We present a method based on Dickson’s lemma to compute the “approximate radical” of a zero dimensional ideal Ĩ in C[x1, . . . , xm] which has zero clusters: the approximate radical ideal has exactly one root in each cluster for sufficiently small clusters. Our method is “global” in the sense that it does not require any local approximation of the zero clusters: it reduces the problem to the co...

We construct infinite-dimensional analogues of finite-dimensional simple modules the nonstandard q-deformed enveloping algebra Uq′(son) defined by Gavrilik and Klimyk, we do same for classical universal U(son). In this paper only consider case when q is not a root unity, q→1 case. Extending work Mazorchuk on son, provide rational matrix coefficients these both use with rationalized formulas to ...

In this paper an equalization technique for colour images is introduced. The method is based on n th root and n th power equalization approach but with optimization of the mean of the image in different colour channels such as RGB and HSI. The performance of the proposed method has been measured by the means of peak signal to noise ratio. The proposed algorithm has been compared with convention...

We present a method based on Dickson’s lemma to compute the “approximate radical” of a zero dimensional ideal Ĩ in C[x1, . . . , xm] which has zero clusters: the approximate radical ideal has exactly one root in each cluster for sufficiently small clusters. Our method is “global” in the sense that it does not require any local approximation of the zero clusters: it reduces the problem to the co...

It is shown that the finite dimensional ireducible representations of the quantum matrix algebra Mq(3) ( the coordinate ring of GLq(3) ) exist only when q is a root of unity ( q = 1 ). The dimensions of these representations can only be one of the following values: p3 , p 3 2 , p 4 , or p 8 . The topology of the space of states ranges between two extremes , from a 3-dimensional torus S1 × S1 × ...

Let F be a global field with ring o of integers, and let μn denote the group of n-th roots of unity in F . Let Γ(f) be the principal congruence subgroup of SL3(o) consisting of elements that are congruent to the identity modulo f. The Kubota symbol κ : Γ(f) −→ μn is a character constructed by Bass, Milnor and Serre [1]. We will give a direct construction, obtaining on the way new formulas for t...

We develop a theory of the pole topology of the Laplace transform of the structure functions of continuous N component systems based on the Wiener-Hopf technique. We classify systems according to the spectrum of the NxN matrix Q(t), with elements Q(ij)(t)=delta(ij)-2pi square root [rho(i)rho(j)]integrale(-tr)q(ij)(r)dr, associated with their factor functions q(ij)(r). For the simplest nontrivia...

It is shown that the finite dimensional irreducible representations of the quantum matrix algebra Mq(n) ( the coordinate ring of GLq(n) ) exist only when q is a root of unity ( q = 1 ). The dimensions of these representations can only be one of the following values: p N 2 where N = n(n−1) 2 and k ∈ {0, 1, 2, ...N} For each k the topology of the space of states is (S1)×(N−k) × [0, 1](×(k) (i.e. ...