Noetherity criterion and a formula for the index of a singular integral functional operator of first order in the continuous case

1994 ◽  
pp. 37-100
Author(s):  
Victor G. Kravchenko ◽  
Georgii S. Litvinchuk
Keyword(s):  
Singular Integral ◽  
Integral Functional ◽  
Continuous Case ◽  
Functional Operator ◽  
First Order

First-emptiness problems in applied probability under first-order dependent input and general output conditions

1973 ◽  
Vol 10 (02) ◽  
pp. 330-342 ◽  
Author(s):  
J. P. Lehoczky
Keyword(s):  
Markov Chain ◽  
Integral Functional ◽  
Applied Probability ◽  
Input Process ◽  
First Order ◽  
Infinite Reservoir

Results for the first-emptiness time of a semi-infinite reservoir and the integral functional of the process up to first-emptiness time are derived under Markov chain input conditions and general output conditions. The results are further extended to allow an input process which is the sum of k consecutive elements of the Markov chain, k ≧ 1.

First Order Partial Functional Differential Equations with Unbounded Delay

2003 ◽  
Vol 10 (3) ◽  
pp. 509-530
Author(s):  
Z. Kamont ◽  
S. Kozieł
Keyword(s):  
Differential Equations ◽  
Integral Functional ◽  
Functional Differential Equations ◽  
Generalized Solutions ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
First Order ◽  
Unbounded Delay ◽  
The Cauchy Problem ◽  
Functional Differential

Abstract The phase space for nonlinear hyperbolic functional differential equations with unbounded delay is constructed. The set of axioms for generalized solutions of initial problems is presented. A theorem on the existence and continuous dependence upon initial data is given. The Cauchy problem is transformed into a system of integral functional equations. The existence of solutions of this system is proved by the method of successive approximations and by using theorems on integral inequalities. Examples of phase spaces are given.

scholarly journals The distribution of the maximum of a first order moving average: the continuous case

Extremes ◽  
2013 ◽  
Vol 17 (1) ◽  
pp. 1-24 ◽  
Author(s):  
Christopher S. Withers ◽  
Saralees Nadarajah
Keyword(s):  
Moving Average ◽  
Continuous Case ◽  
First Order ◽  
Distribution Of The Maximum

Closed 𝓐-p Quasiconvexity and Variational Problems with Extended Real-Valued Integrands

2018 ◽  
Vol 24 (4) ◽  
pp. 1605-1624
Author(s):  
Adam Prosinski
Keyword(s):  
Vector Fields ◽  
Additional Assumption ◽  
Integral Functional ◽  
Variational Problems ◽  
Constant Rank ◽  
Differential Constraint ◽  
First Order ◽  
Characteristic Cone ◽  
Lower Semi ◽  
Continuity Assumption

This paper relates the lower semi-continuity of an integral functional in the compensated compactness setting of vector fields satisfying a constant-rank first-order differential constraint, to closed 𝓐-p quasiconvexity of the integrand. The lower semi-continuous envelope of relaxation is identified for continuous, but potentially extended real-valued integrands. We discuss the continuity assumption and show that when it is dropped our notion of quasiconvexity is still equivalent to lower semi-continuity of the integrand under an additional assumption on the characteristic cone of 𝓐.

On a class of systems of singular integral equations on a bounded domain

1979 ◽  
Vol 83 (3-4) ◽  
pp. 347-364 ◽  
Author(s):  
A. Džuraev
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Boundary Curve ◽  
Adjoint Problem ◽  
Bergman Kernel Function ◽  
One Dimensional ◽  
First Order ◽  
Order Elliptic System ◽  
Type Boundary

SynopsisA class of systems of two-dimensional singular integral equations with even kernels over bounded domains in the plane is studied. The applications include integral equations with the Bergman kernel function. The method of investigation is the following: the integral equation is reduced to a Riemann type boundary value problem for a first order elliptic system. This is solved by means of one-dimensional singular integral equations over the boundary curve. An adjoint problem is formulated, the Noetherian theorems are established, and a formula for the index is given.

scholarly journals On approximation of two-dimensional potential and singular operators

2019 ◽  
Vol 2019 (1) ◽  
pp. 68-83
Author(s):  
Charyyar Ashyralyyev ◽  
Sedanur Efe
Keyword(s):  
Numerical Calculation ◽  
Singular Integral ◽  
Numerical Experiments ◽  
Spline Approximation ◽  
Integral Operators ◽  
Quadrature Formulas ◽  
Two Dimensional ◽  
Order Of Accuracy ◽  
First Order ◽  
Order Spline

Abstract The purpose of this paper is the construction of second-order of accuracy quadrature formulas for the numerical calculation of the Vekua types two-dimensional potential and singular integral operators in the unit disk of complex plane. We propose quadrature formulas for these integrals which based on first-order spline approximation of two-dimensional function. MATLAB programs are used for numerical experiments in test examples.

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