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/\

The notion of smooth biproximity space  where $delta_1,delta_2$ are gradation proximities defined by Ghanim et al. [10]. In this paper, we show every smooth biproximity space $(X,delta_1,delta_2)$ induces a supra smooth proximity space $delta_{12}$ finer than $delta_1$ and $delta_2$. We study the relationship between $(X,delta_{12})$ and the $FP^*$-separation axioms which had been introduced by...

Copyright q 2012 K. Kannan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Many investigations are undergoing of the relationship between topological spaces and graph theory. The aim of this short communication is to study the na...

We consider the mesoscopic normal persistent current (PC) in a very low-temperature superconductor with a bare transition temperature T_0(c) much smaller than the Thouless energy E(c). We show that in a rather broad range of pair-breaking strength, T_0(c) < or = Planck's/tau(s)< or =E(c), the transition temperature is renormalized to zero, but the PC is hardly affected. This may provide an expl...

By using m-open multifunctions from a topological space into an m-space, we establish the unified theory for several weak forms of open multifunctions in the sense of Kuratowski between bitopological spaces.

If U and V are topologies on an abstract set X, then the triple (X, U, V) is a bitopological space. Using the theorem of Priestley on the representation of distributive lattices, results of Dilworth concerning the normal completion of the lattice of bounded, continuous, realvalued functions on a topological space are extended to include the lattice of bounded, semi-continuous, real-valued funct...

By using m-open functions from a topological space into an m-space, we establish the unified theory for several weak forms of open functions in the sense of Kuratowski between bitopological spaces.

The purpose of this paper is to study the distribution zeros solutions a first-order neutral differential equation form \begin{equation*} \left[x(t) + p(t) x(t-\tau)\right]' q(t) x(t-\sigma) = 0, \quad t \geq t_0, \end{equation*} where $p\in C([t_0,\infty),[0,\infty))$, $q \in C([t_0,\infty),(0,\infty))$, $\tau,\sigma>0$, and $\sigma>\tau$. We obtain new upper bound estimates for distance betwe...

We construct a completely regular ordered space (X, T ,≤) such that X is an I-space, the topology T of X is metrizable and the bitopological space (X, T ♯,T ♭) is pairwise regular, but not pairwise completely regular. (Here T ♯ denotes the upper topology and T ♭ the lower topology of X.)