While most approaches in formal methods address system correctness, ensuring robustness has remained a challenge. In this paper we present and study the logic rLTL which provides means to formally reason about both correctness design. Furthermore, identify large fragment of for verification problem can be efficiently solved, i.e., done by using an automaton, recognizing behaviors described form...

For a convex body $K$ in $\mathbb{R}^n$, we introduce and study the extremal general affine surface areas, defined by \[ {\rm IS}_{\varphi}(K):=\sup_{K^\prime\subset K}{\rm as}_{\varphi}(K),\quad os}_{\psi}(K):=\inf_{K^\prime\supset as}_{\psi}(K) \] where ${\rm as}_{\varphi}(K)$ as}_{\psi}(K)$ are $L_\varphi$ $L_\psi$ area of $K$, respectively. We prove that there exist bodies achieve supremum ...

Let $varphi(z)=z^m, z in mathbb{U}$, for some positive integer $m$, and $C_varphi$ be the composition operator on the Bergman space $mathcal{A}^2$ induced by $varphi$. In this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $C^*_varphi C_varphi, C_varphi C^*_varphi$ as well as self-commutator and anti-self-commutators of $C_...

It has been known that endothelin-1 (ET-1) exerts important actions in gastrointestinal smooth muscle motility, but its precise mechanism remains unsolved. We investigated the intracellular mechanism of ET-1-induced circular smooth muscle cell contraction in cat esophagus. ET-1 produced contraction of smooth muscle cells isolated by enzymatic digestion. The contraction in response to ET-1 was c...

Abstract Assume that $$\Omega \subset \mathbb {R}^k$$ Ω ⊂ R k is an open set, V a real separable Banach space and $$f_1,\ldots ,f_N :\Omega \rightarrow \Omega $$ f 1 </...

This paper presents an abstract, mathematical formulation of classical propositional logic. It proceeds layer by layer: (1) abstract, syntax-free propositions; (2) abstract , syntax-free contraction-weakening proofs; (3) distribution ; (4) axioms p ∨ p. Abstract propositions correspond to objects of the category G(Rel L) where G is the Hyland-Tan double glue-ing construction, Rel is the standar...

This paper presents an abstract, mathematical formulation of classical propositional logic. It proceeds layer by layer: (1) abstract, syntax-free propositions; (2) abstract , syntax-free contraction-weakening proofs; (3) distribution ; (4) axioms p ∨ p. Abstract propositions correspond to objects of the category G(Rel L) where G is the Hyland-Tan double glue-ing construction, Rel is the standar...

It is well-known that the number of spanning trees, denoted by $\tau(G)$, in a connected multi-graph $G$ can be calculated Matrix-Tree theorem and Tutte's deletion-contraction theorem. In this short note, we find an alternate method to compute $\tau(G)$ degrees vertices.