We study here $T_{0}$-$Q$-bitopological spaces and sober $Q$-bitopological spaces and their relationship with two particular Sierpinski objects in the category of $Q$-bitopological spaces. The epireflective hulls of both these Sierpinski objects in the category of $Q$-bitopological spaces turn out to be the category of $T_0$-$Q$-bitopological spaces. We show that only one of these Sierpinski ob...

In this paper we introduce the notion of fuzzy bitopological ideals .The concept of fuzzy pairwise local function is also introduced here by utilizing the q-neighborhood structure for a fuzzy topological space .These concepts are discussed fuzzy bitopologies and several relations between different fuzzy bitopological ideals .

In this paper we study a gradient flow generated by the Landau--de Gennes free energy that describes nematic liquid crystal configurations in space of $Q$-tensors. This density functional is composed three quadratic terms as elastic part, and singular potential bulk part considered natural enforcement physical constraint on eigenvalues $Q$. The system nondiagonal parabolic with which trends to ...

Assume that $${\mathbb {F}}$$ is an algebraically closed field and let q denote a nonzero scalar in not root of unity. The universal Askey–Wilson algebra $$\triangle _q$$ unital associative -algebra defined by generators relations. are A, B, C the relations state each $$\begin{aligned} A+\frac{q BC-q^{-1} CB}{q^2-q^{-2}}, \qquad B+\frac{q CA-q^{-1} AC}{q^2-q^{-2}}, C+\frac{q AB-q^{-1} BA}{q^2-q...

ABSTARCT: We define and characterize a fuzzy pairwise strongly pre-continuous mappings on a fuzzy bitopological space. We investigate some of their properties. We establish some equivalent conditions of fuzzy pairwise strongly precontinuous mappings on a fuzzy bitopological space.

In this paper we introduce the concept of (i,j)–πgβ-closed set in intuitionistic fuzzy bitopological spaces as a generalization of πgβ-closed set in fuzzy bitopological space and study their related notions in bitopological spaces. Next, we introduce (i,j)–πgβopen sets in intuitionistic fuzzy bitopological spaces, and investigate some of their basic properties. Using these concepts, the charact...

A class B of bitopological structures is a bitopological representation of a class C of continuous mappings of topological spaces if C coinsides with the class of all bicontinuous mappings f : (X;) ?! (X 0 ; 0) for all ; 0 2 B. The paper contains a short survey of old author's results and some new results on bitopological representations of classes of metric space mappings.

In this paper, we used the supra fuzzy topology which generated from a fuzzy bitopological space [1] to introduce and study the concepts of continuity (resp. openness, closeness) of mapping, separation axioms and compactness for a fuzzy bitopological spaces. Our definition preserve much of the correspondence between concepts of fuzzy bitopological spaces and the associated fuzzy topological spa...

It is well-known that observability (and, by duality, controllability) of the elliptic wave equation, i.e., with a Riemannian Laplacian, in time $T_0$ almost equivalent to Geometric Control Condition (GCC), which stipulates any geodesic ray meets control set within $T_0$. We show subelliptic setting, GCC never verified, and equations are observable finite time. More precisely, given Laplacian $...

Let $E/\mathbb Q(t)$ be an elliptic curve and let $t_0 \in \mathbb Q$ a rational number for which the specialization $E_{t_0}$ is curve. In 2015, Gusić Tadić gave easy-to-check criterion, based only on Weierstrass equation $E/\