Starting with the Iwasawa-type decomposition of a first-order optical system (or ABCD system) as a cascade of a lens, a magnifier, and an orthosymplectic system (a system that is both symplectic and orthogonal), a further decomposition of the orthosymplectic system in the form of a separable fractional Fourier transformer embedded between two spatial-coordinate rotators is proposed. The resulti...

A new method called Boundary Integral-based Domain Decomposition is proposed for the fast solution of the Laplace equation on regular and irregular regions. The idea of the method is to adopt the domain decomposition approach by partitioning into subdomains and use an integral equation formulation to compute the interface values. The method provides a particularly eecient algorithm for parallel...

Currents represent generalized surfaces studied in geometric measure theory. They range from relatively tame integral currents representing oriented compact manifolds with boundary and integer multiplicities, to arbitrary elements of the dual space of differential forms. The flat norm provides a natural distance in the space of currents, and works by decomposing a d-dimensional current into dan...

In this paper we give a nesessary and sufficient condition for a Choquet integral model to be decomposable into an equivalent hierarchical Choquet integral model constructed by hierarchical combinations of some ordinary Choquet integral models. The condition is obtained by Inclution-Exclusion Covering (IEC). Moreover we show some properties on the set of IECs.

We review non-conformal domain decomposition methods (DDMs) and their applications in solving electrically large and multi-scale electromagnetic (EM) radiation and scattering problems. In particular, a finite-element DDM, together with a finite-element tearing and interconnecting (FETI)-like algorithm, incorporating Robin transmission conditions and an edge corner penalty term, are discussed in...

The topic of the Adomian decomposition method has been rapidly growing in recent years. The concept of this method was first introduced by G. Adomian in the beginning of 1980’s [1, 2]. In this method the solution of a functional equations is considered as the sum of an infinite series usually converging to the solution [3]. The Adomian decomposition method for solving linear and nonlinear integ...

Domain decomposition methods are designed to deal with coupled or transmission problems for partial differential equations. Since the original boundary value problem is replaced by local problems in substructures, domain decomposition methods are well suited for both parallelization and coupling of different discretization schemes. In general, the coupled problem is reduced to the Schur complem...

A complex of Cu(II) with 1-(6-HydroxyNaphthalen-2-yl) Butane-1,3-Dione (HNBD) was synthesized and characterized by elemental analysis, IR, UV and DTA-TG-DTG techniques.    IR spectra as well as UV-visible absorption measurements indicated that Cu(II) ion was coordinated to the HNBD ligand. The TG-DTA-DTG curves showed that thermal decomposition o...

The present paper is devoted to analyzing the lack of compactness bounded sequences in inhomogeneous Sobolev spaces, where might fail be compact due an isometric group action, that is, translation. It will proved every sequence (un) has (possibly infinitely many) profiles, and then asymptotically decomposed into a sum translated profiles double-suffix residual term, term becomes arbitrarily sma...