University of Qom, Qom, Iran


Applied Mathematics and Physics. 2014, 2(4), 124-127
DOI: 10.12691/amp-2-4-1
Copyright © 2014 Science and Education Publishing

Cite this paper:
Mahdi Ahmadinia, Zeinab Safari. Two Numerical Methods to Solve the Second Order Multi-pantograph Equation with Boundary Conditions. Applied Mathematics and Physics. 2014; 2(4):124-127. doi: 10.12691/amp-2-4-1.

Correspondence to: Mahdi  Ahmadinia, Department Mathematics, University of Qom, Qom, Iran. Email: mahdiahmadinia72@gmail.com & m-ahmadinia@qom.ac.ir

Abstract

In this article, we present two numerical methods to solve the second order multi-pantograph equation with boundary conditions. The multi-pantograph equation is converted to an integral equation then the integral equation is solved by two projective methods. Some properties of Chebyshev polynomials are employed to prove the convergence analysis of the two proposed methods. Finally, numerical examples also are given to illustrate the efficiency and validity of the two proposed methods.

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References

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[6]  M. Sezer and A. Akyüz-Daşcıoğlu, “A Taylor method for numerical solution of generalized pantograph equations with linear functional argument,”J. Comput. Appl. Math., 200. 217-225. 2007.
 
[7]  M. Sezer, S. Yalçinbaş and M. Gülsu,“A Taylor polynomial approach for solving generalized pantograph equations with nonhomogeneous term,” Int. J. Comput. Math., 85(7), 1055-1063. 2008.
 
[8]  M. Sezer, S. Yalçinbaş and N. Şahin, “Approximate solution of multi-pantograph equation with variable coefficients,” J. Comput. Appl. Math., 214. 406-416. 2008.
 
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[10]  E.Yusufoğlu, “An efficient algorithm for solving generalized pantograph equations with linear function alargument,” Appl. Math. Comput, 217(7). 3591-3595. 2010.
 
[11]  Ş. Yüzbaşi, “An efficient algorithm for solving multi-pantograph equations systems,” Comput. Math. Appl, 64, 589-603, 2012.
 
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[15]  Z. H. Yu, “Variational iteration method for solving the multi-pantograph delay equation,” Phys. Lett. A, 372(43). 6475-6479. 2008.
 
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Article

On ’t Hooft–Polyakov Monopole, Julia–Zee Dyon, and Higgs Field, throughout the Generalized Bogomoln’yi Equations

1B.M. Birla Science Centre, Hyderabad, India


Applied Mathematics and Physics. 2014, 2(3), 119-123
DOI: 10.12691/amp-2-3-8
Copyright © 2014 Science and Education Publishing

Cite this paper:
Lukasz Andrzej Glinka. On ’t Hooft–Polyakov Monopole, Julia–Zee Dyon, and Higgs Field, throughout the Generalized Bogomoln’yi Equations. Applied Mathematics and Physics. 2014; 2(3):119-123. doi: 10.12691/amp-2-3-8.

Correspondence to: Lukasz  Andrzej Glinka, B.M. Birla Science Centre, Hyderabad, India. Email: laglinka@gmail.com; lukaszglinka@wp.eu

Abstract

In this paper, making use of the’tHooft–Polyakov–Julia–Zeeansatz for the SU(2) Yang–Mills–Higgs gauge field theory, we present the straightforward generalization of the Bogomoln’yi equations and its several consequences. Particularly, this is shown that this idea is able to generate new types of non-abelian both dyons and magnetic monopoles and, moreover, that within the new model the scalar field can be described through the Coulomb potential, whereas, upto aconstant, the non-abelian gauge field becomes the Wu–Yang monopole.

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References

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Article

Massive Electrodynamic Gravity

1B.M. Birla Science Centre, Hyderabad, India


Applied Mathematics and Physics. 2014, 2(3), 112-118
DOI: 10.12691/amp-2-3-7
Copyright © 2014 Science and Education Publishing

Cite this paper:
Lukasz Andrzej Glinka. Massive Electrodynamic Gravity. Applied Mathematics and Physics. 2014; 2(3):112-118. doi: 10.12691/amp-2-3-7.

Correspondence to: Lukasz  Andrzej Glinka, B.M. Birla Science Centre, Hyderabad, India. Email: laglinka@gmail.com; lukaszglinka@wp.eu

Abstract

In this paper, an effcient combination of the diverse theoretical approaches, such like the Einstein gravitational waves, the Lifshitz cosmological perturbation theory, the Veltman perturbative quantum gravity, and the Maxwell electrodynamics, leads to an essentially new discussion of either massless and massive gravitons. The new force law of gravitation is established. The case of the Planckian particle is considered in the context of the Markov hypothesis.

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References

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Article

Challenging Photon Mass: from Scalar Quantum Electrodynamics to String Theory

1B.M. Birla Science Centre, Hyderabad, India


Applied Mathematics and Physics. 2014, 2(3), 103-111
DOI: 10.12691/amp-2-3-6
Copyright © 2014 Science and Education Publishing

Cite this paper:
Lukasz Andrzej Glinka. Challenging Photon Mass: from Scalar Quantum Electrodynamics to String Theory. Applied Mathematics and Physics. 2014; 2(3):103-111. doi: 10.12691/amp-2-3-6.

Correspondence to: Lukasz  Andrzej Glinka, B.M. Birla Science Centre, Hyderabad, India. Email: laglinka@gmail.com; lukaszglinka@wp.eu

Abstract

A massless photon, originated already through the Maxwell theory of electromagnetism, is one of the basic paradigms of modern physics, ideally supported throughout both the quantum electrodynamics and the Higgs mechanism of spontaneous symmetry breaking which lays the foundations of the Standard Model of elementary particles and fundamental interactions. Nevertheless, the physical interpretation of the optical experimental data, such like observations of total internal reflection of the beam shift in the Goos–H¨anchen effect, concludes a photon mass. Is, therefore, light diversified onto two independent species - gauge photons and optical photons? Can such a state of affairs be consistently described through a unique theoretical model? In this paper, two models of a photon mass, arising from the scalar quantum electrodynamics with the Higgs potential, are discussed. The first scenario leads to a neutral scalar mass estimable throughout the experimental limits on a photon mass. In the modified mechanism, a neutral scalar mass in not affected throughout a photon mass and is determinable through the experimental data, while a massless dilaton is present and a non-kinetic massive vector field effectively results in the string theory of non-interacting invariant both a free photon and a neutral scalar, and the Aharonov–Bohm effect is considered. The Markov hypothesis on maximality of the Planck mass is applied.

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References

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Show Less References

Article

Towards Superluminal Physics: Compromising Einstein's Special Relativity and Faster-Than-Light Particles

1B.M. Birla Science Centre, Hyderabad, India


Applied Mathematics and Physics. 2014, 2(3), 94-102
DOI: 10.12691/amp-2-3-5
Copyright © 2014 Science and Education Publishing

Cite this paper:
Lukasz Andrzej Glinka. Towards Superluminal Physics: Compromising Einstein's Special Relativity and Faster-Than-Light Particles. Applied Mathematics and Physics. 2014; 2(3):94-102. doi: 10.12691/amp-2-3-5.

Correspondence to: Lukasz  Andrzej Glinka, B.M. Birla Science Centre, Hyderabad, India. Email: laglinka@gmail.com; lukaszglinka@wp.eu

Abstract

Throughout the violation of momentum-velocity parallelism and deformation of the Einstein equivalence principle, the model of faster- than-light motion, wherein both the Minkowski energy-momentum space and the Lorentz invariance, laying the foundations of Special Relativity and Standard Model, is constructed. Recently announced and denounced CERN's superluminal neutrinos are confronted.

Keywords

References

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Article

Objective Quantum Gravity, Its Possible Relation to Gauge Theories and Strings

1B.M. Birla Science Centre, Hyderabad, India


Applied Mathematics and Physics. 2014, 2(3), 82-93
DOI: 10.12691/amp-2-3-4
Copyright © 2014 Science and Education Publishing

Cite this paper:
Lukasz Andrzej Glinka. Objective Quantum Gravity, Its Possible Relation to Gauge Theories and Strings. Applied Mathematics and Physics. 2014; 2(3):82-93. doi: 10.12691/amp-2-3-4.

Correspondence to: Lukasz  Andrzej Glinka, B.M. Birla Science Centre, Hyderabad, India. Email: laglinka@gmail.com; lukaszglinka@wp.eu

Abstract

In this paper the model of quantum gravity for the higher dimensional Lorentzian space-times, in the sense of the analogy with the Arnowitt–Deser–Misner decomposition well-known from General Relativity, is presented. The model is constructed through making use of the quantum geometrodynamics supplemented by the global onedimensionality conjecture, and considers the objective wave functionals. The framework of quantum field theory is applied in order to establish the phenomenological efficiency in accordance with high energy physics. The empirical deductions on the spatial dimensionality are presented as the relationship between the model and gauge theories, especially string theory.

Keywords

References

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Article

Novel Solution of Wheeler-DeWitt Theory

1B.M. Birla Science Centre, Hyderabad, India


Applied Mathematics and Physics. 2014, 2(3), 73-81
DOI: 10.12691/amp-2-3-3
Copyright © 2014 Science and Education Publishing

Cite this paper:
Lukasz Andrzej Glinka. Novel Solution of Wheeler-DeWitt Theory. Applied Mathematics and Physics. 2014; 2(3):73-81. doi: 10.12691/amp-2-3-3.

Correspondence to: Lukasz  Andrzej Glinka, B.M. Birla Science Centre, Hyderabad, India. Email: laglinka@gmail.com; lukaszglinka@wp.eu

Abstract

Taking into account the global one-dimensionality conjecture recently proposed by the author, the Cauchy-like analytical wave functional of the Wheeler-DeWitt theory is derived. The crucial point of the integration strategy is canceling of the singular behavior of the effective potential, which is performed through the suitable change of variables introducing the invariant global dimension. In addition, the conjecture is extended onto the wave functionals dependent on both Matter felids as well as the invariant global dimension. Through application of the reduction within the quantum gravity model, the appropriate Dirac equation is obtained and than solved. The case of superposition is also briey discussed.

Keywords

References

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Article

Thermodynamical Quantum Gravity

1B.M. Birla Science Centre, Hyderabad, India


Applied Mathematics and Physics. 2014, 2(3), 66-72
DOI: 10.12691/amp-2-3-2
Copyright © 2014 Science and Education Publishing

Cite this paper:
Lukasz Andrzej Glinka. Thermodynamical Quantum Gravity. Applied Mathematics and Physics. 2014; 2(3):66-72. doi: 10.12691/amp-2-3-2.

Correspondence to: Lukasz  Andrzej Glinka, B.M. Birla Science Centre, Hyderabad, India. Email: laglinka@gmail.com; lukaszglinka@wp.eu

Abstract

The canonically quantized 3+1 General Relativity with the global one dimensionality conjecture defines the model, which dimensionally reduced and secondary quantized yields the one-dimensional quantum field theory wherein the generic one-point correlations create a boson mass responsible for quantum gravity. In this paper, this simple model is developed in a wider sense. We propose to consider the thermodynamics of space quanta, constructed ab initio from the entropic formalism, as the quantum gravity phenomenology.

Keywords

References

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[[2]  D. J. Gross, T. Piran, and S. Weinberg (eds.), Two Dimensional Quan- tum Gravity and Random Surfaces, World Scientific (1992).
 
[[3]  G. W. Gibbons and S. W. Hawking (eds.), Euclidean Quantum Grav- ity, World Scientific (1993).
 
[[4]  G. Esposito, Quantum Gravity, Quantum Cosmology and Lorentzian Geometries, Springer (1994).
 
[[5]  J. Ehlers and H. Friedrich (eds.), Canonical Gravity: From Classical to Quantum, Springer (1994).
 
Show More References
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[8]  G. Esposito, A. Yu. Kamenshchik, and G. Pollifrone, Euclidean Quan- tum Gravity on Manifolds with Boundary, Springer (1997).
 
[9]  P. Fré, V. Gorini, G. Magli, and U. Moschella, Classical and Quantum Black Holes, Institute of Physics Publishing (1999).
 
[10]  I. G. Avramidi, Heat Kernel and Quantum Gravity, Springer (2000).
 
[11]  B. N. Kursunoglu, S. L. Mintz, and A. Perlmutter (eds.), Quantum Gravity, Generalized Theory of Gravitation and Superstring Theory- Based Unification, Kluwer (2002).
 
[12]  S. Carlip, Quantum Gravity in 2+1 Dimensions, Cambridge University Press (2003).
 
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[14]  C. Rovelli, Quantum Gravity, Cambridge University Press (2004);
 
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Article

Bosonic Quantum Gravity According to the Global One-Dimensionality Conjecture

1Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research in Dubna, Russia


Applied Mathematics and Physics. 2014, 2(3), 59-65
DOI: 10.12691/amp-2-3-1
Copyright © 2014 Science and Education Publishing

Cite this paper:
Lukasz Andrzej Glinka. Bosonic Quantum Gravity According to the Global One-Dimensionality Conjecture. Applied Mathematics and Physics. 2014; 2(3):59-65. doi: 10.12691/amp-2-3-1.

Correspondence to: Lukasz  Andrzej Glinka, Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research in Dubna, Russia. Email: laglinka@gmail.com; lukaszglinka@wp.eu

Abstract

In this paper, making use of the global one-dimensionality conjecture, we discuss the reduction of the Wheeler–DeWitt quantum geometrodynamics to the Klein–Gordon equation describing the scalar bosonic particle. The method of second quantization in the appropriate Fock space is applied, and, employing both the Bogoliubov transformation as well as Heisenberg equations of motion, the quantum gravity is expressed as evolution of the creators and annihilators related to the initial data. It is shown that this procedure leads to the understanding of the boson mass, through the one-point two-boson quantum correlations, as a scaled initial data mass.

Keywords

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Article

The Effects of Golden Mean on the Diffraction by Monatomic One-Dimensional Quasicrystal

1Department of Physics, Sa’adatu Rimi College of Education, Kano-Nigeria

2Department of Physics, Bayero University, Kano-Nigeria

3Department of Physics, Kaduna State University, Kaduna-Nigeria


Applied Mathematics and Physics. 2014, 2(2), 53-58
DOI: 10.12691/amp-2-2-5
Copyright © 2014 Science and Education Publishing

Cite this paper:
M. Sa’Id, G. Babaji, S.G. Abdu. The Effects of Golden Mean on the Diffraction by Monatomic One-Dimensional Quasicrystal. Applied Mathematics and Physics. 2014; 2(2):53-58. doi: 10.12691/amp-2-2-5.

Correspondence to: S.G.  Abdu, Department of Physics, Kaduna State University, Kaduna-Nigeria. Email: sgabdul@yahoo.com

Abstract

In this work, the code ‘Laue’ was used to simulate the diffraction pattern and to investigate the effects of varying the golden mean in a monatomic linear quasicrystal having a pseudo atomic potential. The work involved setting the parameters of the code required to simulate the diffraction, running the code and exporting the data generated to excel for analysis. It was found that the shape of the diffraction pattern and the background intensity for a given value of the golden mean is unique. Both the width of the diffraction pattern and the intensity of the central peak decrease with increasing golden mean. Results obtained illustrated the features of the diffraction by quasicrystal and proved the suitability and accuracy of the code in simulating the dynamics of quasicrystals.

Keywords

References

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Article

Contact-Boundary Value Problem in the Non-Classical Treatment for One Pseudo-Parabolic Equation

1Institute of Cybernetics Azerbaijan National Academy of Sciences, Baku, Azerbaijan


Applied Mathematics and Physics. 2014, 2(2), 49-52
DOI: 10.12691/amp-2-2-4
Copyright © 2014 Science and Education Publishing

Cite this paper:
Ilgar G. Mamedov. Contact-Boundary Value Problem in the Non-Classical Treatment for One Pseudo-Parabolic Equation. Applied Mathematics and Physics. 2014; 2(2):49-52. doi: 10.12691/amp-2-2-4.

Correspondence to: Ilgar  G. Mamedov, Institute of Cybernetics Azerbaijan National Academy of Sciences, Baku, Azerbaijan. Email: ilgar-mammadov@rambler.ru

Abstract

In this paper substantiated for a differential equation of pseudo-parabolic type with discontinuous coefficients a contact-boundary value problem with non-classical boundary conditions is considered, which requires no matching conditions. Equivalence of these conditions boundary condition is substantiated classical, in the case if the solution of the problem in the izotropic S.L. Sobolev's space is found. The considered equation as a pseudo-parabolic equation generalizes not only classic equations of mathematical physics (heat-conductivity equations, string vibration equation) and also many models differential equations (Aller's equation, Manjeron equation, telegraph equation, moisture transfer generalized equation, Boussinesq - Love equation and etc.). It is grounded that the contact-boundary conditions in the classic and non-classic treatment are equivalent to each other, and such boundary conditions are demonstrated in geometric form. Even from geometric interpretation can see that the grounded non-classic treatment doesn't require any additional conditions of agreement type. Thus, namely in this paper, the non-classic problem with contact-boundary conditions is grounded for a pseudo-parabolic equation. For simplicity, this was demonstrated for one model case in one of S.L. Sobolev izotropic space Wp(4,4)(G).

Keywords

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[7]  I.G. Mamedov, Goursat non - classic three dimensional problems for a hyperbolic equation with discontinuous coefficients, Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta, Ser. Fiz.-Mat. Nauki, No. 1 (20), (2010), 209-213 (in Russian).
 
[8]  I.G. Mamedov, Fundamental solution of initial boundary value problem for a fourth order pseudo-parabolic equation with non-smooth coefficients, Vladikavkazskii Matematicheskii Zhurnal, vol. 12, No 1, (2010), 17-32 (in Russian).
 
[9]  I.G. Mamedov, A non-classical formula for integration by parts related to Goursat problem for a pseudo-parabolic equation, Vladikavkazskii Matematicheskii Zhurnal, vol. 13, No 4, (2011), 40-51 (in Russian).
 
[10]  I.G. Mamedov, Contact-boundary value problem for a hyperbolic equation with multiple characteristics, Functional analysis and its applications, Proceedings of the International Conference devoted to the centenary of academician Z. I. Khalilov, Baku, (2011), 230-232 (in Russian).
 
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Article

A New Approximation Method for the Systems of Nonlinear Fredholm Integral Equations

1Department of Mathematics, Faculty of Science and Arts, Celal Bayar University, Manisa, Turkey


Applied Mathematics and Physics. 2014, 2(2), 40-48
DOI: 10.12691/amp-2-2-3
Copyright © 2014 Science and Education Publishing

Cite this paper:
Salih Yalçınbaş, Kübra Erdem. A New Approximation Method for the Systems of Nonlinear Fredholm Integral Equations. Applied Mathematics and Physics. 2014; 2(2):40-48. doi: 10.12691/amp-2-2-3.

Correspondence to: Salih  Yalçınbaş, Department of Mathematics, Faculty of Science and Arts, Celal Bayar University, Manisa, Turkey. Email: salih.yalcinbas@cbu.edu.tr

Abstract

In this paper, we present a new approximate method for solving systems of nonlinear Fredholm integral equation. This method is based on, first, differentiating both sides of integral equations n times and then substituting the Taylor series the unknown functions in the resulting equation and later, transforming to a matrix equation. By merging these results, a new system which corresponds to a system of linear algebraic equations is obtained. The solution of this system yields the Taylor coefficients of the solution function. Numerical results and comparisons with the exact solution are included to demostrate the validity and applicability of the technique.

Keywords

References

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[11]  K. Maleknejad and K. M. Tavassoli, Solving linear integro-differential equation system by Galerkin methods with hybrid functions, Appl. Math. Comput. 159, 603-612, 2004.
 
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[16]  S. Yalçınbaş, Taylor polynomial solutions of nonlinear Volterra-Fredholm integral equations, Appl. Math. Comput., 127, 195-206, 2002.
 
[17]  S. Yalçınbaş, A. Şahiner, M. Demirbaş, B. Altınay and S. Kocakuş, The approximate solution of high-order linear differential equation systems with variable coefficients in terms of Taylor polynomials, The third international conference ‘‘Tools for mathematical modelling’’, Saint Petersburg, 18-23 June 2001, 8, 175-188, 2001.
 
[18]  Yalçınbaş and F. Yeniçerioğlu, The approximate solutions of high-order linear differential equation systems with variable coefficients, Far East Journal of Dynamical Systems, 6, 2, 139-157, 2004.
 
[19]  A. Akyüz-Daşçıoğlu and M. Sezer, Chebyshev polynomial solutions of systems of higher-order linear Fredholh-Volterra integro-differential equations, J. Franklin Institute 342, 688-701, 2005.
 
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[21]  S. Yalçınbaş and K. Erdem, Approximate solutions of nonlinear Volterra integral equation systems, International Journal of Modern Physics B, 24, 32, 6235-6258, 2010.
 
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Article

Fermat Collocation Method for Solvıng a Class of the Second Order Nonlinear Differential Equations

1Department of Mathematics Celal Bayar University, Muradiye, Manisa, Turkey


Applied Mathematics and Physics. 2014, 2(2), 33-39
DOI: 10.12691/amp-2-2-2
Copyright © 2014 Science and Education Publishing

Cite this paper:
Salih Yalçınbaş, Dilek Taştekin. Fermat Collocation Method for Solvıng a Class of the Second Order Nonlinear Differential Equations. Applied Mathematics and Physics. 2014; 2(2):33-39. doi: 10.12691/amp-2-2-2.

Correspondence to: Salih  Yalçınbaş, Department of Mathematics Celal Bayar University, Muradiye, Manisa, Turkey. Email: salih.yalcinbas@cbu.edu.tr

Abstract

In this paper, a matrix method based on collocation points on any interval [a,b] is proposed for the approximate solution of some second order nonlinear ordinary differential equations with the mixed conditions in terms of Fermat polynomials. The method, by means of collocation points, transforms the differential equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Fermat coefficients. Also, the method can be used for solving Riccati equation. The numerical results show the effectiveness of the method for this type of equation. Comparing the methodology with some known techniques shows that the present approach is relatively easy and high accurate.

Keywords

References

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[[1]  G.F.Corliss, Guarented error bounds for ordinary differential equations, in theory and numeric of ordinary and partial equations (M.Ainsworth, J.Levesley, W.A Light, M.Marletta, Eds), Oxford Universty press, Oxford, pp. 342 (1995).
 
[[2]  H. Bulut, D.J. Evens, on the solution of Riccati equation by the Decomposition method, Intern. J. Computer Math., 79(1) (2002) 103-109.
 
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[[4]  V. Hernandez, J.J. Ibonez, J. Peinodo, E. Arias, A GMRES-based BDF method for solving Differential Riccati Equations, Appl. Math. Comput. amc. 2007. 06. 021.
 
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[6]  D. Taştekin, S. Yalçınbaş, M. Sezer, Taylor collocation method for solving a class of the first order nonlinear differential equations, Mathematical and Computational Applications, vol.18, no.3, pp. 383-391, 2013.
 
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[10]  S. Yalçınbaş, Taylor polynomial solutions of nonlinear Volterra-Fredholm integral equations, Applied Mathematics and Computation 127, 195-206, 2002.
 
[11]  S. Yalçınbaş, K. Erdem, Approximate solutions of nonlinear Volterra integral equation systems, International Journal of Modern Physics B 24(32), 6235-6258, 2010.
 
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Article

Stable Laws and the Number of Ordinary

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


Applied Mathematics and Physics. 2014, 2(2), 27-32
DOI: 10.12691/amp-2-2-1
Copyright © 2014 Science and Education Publishing

Cite this paper:
P.M. Mazurkin. Stable Laws and the Number of Ordinary. Applied Mathematics and Physics. 2014; 2(2):27-32. doi: 10.12691/amp-2-2-1.

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

Abstract

Power total number of primes from the discharge of the decimal system is identified by the law of exponential growth with 14 fundamental physical constants. Model obtained on the parameters of the physical constants, proved less of the error and it gives more accurate predictions of the relative power of the set of prime numbers. The maximum absolute error of power (the number of primes), the traditional number is three times higher than suggested by us complete a number of prime numbers. Therefore, the traditional number 2, 3, 5, 7,. .. is only a special case. The transformation In10=2,30285… it was a rough rounded, leading to false identification of physico-mathematical regularities of different series of prime numbers. Model derived from physical constants, proved more accurate than the relative accuracy, and it gives more accurate predictions of the relative power of the set of prime numbers with increasing discharge the decimal number system.

Keywords

References

[[1]  Don Zagier. The first 50 million prime numbers. URL: http://www.ega-math.narod.ru/Liv/Zagier.htm.
 
[[2]  Number. URL: http://ru.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%BE.
 
[[3]  Mazurkin P.M. Biotechnical principle and sustainable laws of distribution // Successes of modern natural sciences. 2009. № 9, 93-97.
 
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[[5]  Fundamental physical constants. URL; http://www.akin.ru/spravka/s_fund.htm.
 

Article

The Dynamic Behavior of the Electrically Charged Cloud of the Ice Crystals

1Department of Structural Mechanic, Technical University of Lodz, Lodz, Poland


Applied Mathematics and Physics. 2014, 2(1), 19-26
DOI: 10.12691/amp-2-1-6
Copyright © 2014 Science and Education Publishing

Cite this paper:
Artur Wirowski. The Dynamic Behavior of the Electrically Charged Cloud of the Ice Crystals. Applied Mathematics and Physics. 2014; 2(1):19-26. doi: 10.12691/amp-2-1-6.

Correspondence to: Artur  Wirowski, Department of Structural Mechanic, Technical University of Lodz, Lodz, Poland. Email: artur.wirowski@p.lodz.pl

Abstract

The paper includes the derivation of the equation of the two-dimensional, dynamic behavior of electrically charged cloud of ice crystals. A large crystal rotation angles and a continuous distribution of charges on the surface of the crystals are included in deliberations. Finally, possible solutions of model equation are discussed and compared with solutions available in the literature. The resulting model can be used as a mechanical basis for optic models of the atmospheric phenomenon called the “miracle of the sun”.

Keywords

References

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[[1]  A. Wirowski, The Non-linear Modeling of the Rotational Vibrations of the Electrically Charged Cloud of the Ice Crystals, Open Journal of Mathematical Modeling, Vol. 1, No. 2 (2013), p. 46-57.
 
[[2]  A. Wirowski, Modelling of the phenomenon known as the miracle of the Sun as the reflection of light from ice crystals oscillating synchronously, Journal of Modern Physics, Vol. 3 No. 3, 2012, pp. 282-289.
 
[[3]  A.A. Soliman, H.A. Abdo, New Exact Solutions of Non-linear Variants of the RLW, the PHI-four and Boussinesq Equations Based on Modified Extended Direct Algebraic Method, International Journal of Non-linear Science, Vol. 7 (2009), No. 3.
 
[[4]  A. Bekir, New Exact Travelling Wave Solutions for Regularized Long-wave, Phi-Four and Drinfeld-Sokolov Equations, International Journal of Non-linear Science, Vol. 6 (2008), No. 1.
 
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[10]  P. Daveze, B. Payet, L. Delaunay, Using dynamic Cotton and Mouton effect to study Brownian relaxation and magnetization of ferrofluids, Proc. SPIE 3098, Optical Inspection and Micromeasurements II, 456 (July 4, 1997).
 
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Article

A New Collocation Method for Systems of Nonlinear Fredholm Integral Equations

1Department of Mathematics, Tonekabon Branch, Islamic Azad University, Tonekabon, Iran


Applied Mathematics and Physics. 2014, 2(1), 15-18
DOI: 10.12691/amp-2-1-5
Copyright © 2014 Science and Education Publishing

Cite this paper:
S.A. Edalatpanah, E. Abdolmaleki. A New Collocation Method for Systems of Nonlinear Fredholm Integral Equations. Applied Mathematics and Physics. 2014; 2(1):15-18. doi: 10.12691/amp-2-1-5.

Correspondence to: S.A.  Edalatpanah, Department of Mathematics, Tonekabon Branch, Islamic Azad University, Tonekabon, Iran. Email: saedalat@yahoo.com

Abstract

In this paper we present a new method for solving nonlinear Fredholm integral equations system in terms of continuous Legendre multi-wavelets on the interval [0, 1). To begin with we describe the characteristic of Legendre multi-wavelets and will go on to indicate that through this method a system of Fredholm integral equations can be reduced to an algebraic equation. Convergence analysis of this method is also presented. Finally, numerical results are given which support the theoretical results.

Keywords

References

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[[1]  K.E. Atkinson, The numerical solution of integral equations of the second kind, Cambridge University Press, Cambridge, 1997.
 
[[2]  R. Kress, Linear integral equations, Springer-Verlag, NewYork, 1999.
 
[[3]  P.K. Kythe, P. Puri, Computational methods for linear integral equations, BirkhauserVerlag, Springer, Boston, 2002.
 
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[[5]  K. Maleknejad, F. Mirzaee, Numerical solution of linear Fredholm integral equations system by rationalized Haar functions method. Int J Comput Math 80 (2003) 1397-405.
 
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[6]  E. Babolian, J. Biazar, and A.R. Vahidi, The decomposition method applied to system of Fredholm integral equations of the second kind, Appl. Math. Comput. 148 (2004) 443-452.
 
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[8]  K. Maleknejad, M. Shahrezaee, Rung-Kutta method for numerical solution of the system of Volterra integral equation, Appl. Math. Comput., 149 (2004) 399-410.
 
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Article

Photon Dose Calculation Algorithms in the Presence of Low-Density Heterogeneity-a Mini Literature Review

1Department of Clinical Research, Hebeii Hospital, Shijiazhuang, China


Applied Mathematics and Physics. 2014, 2(1), 13-14
DOI: 10.12691/amp-2-1-4
Copyright © 2014 Science and Education Publishing

Cite this paper:
Chang Lau. Photon Dose Calculation Algorithms in the Presence of Low-Density Heterogeneity-a Mini Literature Review. Applied Mathematics and Physics. 2014; 2(1):13-14. doi: 10.12691/amp-2-1-4.

Correspondence to: Chang  Lau, Department of Clinical Research, Hebeii Hospital, Shijiazhuang, China. Email: changlau55@gmail.com

Abstract

Dose prediction accuracy in photon dose calculation algorithms is important to ensure accurate delivery of prescribed dose to the tumor during radiation therapy. The main objective of this article is to provide a brief review on most recent dose calculation algorithm called Acuros XB, which is used to calculate the cancer treatment plans in external beam radiation therapy.

Keywords

References

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[[1]  Vassiliev O, Wareing T, McGhee J, Failla G, Salehpour M, Mourtada F. Validation of a new grid based Blotzmann equation solver for dose calculation in radiotherapy with photon beams. Phys Med Biol 2010; 55: 581-98.
 
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[[3]  Han T, Followill D, Mikell J, Repchak R, Molineu A, Howell R, Salehpour M, Mourtada F. Dosimetric impact of Acuros XB deterministic radiation transport algorithm for heterogeneous dose calculation in lung cancer. Med Phys. 2013 May; 40 (5): 051710.
 
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Article

k-Generalized Fibonacci Numbers

1Department of Mathematics and MCA, Mandsaur Institute of Technology, Mandsaur, India

2Department of Mathematical Sciences and Computer Application, Bundelkhand University, Jhansi (U. P.), India


Applied Mathematics and Physics. 2014, 2(1), 10-12
DOI: 10.12691/amp-2-1-3
Copyright © 2014 Science and Education Publishing

Cite this paper:
Yashwant K. Panwar, Mamta Singh. k-Generalized Fibonacci Numbers. Applied Mathematics and Physics. 2014; 2(1):10-12. doi: 10.12691/amp-2-1-3.

Correspondence to: Yashwant  K. Panwar, Department of Mathematics and MCA, Mandsaur Institute of Technology, Mandsaur, India. Email: yashwantpanwar@gmail.com

Abstract

In this paper, we present the k-Generalized Fibonacci sequence. This sequence generalizes other, Generalized Fibonacci sequence. Generalized Fibonacci sequence was introduced by Gupta, Panwar and Sikhwal in 2012. We establish some of the interesting properties of k- Generalized Fibonacci sequence.

Keywords

References

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[[1]  A. F. Horadam, A generalized Fibonacci sequence. Math Mag., 68 (1961), 455-459.
 
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[[4]  S. Falco´n, On the k-Lucas numbers. International Journal of Contemporary Mathematical Sciences, 6 (21) (2011), 1039-1050.
 
[[5]  S. Falco´n, On the Lucas Triangle and its Relationship with the k-Lucas numbers. Journal of Mathematical and Computational Science, 2 (3) (2012), 425-434.
 
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[6]  S. Falco´n, Plaza, A.: On the Fibonacci k-numbers. Chaos, Solitons & Fractals, 32 (5) (2007), 1615-1624.
 
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[8]  S. Falco´n, Plaza, A.: The k-Fibonacci sequence and the Pascal 2-triangle. Chaos, Solitons & Fractals, 33 (1) (2007), 38-49.
 
[9]  S. Vajda, Fibonacci and Lucas numbers, and the golden section. Theory and applications. Chichester: Ellis Horwood limited (1989).
 
[10]  T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley, New York. (2001).
 
[11]  V. K. Gupta and Y. K. Panwar “Common factors of generalized Fibonacci, Jacobstha and Jacobsthal-Lucas numbers”, International Journal of Applied Mathematica Research, Vol.1, No.4 (2012), 377-382.
 
[12]  V. K. Gupta, Y. K. Panwar and O. Sikhwal, “Generalized Fibonacci sequences” Theoretical Mathematics & Applications, Vol.2, No.2 (2012), 115-124.
 
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Article

The Application of Parseval’s Theorem to Integral Problems

1Department of Management and Information, Nan Jeon University of Science and Technology, Tainan City, Taiwan


Applied Mathematics and Physics. 2014, 2(1), 4-9
DOI: 10.12691/amp-2-1-2
Copyright © 2014 Science and Education Publishing

Cite this paper:
Chii-Huei Yu. The Application of Parseval’s Theorem to Integral Problems. Applied Mathematics and Physics. 2014; 2(1):4-9. doi: 10.12691/amp-2-1-2.

Correspondence to: Chii-Huei  Yu, Department of Management and Information, Nan Jeon University of Science and Technology, Tainan City, Taiwan. Email: chiihuei@nju.edu.tw

Abstract

This paper uses the mathematical software Maple as an auxiliary tool to study six types of definite integrals. We can obtain the infinite series forms of these definite integrals by using Parseval’s theorem. On the other hand, we provide some examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying the answers by using Maple.

Keywords

References

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[[4]  C. -H. Yu, “Using Maple to study two types of integrals,” International Journal of Research in Computer Applications and Robotics, Vol. 1, pp. 14-22, 2013.
 
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[6]  C. -H. Yu, “A study on integral problems by using Maple,” International Journal of Advanced Research in Computer Science and Software Engineering, Vol. 3, pp. 41-46, 2013.
 
[7]  C. -H. Yu, “Evaluating some integrals with Maple,” International Journal of Computer Science and Mobile Computing, Vol. 2, pp. 66-71, 2013.
 
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[11]  C. -H. Yu, “Application of Maple on the integral problem of some type of rational functions,”Proceedings of the Annual Meeting and Academic Conference for Association of IE, D357-D362, 2012.
 
[12]  C. -H. Yu, “A study of the integrals of trigonometric functions with Maple,” Proceedings of the Institute of Industrial Engineers Asian Conference 2013, Springer, Vol. 1, pp. 603-610, 2013.
 
[13]  C. -H. Yu, “Application of Maple on some integral problems,” Proceedings of the International Conference on Safety & Security Management and Engineering Technology 2012, pp. 290-294, 2012.
 
[14]  C. -H. Yu, “Application of Maple on evaluating the closed forms of two types of integrals,” Proceedings of the 17th Mobile Computing Workshop, ID16, 2012.
 
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Article

A Simple Scheme for Generation of N-Qubits Entangled Stated

1Department of Physics, University of Zanjan, Zanjan, Iran


Applied Mathematics and Physics. 2014, 2(1), 1-3
DOI: 10.12691/amp-2-1-1
Copyright © 2013 Science and Education Publishing

Cite this paper:
Siamak Khademi, Ghasem Naeimi, Ozra Heibati. A Simple Scheme for Generation of N-Qubits Entangled Stated. Applied Mathematics and Physics. 2014; 2(1):1-3. doi: 10.12691/amp-2-1-1.

Correspondence to: Siamak  Khademi, Department of Physics, University of Zanjan, Zanjan, Iran. Email: khademi@znu.ac.ir

Abstract

Generation and manipulation of multi-qubits or multi-partite entangled states are cornerstones of manufacturing quantum computers and developing quantum information. In this paper, we develop a new scheme for the generation of a multi-partite maximally entangled state generation. This method has less limitation and is simpler than the previous ones. It is based on the interactions of a chain of Rydberg Rubidium atoms with an array of five high quality cavities, including four classical and one quantum cavity in the middle.

Keywords

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Article

Control Processes Optimization for Mechanical Systems with Active, Semi-Passive and Passive Actuators

1Department of Nonlinear Mathematical Analysis, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine, Lviv, Ukraine


Applied Mathematics and Physics. 2013, 1(4), 147-150
DOI: 10.12691/amp-1-4-8
Copyright © 2013 Science and Education Publishing

Cite this paper:
Olexandr Polishchuk. Control Processes Optimization for Mechanical Systems with Active, Semi-Passive and Passive Actuators. Applied Mathematics and Physics. 2013; 1(4):147-150. doi: 10.12691/amp-1-4-8.

Correspondence to: Olexandr  Polishchuk, Department of Nonlinear Mathematical Analysis, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine, Lviv, Ukraine. Email: od_polishchuk@mail.ru

Abstract

The influence of the geometric parameters of two-link manipulator on the energy expenditure necessary for the implementation of a given movement is investigated. It is proposed approximation-compensatory approach to replace the active actuators in the joints of the manipulator on semi-passive and entirely passive actuators. Advantages and disadvantages of such replacement are analyzed and the fields of use of such manipulators are proposed.

Keywords

References

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Article

Lead Phosphate Glass Containing Boron and Lithium Oxides as a Shielding Material for Neutron- and Gamma-Radiation

1Physics Department, Faculty of Science, Al-Azhar University, Girls Branch, Nasr City, Cairo, Egypt


Applied Mathematics and Physics. 2013, 1(4), 143-146
DOI: 10.12691/amp-1-4-7
Copyright © 2013 Science and Education Publishing

Cite this paper:
H. A. Saudi. Lead Phosphate Glass Containing Boron and Lithium Oxides as a Shielding Material for Neutron- and Gamma-Radiation. Applied Mathematics and Physics. 2013; 1(4):143-146. doi: 10.12691/amp-1-4-7.

Correspondence to: H.  A. Saudi, Physics Department, Faculty of Science, Al-Azhar University, Girls Branch, Nasr City, Cairo, Egypt. Email: heba_saudi@yahoo.com

Abstract

A glass system with chemical formula: xLi2O– (50_x) B2O3–40PbO–10P2O5 mole % is prepared to be used as radiation shield. The mass attenuation coefficient and half value layer of the glass system to gamma rays have been measured experimentally and compared with those determined from theoretical calculations using the mixture rule of WinXCom program. A database of effective mass removal cross-sections for fast neutrons is also introduced in this work.

Keywords

References

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Article

The Parallel Postulate is Depended on the Other Axioms

1Larnaca, Cyprus


Applied Mathematics and Physics. 2013, 1(4), 129-142
DOI: 10.12691/amp-1-4-6
Copyright © 2013 Science and Education Publishing

Cite this paper:
Markos Georgallides. The Parallel Postulate is Depended on the Other Axioms. Applied Mathematics and Physics. 2013; 1(4):129-142. doi: 10.12691/amp-1-4-6.

Correspondence to: Markos  Georgallides, Larnaca, Cyprus. Email: georgallides.marcos@cytanet.com.cy

Abstract

In the manuscript is proved that parallel postulate is only in Plane (three points only) and is based on the four Postulates for Constructions, where all properties of Euclidean geometry compactly exist as Extrema on points, lines, planes, circles and spheres. Projective, Hyperbolic and Elliptic geometry is proved to be an Extrema (deviations) in Euclidean geometry where on them Einstein's theory of general relativity is implicated approximately to the properties of physical space.

Keywords

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Article

Identities of Common Factors of Generalized Fibonacci, Jacobsthal and Jacobsthal-Lucas Numbers

1Department of Mathematics and MCA, Mandsaur Institute of Technology, Mandsaur, India

2School of Studies in Mathematics, Vikram University Ujjain, India

3Department of Mathematics, Govt. Madhav Science College, Ujjain, India


Applied Mathematics and Physics. 2013, 1(4), 126-128
DOI: 10.12691/amp-1-4-5
Copyright © 2013 Science and Education Publishing

Cite this paper:
Yashwant K. Panwar, Bijendra Singh, V. K. Gupta. Identities of Common Factors of Generalized Fibonacci, Jacobsthal and Jacobsthal-Lucas Numbers. Applied Mathematics and Physics. 2013; 1(4):126-128. doi: 10.12691/amp-1-4-5.

Correspondence to: Yashwant  K. Panwar, Department of Mathematics and MCA, Mandsaur Institute of Technology, Mandsaur, India. Email: yashwantpanwar@gmail.com

Abstract

The Fibonacci sequence is famous for possessing wonderful and amazing properties. In this paper, we present generalized identities involving common factors of generalized Fibonacci, Jacobsthal and jacobsthal-Lucas numbers and related identities consisting even and odd terms. Binet’s formula will employ to obtain the identities.

Keywords

References

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[[1]  Gupta, V. K. & Panwar, Y. K., Common factors of generalized Fibonacci, Jacobsthal and Jacobsthal-Lucas numbers, International Journal of Applied Mathematical Research, 1(4), 377-382, 2012.
 
[[2]  Gupta, V. K., Panwar, Y. K. & Sikhwal, O., Generalized Fibonacci sequences, Theoretical Mathematics & Applications, 2(2), 115-124, 2012.
 
[[3]  Horadam, F., Jacobsthal Representation Numbers, The Fibonacci Quarterly, 34(1), 40-54, 1996.
 
[[4]  Hoggatt, V.E. Jr., Fibonacci and Lucas numbers. Houghton – Mifflin Co., Boston, 1969.
 
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[6]  Koshy, T., Fibonacci and Lucas Numbers with Applications, John Wiley, New York, 2001.
 
[7]  Panwar, Y. K., Generalized Fibonacci sequences, LAP, Germany, 2012.
 
[8]  Panwar, Y. K., Singh, B. & Gupta, V. K., Generalized Identities Involving Common factors of generalized Fibonacci, Jacobsthal and Jacobsthal-Lucas numbers, International Journal of Analysis and Application, 3(1), 53-59, 2013.
 
[9]  Singh, B., Bhadouria, P. & Sikhwal, O., Generalized Identities Involving Common Factors of Fibonacci and Lucas Numbers, International Journal of Algebra, 5(13), 637-645, 2011.
 
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Article

Solution of Nonlinear Equations in Science through Lagrange’s Inversion Theorem

1Department of Statistics, University of Brasilia, Brasilia, Brazil

2Department of Civil Engineering, ITM University, Gurgaon, India

3Department of Civil and Environmental Engineering, University of Brasilia, Brasilia, Brazil


Applied Mathematics and Physics. 2013, 1(4), 120-125
DOI: 10.12691/amp-1-4-4
Copyright © 2013 Science and Education Publishing

Cite this paper:
Pushpa N. Rathie, Prabhata K. Swamee, Luan Carlos de S. M. Ozelim. Solution of Nonlinear Equations in Science through Lagrange’s Inversion Theorem. Applied Mathematics and Physics. 2013; 1(4):120-125. doi: 10.12691/amp-1-4-4.

Correspondence to: Pushpa  N. Rathie, Department of Statistics, University of Brasilia, Brasilia, Brazil. Email: pushpanrathie@yahoo.com

Abstract

Nonlinear problems arise in most of the scientific fields. In general, such behavior is represented by a nonlinear equation, whose solution is sought. Analytical and numerical methods have been applied to the solution of this class of equations, notwithstanding, in cases where highly nonlinear phenomena are analyzed, the number of iterations and computational effort necessary to achieve the minimum required accuracy is very high. Lagrange´s Inversion Theorem (LIT) has been applied to solve this kind of problems analytically, giving the solution as an infinite power series. This way, the accuracy can be as high as necessary by taking more terms from the series solution, which is easily computationally implemented. Also, in some cases it is possible to relate the series obtained to the expansion of special and elementary functions, which enables one to exactly solve the desired equation. In the present review paper, a total of eleven applications have been discussed in order to show the role of LIT in various areas of nonlinear sciences.

Keywords

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Article

Introduction of Derivatives and Integrals of Fractional Order and Its Applications

1Islamic Azad University, Bardaskan Branch, Department of Mathematics, Bardaskan, Iran


Applied Mathematics and Physics. 2013, 1(4), 103-119
DOI: 10.12691/amp-1-4-3
Copyright © 2013 Science and Education Publishing

Cite this paper:
Mehdi Delkhosh. Introduction of Derivatives and Integrals of Fractional Order and Its Applications. Applied Mathematics and Physics. 2013; 1(4):103-119. doi: 10.12691/amp-1-4-3.

Correspondence to: Mehdi  Delkhosh, Islamic Azad University, Bardaskan Branch, Department of Mathematics, Bardaskan, Iran. Email: mehdidelkhosh@yahoo.com

Abstract

Fractional calculus is a branch of classical mathematics, which deals with the generalization of operations of differentiation and integration to fractional order. Such a generalization is not merely a mathematical curiosity but has found applications in various fields of physical sciences. In this paper, we review the definitions and properties of fractional derivatives and integrals, and we express the prove some of them.

Keywords

References

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Article

Vibration of Non-Homogeneous Rectangular Plate Having Parabolically Varying Thickness in Both Directions with Exponentially Temperature Distribution

1Department of Mathematics, M. S. College, Saharanpur, U.P., India

2Department of MCA, Institute of Management Studies, Dehradun, India


Applied Mathematics and Physics. 2013, 1(4), 94-102
DOI: 10.12691/amp-1-4-2
Copyright © 2013 Science and Education Publishing

Cite this paper:
Arun Kumar Gupta, Vaibhav Panwar. Vibration of Non-Homogeneous Rectangular Plate Having Parabolically Varying Thickness in Both Directions with Exponentially Temperature Distribution. Applied Mathematics and Physics. 2013; 1(4):94-102. doi: 10.12691/amp-1-4-2.

Correspondence to: Vaibhav  Panwar, Department of MCA, Institute of Management Studies, Dehradun, India. Email: vaibhav@gmail.com

Abstract

An analysis is presented for frequencies of non-homogeneous rectangular plates of bi-parabolically thickness variation with exponentially temperature distribution on the basis of classical plate theory. An approximate but quiet convenient frequency equation is derived by using Rayleigh-Ritz technique with a two term deflection function. Effect of non-homogeneity together with taper constants and thermal gradient on the natural frequencies of vibration of a clamped rectangular plate on the first two modes of vibration have been analysed. Results are presented in tabular and graphical form both.

Keywords

References

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Article

A Preconditioned ELMRES Implementation

1Department of Mathematics, Islamic Azad University, Bardaskan Branch, Bardaskan, Iran


Applied Mathematics and Physics. 2013, 1(4), 90-93
DOI: 10.12691/amp-1-4-1
Copyright © 2013 Science and Education Publishing

Cite this paper:
Mehdi Delkhosh, Hossein Zareamoghaddam. A Preconditioned ELMRES Implementation. Applied Mathematics and Physics. 2013; 1(4):90-93. doi: 10.12691/amp-1-4-1.

Correspondence to: Mehdi Delkhosh, Department of Mathematics, Islamic Azad University, Bardaskan Branch, Bardaskan, Iran. Email: mehdidelkhosh@yahoo.com

Abstract

In this paper we review the ELMentary RESidual(ELMRES) algorithm for solving linear system of equations. ELMRES is a krylov subspace method which uses the Hessenberg transformation as the projection technique for reducing the dimension of original matrix A. We apply some preconditioned techniques for this algorithm. At the end of this paper, some numerical examples have been shown to compare the preconditioned ELMRES with the original version.

Keywords

References

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[[4]  Lewis B., Reichel L., Arnoldi-Tikhonov regularization methods, J. Comput. Appl. Math., 226 (2009) 92-102.
 
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[7]  Saberi Najafi H., Zareamoghaddam H., A new computational GMRES method, Appl. Math. Comput. 2 (2008) 527-534.
 
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Article

Entropy Generation in MHD Porous Channel Flow Under Constant Pressure Gradient

1Department of Mathematics, University of Gour Banga, Malda, India

2Department of Applied Mathematics, Vidyasagar University, Midnapore, India


Applied Mathematics and Physics. 2013, 1(3), 78-89
DOI: 10.12691/amp-1-3-5
Copyright © 2013 Science and Education Publishing

Cite this paper:
Sanatan Das, Rabindra Nath Jana. Entropy Generation in MHD Porous Channel Flow Under Constant Pressure Gradient. Applied Mathematics and Physics. 2013; 1(3):78-89. doi: 10.12691/amp-1-3-5.

Correspondence to: Sanatan Das, Department of Mathematics, University of Gour Banga, Malda, India. Email: jana261171@yahoo.co.in