It is known that if a symmetric matrix differential equation has the order preserving property and dimension at least 2, then this Riccati (see [20]). In paper we prove similar statement holds for discrete equations as well. proof use new approach, in which extend function to continuous one by using iteration theory apply result case.

an operator associated with the wright function is introduced in the open unit disk. differential subordination and superordination results associated with this operator are obtained by investigating appropriate classes of admissible functions. in particular, some inequalities for modified bessel functions are also obtained.

We consider lower bounding the maximum achievable rate of a differential unitary spacetime transmission subject to a prescribed performance. We characterize the performance using a suitably defined distance between two unitary matrices, which was previously obtained through pairwise error probability analysis. Considering the set of all unitary or orthogonal matrices as a compact manifold with ...

We propose a definition of regularity of a linear differential system with coefficients in a monomial extension of a differential field, as well as a global and truly rational (i.e. factorisation–free) iteration that transforms a system with regular finite singularities into an equivalent one with simple finite poles. We then apply our iteration to systems satisfied by bases of algebraic functi...

The extracellular matrix is a three-dimensional network of proteins, glycosaminoglycans and other macromolecules. It has a structural support function as well as a role in cell adhesion, migration, proliferation, differentiation, and survival. The extracellular matrix conveys signals through membrane receptors called integrins and plays an important role in pituitary physiology and tumorigenesi...

In this paper, we have considered phase synchronizations in coupled chaotic systems presented by fractional differential equations. This synchronization occurs when some eigenvalues of the matrix found in the linear approximation of difference evolutional equation between coupled chaotic systems have zero real parts. Here, we have used nonlinear feedback function for synchronization. We have al...

Abstract This paper presents an appropriate numerical method to solve nonlinear Fredholm integro-differential equations with time delay. Its approach is based on the Taylor expansion. This method converts the integro-differential equation and the given conditions into the matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Taylor expansion coefficients, s...

In this paper we consider the stability of motion an unbalanced gyroscope with a flexible shaft in gimbal suspension.Gyroscopes are used to control boom tower cranes. First, linear Hamiltonian systems differential equations. The arise transportation problems. We prove several properties matrix. Next, normalization solve system matrix equations find generating function canonical transformation. ...