Related papers: A Functional Model for SMP Matrices and the Jacobi…
We consider a class of semi-Markov processes (SMP) such that the embedded discrete time Markov chain may be non-homogeneous. The corresponding augmented processes are represented as semi-martingales using stochastic integral equation…
Entropy stable schemes replicate an entropy inequality at the semi-discrete level. These schemes rely on an algebraic summation-by-parts (SBP) structure and a technique referred to as flux differencing. We provide simple and efficient…
We consider a set of measures on the real line and the corresponding system of multiple orthogonal polynomials (MOPs) of the first and second type. Under some very mild assumptions, which are satisfied by Angelesco systems, we define…
Motivated by recent results in random matrix theory we will study the distributions arising from products of complex Gaussian random matrices and truncations of Haar distributed unitary matrices. We introduce an appropriately general class…
Stochastic fluid-fluid models (SFFMs) offer powerful modeling ability for a wide range of real-life systems of significance. The existing theoretical framework for this class of models is in terms of operator-analytic methods. For the first…
This paper describes extension of the Master Stability Function for arrays of non-smooth oscillators. This extension is based on the previously introduced Jacobi matrix estimation method, which can be applied to networks of non-smooth…
The problem of two-phase flow in straight capillaries of polygonal cross section displays many of the dynamic characteristics of rapid interfacial motions associated with pore-scale displacements in porous media. Fluid inertia is known to…
In this manuscript we study algebraic and analytic properties of the sequence of monic polynomials orthogonal with respect to a Jacobi differential operator. A fluid dynamics model for source points location of a flow of an incompressible…
We consider periodic matrix-valued Jacobi operators. The spectrum of this operator is absolutely continuous and consists of intervals separated by gaps. We define the Lyapunov function, which is analytic on an associated Riemann surface. On…
In this work the spectral theory of self-adjoint operator $A$ represented by Jacobi matrix is considered. The approach is based on the continued fraction representation of the resolvent matrix element of $A$. Different criteria of absolute…
We consider the inverse dynamical problem for the dynamical system with discrete time associated with the semi-infinite Jacobi matrix. We solve the inverse problem for such a system and answer a question on the characterization of the…
We consider the inverse dynamic problem for a dynamical system with discrete time associated with a semi-infinite complex Jacobi matrix. We propose two approaches of recovering coefficients from dynamic response operator and answer a…
We consider a family of steady free-surface flow problems in two dimensions, concentrating on the effect of nonlinearity on the train of gravity waves that appear downstream of a disturbance. By exploiting standard complex variable…
We study the J-flow on the toric manifolds, through study the transition map between the moment maps induced by two K\"{a}hler metrics, which is a diffeomorphism between polytopes. This is similar to the work of Fang-Lai, under the…
A systematic exposition of scale functions is given for positive self-similar Markov processes (pssMp) with one-sided jumps. The scale functions express as convolution series of the usual scale functions associated with spectrally one-sided…
The discrete spectrum of complex Jacobi matrices that are compact perturbations of the discrete laplacian is under consideration. The rate of stabilization for the the matrix entries which provides finiteness of the discrete spectrum and is…
Degrees of freedom for high-order binary constrained flows of soliton equations admitting $2\times 2$ Lax matrices are $2N+k_0$. It is known that $N+k_0$ pairs of canonical separated variables for their separation of variables can be…
We consider the 1D periodic Jacobi matrices. The spectrum of this operator is purely absolutely continuous and consists of intervals separated by gaps. We solve the inverse problem (including characterization) in terms of vertical slits on…
Using a matrix approach, we define the free Jacobi process as the limit of the complex Jacobi matrix process. The we derive a free SDE which is analogous to its classical counterpart. To proceed, we prove that fro suitable parameters the…
The class of three-diagonal Jacobi matrix with exponentially increasing elements is considered. Under some assumptions the matrix corresponds to unbounded self-adjoint operator in the weighted space. The weight depends on elements of the…