Related papers: Open problems on GKK tau-matrices
We show cocycle stability for linear maps with a weak irreducibility condition and their jointly integrable perturbations.
In this survey, we discuss some basic problems concerning random matrices with discrete distributions. Several new results, tools and conjectures will be presented.
The Gaussian-filtered Navier-Stokes equations are examined theoretically and a generalized theory of their numerical stability is proposed. Using the exact expansion series of subfilter-scale stresses or integration by parts, the terms…
We review various aspects of disk instability models. We discuss problems and difficulties and present ways that have been suggested to solve them.
A problem of constructing quantum groups from classical r-matrices is discussed.
We consider theories with one gauge group (SU, SO or Sp) and one scalar in a two-index representation. The renormalizable action often has accidental symmetries (such as global U(1) or unusual group parities) that lead to one or more stable…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system Hamiltonian. Some general stability results are given for different classes of perturbations to the…
We introduce the idea of natural mass matrices, an organizing principle useful in the search for GUT scale quark mass matrix patterns that are consistent with known CKM constraints and quark mass eigenvalues. An application of this idea is…
We propose a list of open problems in pluripotential theory partially motivated by their applications to complex differential geometry. The list includes both local questions as well as issues related to the compact complex manifold…
The concepts of differentiation and integration for matrices are known. As far as each matrix is differentiable, it is not clear a priori whether a given matrix is integrable or not. Recently some progress was obtained for diagonalizable…
We discuss stability of Q-balls interacting with fermions in theory with small coupling constant g. We argue that for configurations with large global U(1)-charge Q the problem of classical stability becomes more subtle. For example, in…
We consider the simplest gauge theories given by one- and two- matrix integrals and concentrate on their stringy and geometric properties. We remind general integrable structure behind the matrix integrals and turn to the geometric…
In this paper, we consider a matroid generalization of the stable matching problem. In particular, we consider the setting where preferences may contain ties. For this generalization, we propose a polynomial-time algorithm for the problem…
The behaviour of magnetic monopole solutions of the Einstein-Yang-Mills-Higgs equations subject to linear spherically symmetric perturbations is studied. Using Jacobi's criterion some of the monopoles are shown to be unstable. Furthermore…
Explicit expressions for multimatrix models with complex and unitary matrices allows to couple these models with well-known unitary, orthogonsl and sympletic ensembles. We consider examples of such mixed ensembles which are solvable in the…
In this small paper we bring together various open problems on geometric multidimensional continued fractions.
In this paper, we investigate the computational complexity of the knapsack problem and subset sum problem for the following tropical algebraic structures. We consider the semigroup of square matrices of size $k \times k$ with non-negative…
We are interested in the phenomenon of the essential spectrum instability for a class of unbounded (block) Jacobi matrices. We give a series of sufficient conditions for the matrices from certain classes to have a discrete spectrum on a…
In this paper, some new Gronwall type inequalities involving iterated integrals are given.
We propose a list of open problems in numerical semigroups.