In this paper a definition of n‐valued system in the context of the algebraizable logics is proposed. We define and study the variety V3, showing that it is definitionally equivalent to the equivalent quasivariety semantics for the “Three‐valued BCK‐logic”. As a consequence we find an axiomatic definition of the above system. 相似文献
A quasivariety is said to be implicative if it is generated by a class of algebras with equationally‐definable implication of equalities. Implicative finitely‐generated quasivarieties appear naturally within logic, for instance, as equivalent quasivarieties of Gentzen‐style calculi for finitely‐valued propositional logics with equality determinant (cf. [17], [18, Subsection 7.5] and Section A). Furthermore, any discriminator quasivariety is implicative. We prove that, for any implicative locally‐finite quasivariety ? and any skeleton S of the class of all finite ?‐simple members of ?, the image of the first component of a natural Galois connection between the dual poset of subquasivarieties of ? and the poset of all sets of finite subsets of S is the closure system of all US‐ideals of the poset 〈S, ?〉, where ? is the embeddability relation and US is the up‐set on S constituted by all members of S having a one‐element subalgebra, with closure basis determined by the sets of all principal and non‐empty finitely‐generated up‐sets on S. It is also shown that the first component of the Galois connection under consideration is injective if and only if, for each finite sequence
Vector‐valued frames were first introduced under the name of superframes by Balan in the context of signal multiplexing and by Han and Larson from the mathematical aspect. Since then, the wavelet and Gabor frames in have interested many mathematicians. The space models vector‐valued causal signal spaces because of the time variable being nonnegative. But it admits no nontrivial shift‐invariant system and thus no wavelet or Gabor frame since is not a group by addition (not as ). Observing that is a group by multiplication, we, in this paper, introduce a class of multiplication‐based dilation‐and‐modulation ( ) systems, and investigate the theory of frames in . Since is not closed under the Fourier transform, the Fourier transform does not fit . We introduce the notion of Θa transform in , and using Θa‐transform matrix method, we characterize frames, Riesz bases, and dual frames in and obtain an explicit expression of duals for an arbitrary given frame. An example theorem is also presented. 相似文献
Abstract The main aim of this paper is to describe the space of operator‐valued predictable processes, which are integrable with respect to a Hilbert space valued quasi‐left continuous semimartingale. The space of integrable processes is a randomized Musielak‐Orlicz space with a modular explicitely expressed in terms of Jacod‐Grigelionis characteristics. 相似文献
The concept of (α,ψ)‐contractions was introduced by Samet et al. in this paper, we introduce (α,ψ)‐generalized contractions in a Hausdorff partial metric space. We discuss its significance and obtain some common fixed point theorems for a pair of self‐mappings. Some examples are given to support the theory. 相似文献
Abstract Thanks to the Stroock and Varadhan “Support Theorem” and under convenient regularity assumptions, stochastic viability problems are equivalent to invariance problems for control systems (also called tychastic viability), as it has been singled out by Doss in 1977 for instance. By the way, it is in this framework of invariance under control systems that problems of stochastic viability in mathematical finance are studied. The Invariance Theorem for control systems characterizes invariance through first‐order tangential and/or normal conditions whereas the stochastic invariance theorem characterizes invariance under second‐order tangential conditions. Doss's Theorem states that these first‐order normal conditions are equivalent to second‐order normal conditions that we expect for invariance under stochastic differential equations for smooth subsets. We extend this result to any subset by defining in an adequate way the concept of contingent curvature of a set and contingent epi‐Hessian of a function, related to the contingent curvature of its epigraph. This allows us to go one step further by characterizing functions the epigraphs of which are invariant under systems of stochastic differential equations. We shall show that they are (generalized) solutions to either a system of first‐order Hamilton‐Jacobi equations or to an equivalent system of second‐order Hamilton‐Jacobi equations. 相似文献
The dual space of B ‐valued martingale Orlicz–Hardy space with a concave function Φ, which is associated with the conditional p‐variation of B ‐valued martingale, is characterized. To obtain the results, a new type of Campanato spaces for B ‐valued martingales is introduced and the classical technique of atomic decompositions is improved. Some results obtained here are connected closely with the p‐uniform smoothness and q‐uniform convexity of the underlying Banach space. 相似文献