By making use of some rather elementary techniques based upon certain inverse pairs of symbolic operators, the authors investigate several decomposition formulas associated with Lauricella’s hypergeometric function F (r) A in r variables (r = 2, 3, 4, . . .) and also with other multiple hypergeometric functions. Alternative derivations of some of these decomposition formulas by means of (for ex...

We consider the quantum double D(G) of a compact group G, following an earlier paper. We use the explicit comultiplication on D(G) in order to build tensor products of irreducible ∗-representations. Then we study their behaviour under the action of the R-matrix, and their decomposition into irreducible ∗-representations. The example of D(SU(2)) is treated in detail, with explicit formulas for d...

Algebraic approach to the integrability condition called shape invariance is briefly reviewed. Various applications of shape-invariance available in the literature are listed. A class of shape-invariant bound-state problems which represent two-level systems are examined. These generalize the Jaynes-Cummings Hamiltonian. Coherent states associated with shape-invariant systems are discussed. For ...

We describe the application of domain decomposition on a boundary integral method for the study of nonlinear surface waves on water in a test case for which the domain decomposition approach is an important tool to reduce the computational effort. An important aspect is the determination of the optimum number of domains for a given parallel architecture. Previous work on heterogeneous clusters ...

We present a decomposition of the space of twisted arcs of a toric stack. As a consequence, we give a combinatorial description of the motivic integral associated to a torus-invariant divisor of a toric stack.

Abstract. We show that for a quantum L-martingale (X(t)), p > 2, there exists a Doob-Meyer decomposition of the submartingale (|X(t)|). A noncommutative counterpart of a classical process continuous with probability one is introduced, and a quantum stochastic integral of such a process with respect to an L-martingale, p > 2, is constructed. Using this construction, the uniqueness of the Doob-Me...

where d×x denotes a Haar measure on G. Up to constants, for (additive) Haar measure dx on A, d×x = dx/|detx|. For brevity, write |x| for |detx| when possible. [0.1] Convergence The integral defining us converges absolutely in Re(s) > n− 1: Recall the Iwasawa decomposition G = P ·K with P the parabolic subgroup of upper-triangular matrices. Since K is open in G, Haar measure on G restricted to K...

This work is focused on structural approaches to studying diagnosability properties given a system model taking into account, both simultaneously or separately, integral and differential causal interpretations for differential constraints. We develop a model characterization and corresponding algorithms, for studying system diagnosability using a structural decomposition that avoids generating ...

the food chain refers to a natural system by which energy is transmitted from one organism to another. in fact, a food chain consists of producers, consumers and decomposition. presence of complex food web increase the stability of the ecosystem. classical food chain theory arises from lotka-volterra model. in the present paper, the dynamics behavior of three level food chain is studied. a syst...

In this paper, we study the traces of Orlicz-Sobolev spaces on a regular rooted tree. After giving dyadic decomposition boundary tree, present characterization trace those first order whose Young function is form t p log ? ? ( e + ) , based integral averages elements decomposition.