The notion of completeness on L-semi-uniform spaces is introduced in this paper. We have established that completeness is weakly hereditary and preserved under L-semi-uniform isomorphism. Finally, we have shown that in a totally bounded L-semi-uniform space, completeness is equivalent to compactness. 2010 AMS Classification: 54A40

Let X be a subset of N or Z. We can associate with X a function GX : N t −→ N which returns, for every (n1, . . . , nt) ∈ N , the number GX(n1, . . . , nt) of all vectors x ∈ X such that, for every i = 1, . . . , t, |xi| ≤ ni. This function is called the growth function of X. The main result of this paper is that the growth function of a semi-linear set of N or Z is a box spline. By using this ...

The synthesis of a series of euphorbioside derivatives is described, starting from euphorbioside isolated from fresh latex of Euphorbia resinifera Berg. Their structures have been established on the basis of spectral data. All compounds were evaluated for antibacterial activities against Escherichia coli and Staphyloccus aureus strains and antifungal activity against Candida albicans and Asperg...

We study semi-stable degenerations of toric varieties determined by certain partitions of their moment polytopes. Analyzing their defining equations we prove a property of uniqueness.

We consider the GNS Hilbert space H of a uniformly hyper-finite C∗algebra and study a class of unbounded Lindbladian arises from commutators. Exploring the local structure of UHF algebra, we have shown that the associated Hudson-Parthasarathy type quantum stochastic differential equation admits a unitary solution. The vacuum expectation of homomorphic cocycle, implemented by the Hudson-Parthasa...

Let p be an odd prime, K a finite extension of Qp, GK = Gal(K̄/K) its absolute Galois group and e = e(K/Qp) its absolute ramification index. Suppose that T is a p-torsion representation of GK that is isomorphic to a quotient of GK -stable Zp-lattices in a semi-stable representation with HodgeTate weights {0, . . . , r}. We prove that there exists a constant μ depending only on n, e and r such th...

let $g$ be a group and $h$ a subgroup of $g$‎. ‎ $h$ is said to have semi-$pi$-property in $g$ if there is a subgroup $t$ of $g$ such that $g=ht$ and $hcap t$ has $pi$-property in $t$‎. ‎in this paper‎, ‎investigating on semi-$pi$-property of subgroups‎, ‎we shall obtain some new description of finite groups‎.