The purpose of this note is to prove an abstract operator version of certain existence theorems for differential and Volterra integral equations which deal with stability properties of solutions. We will do this in such a way that the results unify, as well as generalize, many of the basic theorems concerning stability of such equations. Thus, our main result(Theorem2)is an abstract version of ...

The group $2^6{{}^{cdot}} G_2(2)$ is a maximal subgroup of the Rudvalis group $Ru$ of index 188500 and has order 774144 = $2^{12}.3^3.7$. In this paper, we construct the character table of the group $2^6{{}^{cdot}} G_2(2)$ by using the technique of Fischer-Clifford matrices.

The domination game is played on an arbitrary graph $G$ by two players, Dominator and Staller. It is known that verifying whether the game domination number of a graph is bounded by a given integer $k$ is PSPACE-complete. On the other hand, it is showed in this paper that the problem can be solved for a graph $G$ in $mathcal O(Delta(G)cdot |V(G)|^k)$ time. In the special case when $k=3$ and the...

A Valued Constraint Satisfaction Problem (VCSP) provides a common framework that can express a wide range of discrete optimization problems. A VCSP instance is given by a finite set of variables, a finite domain of labels, and an objective function to be minimized. This function is represented as a sum of terms where each term depends on a subset of the variables. To obtain different classes of...

Random dot patterns (RDPs) have been used to stimulate in isolation either of two binocular mechanisms for motion in depth: interocular velocity difference (IOVD), and changing disparity over time (CDOT). First, we examined how these stimuli isolate either mechanism using models based on motion/disparity energy detection. In the model, the IOVD mechanism calculates the difference in motion sign...

In this manuscript, we will study the asymptotic behavior for a class of nonlocal diffusion equations associated with weighted fractional $$\wp (\cdot )$$ -Laplacian operator involving constant/variable exponent, ^{-}:=\min _{(x,y) \in {\overline{\Omega }}\times }}} \wp (x,y)\geqslant \max \left\{ 2N/(N+2s),1\right\} $$ and $$s\in (0,1).$$ case constant exponents, under some appropriate conditi...

By left magma-$e$-magma, I mean a set containingthe fixed element $e$, and equipped by two binary operations "$cdot$", $odot$ with the property $eodot (xcdot y)=eodot(xodot y)$, namelyleft $e$-join law. So, $(X,cdot,e,odot)$ is a left magma-$e$-magmaif and only if $(X,cdot)$, $(X,odot)$ are magmas (groupoids), $ein X$ and the left $e$-join law holds.Right (and two-sided) magma-$e$-magmas are de...

Fixed automated spray technology (FAST) systems are designed as a fi xed-asset technology for anti-icing at specifi c target areas, such as bridges, tunnels, ramps and other elevated roadways. They remotely sense the potential for frost or ice formation on pavement in light of atmospheric and pavement data from a road weather information system (RWIS) or an environmental sensor system (ESS) and...

in this paper, we introduce and study fuzzy variational-like inclusion, fuzzy resolvent equation and $h(cdot,cdot)$-$phi$-$eta$-accretive operator in real  uniformly smooth banach spaces. it is established that fuzzy variational-like inclusion is equivalent to a fixed point problem as well as to a fuzzy resolvent equation. this equivalence is used to define an iterative algorithm for solving fu...