In this study, the existence and uniqueness of the solution of a class of nonlinear finite-part singular integral equations with Carleman shift preserving orientation has been investigated in the generalized Holder space () Γ ϕ H. 1. Introduction Many important problems of engineering mechanics like elasticity, plasticity, and fracture mechanics and aerodynamics can be reduced to the solution o...

This paper considers linear time-invariant decentralized singular systems which are either nonregular or, if they are regular, they have impulsive modes. It derives algebraic necessary and sufficient conditions for making a singular system both regular and impulsefree by decentralized output feedback control laws and decentralized proportional-plus-derivative output feedback control laws.

Consider the linear time-invariant singular system Eẋ(t) = Ax(t) + Bu(t) (1) where E, A ∈ Rn×n, B ∈ Rm×n ,C ∈ R p×n and D ∈ R p×m . The system is assumed to be regular det [s E − A] = 0. Systems of the above form are usually called singular systems, descriptor systems, generalized state space systems, semistate systems, etc. It is easily seen that when E is non-singular then (1) may be rewritte...

This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construction uses a single linear differential form defined from the Jacobian matrix of the input, and defines the deflated system by applying this differential form to the original system. The advantages of this new deflation is ...

using the fixed point theorem in a‎ ‎cone‎, ‎the existence and multiplicity of radial convex solutions of‎ ‎singular system of monge-amp`{e}re equations are established‎.‎

using the fixed point theorem in a‎ ‎cone‎, ‎the existence and multiplicity of radial convex solutions of‎ ‎singular system of monge-amp`{e}re equations are established‎.‎

In this paper, necessary and sufficient conditions for the positive invariance of convex polyhedra with respect to linear discrete-time singular systems subject to bounded additive disturbances are established. New notions of ∆-invariance under different assumptions on the initial conditions are defined. Specifically, the notions of simple and weak ∆invariance are considered. They can be seen a...