Let B be a real vector lattice and a Banach space under a semimonotonic norm. Suppose T is a linear operator on B which is positive and eventually compact, y is a positive vector, and A is a positive real. It is shown that (XI—TY1y is positive if, and only if, y is annihilated by the absolute value of any generalized eigenvector of T* associated with a strictly positive eigenvalue not less than...

Recently it was shown that for the linear time-invariant plant ASPR(Almost Strictly Positive Real)/ASNR(Almost Strictly Negative Real) property can be used to design an adaptive multi-periodic repetitive control system that guarantee the Lyapunov stability of the whole system. This paper attempts to extend this concept to SP(Strictly Passive)/ASP(Almost Strictly Passive) nonlinear plant. The ge...

We consider maps fK(v) = minA∈K Av and gK(v) = maxA∈KAv, where K is a finite set of nonnegative matrices and by “min” and “max” we mean component-wise minimum and maximum. We transfer known results about properties of gK to fK. In particular we show existence of nonnegative generalized eigenvectors of fK, give necessary and sufficient conditions for existence of strictly positive eigenvector of...

In this paper we study the sequences generated by a neuronal equation of the form xn " 1[!ki"1 aixn#i # Θ], where k is the size of the memory. We show that in the case where all the parameters (ai)1%i%k are strictly positive reals and k is a multiple of 6 (i.e., k " 6m), there exists a subset B " &w1, w2, . . . , wΑ( of &1, 2, . . . , m # 1( and for which there exists a neuronal equation of mem...

‎a new approximation method for the set of common fixed points of‎ ‎nonexpansive mappings and the set of solutions of systems of‎ ‎variational inequalities is introduced and studied‎. ‎moreover‎, ‎we‎ ‎apply our main result to obtain strong convergence theorem to a‎ ‎common fixed point of a nonexpannsive mapping and solutions of ‎a ‎system of variational inequalities of an inverse strongly mono...

The Debye-Hückel theory describes rigorously the thermal equilibrium of classical Coulomb fluids in the high-temperature β → 0 regime (β denotes the inverse temperature). It is generally believed that the Debye-Hückel theory and the systematic high-temperature expansion provide an adequate description also in the region of small strictly positive values of β > 0. This hypothesis is tested in th...

Our concern is the completeness problem for strongly positive (SP) theories, that is, sets of implications between SP-terms built from propositional variables, conjunction and modal diamond operators. Originated in logic, algebra and computer science, SP-theories have two natural semantics: meet-semilattices with monotone operators providing Birkhoff-style calculi, and first-order relational st...