For analytic functions f (z) = z p +a p+1 z p+1 +··· in the open unit disk U and a polynomial Q(z) of degree n > 0, the function F(z) = f (z)[Q(z)] β/n is introduced. The object of the present paper is to determine the radius of p-valently strongly starlikeness of order γ for F(z).

The aim of this paper is to settle a question about the tight closure of Ž 2 2 2 . w x Ž 3 3 3. the ideal x , y , z in the ring R s K X, Y, Z r X q Y q Z where Ž K is a field of prime characteristic p / 3. Lower case letters denote the . images of the corresponding variables. M. McDermott has studied the tight closure of various irreducible ideals in R and has established that Ž 2 2 2 . w x xyz...

A short new proof of the fact that all shifted complexes are fixed by reverse lexicographic shifting is given. A notion of lexicographic shifting, ∆ lex — an operation that transforms a monomial ideal of S = k[x i : i ∈ N] that is finitely generated in each degree into a squarefree strongly stable ideal — is defined and studied. It is proved that (in contrast to the reverse lexicographic case) ...

Gu map-1 is a modified version of GGH map. It uses same ideal lattices for constructing the trapdoors, while the novelty is that no encodings of zero are given. In this short paper we show that Gu map-1 cannot be used for the instance of witness encryption (WE) based on the hardness of 3-exact cover problem. That is, if Gu map-1 is used for such instance, we can break it by soving a combined 3-...

We consider the interaction of quantum light with an ideal semiconductor microcavity. We investigate photon statistics in different conditions and the presence of detuning and exciton-exciton interaction. We show that in the resonant interaction and absence of the exciton-exciton interaction, the state of the whole system can be considered as   coherent state. According to our results, it turns...

We introduce the notion of reset left regular decomposition of an ideal regular language and we prove that there is a one-to-one correspondence between these decompositions and strongly connected synchronizing automata. We show that each ideal regular language has at least a reset left regular decomposition. As a consequence each ideal regular language is the set of synchronizing words of some ...

Definition 1.1. A curved L∞ algebra over A consists of a locally free finitely generated graded A]-module V, together with a cohomological degree 1 and square zero derivation d : Ŝym(V∨[−1])→ Ŝym(V∨[−1]) where V∨ is the A]-linear dual and the completed symmetric algebra is also over A]. There are two additional requirements on the derivation d: (1) The derivation d makes Ŝym(V∨[−1]) into a dga ...

By proposing a predictive method with no adjustable parameter and by using infinite dilution activity coefficients of components in binary mixtures obtained from UNIFAC model, the binary interaction parameters (k12) in van der Waals mixing rule (vdWMR) and Orbey-Sandler mixing rule (OSMR) have been evaluated. The predicted binary interaction parameters are used in Peng-Robinson-S...

It is well known that for the case of a countable partial order, the ideal completion and the chain completion coincide. We investigate the boundary at which the chain and ideal completion do not coincide. We show in particular that the ideal completion is not sequentially adequate; that is it is not possible in general to simply replace the ideal completion with a completion based on sequences...