Kato inequality for operators with infinitely many separated variables

1999 ◽  
Vol 51 (5) ◽  
pp. 799-801
Author(s):  
V. G. Samoilenko
Keyword(s):  
Kato Inequality ◽  
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

Heat equation with a singular potential on the boundary and the Kato inequality

2012 ◽  
Vol 118 (1) ◽  
pp. 161-176 ◽  
Author(s):  
Kazuhiro Ishige ◽  
Michinori Ishiwata
Keyword(s):  
Heat Equation ◽  
Singular Potential ◽  
Kato Inequality

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).

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