We develop explicit formulae for the eigenvalues of various invariants highest weight irreducible representations quantum supergroup $U_q[gl(m|n)]$. The techniques employed make use modified characteristic identity methods and allow evaluation generator matrix elements reduced Wigner coefficients.

We introduce the quasi-Hopf superalgebras which are Z2 graded versions of Drinfeld’s quasi-Hopf algebras. We describe the realization of elliptic quantum supergroups as quasi-triangular quasi-Hopf superalgebras obtained from twisting the normal quantum supergroups by twistors which satisfy the graded shifted cocycle condition, thus generalizing the quasi-Hopf twisting procedure to the supersymm...

We prove well-posedness, convergence, and detail decay estimates for the normal triangular mesh multi-scale transform for C surfaces in the simplest case when the subdivision rule S used for base point prediction is given by edge midpoint insertion. A restrictive assumption is that the initial triangular mesh needs to be quasi-regular and of small enough mesh-size. We also provide numerical evi...

in the traditional hole drilling method the in-plane stresses are studied in detail and the interlaminar stresses are not taken seriously. the interlaminar stresses on the free edge of composite materials are important and can cause matrix cracking and delamination. inserting holes in composite laminates causes free edges and it can induce interlaminar shear and normal stresses. in this researc...

Binary black hole simulations starting from quasi-circular (i.e., zero radial velocity) initial data have orbits with small but nonzero orbital eccentricities. In this paper, the quasi-equilibrium initial-data method is extended to allow nonzero radial velocities to be specified in binary black hole initial data. New low-eccentricity initial data are obtained by adjusting the orbital frequency ...

The purpose of this article is to study determinants of matrices which are known as generalized Pascal triangles (see [1]). We present a factorization by expressing such a matrix as a product of a unipotent lower triangular matrix, a Töeplitz matrix and a unipotent upper triangular matrix. The determinant of a generalized Pascal matrix equals thus the determinant of a Töeplitz matrix. This equa...

Systems of the form (R(1) · · ·R(p) − λI)x = b, where each R(i) is an n-by-n upper triangular matrix, can be solved in O(pn3) flops if the matrix of coefficients is explicitly formed. We develop a new method for this system that circumvents the explicit product and requires only O(pn2) flops to execute. The error bounds for the new algorithm are essentially the same as the error bounds for the ...

Whether or not system is unitary can be seen from the way it, if perturbed, relaxes back to equilibrium. The relaxation of semiclassical black hole can be described in terms of correlation function which exponentially decays with time. In the momentum space it is represented by infinite set of complex poles to be identified with the quasi-normal modes. This behavior is in sharp contrast to the ...

We calculate the Gerstenhaber bracket on Hopf algebra and Hochschild cohomologies of Taft Tp for any integer p>2 which is a nonquasi-triangular algebra. show that indeed zero cohomology Tp, as in all known quasi-triangular algebras. This example first computation Also, we find general formula with bijective antipode bar resolution reminiscent Gerstenhaber's original cohomology.

We start by pointing out that certain Riemann surfaces appear rather naturally in the context of wave equations in the black hole background. For a given black hole there are two closely related surfaces. One is the Riemann surface of complexified “tortoise” coordinate. The other Riemann surface appears when the radial wave equation is interpreted as the Fuchsian differential equation. We study...