Related papers: Infinite J-matrices and a matrix moment problem
This is an expository survey of the Jacobian problem for the class of Pluriharmonic functions.
The fundamental matrix and the delay Lyapunov matrix of linear delay difference equations are introduced. Some properties of the Lyapunov matrix, and the jump discontinuities of its derivative are proven, leading to its construction in the…
The paper proposes a logical model of combinatorial problems, also it gives an example of a problem of the class NP that can not be solved in polynomial time on the dimension of the problem.
We study the computability of the operator norm of a matrix with respect to norms induced by linear operators. Our findings reveal that this problem can be solved exactly in polynomial time in certain situations, and we discuss how it can…
In this work we study the existence of periodic and asymptotically periodic solutions of a system of nonlinear Volterra difference equations with infinite delay. By means of fixed point theory, we furnish conditions that guarantee the…
We make a relativistic extension of the one-dimensional J-matrix method of scattering. The relativistic potential matrix is a combination of vector, scalar, and pseudo-scalar components. These are non-singular short-range potential…
We show that the partial transpose of $9\times 9$ positive semidefinite matrices do not have inertia (4,1,4) and (3,2,4). It solves an open problem in "LINEAR AND MULTILINEAR ALGEBRA, Changchun Feng et al, 2022". We apply our results to…
There has been significant interest in studying the asymptotics of certain generalised moments, called the moments of moments, of characteristic polynomials of random Haar-distributed unitary and symplectic matrices, as the matrix size $N$…
In this paper I have presented Comment on Anandan's paper (J. Anandan, Phys. Rev. Lett. 85, 1354 (2000)) [hep-th/9910018].
We describe a list of open problems in random matrix theory and integrable systems which was presented at the conference ``Integrable Systems, Random Matrices, and Applications'' at the Courant Institute in May 2006.
Let n\geq3 and J_{n}:=circ(J_{1},J_{2},...,J_{n}) and j_{n}:=\circ(j_{0},j_{1},...,j_{n-1}) be the n\timesn circulant matrices, associated with the nth Jacobsthal number J_{n} and the nth Jacobsthal-Lucas number j_{n}, respectively. The…
We argue that our analysis of the J-Q model, presented in Phys. Rev. B 80, 174403 (2009), and based on a field-theory description of coupled dimers, captures properly the strong quantum fluctuations tendencies, and the objections outlined…
For a Jacobi matrix J on l^2(Z_+) with Ju(n)=a_{n-1} u(n-1) + b_n u(n) + a_n u(n+1), we prove that \sum_{|E|>2} (E^2 -4)^{1/2} \leq \sum_n |b_n| + 4\sum_n |a_n -1|. We also prove bounds on higher moments and some related results in higher…
The Annals of Applied Probability (2002) 12 1114-1137
Among seven problems, proposed for XXI century by Clay Mathematical Institute, there are two stemming from physics. One of them is called "Yang-Mills Existence and Mass Gap". The detailed statement of the problem, written by A. Jaffe and E.…
The article is devoted to the existence of solutions of a certain system of quadratic integral equations in H^1(R, R^N). We show the existence of a perturbed solution by using a fixed point technique in the Sobolev space on the real line.
This paper provides a new formulation of second order stochastic target problems introduced in [SIAM J. Control Optim. 48 (2009) 2344-2365] by modifying the reference probability so as to allow for different scales. This new ingredient…
Polar decompositions of quaternion matrices with respect to a given indefinite inner product are studied. Necessary and sufficient conditions for the existence of an $H$-polar decomposition are found. In the process an equivalent to Witt's…
An exponential representation of the S-matrix provides a natural framework for understanding the semi-classical limit of scattering amplitudes. While sharing some similarities with the eikonal formalism it differs from it in details.…
For many applications, it is convenient to have good upper bounds for the norm of the inverse of a given matrix. In this paper, we obtain such bounds when A is a Nekrasov matrix, by means of a scaling matrix transforming A into a strictly…