Fixed any term-ordering < on the set T(n) of terms in n variables x1, . . . , xn, we study homogeneous ideal a ⊆ P(n) of the ring of polynomials in n variables over a field k, via the associated order-ideal N (a), consisting of all the terms which are not maximal terms of elements of a and called sous-éscalier of a [7, 12, 14]. In particular we will focus our attention on the following combinat...

Triangular systems play a fundamental role in matrix computations. It has been prominently stated in the literature, but is perhaps not widely appreciated, that solutions to triangular systems are usually computed to high accuracy--higher than the traditional condition numbers for linear systems suggest. This phenomenon is investigated by use of condition numbers appropriate to the componentwis...

The classical theorem of Weitzenböck states that the algebra of invariants K[X] of a single unipotent transformation g ∈ GLm(K) acting on the polynomial algebra K[X] = K[x1, . . . , xm] over a field K of characteristic 0 is finitely generated. This algebra coincides with the algebra of constants K[X] of a linear locally nilpotent derivation δ of K[X]. Recently the author and C. K. Gupta have st...

I referred her to [2], where Theorem 3.6 asserts that K1(R) is R /Ẽ, where Ẽ is the group generated by (1 + xy)/(1 + yx) with x, y in R and 1 + xy in R and where the last sentence in §3 says that Ẽ is not [R, R] in the case when R = M2(Z/2Z) is the ring of 2 by 2 matrices over a field of two elements (Z is the ring of integers). Moreover, in this case the group K1(R) is trivial while R/[R , R] ...

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.

let = be a non-negative matrix. denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. if we used instead of the purpose of this paper is to establish a hardy type formula for , where is hausdorff matrix and a similar result is also established for where in particular, we apply our results to the cesaro...

The Extended Euclidean algorithm for matrix Pade approximants is applied to compute matrix Pade approximants in rectangular full packed format (RFP) if the coefficient matrices of the input matrix polynomial are triangular. The procedure given by Gustavson et al for packing a triangular matrix in rectangular full packed format is applied to pack sequence of lower triangular matrices of a matrix...

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 innite 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, the notions of $(T,S)$-composition matrix and$(T,S)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(T,S)$ is a dual pair of triangular module. Theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. Furthermore, theirproperties and characterizations are presented. Then a new methodbased on $tilde{...

In this paper, an atomistic based finite element model is developed to investigate the influence of topological defects on mechanical properties of graphene. The general in-plane stiffness matrix of the hexagonal network structure of graphene is found. Effective elastic modulus of a carbon ring is determined from the equivalence of molecular potential energy related to stretch and angular defor...