In this paper we define $q$-spherical surfaces as the that contain absolute conic of Euclidean space a $q-$fold curve. Particular attention is paid to with singular points highest order. Two classes such surfaces, one and two $n-$fold points, are discussed in detail. We study their properties, give algebraic equations visualize them program {\it Mathematica}.

Abstract The coexistence of air and water as a mixture in void spaces unsaturated soils, makes its mechanical behaviour relatively complex difficult to be addressed by classical saturated soil mechanics principles. In addition, many engineering problems encountered practical situations had some part deal with soils therefore the clear understanding various behavioural patterns is crucial. To da...

We report anisotropic resistivity measurements of the heavy-fermion superconductor CeRh$_2$As$_2$ in magnetic fields up to 16 T and temperatures down 0.35 K. The measured shows a signature corresponding suggested quadrupole density wave order state at $T_0 \sim$ 0.5 K for both directions. For field applied along tetragonal $a$ axis, $T_0$ is enhanced with reaching $\sim$1.75 T. Further, field-i...

Considering a countable number of topologies on a set X, we introduce the notion of (א0)topological spaces as a generalization of the notions of both bitopological spaces and (ω)topological spaces, and study some of their properties. AMS Mathematics Subject Classification (2000): 54A10

In this paper we define pairwise-$\alpha$-paracompact subsets as a generalisation of $\alpha$-paracompact in topological spaces and study their properties its relations with other bitopological spaces. Several theorems are obtained concerning sets. We introduced the definition $p$-paracompact bitoplogical

In this paper, we characterize explicitly the separation properties $T_0$ and $T_1$ at a point p in topological category of quantale-valued preordered spaces investigate how these characterizations are related. Moreover, prove that local hereditary productive.

The concept of pairwise S-closedness in bitopological spaces has been introduced and some properties of such spaces have been studied in this paper. EY WORDS AND PHRASES. Pairwise semi-open, Pairwise almost compact, Pairwise S-closed, Pairwise regularly open and regularly closed, Pairwise extremal disconnectedness, Pairwise semi-continuous and irresolute functions. 1980 AMS MATHEMATICS SUBJECT ...