相关论文: Open problems on GKK tau-matrices
The construction of quantum knot invariants from solutions of the Yang--Baxter equation (R-matrices) is reviewed with the emphasis on a class of R-matrices admitting an interpretation in intrinsically three-dimensional terms.
Two new neutrino mass matrix textures exhibiting the \emph{mixed $\mu$-$\tau$ symmetry} are proposed. The mass matrices hint for a promising neutrino mixing schemes and find their connections with $\Delta(27)$ and $A_{4}$ discrete symmetry…
Motivated by questions in robust control and switched linear dynamical systems, we consider the problem checking whether all convex combinations of k matrices in R^{n x n} are stable. In particular, we are interested whether there exist…
In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a…
In this paper, we address the problem of estimating a covariance matrix of a multivariate Gaussian distribution, relative to a Stein loss function, from a decision theoretic point of view. We investigate the case where the covariance matrix…
Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.
We develop a systematic analysis of quark mass matrices which, starting with the measured values of quark masses and mixing angles, allows for a model independent search for all possible (symmetric or hermitian) mass matrices having texture…
The Nystr\"om method is a widely used technique for improving the scalability of kernel-based algorithms, including kernel ridge regression, spectral clustering, and Gaussian processes. Despite its popularity, the numerical stability of the…
Let K/F be a cyclic field extension of odd prime degree. We consider Galois embedding problems involving Galois groups with common quotient Gal(K/F) such that corresponding normal subgroups are indecomposable Fp[Gal(K/F)]-modules. For these…
In this paper we have discussed different possible orthogonalities in matrices, namely orthogonal, quasi-orthogonal, semi-orthogonal and non-orthogonal matrices including completely positive matrices, while giving some of their…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
The goal of this presentation is to highlight various computational techniques used to study dynamics of quantum many-body systems. We examine the projection and variable phase methods being applied to multi-channel problems of scattering…
A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted by an infinite square well, and in expressing the…
We show that a fast algorithm for the QR factorization of a Toeplitz or Hankel matrix A is weakly stable in the sense that R^T.R is close to A^T.A. Thus, when the algorithm is used to solve the semi-normal equations R^T.Rx = A^Tb, we obtain…
A review of some recent results on the dynamical theory of the Yang-Baxter maps (also known as set-theoretical solutions to the quantum Yang-Baxter equation) is given. The central question is the integrability of the transfer dynamics. The…
We consider the quantum inverse scattering method for several mixed integrable models based on the rational SU(N) R-matrix with general toroidal boundary conditions. This includes systems whose Hilbert spaces are invariant by the discrete…
In this paper, we have constructed the higher order k-bonacci matrices and studied some of their basic properties. We have also shown that these matrices satisfying some new and interesting relations in k-bonacci recurrence. This is the…
Rigorous mathematical proofs of the security of continuous-variable quantum key distribution (CV QKD) have been obtained recently. Unfortunately, these security proofs rely on assumptions that are hardly met in experimental practice. Here I…
Solutions of the system of evolutionary equations in the short-wavelength approximation are found and studied. A connection is established between the problem of the evolution of short-wavelength gravitational-scalar perturbations and the…
The status of several representative gauge theories on various quantum space-times, mainly focusing on Yang-Mills type extensions together with a few matrix model formulations is overviewed. The common building blocks are derivation based…