1 Structure Sheaves 7 1.1 C-Valued Sheaves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3 The Factorization System on StrG(X) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.4 Classifying ∞-Topoi . . . . . . . . . . . . ....

in this paper, we consider an arbitrary binary polynomial sequence {a_n} and then give a lower triangular matrix representation of this sequence. as main result, we obtain a factorization of the in nite generalized pascal matrix in terms of this new matrix, using a riordan group approach. further some interesting results and applications are derived.

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.

1 Structure Sheaves 7 1.1 C-Valued Sheaves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2 Geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3 The Factorization System on StrG(X) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.4 Classifying ∞-Topoi . . . . . . . . . . . . ....

In this paper we present a specialized matrix factorization procedure for computing the dual step in a primal-dual path-following interior point algorithm for solving two-stage stochastic linear programs with restricted recourse. The algorithm, based on the Birge-Qi factorization technique, takes advantage of both the dual block-angular structure of the constraint matrix and of the special stru...

The QCD treatment of the photon structure is recalled. Emphasis is given to the recently derived momentum sum rule, and to the proper choice of the factorization scheme and/or boundary conditions for the evolution equations beyond the leading order. Parametrizations of the photon’s parton content are examined and compared. The small-x behaviour of the photon structure is briefly discussed. ∗ In...