1 Definitions Definition 1. A graded ring is a ring S together with a set of subgroups Sd, d ≥ 0 such that S = ⊕ d≥0 Sd as an abelian group, and st ∈ Sd+e for all s ∈ Sd, t ∈ Se. One can prove that 1 ∈ S0 and if S is a domain then any unit of S also belongs to S0. A homogenous ideal of S is an ideal a with the property that for any f ∈ a we also have fd ∈ a for all d ≥ 0. A morphism of graded r...

We define type A, type B, type C as well as C∗-semi-finite C∗-algebras. It is shown that a von Neumann algebra is a type A, type B, type C or C∗-semi-finite C∗-algebra if and only if it is, respectively, a type I, type II, type III or semi-finite von Neumann algebra. Moreover, any type I C∗-algebra is of type A (actually, type A coincides with the discreteness as defined by Peligrad and Zsidó),...

then the ideal (F1, ..., FN) they generate in the Paley-Wiener algebra Ê ′(Rn) is slowly decreasing respect to the Paley-Wiener weight p(z) = log |z| + |Im z|. As a consequence, this ideal is closed in Ê ′(Rn). It coincides with the ideal [I(F1, ..., FN)]loc, which consists of elements in Ê ′(Rn) that belong locally to the ideal generated by F1, ..., FN in the algebra of entire functions in n v...

Let (A, m) be an excellent normal local ring with algebraically closed residue class field. Given integrally closed m-primary ideals I ⊃ J , we show that there is a composition series between I and J , by integrally closed ideals only. Also we show that any given integrally closed m-primary ideal I, the family of integrally closed ideals J ⊂ I, lA(I/J) = 1 forms an algebraic variety with dimens...

In this paper we consider the open complement U of a hypersurface Y = V (a) in an affine scheme X. We study the relations between the affineness of U , the intersection of Y with closed subschemes, the property that every closed surface in U is affine, the property that every analytic closed surface is Stein and the superheight of a defining ideal a.

This paper studies the Ratliff-Rush closure of ideals in integral domains. By definition, the Ratliff-Rush closure of an ideal I of a domain R is the ideal given by Ĩ := S (I :R I ) and an ideal I is said to be a Ratliff-Rush ideal if Ĩ = I. We completely characterize integrally closed domains in which every ideal is a Ratliff-Rush ideal and we give a complete description of the Ratliff-Rush cl...

This thesis study involves designing, implementing and testing of a novel radio resource control algorithm for the closed loop power control in the LTE uplink. Different values of the path loss compensation factor are investigated in the range 0.7-1.0 and an optimal value of 0.8 as allowed by the LTE standard is proposed. Both the ideal and a more realistic case modeled by including delay, erro...

In identification for control with no unmodelled dynamics, the best controller performance is achieved by performing the identification in closed loop. Alan'S-We compare open loop versus closed loop identification when the identified model is used for control design, and when the system itself belongs to the model class, so that only variance errors are relevant. Our measure of controller perfo...

‎let $x=left(‎ ‎begin{array}{llll}‎ ‎ x_1 & ldots & x_{n-1}& x_n‎ ‎ x_2& ldots & x_n & x_{n+1}‎ ‎end{array}right)$ be the hankel matrix of size $2times n$ and let $g$ be a closed graph on the vertex set $[n].$ we study the binomial ideal $i_gsubset k[x_1,ldots,x_{n+1}]$ which is generated by all the $2$-minors of $x$ which correspond to the edges of $g.$ we show that...