The notion of a <7-continuous matrix-valued positive definite distribution on 5/v(2a) x RM x G is introduced, where G is an abelian separable locally compact group and where Sp/(2a) is an open ball around zero in RA' with radius la > 0 . This notion generalizes that one of strongly continuous positive definite operator-valued functions. For these objects, a Bochner-type theorem gives a suitable...

This paper presents an experiment with human subjects concerning the vague spatial relation ‘near’ in environmental space. After the topic is introduced and relevant previous work surveyed, the experiment is described. Three approaches to experimental analysis are presented and discussed: nearness neighbourhoods as regions with broad boundaries, fuzzy nearness and distance measures, and four-va...

A Tychonoff space $X$ is called $\kappa$-pseudocompact if for every continuous mapping $f$ of into $\mathbb{R}^\kappa$ the image $f(X)$ compact. This notion generalizes pseudocompactness and gives a stratification spaces lying between pseudocompact compact spaces. It well known that determined by uniform structure function $C_p(X)$ real-valued functions on endowed with pointwise topology. In re...

Kleene’s strong three-valued logic extends naturally to a four-valued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it four-valued analogs of Kleene’s weak three-valued logic, and the asymmetric logic of Lisp are also available. We propose an extension of these ideas to the family of distributive bi...

We prove that NIP valued fields of positive characteristic are henselian, and we begin to generalize the known results on dp-minimal dp-finite fields. On any unstable field K, define a type-definable group “infinitesimals,” corresponding canonical topology (K,+). reduce classification construction non-trivial Aut(K/A)-invariant valuation rings.

Ranking interval-valued fuzzy soft sets is an increasingly important research issue in decision making, and provides support for makers order to select the optimal alternative under uncertain environment. Currently, there are three set-based decision-making algorithms literature. However, these not able overcome of comparable alternatives and, fact, might be ignored due lack a comprehensive pri...

Entropy rate is a real valued functional on the space of discrete random sources which lacks a closed formula even for subclasses of sources which have intuitive parameterizations. A good way to overcome this problem is to examine its analytic properties relative to some reasonable topology. A canonical choice of a topology is that of the norm of total variation as it immediately arises with th...

Reconstruction of an image from noisy data using Markov Random Field theory has been explored by both the graph-cuts and continuous max-flow community in the form of the Potts and Ishikawa models. However, neither model takes into account the particular cyclic topology of specific intensity types such as the hue in natural colour images, or the phase in complex valued MRI. This paper presents c...

Let E be a completely regular topological space. Mitoma [9 ], extending the classical case E = R 1, has recently introduced the Skorokhod topology on the space D( [0, 1 ] : E). This topology is investigated in detail. We find families of continuous functions which generate the topology, examine the structure of the Borel and Baire a-algebras of D( [0, 1 ] : E) and prove tightness criteria for E...

In this paper, we introduce the new definition of rough membership function using continuous and discuss several concepts properties set value functions as results on function. Moreover, extend to topology spaces by substituting an equivalence class prove some theorems certain types more general fundamental generalized sets. Our result concept valued theory.