We introduce the concept of the intuitionistic fuzzy proximity as a generalization of fuzzy proximity, and investigate its properties. Also we investigate the relationship among intu-itionistic fuzzy proximity and fuzzy proximity, and intuitionistic fuzzy topology. 1. Introduction. As a generalization of fuzzy sets, the concept of intuitionistic fuzzy sets was introduced by Atanassov [1]. Recen...

partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...

Abstract. Let L be a lattice and M a bounded distributive lattice. Let ConL denote the congruence lattice of L, P (M) the Priestley dual space of M , and L (M) the lattice of continuous order-preserving maps from P (M) to L with the discrete topology. It is shown that Con(L ) ∼= (ConL) P (ConM) Λ , the lattice of continuous order-preserving maps from P (ConM) to ConL with the Lawson topology. V...

We propose a finite volume scheme to discretize the one-dimensional Vlasov–Poisson system. We prove that, if the initial data are positive, bounded, continuous, and have their first moment bounded, then the numerical approximation converges to the weak solution of the system for the weak topology of L. Moreover, if the initial data belong to BV , the convergence is strong in C(0, T ;L loc ). To...

This paper focuses on the relationships between stratified $L$-conver-gence spaces, stratified strong $L$-convergence spaces and stratifiedlevelwise  $L$-convergence spaces. It has been known that: (1) astratified $L$-convergence space is precisely a left-continuousstratified levelwise $L$-convergence space; and (2) a  stratifiedstrong $L$-convergence space is naturally a stratified $L$-converg...

We proposed the theory of multi-fuzzy sets [Sabu and Ramakrishnan (2010a), (2011a)] as an extension of theories of fuzzy sets, L-fuzzy sets [Goguen (1967)] and intuitionistic fuzzy sets [Atanassov (1986)]. Theory of multi-fuzzy sets deals with multi-level fuzziness and multi-dimensional fuzziness. Our previous papers discussed the basic notions of multi-fuzzy sets, multi-fuzzy topology, and mul...

Strong laws of large numbers are given for L-statistics (linear com­ binations of order statistics) and for U -statistics (averages of kernels of ran­ dom samples) for ergodic stationary processes, extending classical theorems of Hoeffding and of Helmers for iid sequences. Examples are given to show that strong and even weak convergence may fail if the given sufficient conditions are not satisf...

Two new Co(II) coordination polymers with a pyridinedicarboxylate ligand, {[Co(L)(H(2)O)]·H(2)O}(n) (1) and [Co(3)(HCOO)(2)(L)(2)(H(2)O)(2)](n) (2) (H(2)L = 5-(pyridin-4-yl)isophthalic acid), have been synthesized and structurally characterized by elemental analysis, IR, XRPD, and single-crystal X-ray diffraction. Structure analyses show that complex 1 has a two-dimensional (2D) double-layered ...

L. Lambán et al. () ACL2 and Algebraic Topology 1 / 23 Introduction Kenzo symbolic computation system: a Common Lisp program devoted to Algebraic (Simplicial) Topology. ◮ A research tool: used to obtain relevant results in the field, neither confirmed nor refuted by any other means. The following question makes sense: Is it Kenzo correct? Our goal: we want to formally prove correcteness propert...