When Is σ (A(t)) ⊂ {z ∈ ℂ; ℜz ≤ −α < 0} the Sufficient Condition for Uniform Asymptotic Stability of LTV System ẋ = A(t)x?

In this paper, the class of matrix functions A(t) is determined for which the condition that the pointwise spectrum σ(A(t))⊂z∈C;ℜz≤−α for all t≥t0 and some α>0 is sufficient for uniform asymptotic stability of the linear time-varying system x˙=A(t)x. We prove that this class contains as a proper subset the matrix functions with the values in the special orthogonal group SO(n).

On the Matrix Versions of Incomplete Extended Gamma and Beta Functions and Their Applications for the Incomplete Bessel Matrix Functions

In this paper, we first introduce the incomplete extended Gamma and Beta functions with matrix parameters; then, we establish some different properties for these new extensions. Furthermore, we give a specific application for the incomplete Bessel matrix function by using incomplete extended Gamma and Beta functions; at last, we construct the relation between the incomplete confluent hypergeometric matrix functions and incomplete Bessel matrix function.

Silica/Protein and Silica/Polysaccharide Interactions and Their Contributions to the Functional Properties of Derived Hybrid Wound Dressing Hydrogels

Multifunctional and biocompatible hydrogels are on the focus of wound healing treatments. Protein and polysaccharides silica hybrids are interesting wound dressing alternatives. The objective of this review is to answer questions such as why silica for wound dressings reinforcement? What are the roles and contributions of silane precursors and silica on the functional properties of hydrogel wound dressings? The effects of tailoring the porous, morphological, and chemical characteristics of synthetic silicas on the bioactivity of hybrid wound dressings hydrogels are explored in the first part of the review. This is followed by a commented review of the mechanisms of silica/protein and silica/polysaccharide interactions and their impact on the barrier, scaffold, and delivery matrix functions of the derived hydrogels. Such information has important consequences for wound healing and paves the way to multidisciplinary researches on the production, processing, and biomedical application of this kind of hybrid materials.

Mathematical Modeling and Functional Order Pursuits with Separated Dynamics

This work is devoted to the study of the pursuit problem in controlled systems described by a fractional-order equation with divided dynamics. For fixed player controls, representations of solutions are established in the form of analogs of the Cauchy formula using generalized matrix functions. Sufficient conditions are obtained for the possibility of completing the pursuit. Specific types of fractional differential equations and models of fractional dynamical systems are considered. The qualitative dynamics, issues of stability and controllability of such systems are discussed. Considered, try which, the motion of the equation is described with irrational orders. Problems of the type under study are encountered in modeling the processes of economic growth and in problems of stabilizing dynamic systems.

Some Results on the Extended Hypergeometric Matrix Functions and Related Functions

In this article, we discuss certain properties for generalized gamma and Euler’s beta matrix functions and the generalized hypergeometric matrix functions. The current results for these functions include integral representations, transformation formula, recurrence relations, and integral transforms.

Computation of Fourier transform representations involving the generalized Bessel matrix polynomials

Motivated by the recent studies and developments of the integral transforms with various special matrix functions, including the matrix orthogonal polynomials as kernels, in this article we derive the formulas for Fourier cosine and sine transforms of matrix functions involving generalized Bessel matrix polynomials. With the help of these transforms several results are obtained, which are extensions of the corresponding results in the standard cases. The results given here are of general character and can yield a number of (known and new) results in modern integral transforms.