suppose $t$ and $s$ are moore-penrose invertible operators betweenhilbert c*-module. some necessary and sufficient conditions are given for thereverse order law $(ts)^{ dag} =s^{ dag} t^{ dag}$ to hold.in particular, we show that the equality holds if and only if $ran(t^{*}ts) subseteq ran(s)$ and $ran(ss^{*}t^{*}) subseteq ran(t^{*}),$ which was studied first by greville [{it siam rev. 8 (1966...

‎in this paper some properties of weak regular injectivity for $s$-posets‎, ‎where $s$ is a pomonoid‎, ‎are studied‎. ‎the behaviour‎ ‎of different kinds of weak regular injectivity with products‎, ‎coproducts and direct sums is considered‎. ‎also‎, ‎some‎ ‎characterizations of pomonoids over which all $s$-posets are of‎ ‎some kind of weakly regular injective are obtained‎. ‎further‎, ‎we‎ ‎giv...

In this paper, a new T-S fuzzy hyperbolic delay model for a class of nonlinear systems with time-varying delay, is presented to address the problems of stability analysis and feedback control. Fuzzy controller is designed based on the parallel distributed compensation (PDC), and with a new Lyapunov function, delay dependent asymptotic stability conditions of the closed-loop system are derived v...

Let $S$ be a dense subsemigroup of $(0,+infty)$. In this paper, we state   definition of thick near zero, and also  we will introduce a definition that is equivalent to the definition of piecewise syndetic near zero which presented by Hindman  and Leader in [6].  We define density near zero for subsets of $S$ by a collection of nonempty finite subsets of $S$ and we investigate the conditions un...

A. Regularity Conditions Within the text we have referred to regularity conditions on the MDP: Regularity conditions A.1: p(s′|s, a), ∇ap(s|s, a), μθ(s), ∇θμθ(s), r(s, a), ∇ar(s, a), p1(s) are continuous in all parameters and variables s, a, s′ and x. Regularity conditions A.2: there exists a b and L such that sups p1(s) < b, supa,s,s′ p(s′|s, a) < b, supa,s r(s, a) < b, supa,s,s′ ||∇ap(s|s, a)...

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In this paper we give a characterization for all semigroups whose square is a group. Moreover, we axiomatize such semigroups and study some relations between the class of these semigroups and Grouplikes,introduced by the author. Also, we observe that this paper characterizes and axiomatizes a class of Homogroups (semigroups containing an ideal subgroup).  Finally, several equivalent conditions ...

‎In this paper some properties of weak regular injectivity for $S$-posets‎, ‎where $S$ is a pomonoid‎, ‎are studied‎. ‎The behaviour‎ ‎of different kinds of weak regular injectivity with products‎, ‎coproducts and direct sums is considered‎. ‎Also‎, ‎some‎ ‎characterizations of pomonoids over which all $S$-posets are of‎ ‎some kind of weakly regular injective are obtained‎. ‎Further‎, ‎we‎ ‎giv...

In order to solve backward parabolic problems F. John [Comm. Pure. Appl. Math. (1960)] introduced the two constraints “‖u(T )‖ ≤ M” and ‖u(0) − g‖ ≤ δ where u(t) satisfies the backward heat equation for t ∈ (0, T ) with the initial data u(0). The slow-evolution-from-the-continuation-boundary (SECB) constraint has been introduced by A. Carasso in [SIAM J. Numer. Anal. (1994)] to attain continuou...