A new operator is considered, allowing compact formulae and proofs in the context of the derivation of a transfer matrix with respect to another matrix. The problem of the parametric sensitivity matrix calculation is chosen for illustration. It consists in deriving a Multiple Input Multiple Output transfer function with respect to a parametric matrix and is central in robust control theory. Eff...

Bivariate matrix functions provide a unified framework for various tasks in numerical linear algebra, including the solution of linear matrix equations and the application of the Fréchet derivative. In this work, we propose a novel tensorized Krylov subspace method for approximating such bivariate matrix functions and analyze its convergence. While this method is already known for some instance...

In this article, the backstepping control scheme is proposed to stabilize fractional order Riccati matrix differential equation with retarded arguments in which derivative presented using Caputo's definition of derivative. The results are established Mittag-Leffler stability. Lyapunov function defined at each stage and negativity an overall ensured by proper selection law. Numerical simulation ...

Matrix exponentials and their derivatives play an important role in the perturbation analysis, control and parameter estimation of linear dynamical systems. The well-known integral representation of the matrix exponential’s directional derivative, , enables us to derive a number of new properties of this derivative, along with spectral, series and exact representations. Many of these results ex...

Algorithms for solving numerical optimization problems and nonlinear systems of equations that rely on derivative information require the repeated estimation of Jacobian and Hessian matrices. The problem of minimizing the number of function evaluations needed to estimate the derivative matrices, within a finite difference method or an automatic differentiation method, has been formulated as a c...

We previously reported that EMD (Enamel Matrix Derivative) induces proliferation of human gingival fibroblasts via activation of Extracellular Regulated Kinase (ERK), and this study assessed the possible mediatory role of EGFR (Epidermal Growth Factor Receptor) in this effect. Treatment of gingival fibroblasts with EMD resulted in tyrosine phosphorylation of the EGFR, as assessed by immunoblott...

Emdogain, a formulation of Enamel Matrix Proteins, is used clinically for periodontal regeneration to stimulate PDL (periodontal ligament), cementum, and bone formation. Its effects on gingival fibroblasts and tissue have not been thoroughly studied. Therefore, we investigated the mechanisms by which Emdogain affects the cell cycle of human gingival fibroblasts. Without serum, Emdogain (50 micr...

M -theory is believed to be described in various dimensions by large N field theories. It has been further conjectured that at finite N , these theories describe the discrete light cone quantization (DLCQ) of M theory. Even at low energies, this is not necessarily the same thing as the DLCQ of supergravity. It is believed that this is only the case for quantities which are protected by non-reno...

INTRODUCTION Direct pulp capping procedure is a therapeutic application of a drug on exposed tooth pulp in order to ensure the closure of the pulp chamber and to allow the healing process to take place. OBJECTIVE The aim of this study was to examine the histological effects of Emdogain® on exposed tooth pulp of a Vietnamese pig (Sus scrofa verus). METHODS The study comprised 20 teeth of a V...