The majority of existing probabilistic model checking case studies are based on well understood theoretical models and distributions. However, real-life probabilistic systems usually involve distribution parameters whose values are obtained by empirical measurements and thus are subject to small perturbations. In this paper, we consider perturbation analysis of reachability in the parametric mo...

In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...

and Applied Analysis 3 Definition 2.3 see 16 . Let X,F, T be a probabilistic metric space. A mapping f : X → X is said to be a Sehgal contraction or B-contraction if the following relation holds: Ff p f q kt ≥ Fpq t , ( p, q ∈ X, t > 0. 2.1 Theorem 2.4 see 17 . Let X,F, T be a complete probabilistic metric space with T of Hadžić-type and f : X → X be a B-contraction. Then f has a fixed point if...

The paper is devoted to discretization of integral norms functions from a given finite dimensional subspace. Even though this problem extremely important in applications, its systematic study has begun recently. In we obtain conditional theorem for all $L_q$, $1\le q<\infty$, which an extension known results $q=1$. To discretize the successfully, introduce new technique, combination probabilist...

This paper is concerned with the Sobolev type weak solutions of one class second order quasilinear parabolic partial differential equations (PDEs, for short). First all, similar to Feng, Wang and Zhao [9] Wu Yu [29], we use a family coupled forward-backward stochastic (FBSDEs, short) which satisfy monotonous assumption represent classical PDEs. Then, based on PDEs approximating PDEs, prove exis...

In this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~The idea of equivalent quasi-norm families is introduced.~Riesz lemma is established in this space.~Finally,~we re-define B-S fuzzy norm and prove that it induces a generating space of quasi-norm family.

interpretation setting that we use, a bounded linear operator and its Moore-Penrose Pseudo Inverse are the analogue of the adjoined pair of monotonic functions in a Galois insertion. The abstract systems are obtained by lumping states, i.e. by identifying each concrete state si with a class C j of states which are all behavioural equivalent to each other. Concretely, we compute this via n×m mat...

This study examines the issue of norm construction in al-Ghazālī’s thought focusing on grounds advanced to support his radical infallibilist position. To fulfill such end, al-Ghazālī, I explain, relies two types arguments, first one relates presumptive nature legal texts order highlight their fundamental indeterminacy and second links interpreter show impossibility fall into error. buttress the...

We propose a model of full propositional linear logic based on topological vector spaces. The essential feature is that we consider partially ordered vector spaces, or, rather, positive cones in such spaces. Thus we introduce a category whose objects are dual pairs of normed cones satisfying certain specific completeness properties, such as existence of norm-bounded monotone suprema, and whose ...