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Fast and rigorous calculation method for MoM matrix elements in planar microstrip structures

ELECTRONICS LETTERS 2000年第9期36卷 801-803页

作者： Samet, A Bouallegue, A Univ Tunis Commun Syst Lab Tunis Tunisia

An analytical integration technique is proposed for evaluating the elements of the impedance matrix obtained by using the spatial-domain method of moments (MoM) applied to the mixed-potential integral equation (MPIE). This technique is based on a Taylor series expansion of the integrands involving only polynomial functions, and thus allowing immediate analytical integration.

关键词： MPIE microstrip components integral equations MoM matrix elements mixed-potential integral equation spatial-domain MOM Taylor series expansion integration polynomial functions calculation method planar microstrip structures impedance matrix method of moments analytical integration technique Galerkin method

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An Algorithm for System Identification of a Discrete-Time polynomial System without Inputs

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IFAC-PapersOnLine 2015年第28期48卷 166-171页

作者： Némcová, Jana Petreczky, Mihály van Schuppen, Jan H. Department of Mathematics Institute of Chemical Technology Prague Czech Republic Dept. of Comp. Science & Automatic Control Écoles des Mines de Douai Douai France Van Schuppen Control Research Amsterdam Netherlands

A subalgebraic approximation algorithm is proposed to estimate from a set of time series the parameters of the observer representation of a discrete-time polynomial system without inputs which can generate an approximation of the observed time series. A major step of the algorithm is to construct a set of generators for the polynomial function from the past outputs to the future outputs. For this singular value decompositions and polynomial factorizations are used. A detailed example is described. © 2015

关键词： Approximation algorithms Algorithms Identification (control systems) Nonlinear systems polynomial approximation Religious buildings Singular value decomposition Time series Algebraic system Discrete time polynomial factorization polynomial functions

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Alienation of two general linear functional equations

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AEQUATIONES MATHEMATICAE 2020年第2期94卷 287-301页

作者： Szostok, Tomasz Inst Math Bankowa 14 PL-40007 Katowice Poland

We study the alienation problem for two general linear equations i.e. we compare the solutions of the system of equations (sic) with the solutions of the single equation. (sic) To this end we introduce the notion of l-alienation-alienation in the class of monomial functions of order l. We use our results among others to study the alienation properties of two monomial functional equations.

关键词： Functional equations Alienation Linear equations polynomial functions

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polynomial clones on squarefree groups

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INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION 2008年第4期18卷 759-777页

作者： Mayr, Peter Johannes Kepler Univ Linz Inst Algebra A-4040 Linz Austria

We prove that, on a set of size n, the number of clones that contain a group operation and all constant functions is finite if n is squarefree. This confirms a conjecture by Pawel Idziak from [5] where the converse implication was shown. Our result follows from the observation that the polynomial clone of an expansion of a squarefree group is uniquely determined by its binary functions. We also note that, in general, such a clone is not determined by the congruence lattice and the commutator operation of the corresponding algebra. This refutes a second conjecture from [5].

关键词： clones of operations polynomial functions commutator theory

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Integer-valued polynomials on algebras

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JOURNAL OF ALGEBRA 2013年 373卷 414-425页

作者： Frisch, Sophie Graz Univ Technol Inst Math A A-8010 Graz Austria

Let D be a domain with quotient field K and A a D-algebra. A polynomial with coefficients in K that maps every element of A to an element of A is called integer-valued on A. For commutative A we also consider integer-valued polynomials in several variables. For an arbitrary domain D and I an arbitrary ideal of D we show I-adic continuity of integer-valued polynomials on A. For Noetherian one-dimensional D, we determine spectrum and Krull dimension of the ring IntD(A) of integer-valued polynomials on A. We do the same for the ring of polynomials with coefficients in M-n(K), the K-algebra of n x n matrices, that map every matrix in M-n(D) to a matrix in M-n(D). (C) 2012 Elsevier Inc. All rights reserved.

关键词： Integer-valued polynomials Spectrum Krull dimension Matrix algebras polynomial rings I-adic topology Non-commutative algebras Non-commuting variables polynomial functions polynomial mappings

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On alienation of two functional equations of quadratic type

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AEQUATIONES MATHEMATICAE 2021年第6期95卷 1169-1180页

作者： Ger, Roman Silesian Univ Inst Math Katowice Poland

We deal with an alienation problem for an Euler-Lagrange type functional equation f(alpha x + beta y) + f(alpha x - beta y) = 2 alpha(2)f(x) + 2 beta(2)f(y) assumed for fixed nonzero real numbers alpha, alpha, 1 not equal alpha(2) not equal beta(2), and the classic quadratic functional equation g(x + y) + g(x - y) = 2g(x) + 2g(y). We were inspired by papers of Kim et al. (Abstract and applied analysis, vol. 2013, Hindawi Publishing Corporation, 2013) and Gordji and Khodaei (Abstract and applied analysis, vol. 2009, Hindawi Publishing Corporation, 2009), where the special case g = gamma f was examined.

关键词： Functional equations Alienation Quadratic type equations polynomial functions Szekelyhidi's theorem

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Using Decoupling Methods to Reduce polynomial NARX Models

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IFAC-PapersOnLine 2018年第15期51卷 796-801页

作者： Westwick, David T. Hollander, Gabriel Karami, Kiana Schoukens, Johan Department of Electrical and Computer Engineering Schulich School of Engineering University of Calgary 2500 University Drive NW Calgary AlbertaT2N 1N4 Canada Pleinlaan 2 Brussels1050 Belgium

The polynomial NARX model, where the output is a polynomial function of past inputs and outputs, is a commonly used equation error model for nonlinear systems. While it is linear in the variables, which simplifies its identification, it suffers from two major drawbacks: the number of parameters grows combinatorially with the degree of the nonlinearity, and it is a black box model, which makes it difficult to draw any insights from the identified model. polynomial decoupling techniques are used to replace the multiple-input single-output polynomial with a decoupled polynomial structure comprising a transformation matrix followed by bank of SISO polynomials, whose outputs are then summed. This approach is demonstrated on two benchmark systems: The Bouc-Wen friction model and the data from the Silverbox model. In both cases, the decoupling results in a substantial reduction in the number of parameters, and allows some insight into the nature of the nonlinearities in the system. © 2018

关键词： polynomials Linear transformations Nonlinear equations Nonlinear systems Decoupling methods Decoupling technique Multiple input single outputs NARX models polynomial functions polynomial structure Substantial reduction Transformation matrices

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On the deformation quantization of coadjoint orbits of semisimple groups

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PACIFIC JOURNAL OF MATHEMATICS 2001年第2期198卷 411-436页

作者： Fioresi, R Lledó, MA Univ Bologna I-40125 Bologna Italy Ist Nazl Fis Nucl Sex Torino Turin Italy Politecn Torino Dipartimento Fis I-10129 Turin Italy

In this paper we consider the problem of deformation quantization of the algebra of polynomial functions on coadjoint orbits of semisimple Lie groups. The deformation of an orbit is realized by taking the quotient of the universal enveloping algebra of the Lie algebra of the given Lie group, by a suitable ideal. A comparison with geometric quantization in the case of SU(2) is done, where both methods agree.

关键词： .universal enveloping symplectic manifold classical system semisimple Lie deformation quantization Poisson bracket geometric quantization coadjoint orbits polynomial functions

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BEM performance with the addition of polynomials solving stationary thermal problems with functional gradation

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INTERNATIONAL JOURNAL FOR COMPUTATIONAL METHODS IN ENGINEERING SCIENCE & MECHANICS 2024年第6期25卷 396-405页

作者： Loeffler, Carlos Friedrich Lara, Luciano de Oliveira Castro Barcelos, Hercules de Melo Univ Fed Espirito Santo Mech Engn Dept PPGEM UFES BR-29075910 Vitoria ES Brazil Natl Inst Metrol Qual & Technol INMETRO Duque De Caxias RJ Brazil

This work presents the formulation and numerical results of the Dual Reciprocity Boundary Element Method (DRBEM), adapted to include the procedure known as the addition of polynomial functions. This technique is used to improve the interpolation scheme's accuracy using radial basis functions. This idea works quite effectively in simple interpolation procedures, especially when the field profile to be approximated has similarities with added polynomials. Although applied as a supplementary resource in some works, the efficiency and restrictions of the procedure were not discussed in detail as necessary. In this article, the addition of functions is applied to solve non-homogeneous stationary heat transfer problems. The main objective is to analyze its capability, especially in reducing the demand for internal interpolation points. The three simulations show that although introducing polynomials can improve the results, other characteristics are mandatory for achieving suitable accuracy. Three examples of numerical simulation are solved and show that its effectivity is relative, mainly limited by the type of application.

关键词： Boundary element method non-homogeneous problems dual reciprocity radial basis functions polynomial functions

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Sylow p-groups of polynomial permutations on the integers mod pⁿ

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JOURNAL OF NUMBER THEORY 2013年第12期133卷 4188-4199页

作者： Frisch, Sophie Krenn, Daniel Graz Univ Technol Inst Math A A-8010 Graz Austria Graz Univ Technol Inst Math B A-8010 Graz Austria

We enumerate and describe the Sylow p-groups of the groups of polynomial permutations of the integers mod p(n) for n >= 1 and of the pro-finite group which is the projective limit of these groups. (C) 2013 The Auth... 详细信息

关键词： polynomial permutations polynomial functions polynomial mappings p-Groups Pro-p-groups Sylow p-groups Finite rings

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