相关论文: Open problems on GKK tau-matrices
There exists an exact relationship between the quasi-exactly solvable problems of quantum mechanics and models of square and rectangular random complex matrices. This relationship enables one to reduce the problem of constructing…
In this thesis, a Bayes linear methodology for the adjustment of covariance matrices is presented and discussed. A geometric framework for quantifying uncertainties about covariance matrices is set up, and an inner-product for spaces of…
We examine the phenomenon of nonlinear stabilization, exhibiting a variety of related examples and counterexamples. For G\^ateaux differentiable maps, we discuss a mechanism of nonlinear stabilization, in finite and infinite dimensions,…
We present 35 open problems on combinatorial, geometric and algebraic aspects of k-orbit abstract polytopes. We also present a theory of rooted polytopes that has appeared implicitly in previous work but has not been formalized before.
The purpose of this paper is two-fold: we present some matrix inequalities of log-majorization type for eigenvalues indexed by a sequence; we then apply our main theorem to generalize and improve the Hua-Marcus' inequalities. Our results…
It is shown how to construct exactly gauge-invariant S-matrix elements for processes involving unstable gauge particles such as the $Z^0$ boson. The results are applied to derive a physically meaningful expression for the cross-section…
We prove that Runge-Kutta (RK) methods for numerical integration of arbitrarily large systems of Ordinary Differential Equations are linearly stable. Standard stability arguments -- based on spectral analysis, resolvent condition or strong…
Neutrino-mass textures proposed at high-scales are known to be unstable against radiative corrections especially for nearly degenerate eigen values. Within the renormalization group constraints we find a mechanism in a class of gauge…
Under certain mild assumption, we establish a one-to-one correspondence between solutions of the Nehari-Takagi problem and solutions of some Takagi-Sarason interpolation problem. The resolvent matrix of the Nehari-Takagi problem is shown to…
We consider solvable matrix models. We generalize Harish-Chandra-Itzykson-Zuber and certain other integrals (Gross-Witten integral and integrals over complex matrices) using the notion of tau function of matrix argument. In this case one…
There are well-known constructions of integrable systems which are chains of infinitely many copies of the equations of the KP hierarchy ``glued'' together with some additional variables, e.g., the modified KP hierarchy. Another…
Some Open Problems Concerning Orthogonal Polynomials.
This paper gives an overview on and summarizes existing complexity and algorithmic results of some variants of the Stable Marriage and the Stable Roommates problems. The last section defines a list of stable matching problems mentioned in…
We review the construction and classification of three-family grand unified models within the framework of asymmetric orbifolds in perturbative heterotic superstring. We give a detailed survey of all such models which is organized to aid…
Due to their conceptual simplicity, k-means algorithm variants have been extensively used for unsupervised cluster analysis. However, one main shortcoming of these algorithms is that they essentially fit a mixture of identical spherical…
In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis…
Turing patterns on unbounded domains have been widely studied in systems of reaction-diffusion equations. However, up to now, they have not been studied for systems of conservation laws. Here, we (i) derive conditions for Turing instability…
We discuss various problems in frame theory that have been open for some years. A short discussion of frame theory is also provided, but it only contains the information that is necessary in order to understand the open problems and their…
This article is a snap-shot of a web site, which has been collecting open problems in quantum information for several years, and documenting the progress made on these problems. By posting it we make the complete collection available in one…
We introduce a new class of large structured random matrices characterized by four fundamental properties which we discuss. We prove that this class is stable under matrix-valued and pointwise non-linear operations. We then formulate an…