A criterion for the primeness of ideals generated by polynomials with separated variables

1999 ◽  
Vol 113 (1) ◽  
pp. 1-13
Author(s):  
Konrad Neumann
Keyword(s):  
Separated Variables

scholarly journals Dual separated variables and scalar products

2020 ◽  
Vol 806 ◽  
pp. 135494 ◽  
Author(s):  
Nikolay Gromov ◽  
Fedor Levkovich-Maslyuk ◽  
Paul Ryan ◽  
Dmytro Volin
Keyword(s):  
Scalar Products ◽  
Separated Variables

Elastodynamic Local Fields for a Crack Running in an Orthotopic Medium

1991 ◽  
Vol 58 (4) ◽  
pp. 982-987 ◽  
Author(s):  
A. Piva ◽  
E. Radi
Keyword(s):  
Dynamic Stress ◽  
Equations Of Motion ◽  
Local Fields ◽  
Stress Fields ◽  
Orthotropic Materials ◽  
Displacement Fields ◽  
First Order ◽  
Stress And Displacement Fields ◽  
Order Elliptic System ◽  
Separated Variables

The dynamic stress and displacement fields in the neighborhood of the tip of a crack propagating in an orthotropic medium are obtained. The approach deals with the methods of linear algebra to transform the equations of motion into a first-order elliptic system whose solution is sought under the assumption that the local displacement field may be represented under a scheme of separated variables. The analytical approach has enabled the distinction between two kinds of orthotropic materials for which explicit espressions of the near-tip stress fields are obtained. Some results are presented graphically also in order to compare them with the numerical solution given in a quoted reference.

scholarly journals Diophantine equations in separated variables and lacunary polynomials

2017 ◽  
Vol 13 (08) ◽  
pp. 2055-2074 ◽  
Author(s):  
Dijana Kreso
Keyword(s):  
Number Field ◽  
Diophantine Equations ◽  
Lower Degree ◽  
Independent Interest ◽  
Infinitely Many Solutions ◽  
Functional Composition ◽  
Type Formula ◽  
Finiteness Criterion ◽  
Separated Variables

We study Diophantine equations of type [Formula: see text], where [Formula: see text] and [Formula: see text] are lacunary polynomials. According to a well-known finiteness criterion, for a number field [Formula: see text] and nonconstant [Formula: see text], the equation [Formula: see text] has infinitely many solutions in [Formula: see text]-integers [Formula: see text] only if [Formula: see text] and [Formula: see text] are representable as a functional composition of lower degree polynomials in a certain prescribed way. The behavior of lacunary polynomials with respect to functional composition is a topic of independent interest, and has been studied by several authors. In this paper, we utilize known results on the latter topic, and develop new ones, in relation to Diophantine applications.

scholarly journals Computing of the separated variables for the Hamilton-Jacobi equation on a computer

2005 ◽  
pp. 163-179
Author(s):  
Y. A. Grigoryev ◽  
◽  
A. V. Tsiganov ◽  
Keyword(s):  
Jacobi Equation ◽  
Hamilton Jacobi Equation ◽  
Separated Variables

scholarly journals Korous Type Inequalities for Orthogonal Polynomials in two Variables

2014 ◽  
Vol 58 (1) ◽  
pp. 1-12
Author(s):  
Branislav Ftorek ◽  
Pavol Oršansky
Keyword(s):  
Weight Function ◽  
Orthogonal Polynomials ◽  
Uniform Boundedness ◽  
Separated Variables

ABSTRACT J. Korous reached an important result for general orthogonal polynomials in one variable. He dealt with the boundedness and uniform boundedness of polynomials { Pn(x)}∞n=0 orthonormal with the weight function h(x) = δ(x) ̃h(x), where ̃h(x) is the weight function of another system of polynomials { ̃Pn(x) }∞n=0 orthonormal in the same interval and δ(x) ≥ δ0 > 0 is a certain function. We generalize this result for orthogonal polynomials in two variables multiplying their weight function h(x, y) by a polynomial, dividing h(x, y) by a polynomial, and multiplying h(x, y) with separated variables by a certain function δ(x, y).

An Entropy Function Implementation of Quadratic Programming

2012 ◽  
Vol 226-228 ◽  
pp. 2227-2230
Author(s):  
Xiao Guang Wang ◽  
Chun Juan Hou
Keyword(s):  
Quadratic Programming ◽  
Programming Problem ◽  
Constraint Programming ◽  
Lagrange Function ◽  
Good Method ◽  
Entropy Function ◽  
Taylor Formula ◽  
Quadratic Programming Problems ◽  
Ks Function ◽  
Separated Variables

This paper is intended to describe a new algorithm, which makes entropy function method with Lagrange function and Taylor formula for solving inseparable variables of quadratic programming. Quadratic programming problem are an important in the fields of nonlinear programming problem. Entropy function also called KS function. The nature and related certificate of KS function and its convergence have already been proved at home and abroad. The application of KS function nature for solving quadratic programming is a very good method, and it is one of the advantages of making more constraint programming problem become a single constraint programming problem, and the original problems are simplified. Electing three examples of separated variables for quadratic programming problems, that is cross terms of zero, and then contrasted with the new method. The algorithm resolves implementation of separated variables of quadratic programming. Our numerical experiments show the proposed algorithm is feasible.

scholarly journals Frobenius nonclassical components of curves with separated variables

2016 ◽  
Vol 159 ◽  
pp. 402-425 ◽  
Author(s):  
Herivelto Borges
Keyword(s):  
Separated Variables
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