Related papers: Differential systems with reflection and matrix in…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…
The persistence theory has been employed by several authors in order to study persistence properties of dynamical systems generated by ordinary differential equations or maps across diverse disciplines. In this note, the author discusses a…
In this note, we consider applications of Ratner's theorem to constructions of families of polynomials with dense values on the set of primitive integer points from the viewpoint of invariant theory.
A simple construction of Euclidean invariant and reflection positive measures on the cylindrical compactification is performed under a weaker hypothesis than has recently been obtained. Moreover, the results are extended to the case when…
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 state some elementary problems concerning the relation between difference calculus and differential calculus, and we try to convince the reader that, in spite of the simplicity of the statements, a solution of these problems would be a…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
We revisit the relative perturbation theory for invariant subspaces of positive definite matrix pairs. As a prototype model problem for our results we consider parameter dependent families of eigenvalue problems. We show that new estimates…
We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the…
An abstract theory of ultradifferentiable sheafs is developed. Moreover, various applications to the theory of linear partial differential equations, differential geometry and, in particular, CR geometry are discussed.
It is known that discrete scale invariance leads to log-periodic corrections to scaling. We investigate the correlations of a system with discrete scale symmetry, discuss in detail possible extension of this symmetry such as translation and…
For a class of stochastic differential equations with reflection for which a certain ${\mathbb{L}}^p$ continuity condition holds with $p>1$, it is shown that any weak solution that is a strong Markov process can be decomposed into the sum…
This note presents a summary and review of various conditions and characterizations for matrix stability (in particular diagonal matrix stability) and matrix stabilizability.
A survey of some results and open questions related to the following algebraic invariants of compact complex manifolds, that can be obtained from differential forms: cohomology groups, Chern classes, rational homotopy groups, and higher…
In the following short paper we list some useful results concerning determinants and inverses of matrices. First we show, how to calculate determinants of $d \times d$ matrices, if their traces are known. As a next step $4 \times 4$…
We determine the most general group of equivalence transformations for a family of differential equations defined by an arbitrary vector field on a manifold. We also find all invariants and differential invariants for this group up to the…
Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…
This work considers the algebras of functions in the quantum matrix ball. An explicit formula for a positive invariant integral is presented.
In this paper explicit decompositions are provided of the Weyl reflections in affine Lie algebras, in terms of fundamental Weyl reflections.
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new…