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Alternative scattering kernels for the first estimates of a reactor:diffusion length

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Nuclear Science and Techniques 2018年第3期29卷 86-91页

作者： Hakan Oztürk Ayca Simsek Yapar Department of Physics Faculty of Arts and SciencesOsmaniye Korkut Ata University80000 OsmaniyeTurkey

Diffusion-length calculations of neutrons are performed using the Chebyshev polynomials of the second kind. The neutrons are assumed to move with constant energy in a uniform homogeneous slab. An alternative scattering kernel called an Anl?–Gngr phase function and a traditional Henyey–Greenstein phase function are used for the scattering function in the stationary neutron transport equation. First, analytic expressions and then numerical results are obtained for the diffusion length for various values of the scattering and cross-sectional parameters.Numerical results obtained from both scattering kernels for the diffusion length of the neutrons are given in tables side by side for comparison. The applicability of the method is easily demonstrated by these results.

关键词： Scattering kernel Diffusion length Chebyshev polynomials Transport equation

Several Expressions of Dirichlet L-function at Positive Integers

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Acta Mathematica Sinica,English Series 2019年第9期35卷 1549-1562页

作者： Yuan HE School of Mathematics and Information Science Neijiang Normal University

In this paper, by making use of Abel’s theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet Lfunction at positive integers by means of some finite sums of different types. Some special cases as well as immediate consequences of the results presented here are also considered.

关键词： Dirichlet L-function trigonometric sums gauss sums bernoulli polynomials combinatorial identities

A Multiple Model Approach to Modeling Based on LPF Algorithm

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Journal of Systems Engineering and Electronics 2001年第3期12卷 64-70页

作者： Li, N. Li, S. Xi, Y. Institute of Automation Shanghai Jiaotong University Shanghai 200030 China

Input-output data fitting methods are often used for unknown-structure nonlinear system modeling. Based on model-on-demand tactics, a multiple model approach to modeling for nonlinear systems is presented. The basic idea is to find out, from vast historical system input-output data sets, some data sets matching with the current working point, then to develop a local model using Local Polynomial Fitting (LPF) algorithm. With the change of working points, multiple local models are built, which realize the exact modeling for the global system. By comparing to other methods, the simulation results show good performance for its simple, effective and reliable estimation.

关键词： Algorithms Computer simulation Data structures Input output programs Mathematical models Parameter estimation polynomials

Mechanical Geometry Theorem Proving Based on Groebner Bases

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Journal of Computer Science & Technology 1997年第1期12卷 10-16页

作者：吴尽昭 Department of Mathematics Peking University Beijing

A new method for the mechanical elementary geometry theorem proving is presented by using Groebner bases of polynomial ideals. It has two main advantages over the approach proposed in literature: (i) It is complete and not a refutational procedure; (ii) The subcases of the geometry statements which are not generally true can be differentiated clearly.

关键词： Geometry statements polynomials ideals generally true mechanical theorem proving Groebner bases

Solution of the Dipoles in Noncommutative Space with Minimal Length

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Communications in Theoretical Physics 2019年第6期71卷 640-646页

作者：张梦瑶隆正文龙超云 College of Physics Guizhou University

The single neutral spin-half particle with electric dipole moment and magnetic dipole moment moving in an external electromagnetic field is studied. The Aharonov-Casher effect and He-McKellar-Wilkens effect are emphatically discussed in noncommutative(NC) space with minimal length. The energy eigenvalues of the systems are obtained exactly in terms of the Jacobi polynomials. Additionally, a special case is discussed and the related energy spectra are plotted.

关键词： Neutral spin-half particle noncommutative space minimal length Jacobi polynomials

On Unitary N-Dilations for Tuples of Circulant Contractions and von Neumann’s Inequality

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American Journal of Computational Mathematics 2023年第4期13卷 594-606页

作者： Joachim Moussounda Mouanda Edwige Josette Maleka Koubemba Djagwa Dehainsala Mathematics Department Blessington Christian University Nkayi Republic of the Congo Mathematics Department N’Djamena University N’Djamena Tchad

We introduce the spectral mapping factorization of tuples of circulant matrices and its matrix version. We prove that every tuple of circulant contractions has a unitary N-dilation. We show that von Neumann’s inequality holds for tuples of circulant contractions. We construct completely contractive homomorphisms over the algebra of complex polynomials defined on .

关键词： Dilations polynomials Matrices

Deriving new operator identities by alternately using normally,antinormally,and Weyl ordered integration technique

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Science China(Physics,Mechanics & Astronomy) 2010年第9期53卷 1626-1630页

作者： FAN HongYi1,YUAN HongChun1 & JIANG NianQuan2 1Department of Physics,Shanghai Jiao Tong University,Shanghai 200030,China 2College of Physics and Electric Information,Wenzhou University,Wenzhou 325035,China Department of Physics Shanghai Jiao Tong University Shanghai China College of Physics and Electric Information Wenzhou University Wenzhou China

Dirac's ket-bra formalism is the language of quantum mechanics.We have reviewed how to apply Newton-Leibniz integration rules to Dirac's ket-bra projectors in previous work.In this work,by alternately using the technique of integration within normal,antinormal,and Weyl ordering of operators we not only derive some new operator ordering identities,but also deduce some new integration formulas regarding Laguerre and Hermite polynomials.This may open a new route of directly deriving some complicated mathematical integration formulas by virtue of the quantum mechanical operator ordering technique,without really performing the integrations in the ordinary way.

关键词： operator ordering identities Laguerre and Hermite polynomials the IWOP technique

Slant path average intensity of finite optical beam propagating in turbulent atmosphere

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Chinese Optics Letters 2006年第10期4卷 559-562页

作者：张逸新王高刚 School of Science Southern Yangtze UniversityWuxi 214036 School of Communication and Control Engineering Southern Yangtze UniversityWuxi 214036

The average intensity of finite laser beam propagating through turbulent atmosphere is calculated from the extended Huygens Fresnel principle. Formulas are presented for the slant path average intensity from an arbitrarily truncated Gaussian beam. The new expressions are derived from the modified von Karman spectrum for refractive-index fluctuations, quadratic approximation of the structure function, and Gaussian approximation for the product of Gaussian function and Bessel function. It is shown that the form of average intensity is not a Gaussian function but a polynomial of the power of the binomial function, Gaussian function, and the incomplete gamma function. The results also show that the mean irradiance of a finite optical beam propagating in slant path turbulent atmosphere not only depends on the effective beam radius at the transmitting aperture plane, propagation distance, and long-term lateral coherence length of spherical wave, but also on the radius of emit aperture.

关键词： Atmospheric turbulence Bessel functions Coherent light polynomials Refractive index

On Fermat’s Last Theorem and Galaxies of Sequences of Positive Integers

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American Journal of Computational Mathematics 2022年第1期12卷 162-189页

作者： Joachim Moussounda Mouanda Mathematics Department Blessington Christian University Nkayi Republic of Congo

We construct sequences of positive integers which are solutions of the equation x2+y2=z2. We introduce Mouanda’s choice functions which allow us to construct galaxies of sequences of positive integers. We give many examples of galaxies of numbers. We show that the equation x2n+y2n=z2n (n ≥2) has no integer solutions. We prove that the equation xn+yn=zn (n ≥3) has no solutions in N. We introduce the notion of the planetary representation of a galaxy of numbers which allow us to predict the structure, laws of the universe and life in every planet system of every galaxy of the universe. We show that every multiverse contains a finite number of universes.

关键词： Fermat’s Equation polynomials Model Theory