The aim of this paper is to introduce the concepts of compatible mappings and compatible mappings of type (R) in non-Archimedean Menger probabilistic normed spaces and to study the existence problems of common fixed points for compatible mappings of type (R), also, we give an applications by using the main theorems.

let $r$ be a commutative ring with zero-divisor set $z(r)$. the total graph of $r$, denoted by$t(gamma(r))$, is the simple (undirected) graph with vertex set  $r$ where two distinct vertices areadjacent if their sum lies in $z(r)$.this work considers minimum zero-sum $k$-flows for $t(gamma(r))$.both for $vert rvert$ even and the case when $vert rvert$ is odd and $z(g)$ is an ideal of $r$it is s...

begin{abstract} The relations between the spectrum of the matrix $Q+R$ and the spectra of the matrices $(gamma + delta)Q+(alpha + beta)R-QR-RQ$, $QR-RQ$, $alpha beta R-QRQ$, $alpha RQR-(QR)^{2}$, and $beta R-QR$ have been given on condition that the matrix $Q+R$ is diagonalizable, where $Q$, $R$ are ${alpha, beta}$-quadratic matrix and ${gamma, delta}$-quadratic matrix, respectively, of ord...

For an arbitrary ring $R$, the zero-divisor graph of $R$, denoted by $Gamma (R)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $R$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. It is well-known that for any commutative ring $R$, $Gamma (R) cong Gamma (T(R))$ where $T(R)$ is the (total) quotient ring of $R$. In this...

This paper contains two directions of work. The first one gives material related to free action (an inner derivation) mappings on a group ring R[G] which is construction involving G and R the dependent elements those in R[G]. other direction deals with generalization definition actions. We concentrate our study elements, satisfy T(x)γ=δx,x∈R[G] some fixed γ,δ∈R[G]. In part we work element. word...

We extend Federer’s coarea formula to mappings f belonging to the Sobolev class W (R;R), 1 ≤ m < n, p > m, and more generally, to mappings with gradient in the Lorentz space L(R). This is accomplished by showing that the graph of f in R is a Hausdorff n-rectifiable set.

The Kuo condition and the second are known as criteria for an r-jet to be V-sufficient in Cr mappings Cr+1 mappings, respectively. In [2] we considered notions of V-sufficiency jets these conditions relative case a given closed set ?, showed that is criterion ?-V-sufficient sufficient mappings. this paper discuss several equivalent or condition.

Under the condition that the values of mapping F are evaluated approximately, we propose a proximal analytic center cutting plane algorithm for solving variational inequalities. It can be considered as an approximation of the earlier cutting plane method, and the conditions we impose on the corresponding mappings are more relaxed. The convergence analysis for the proposed algorithm is also give...

In this paper, we introduce a generalized system of nonlinear relaxed co-coercive variational inclusions involving (A, η)-monotone mappings in the framework of Hilbert spaces. Based on the generalized resolvent operator technique associated with (A, η)-monotonicity, we consider the approximation solvability of solutions to the generalized system. Since (A, η)-monotonicity generalizes A-monotoni...

Second-Order tuple generating dependencies (SO tgds) were introduced by Fagin et al. to capture the composition of simple schema mappings. Testing the equivalence of SO tgds would be important for applications like model management and mapping optimization. However, we prove the undecidability of the logical equivalence of SO tgds. Moreover, under weak additional assumptions, we also show the u...