In this paper, the Fischer matrices of maximal subgroup G = 21+8+ : (U4(2):2) U6(2):2 will be derived from quotient group Q G/Z(21+8+) 28 (U4(2):2), where Z(21+8+) denotes center extra-special 2-group 21+8+. Using approach, and associated ordinary character table are computed in an elegantly simple manner. This approach can used to compute any split extension form 21+2n+ :G, n ∈ N, provided irr...

Fischer provided a new type of binomial determinant for the number alternating sign matrices involving third root unity. In this paper we prove that her formula, when replacing unity by an indeterminate q, actually gives (q?1+2+q)-enumeration matrices. By evaluating generalisation are able to reprove conjecture Mills, Robbins and Rumsey stating Q-enumeration is product two polynomials in Q. Fur...

The non-split extension group $overline{G} = 5^3{^.}L(3,5)$ is a subgroup of order 46500000 and of index 1113229656 in Ly. The group $overline{G}$ in turn has L(3,5) and $5^2{:}2.A_5$ as inertia factors. The group $5^2{:}2.A_5$ is of order 3 000 and is of index 124 in L(3,5). The aim of this paper is to compute the Fischer-Clifford matrices of $overline{G}$, which together with associated parti...

Zeilberger [12] proved the Refined Alternating Sign Matrix Theorem, which gives a product formula, first conjectured by Mills, Robbins and Rumsey [9], for the number of alternating sign matrices with given top row. Stroganov [10] proved an explicit formula for the number of alternating sign matrices with given top and bottom rows. Fischer and Romik [7] considered a different kind of “doubly-ref...

There recently has been much interest in non-interior continuation/smoothingmethods for solving linear/nonlinear complementarity problems. We describe extensions of such methods to complementarity problems defined over the cone of block-diagonal symmetric positive semidefinite real matrices. These extensions involve the ChenMangasarian class of smoothing functions and the smoothed Fischer-Burme...

This paper is focused on the applications of Schur complements to determinant inequalities. It presents a monotonic characterization of Schur complements in the L öwner partial ordering sense such that a new proof of the Hadamard-Fischer-Koteljanski inequality is obtained. Meanwhile, it presents matrix identities and determinant inequalities involving positive semidefinite matrices and extends ...

Zeilberger [12] proved the Refined Alternating Sign Matrix Theorem, which gives a product formula, first conjectured by Mills, Robbins and Rumsey [9], for the number of alternating sign matrices with given top row. Stroganov [10] proved an explicit formula for the number of alternating sign matrices with given top and bottom rows. Fischer and Romik [7] considered a different kind of “doubly-ref...

the subfamily alysiinae (hymenoptera, braconidae) is one of the most peculiar and diverse endoparasitoids of the family braconidae. a sampling survey was done in different parts of iran, mainly in south, central and south eastern provinces. fifteen species are recorded for the first time from iran. they were belonging to tribe alysiini (dinotrema amparoae peris-felipo, 2013; d. borzhomii tobias...

The authors and Fischer recently proved that any hereditary property of two-dimensional matrices (where the row and column order is not ignored) over a finite alphabet is testable with a constant number of queries, by establishing the following (ordered) matrix removal lemma: For any finite alphabet Σ, any hereditary property P of matrices over Σ, and any > 0, there exists fP( ) such that for a...

The analogy between eigenvalues and singular values has many faces. The current review brings together several examples of this analogy. One example regards the similarity between Symmetric Rayleigh Quotients and Rectangular Rayleigh Quotients. Many useful properties of eigenvalues stem are from the Courant-Fischer minimax theorem, from Weyl’s theorem, and their corollaries. Another aspect rega...