In the present paper combinatorial identities involving q-dual sequences or polynomials with coefficients q-dual sequences are derived. Further, combinatorial identities for q-binomial coefficients(Gaussian coefficients), q-Stirling numbers and q-Bernoulli numbers and polynomials are deduced.

Highest weight representations of Uq(su(1, 1)) with q = expπi/N are investigated. The structures of the irreducible hieghesat weight modules are discussed in detail. The Clebsch-Gordan decomposition for the tensor product of two irreducible representations is discussed. By using the results, a representation of SL(2,R) ⊗ Uq(su(2)) is also presented in terms of holomorphic sections which also ha...

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...

The irreducible representations of the cubic space group are described and used to determine the mapping of continuum states to lattice states with non-zero linear momentum. The Clebsch-Gordan decomposition is calculated from the character table for the cubic space group. These results are used to identify multiparticle states which appear in the hadron spectrum on the lattice.

In the present paper, some finite element softwares about interaction of dam and reservoir during earthquake in time domain are discussed. Impedance option is used as boundary condition of absorbent of reservoir and wave. For each software, time history analysis of pressure and displacement are done and finally suitable elements for dam structure and reservoir fluid are introduced comparing the...

This paper is devoted to a sharp investigation of the notion of Lagrange's resolvent and his connections with Galois Theory.

We present an expanded mixed finite element method for solving second-order elliptic partial differential equations on geometrically general domains. For the lowest-order Raviart–Thomas approximating spaces, we use quadrature rules to reduce the method to cell-centered finite differences, possibly enhanced with some face-centered pressures. This substantially reduces the computational complexit...

in this paper we demonstrate the existence of a set of polynomials pi , 1 i  n , which arepositive semi-definite on an interval [a , b] and satisfy, partially, the conditions of polynomials found in thelagrange interpolation process. in other words, if a  a1  an  b is a given finite sequence of realnumbers, then pi (a j )  ij (ij is the kronecker delta symbol ) ; moreover, the sum of ...

The conventional Gibbs energy minimization methods apply elemental amounts of system components as conservation constraints in the form of a stoichiometric conservation matrix. The linear constraints designate the limitations set on the components described by the system constituents. The equilibrium chemical potentials of the constituents are obtained as a linear combination of the component-s...

The paper is devoted to designing an interface preconditioner for the mortar element method. After brief overview of the problem in Introduction, we discuss the mortar element method with different types of the Lagrange multiplier spaces. Next, we consider the domain decomposition technique for the solution of mortar element systems and outline the general framework of the solution of saddle-po...