Asymptotic behavior of the central path for a special class of degenerate SDP problems

The multidimensional integral equation of second kind with a homogeneous of degree (−n) kernel is considered. The special class of continuous functions with a given asymptotic behavior in the neighborhood of zero is defined. It is proved that, if the free term of the integral equation belongs to this class and the equation itself is solvable, then its solution also belongs to this class. To solve this problem, a special research technique is used. The above-mentioned technique is based on the decomposition of both the solution and the free term in spherical harmonics.

Download Full-text

Application of Stieltjes theory for S-fractions to birth and death processes

Advances in Applied Probability ◽

10.1017/s0001867800021388 ◽

1983 ◽

Vol 15 (03) ◽

pp. 507-530 ◽

Cited By ~ 3

Author(s):

G. Bordes ◽

B. Roehner

Keyword(s):

Asymptotic Behavior ◽

Lower Bound ◽

Special Class ◽

Jacobi Matrix ◽

General Theorem ◽

Sufficient Conditions ◽

Death Process ◽

Nearest Neighbour ◽

Birth And Death Process ◽

Birth And Death Processes

We are interested in obtaining bounds for the spectrum of the infinite Jacobi matrix of a birth and death process or of any process (with nearest-neighbour interactions) defined by a similar Jacobi matrix. To this aim we use some results of Stieltjes theory for S-fractions, after reviewing them. We prove a general theorem giving a lower bound of the spectrum. The theorem also gives sufficient conditions for the spectrum to be discrete. The expression for the lower bound is then worked out explicitly for several, fairly general, classes of birth and death processes. A conjecture about the asymptotic behavior of a special class of birth and death processes is presented.

Download Full-text

THE CORNER TRANSFER MATRIX OF SOME FREE-FERMION SYSTEMS AND MEIXNER’S POLYNOMIALS

International Journal of Modern Physics B ◽

10.1142/s0217979290000413 ◽

1990 ◽

Vol 04 (05) ◽

pp. 895-905 ◽

Cited By ~ 11

Author(s):

T.T. TRUONG ◽

I. PESCHEL

Keyword(s):

Asymptotic Behavior ◽

Orthogonal Polynomials ◽

Special Class ◽

Finite Lattice ◽

Free Fermion ◽

Transfer Matrices ◽

Corner Transfer Matrices ◽

Meixner Polynomials ◽

Fermion Systems ◽

Large Lattice

Corner transfer matrices of some free-fermion vertex systems on a finite lattice, are exactly diagonalised in the Hamiltonian limit with the help of a special class of orthogonal polynomials: the Meixner polynomials. We present the derivation, discuss the asymptotic behavior for a large lattice and compare the results with numerical computation.

Download Full-text

Asymptotic Behavior of Solutions of Delayed Difference Equations

Abstract and Applied Analysis ◽

10.1155/2011/671967 ◽

2011 ◽

Vol 2011 ◽

pp. 1-24 ◽

Cited By ~ 2

Author(s):

J. Diblík ◽

I. Hlavičková

Keyword(s):

Asymptotic Behavior ◽

Difference Equations ◽

Special Class ◽

General Theorem ◽

Asymptotic Behavior Of Solutions ◽

Order Difference ◽

First Order ◽

Discrete Equations

This contribution is devoted to the investigation of the asymptotic behavior of delayed difference equations with an integer delay. We prove that under appropriate conditions there exists at least one solution with its graph staying in a prescribed domain. This is achieved by the application of a more general theorem which deals with systems of first-order difference equations. In the proof of this theorem we show that a good way is to connect two techniques—the so-called retract-type technique and Liapunov-type approach. In the end, we study a special class of delayed discrete equations and we show that there exists a positive and vanishing solution of such equations.

Download Full-text

ON SOLVABILITY OF A NONLINEAR DISCRETE SYSTEM IN THE SPREAD THEORY OF INFECTION

Proceedings of the YSU A: Physical and Mathematical Sciences ◽

10.46991/pysu:a/2020.54.2.087 ◽

2020 ◽

Vol 54 (2 (252)) ◽

pp. 87-95

Author(s):

M.H. Avetisyan

Keyword(s):

Asymptotic Behavior ◽

Nonlinear System ◽

Special Class ◽

Discrete System ◽

Mathematical Theory ◽

Algebraic Equations ◽

Uniqueness Of The Solution ◽

Nonlinear Discrete System ◽

Bounded Sequences ◽

Temporal Spread

In this paper a special class of infinite nonlinear system of algebraic equations with Teoplitz matrix is studied. The mentioned system arises in the mathematical theory of the spatial temporal spread of the epidemic. The existence and the uniqueness of the solution in the space of bounded sequences are proved. It is studied also the asymptotic behavior of the constructed solution at infinity. At the end of the work specific examples are given.

Download Full-text

Application of Stieltjes theory for S-fractions to birth and death processes

Advances in Applied Probability ◽

10.2307/1426617 ◽

1983 ◽

Vol 15 (3) ◽

pp. 507-530 ◽

Cited By ~ 16

Author(s):

G. Bordes ◽

B. Roehner

Keyword(s):

Asymptotic Behavior ◽

Lower Bound ◽

Special Class ◽

Jacobi Matrix ◽

General Theorem ◽

Sufficient Conditions ◽

Death Process ◽

Nearest Neighbour ◽

Birth And Death Process ◽

Birth And Death Processes

We are interested in obtaining bounds for the spectrum of the infinite Jacobi matrix of a birth and death process or of any process (with nearest-neighbour interactions) defined by a similar Jacobi matrix.To this aim we use some results of Stieltjes theory for S-fractions, after reviewing them. We prove a general theorem giving a lower bound of the spectrum. The theorem also gives sufficient conditions for the spectrum to be discrete.The expression for the lower bound is then worked out explicitly for several, fairly general, classes of birth and death processes. A conjecture about the asymptotic behavior of a special class of birth and death processes is presented.

Download Full-text