in this paper‎, ‎we determine the simple groups $g=ab$‎, ‎where $b$ is isomorphic to $l_{3}(4)$ and $a$ isomorphic to an alternating or a symmetric group on $ngeq5$‎, ‎letters‎.

Systems of linear equations can be represented by matrix equations of the form A~x = ~b. LU Factorization is a method for solving systems in this form by transforming the matrix A into a form that makes backwards and forward susbstitution feasible. A common algorithm for LU factorization is Gaussian elimination, which I used for my serial and parallel implementations. I investigated using async...

We introduce a technique for proving all-genus wall-crossing formulas in the gauged linear sigma model as stability parameter varies, without assuming factorization properties of virtual class. Implementing this to associated complete intersection weighted projective space, we obtain uniform proof formula both geometric and Landau–Ginzburg phase.

Supernode partitioning for unsymmetric matrices together with complete block diagonal supernode pivoting and asynchronous computation can achieve high gigaflop rates for parallel sparse LU factorization on shared memory parallel computers. The progress in weighted graph matching algorithms helps to extend these concepts further and unsymmetric prepermutation of rows is used to place large matri...

Consider the solution of a sparse linear system Ax = b when the matrix A is symmetric and positive definite. A typical iterative solver is obtained by using the method of Conjugate Gradients (CG) [15] preconditioned with an incomplete Cholesky (IC) factor L̂ [4]. The latter is an approximation to the (complete) Cholesky factor L, where A = LL . Consequently, the process of computing L̂ relies to ...

Let d1 and d2 be discriminants of distinct quadratic imaginary orders and let J(d1, d2) denote the product of differences of CM j-invariants with discriminants d1 and d2. In 1985, Gross and Zagier gave an elegant formula for the factorization of the integer J(d1, d2) in the case that d1 and d2 are relatively prime and discriminants of maximal orders. We generalize their methods and give a compl...

A new algorithm of Demmel et al. for computing the singular value decomposition (SVD) to high relative accuracy begins by computing a rank-revealing decomposition (RRD). Demmel et al. analyse the use of Gaussian elimination with complete pivoting (GECP) for computing the RRD. We investigate the use of QR factorization with complete pivoting (that is, column pivoting together with row sorting or...

The Symmetric Delay Factorization (SDF) is introduced in 1] for synthesizing linear phase paraunitary lter banks and is applied successfully in 2] for designing Time-Varying Filter Banks (TVFB). This paper describes a minimal and complete generalized symmetric delay factorization valid for a larger class of paraunitary lter banks, and for an arbitrary (even and odd) number of channels. The appr...

We systematically investigate the factorization of causal finite impulse response (FIR) paraunitary filterbanks with given filter length. Based on the singular value decomposition of the coefficient matrices of the polyphase representation, a fundamental order-one factorization form is first proposed for general paraunitary systems. Then, we develop a new structure for the design and implementa...

In Niederreiter’s factorization algorithm for univariate polynomials over finite fields, the factorization problem is reduced to solving a linear system over the finite field in question, and the solutions are used to produce the complete factorization of the polynomial into irreducibles. For fields of characteristic 2, a polynomial time algorithm for extracting the factors using the solutions ...