Let \(X\) be a real reflexive Banach space and \(X^*\) its dual space. \(G_1\) \(G_2\) open subsets of such that \(\overline G_2\subset G_1\), \(0\in G_2\), is bounded. \(L: X\supset D(L)\to X^*\) densely defined linear maximal monotone operator, \(A:X\supset D(A)\to 2^{X^*}\) positively homogeneous operator degree \(\gamma>0\), \(C:X\supset D(C)\to bounded demicontinuous type \((S_+)\) with...

‎‎Let $G=(V‎, ‎E)$ be a simple graph with vertex set $V$ and edge set $E$‎. ‎A {em mixed Roman dominating function} (MRDF) of $G$ is a function $f:Vcup Erightarrow {0,1,2}$ satisfying the condition that every element $xin Vcup E$ for which $f(x)=0$ is adjacent‎‎or incident to at least one element $yin Vcup E$ for which $f(y)=2$‎. ‎The weight of an‎‎MRDF $f$ is $sum _{xin Vcup E} f(x)$‎. ‎The mi...

Visual counting, a task that aims to estimate the number of objects from an image/video, is open-set problem by nature as population can vary in $$[0,+\infty )$$ theory. However, collected data are limited reality, which means only closed set observed. Existing methods typically model this through regression, while they prone suffer unseen scenes with counts out scope set. In fact, counting has...

Let $G$ be a finite group. We construct the prime graph of $ G $,which is denoted by $ Gamma(G) $ as follows: the vertex set of thisgraph is the prime divisors of $ |G| $ and two distinct vertices $ p$ and $ q $ are joined by an edge if and only if $ G $ contains anelement of order $ pq $.In this paper, we determine finite groups $ G $ with $ Gamma(G) =Gamma(L_3(q)) $, $2 leq q < 100 $ and prov...

The aim of this paper is to introduce and study two new classes of functions called weakly $e^{*}$-open functions and weakly $e^{*}$-closed functions via the concept of $e^{*}$-open set defined by Ekici cite{erd1}. The notions of weakly $e^{*}$-open and weakly $e^{*}$-closed functions are weaker than the notions of weakly $beta$-open and weakly $beta$-closed functions defined by Caldas and Nava...

For a graph $G$ let $gamma (G)$ be its domination number. We define a graph G to be (i) a hypo-efficient domination graph (or a hypo-$mathcal{ED}$ graph) if $G$ has no efficient dominating set (EDS) but every graph formed by removing a single vertex from $G$ has at least one EDS, and (ii) a hypo-unique domination graph (a hypo-$mathcal{UD}$ graph) if $G$ has at least two minimum dominating sets...