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Some Hall polynomials for representation-finite selfinjective algebra with mod _pΛ without short chains

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Chinese Science Bulletin 1997年第12期42卷 985-988页

作者： ZHANG ShunhuaDepartment of Mathematics, Shandong University, Jinan 250100, China Department of Mathematics Shandong University Jinan China

1 PreliminariesThe Hall algebra H（A） of a finitary ring A was defined by Ringel.H（A）is the freeAbelian group with a basis{u[M]}[M] indexed by the isomorphism classes [M] of finite A-modules M with the multiplicati... 详细信息

关键词： Hall algebras Hall polynomials short chains.

BOUNDS FOR THE ZEROS OF polynomials

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Analysis in Theory and Applications 2004年第1期20卷 16-27页

作者： W.M.Shah A.Liman Bemina College IndiaCollege Srinagar India

Let P(z)= be a polynomial of degree n. In this paper we prove a more general result whichinteralia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generali... 详细信息

关键词： polynomials bounds Enestrom-Kakeya theorem

Characterization and Properties of Bent-Negabent Functions

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Chinese Journal of Electronics 2022年第4期31卷 786-792页

作者： JIANG Niu ZHAO Min YANG Zhiyao ZHUO Zepeng CHEN Guolong School of Mathematical Sciences Huaibei Normal University Fujian Provincial Key Laboratory of Network Security and Cryptology Fujian Normal University School of Cyber Science University of Science and Technology of China School of Computer Engineering Bengbu University

A further characterization of the bentnegabent functions is presented. Based on the concept of complete mapping polynomial, we provide a necessary and sufficient condition for a class of quadratic Boolean functions to be bent-negabent. A new characterization of negabent functions can be described by using the parity of Hamming weight. We further generalize the classical convolution theorem and give the nega-Hadamard transform of the composition of a Boolean function and a vectorial Boolean function. The nega-Hadamard transform of a generalized indirect sum is calculated by this composition method.

关键词： Algebra complete mapping polynomial Integral transforms Function theory, analysis quadratic Boolean functions vectorial Boolean function convolution generalized indirect sum sufficient condition nega-Hadamard transform Algebra, set theory, and graph theory polynomials Boolean functions classical convolution theorem Mathematical analysis Hadamard transforms bent-negabent functions necessary condition

Certain Results for the 2-Variable Peters Mixed Type and Related polynomials

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Analysis in Theory and Applications 2018年第2期34卷 147-164页

作者： Ghazala Yasmin Department of Applied Mathematics Faculty of Engineering Aligarh Muslim University

In this article, the 2-variable general polynomials are taken as base with Peters polynomials to introduce a family of 2-variable Peters mixed type polynomials.These polynomials are framed within the context of monomiality principle and their properties are established. Certain summation formulae for these polynomials are also derived. Examples of some members belonging to this family are considered and numbers related to some mixed special polynomials are also explored.

关键词： 2-Variable general polynomials Peters polynomials 2-variable truncated exponential polynomials Sheffer sequences monomiality principle

ON ROBUST STABILITY OF polynomials AND RELATED TOPICS

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Systems Science and Mathematical Sciences 1992年第1期5卷 42-54页

作者： Hollot C.V. Department of Electrical and Computer Engineering University of MassachusettsUSA

Complex polynomials are of significance in engineering applications.This paper addresses the robust stability of such polynomials.We first system-atically discuss the alternative pair of polynomials and obtain some fundamentalresults.The geometric characterizations of the family of stable complex polyno-mials are investigated.Some connections with Sturm chains and conditions for theconvex combination of polynomials to be aperiodic are established.

关键词： Robust stability complex polynomials Kharitonov’s theorem convex combination

Inequalities Concerning The Maximum Modulus of polynomials

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Analysis in Theory and Applications 2018年第2期34卷 175-186页

作者： B.A.Zargar A.W.Manzoor Shaista Bashir Department of Mathematics University of Kashmir

Let P(z) be a polynomial of degree n having all its zeros in |z|≤k, k ≤1, then for every real or complex number β, with |β|≤ 1 and R ≥ 1, it was shown by A.Zireh et al. [7] that for |z|=1,min|z|=1|P(Rz)+β((R+k)/(1+k))~nP(z)|≥k^(-n)|R^n+β((R+k)/(1+k))~n|min|z|=k|P(z)|.In this paper, we shall present a refinement of the above inequality. Besides, we shall also generalize some well-known results.

关键词： Growth of polynomials minimum modulus of polynomials inequalities

Some Estimates of the Maximum Modulus for polynomials with Gaps

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Analysis in Theory and Applications 2019年第4期35卷 421-426页

作者： Eze R.Nwaeze Department of Mathematics Tuskegee UniversityTuskegeeAL 36088USA

Let p(z)be a polynomial of degree n having some zeros at a point z0 ∈C with |z0|<1 and the rest of the zeros lying on or outside the boundary of a prescribed disk.In this brief note,we consider this class of polynomi... 详细信息

Let p(z)be a polynomial of degree n having some zeros at a point z0 ∈C with |z0|polynomials and obtain some bounds for(max|z|=R|p(z)|)s in terms of (max|z|=1|p(z)|)s for any R≥1 and s∈N.

关键词： polynomials maximum modulus zeros prescribed disk

Representation of the quantum mechanical wavefunction by orthogonal polynomials in the energy and physical parameters

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Communications in Theoretical Physics 2020年第1期72卷 66-80页

作者： A D Alhaidari Saudi Center for Theoretical Physics PO Box 32741Jeddah 21438Saudi Arabia

We present a formulation of quantum mechanics based on the theory of orthogonal polynomials.The wavefunction is expanded over a complete set of square integrable basis where the expansion coefficients are orthogonal polynomials in the energy and physical parameters.Information about the corresponding physical systems(both structural and dynamical)are derived from the properties of these polynomials.We demonstrate that an advantage of this formulation is that the class of exactly solvable quantum mechanical problems becomes larger than in the conventional formulation(see,for example,table 3 in the text).We limit our investigation in this work to the Askey classification scheme of hypergeometric orthogonal polynomials and focus on the Wilson polynomial and two of its limiting cases(the Meixner–Pollaczek and continuous dual Hahn polynomials).Nonetheless,the formulation is amenable to other classes of orthogonal polynomials.

关键词： tridiagonal representation orthogonal polynomials recursion relation asymptotics energy spectrum phase shift

Search for Monic Irreducible polynomials with Decimal Equivalents of polynomials over Galois Field GF(pq)

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Open Journal of Discrete Mathematics 2018年第1期8卷 21-33页

作者： Sankhanil Dey Ranjan Ghosh Institute of Radio Physics and Electronics University of Calcutta Kolkata India

Substitution boxes or S-boxes play a significant role in encryption and de-cryption of bit level plaintext and cipher-text respectively. Irreducible Poly-nomials (IPs) have been used to construct 4-bit or 8-bit substitution boxes in many cryptographic block ciphers. In Advance Encryption Standard, the ele-ments of 8-bit S-box have been obtained from the Multiplicative Inverse (MI) of elemental polynomials (EPs) of the 1st IP over Galois field GF(28) by adding an additive element. In this paper, a mathematical method and the algorithm of the said method with the discussion of the execution time of the algorithm, to obtain monic IPs over Galois field GF(pq) have been illustrated with example. The method is very similar to polynomial multiplication of two polynomials over Galois field GF(pq) but has a difference in execution. The decimal equivalents of polynomials have been used to identify Basic polynomials (BPs), EPs, IPs and Reducible polynomials (RPs). The monic RPs have been determined by this method and have been cancelled out to produce monic IPs. The non-monic IPs have been obtained with multiplication of α where?α∈ GF(pq)?and assume values from 2 to (p −1) to monic IPs.

关键词： Finite Fields Galois Fields Irreducible polynomials Decimal Equivalents