A set-theoretic property called Property S is introduced as a generalization of the well-known Property B. Property S is named for Schrijver who rst used it in a paper 13] in connection with the Boolean prime ideal theorem. It was independently introduced by Kolany 10] to give a uniform treatment for a variety of satissability problems using an abstract resolution method to determine satissabil...

Recall that a ring $R\ $is said to be quasi regular if its total quotient $q(R)\ \textit{von Neumann regular}. It is well known and only it reduced satisfying the property: for each $a\in R,$ $ann_{R}(ann_{R}(a))=ann_{R}(b)$ some $b\in R$. Here, in this study, we extend notion of rings which satisfy aforementioned property modules. We give many characterizations properties these two classes Mor...

This paper considers the computational complexity of the disjunc-tion and existential properties of intuitionistic logic. We prove that the disjunction property holds feasibly for intuitionistic propositional logic; i.e., from a proof of A _ B, a proof either of A or of B can be found in polynomial time. For intuitionistic predicate logic, we prove superexponential lower bounds for the disjunct...

If S, T ∈ B(H) have Bishop's property (β), does S + T have Bishop's property (β)? In this paper, a special case of this question is studied. Also given are a necessary and sufficient condition for a 2 × 2 operator matrix to have Bishop's property (β). Finally, the Helton class of an operator which has Bishop's property (β) is studied. 1. Introduction. Let B(H) be the algebra of all bounded line...

We establish a characterization of almost P-matrices via sign non-reversal property. In this we are inspired by the analogous results for N-matrices. Next, interval hull two m×n matrices A=(aij) and B=(bij), denoted I(A,B), is collection all C∈Rn×n such that each cij convex combination aij bij. Using property, identify finite subset I(A,B) determines if in N-matrices/almost P-matrices. This pro...

This paper considers the computational complexity of the disjunction and existential properties of intuitionistic logic. We prove that the disjunction property holds feasibly for intuitionistic propositional logic; i.e., from a proof of A ∨ B , a proof either of A or of B can be found in polynomial time. For intuitionistic predicate logic, we prove superexponential lower bounds for the disjunct...

Let B(n) be the subset lattice of {1, 2, . . . , n}. Sperner’s theorem states that the width of B(n) is equal to the size of its biggest level. There have been several elegant proofs of this result, including an approach that shows that B(n) has a symmetric chain partition. Another famous result concerning B(n) is that its cover graph is hamiltonian. Motivated by these ideas and by the Middle T...

Abstract In a Banach algebra A it is well known that the usual spectrum has following property: $$\begin{aligned} \sigma (ab) \setminus \{0\} = (ba) \end{aligned}$$ σ ( a b ) \ {</mml:m...

We generalize the classical universal approximation theorem for neural networks to case of complex-valued networks. Precisely, we consider feedforward with a complex activation function σ:C→C in which each neuron performs operation CN→C,z↦σ(b+wTz) weights w∈CN and bias b∈C, σ applied componentwise. completely characterize those functions associated have property, meaning that they can uniformly...

Motivation to revisit the Conley index theory for discrete multivalued dynamical systems stems from the needs of broader real applications, in particular in sampled dynamics or in combinatorial dynamics. The new construction of the index in [B. Batko and M. Mrozek, SIAM J. Applied Dynamical Systems, 15(2016), pp. 1143-1162] based on weak index pairs, under the circumstances of the absence of in...