Related papers: Differential calculus for fully matricial function…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
Four families of special functions, depending on n variables, are studied. We call them symmetric and antisymmetric multivariate sine and cosine functions. They are given as determinants or antideterminants of matrices, whose matrix…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…
We consider the algebra of square matrices of bounded non-commutative (NC) functions over NC operator unit balls (unit balls corresponding to finite-dimensional operator spaces) and characterize cyclic matrix free polynomials with respect…
We study first order differential operators with constant coefficients. The main question is under what conditions a generalized Poincar\'e inequality holds. We show that the constant rank condition is sufficient. The concept of the…
As well known, permanent of a square (0,1)-matrix $A$ of order $n$ enumerates the permutations $\beta$ of $1,2,...,n$ with the incidence matrices $B\leq A.$ To obtain enumerative information on even and odd permutations with condition…
The study of the dynamics of polynomials is now a major field of research, with many important and elegant results. The study of entire functions that are not polynomials -- in other words transcendental entire functions -- is somewhat less…
Entire functions in one complex variable are extremely relevant in several areas ranging from the study of convolution equations to special functions. An analog of entire functions in the quaternionic setting can be defined in the slice…
The theory of fractional calculus has developed in a number of directions over the years, including: the formulation of multiple different definitions of fractional differintegration; the extension of various properties of standard calculus…
In this talk, I will discuss the use of harmonic functions to study the geometry and topology of complete manifolds. In my previous joint work with Luen-fai Tam, we discovered that the number of infinities of a complete manifold can be…
In this paper, we study the consequences of the fundamental theorem of calculus from an algebraic point of view. For functions with singularities, this leads to a generalized notion of evaluation. We investigate properties of such…
A generalized definition of the determinant of matrices is given, which is compatible with the usual determinant for square matrices and keeps many important properties, such as being an alternating multilinear function, keeping…
An exact expression for the determinant of the splitting matrix is derived: it allows us to analyze the asympotic behaviour needed to amend the large angles theorem proposed in Ann. Inst. H. Poincar\'e, B-60, 1, 1994. The asymptotic…
Using the technique of Poincar\'{e} return maps, we disclose an intricate order of the subsequent homoclinics near the primary homoclinic bifurcation of the Shilnikov saddle-focus in systems with reflection symmetry. We also reveal the…
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…
Given standard angular momentum and boost matrices, the commutation rules for vector and momentum matrices are solved. The resulting matrix components are displayed as detailed functions of spin with factors such as the square root of…
We show sufficient and necessary conditions, in terms of some partial differential equations with variable coefficients, for a quaternionic function to admit a continuous derivative in a open set in the sense of C. Schwartz.
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
Complete Lyapunov functions for a dynamical system, given by an autonomous ordinary differential equation, are scalar-valued functions that are strictly decreasing along orbits outside the chain-recurrent set. In this paper we show that we…
We use the theory of fully matricial, or non-commutative, functions to investigate infinite divisibility and limit theorems in operator-valued non-commutative probability. Our main result is an operator-valued analogue of the Bercovici-Pata…