Parallel computers, such as multiprocessors system-on-chip (Mp-SoCs), multicomputers and cluster computers, are consisting of hundreds or thousands multiple processing units and components (such as routers, channels and connectors) connected via some interconnection network that collectively may undergo high failure rates. Therefore, these systems are required to be equipped with fault-tolerant...

A comparison problem for volumes of convex bodies asks whether inequalities fK(ξ) ≤ fL(ξ) for all ξ ∈ S imply that Voln(K) ≤ Voln(L), where K,L are convex bodies in R, and fK is a certain geometric characteristic of K. By linear stability in comparison problems we mean that there exists a constant c such that for every ε > 0, the inequalities fK(ξ) ≤ fL(ξ) + ε for all ξ ∈ S imply that (Voln(K))...

Lagrange multiplier rules for abstract optimization problems with mixed smooth and convex terms in the cost, with smooth equality constrained and convex inequality constraints are presented. The typical case for the equality constraints that the theory is meant for is given by differential equations. Applications are given to L-minimum norm control problems, L∞norm minimization, and a class of ...

Multimodular functions and L-convex functions have been investigated almost independently, but they are, in fact, equivalent objects that can be related through a simple coordinate transformation. Some facts known for L-convex functions can be translated to new results for multimodular functions, and vice versa. In particular, the local optimality condition for global optimality found in the li...

in this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. in particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. then we study fuzzy...

Abstract L-convex sets are one of the most fundamental concepts in discrete convex analysis. Furthermore, Minkowski sum two sets, called L $$_{2}$$ 2 -convex is an intriguing object that closely related to polymatroid intersection. This paper reveals polyhedral description ...

In this note we present a reverse isoperimetric inequality for closed convex curves, which states that if γ is a closed strictly convex plane curve with length L and enclosing an area A, then one gets L ≤ 4π(A+ |Ã|), where à denotes the oriented area of the domain enclosed by the locus of curvature centers of γ, and the equality holds if and only if γ is a circle. MSC 2000: 52A38, 52A40

be the Fourier cosine series. The problem of L-convergence of the Fourier cosine series (1.1) has been settled for various special classes of coefficients. Young [9] found that an logn = o(1), n → ∞ is a necessary and sufficient condition for the L-convergence of the cosine series with convex (△an ≥ 0) coefficients, and Kolmogorov [8] extended this result to the cosine series with quasi-convex ( ∞

Hermite-Hadamard inequality is one of the fundamental applications of convex functions in Theory of Inequality. In this paper, Hermite-Hadamard inequalities for $mathbb{B}$-convex and $mathbb{B}^{-1}$-convex functions are proven.

[1] The channel network (S) is a nonconvex set, while its basin [C(S)] is convex. We remove open-end points of the channel connectivity network iteratively to generate a traveltime sequence of networks (Sn). The convex hulls of these traveltime networks provide an interesting topological quantity, which has not been noted thus far. We compute lengths of shrinking traveltime networks L(Sn) and a...