Related papers: Open problems on GKK tau-matrices
Presentation of set matrices and demonstration of their efficiency as a tool using the path/cycle problem.
This review article will present some recent results and methods in the study of 1-particle quantum or wave scattering systems, in the semiclassical/high frequency limit, in cases where the corresponding classical/ray dynamics is chaotic.…
We prove that static, spherically symmetric, asymptotically flat, regular solutions of the Einstein-Yang-Mills equations are unstable for arbitrary gauge groups, at least for the ``generic" case. This conclusion is derived without explicit…
This is an exposition for mathematicians of some unsolved problems arising in control theory of linear time-independent systems.
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…
In this paper we review a number of issues on the security of quantum key distribution (QKD) protocols that bear directly on the relevant physics or mathematical representation of the QKD cryptosystem. It is shown that the cryptosystem…
We explore the uncertainty relation for unitary operators in a new way and find two uncertainty equalities for unitary operators, which are minimized by any pure states. Additionally, we derive two sets of uncertainty inequalities that…
We give fully explicit upper and lower bounds for the constants in two known inequalities related to the quadratic nonlinearity of the incompressible (Euler or) Navier-Stokes equations on the torus T^d. These inequalities are "tame"…
Multiplicative and additive $D$-stability, diagonal stability, Schur $D$-stability, $H$-stability are classical concepts which arise in studying linear dynamical systems. We unify these types of stability, as well as many others, in one…
Branes and defects in topological Landau-Ginzburg models are described by matrix factorisations. We revisit the problem of deforming them and discuss various deformation methods as well as their relations. We have implemented these…
We provide a determinantal formula for tau-functions of the KP hierarchy in terms of rectangular, constant matrices $A$, $B$ and $C$ satisfying a rank one condition. This result is shown to generalize and unify many previous results of…
This paper pursues a two-fold goal. Firstly, we aim to derive novel second-order characterizations of important robust stability properties of perturbed Karush-Kuhn-Tucker systems for a broadclass of constrained optimization problems…
A modified Gauss's algorithm for solving a system of linear equations in an integral ring is proposed, as well as an appropriate algorithm for calculating the elements of the adjoint matrix.
A unified matrix-vector representation is developed of such solution concepts as the core, the uncovered, the uncaptured, the minimal weakly stable, the minimal undominated, the minimal dominant and the untrapped sets. We also propose…
We construct quark mixing matrices within a group theoretic framework which is easily applicable to any number of generations. Familiar cases are retrieved and related, and it is hoped that our viewpoint may have advantages both…
The gl(N) and U_q(gl(N)) quantum spin chains in the presence of integrable spin impurities are considered. Within the Bethe ansatz formulation, we derive the associated transmission amplitudes, and the corresponding transmission matrices…
In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of…
Some new Gruss type inequalities in inner product spaces and applications for integrals are given.
In this survey article we discuss key open problems which could serve as a guidance for further research directions of multiplicative ideal theory and factorization theory.
We study a variant of algebraic K-theory and prove that it is stable and preserves module structures.