相关论文: Study of the vacuum matrix element of products of …
We present a simple model of the interface between a local homogeneous medium and a potentially nonlocal metamaterial/photonic crystal. This model allows us to calculate the scattering matrix elements of the interface for a plane wave of…
We study the image of $\textrm{SU}(n)$ under the diagonal product map. Using only elementary tools of linear algebra, analysis and general topology, we find the analytical formula for the boundary of this image and find all special unitary…
Gradient vector fields are fundamental objects from both theoretical and practical perspectives, since various phenomena can be modeled within this framework. The ``moduli space'' of such vector fields provides the foundation for describing…
A simple theory of the covariant derivatives, deformed derivatives and relative covariant derivatives of multivector and multiform fields is presented using algebraic and analytical tools developed in previous papers.
We provide formulas for invariants defined on a tensor product of defining representations of unitary groups, under the action of the product group. This situation has a physical interpretation, as it is related to the quantum mechanical…
Graphs are very important mathematical structures used in many applications, one of which is transportation science. When dealing with transportation networks, one deals not only with the network structure, but also with information related…
We use an extension of the diagrammatic rules in random matrix theory to evaluate spectral properties of finite and infinite products of large complex matrices and large hermitian matrices. The infinite product case allows us to define a…
These notes follow my articles [1, 6], and give some new important details. We propose here a new combinatorial method of encoding of measure spaces with measure preserving transformations, (or groups of transformations) in order to give…
We consider certain matrix-products where successive matrices in the product belong alternately to a particular qualitative class or its transpose. The main theorems relate structural and spectral properties of these matrix-products to the…
We analyze the neutrino mass matrix entries and their correlations in a probabilistic fashion, constructing probability distribution functions using the latest results from neutrino oscillation fits. Two cases are considered: the standard…
The QCD vacuum can be studied using external fields. We report here results respectively obtained probing the lattice QCD vacuum by means of an abelian monopole field and of an abelian chromomagnetic field
We find the exact solution for the stationary state measure of the partially asymmetric exclusion process on a ring with multiple species of particles. The solution is in the form of a matrix product representation where the matrices for a…
We present a geometric interpretation of the integration-by-parts formula on an arbitrary vector bundle. As an application we give a new geometric formulation of higher-order variational calculus.
In factoring matrices into the product of two matrices operations are typically performed with elements restricted to matrix subspaces. Such modest structural assumptions are realistic, for example, in large scale computations. This paper…
We give an overview of combinatorial methods to represent 3D data, such as graphs and meshes, from the viewpoint of their amenability to analysis using machine learning algorithms. We highlight pros and cons of various representations and…
This paper investigates some combinatorial and algebraic properties of a Witt type formula for graphs.
This paper studies two topics concerning on the orthogonal complement of one dimensional subspace with respect to a given quadratic form on a vector space over a number field. One is to determine the invariants for the isomorphism class of…
This monograph is a study of the category of polynomial endofunctors on the category of sets and its applications to modeling interaction protocols and dynamical systems. We assume basic categorical background and build the categorical…
The variety of uniform matrix product states arises both in algebraic geometry as a natural generalization of the Veronese variety, and in quantum many-body physics as a model for a translation-invariant system of sites placed on a ring.…
We introduce a method for calculating individual elements of matrix functions. Our technique makes use of a novel series expansion for the action of matrix functions on basis vectors that is memory efficient even for very large matrices. We…