The goal of this work is to construct and study hybrid and multiplicative two-level overlapping Schwarz algorithms with standard coarse spaces for the almost incompressible linear elasticity and Stokes systems, discretized by mixed finite and spectral element methods with discontinuous pressures. Two different approaches are considered to solve the resulting saddle point systems: a) a precondit...

Correspondence: homidan@kfupm. edu.sa Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, P. O. Box 119, Saudi Arabia Abstract Hankel operators and Hankel transforms are required in a number of applications. This article proves a number of theorems that efficiently and accurately approximates a function using Hankel transforms and Hankel sum....

‎The first multiplicative Zagreb index $Pi_1(G)$ is equal to the‎ ‎product of squares of the degree of the vertices and the second‎ ‎multiplicative Zagreb index $Pi_2(G)$ is equal to the product of‎ ‎the products of the degree of pairs of adjacent vertices of the‎ ‎underlying molecular graphs $G$‎. ‎Also‎, ‎the multiplicative sum Zagreb index $Pi_3(G)$ is equal to the product of‎ ‎the sum...

background: for psychiatric disorders, comorbidity is a rule rather than exception. thus it is particularly important to study additive and multiplicative effects of multiple mental disorders on suicidal behaviors. objectives: the aim of this study was to investigate the ethnic differences in multiplicative effects of mental disorders on suicidal ideation among black adults in the united states...

We consider the multiplicative complexity of Boolean functions with multiple bits of output, studying how large a multiplicative complexity is necessary and sufficient to provide a desired nonlinearity. For so-called ΣΠΣ circuits, we show that there is a tight connection between error correcting codes and circuits computing functions with high nonlinearity. Combining this with known coding theo...

In this paper, we study non-central almost subnormal subgroups of the multiplicative group a division ring satisfying nonzero generalized rational identity. The main result generalizes Chiba’s theorem on subgroups. As an application, get algebraic last has several corollaries which generalize completely or partially some previous results.

In this note we give a short and self-contained proof that, for any δ > 0, ∑ x≤n≤x+xδ λ(n) = o(x ) for almost all x ∈ [X, 2X]. We also sketch a proof of a generalization of such a result to general real-valued multiplicative functions. Both results are special cases of results in our more involved and lengthy recent pre-print.