The external Cayley transform is used for the conversion of linear dynamical systems between scattering and impedance forms. We study this transform in the formal setting of colligations which includes all impedance (energy) conservative boundary control systems. Practically motivated sufficient conditions are given to describe when such colligations have well-defined semigroups. We apply these...

In this paper we studyC0-semigroups onX×Lp(−h, 0;X) associated with linear differential equations with delay, whereX is a Banach space. In the case thatX is a Banach lattice with order continuous norm, we describe the associated modulus semigroup, under minimal assumptions on the delay operator. Moreover, we present a new class of delay operators for which the delay equation is well-posed for p...

In this paper the theory of evolution semigroups is developed and used to provide a framework to study the stability of general linear control systems. These include autonomous and nonautonomous systems modeled with unbounded state-space operators acting on Banach spaces. This approach allows one to apply the classical theory of strongly continuous semigroups to timevarying systems. In particul...

In this work we consider a semilinear initial boundary-value problem modelling an elastic thin plate (in the context of the so-called KirchhoffLove theory) coupled with an elastic membrane, regarding homogeneous boundary conditions. By means of the theory of strongly continuous semigroups of linear operators applied to abstract semilinear initial valued problems [16], we obtain existence and un...

This paper introduces the concept of square-mean piecewise almost periodic for impulsive stochastic processes. The existence of square-mean piecewise almost periodic solutions for linear and nonlinear impulsive stochastic differential equations is established by using the theory of the semigroups of the operators and Schauder fixed point theorem. The stability of the square-mean piecewise almos...

This is the second part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. We consider a substitute to the notion of pointwise bounds for kernels of operators which usually is a measure of decay. This substitute is that of off-diagonal estimates expressed in terms of local and scale invariant L − L estimates. We propose a definition in spa...

This is the second part of a series of four articles on weighted norm inequalities, off-diagonal estimates and elliptic operators. We consider a substitute to the notion of pointwise bounds for kernels of operators which usually is a measure of decay. This substitute is that of off-diagonal estimates expressed in terms of local and scale invariant L − L estimates. We propose a definition in spa...

this study recommends a gis-based (geographic information systems) and multi-criteria evaluation for site selection of gas power plant in natanz city of iran. the multi-criteria decision framework integrates legal requirements and physical constraints related to environmental and economic concerns. it also builds a hierarchy model for gas power plant suitability. the methodologies used for site...