where / is a mapping of X into its adjoint space X* such that for all u in X, (J(u)} ^)=|M| 2 d ||/(^)|| HMI* In some recent papers ([7], [8], [9]), we have presented an existence theory for solutions of nonlinear functional equations in uniformly convex Banach spaces X involving nonexpansive and accretive mappings. These results were obtained by interweaving the fixed point theory of nonexpans...

Let C be a nonempty closed convex subset of a smooth Banach space E and let A be an accretive operator of C into E. We first introduce the problem of finding a point u ∈ C such that 〈Au, J(v− u)〉 ≥ 0 for all v ∈ C, where J is the duality mapping of E. Next we study a weak convergence theorem for accretive operators in Banach spaces. This theorem extends the result by Gol’shteı̆n and Tret’yakov i...

A multiple-interval representation of a graph G is a mapping f which assigns to each vertex of G a union of intervals on the real line so that two distinct vertices u and v are adjacent if and only if f(u) ∩ f(v) = ∅. We study the total interval number of G, de0ned as I(G) = min {∑ v∈V #f(v): f is a multiple-interval representation of G } ; where #f(v) is the minimum number of intervals whose u...

The systems engineering V (SE-V) is an established process model to guide the development of complex engineering projects (INCOSE, 2011). The SE-V process involves decomposition and integration of system elements through a sequence of tasks that produce both a system design and its testing specifications, followed by successive levels of build, integration, and test activities. This paper prese...

Mendelian segregation analysis was used to map chromosomal genes for the induction of endogenous N- and B-tropic ecotropic retroviruses (V loci) in high and low leukemic mouse strains. Patterns of virus expression were determined for mice of various inbred strains, congenic lines carrying single V loci, and the linkage testing stocks used in mapping studies. Segregation analysis resulted in the...

For a graph G with a given subgraph H, the backbone coloring is defined as the mapping c : V (G) → N+ such that |c(u)− c(v)| ≥ 2 for each edge {u, v} ∈ E(H) and |c(u)− c(v)| ≥ 1 for each edge {u, v} ∈ E(G). The backbone chromatic number BBC(G,H) is the smallest integer k such that there exists a backbone coloring with maxv∈V (G) c(v) = k. In this paper, we present the algorithm for the backbone...

A variety V has an alg-universal n-expansion if the addition of n nullary operations to algebras from V produces an alg-universal category. It is proved that any semigroup variety V containing a semigroup that is neither an inflation of a completely simple semigroup nor an inflation of a semilattice of groups has an alg-universal 3-expansion. We say that a variety V is var-relatively alg-univer...

Abstract This note is devoted to the splitting algorithm proposed by Davis and Yin (Set-valued Var. Anal. 25 (4), 829–858, 2017) for computing a zero of sum three maximally monotone operators, with one them being cocoercive. We provide direct proof that guarantees its convergence when stepsizes are smaller than four times cocoercivity constant, thus doubling size interval established Yin. As by...

In this paper, focusing on general nonlinear programming problems, we attempt to propose a general and highperformance approximate solution method for them. In recent years, S. Koziel et al. have proposed a floating-point genetic algorithm, GENOCOP V, as a general approximate solution method for nonlinear programming problems and showed its efficiency, there are left some shortcomings of the me...

This paper presents a new algorithm called List-based Load Balancing (LLB) for compile-time task scheduling on distributed-memory machines. LLB is intended as a cluster-mapping and task-ordering step in the multi-step class of scheduling algorithms. Unlike current multistep approaches, LLB integrates cluster-mapping and taskordering in a single step. The benefits of this integration are twofold...