Concerning the Problem of Subsets of Finite Positive Packing Measure

For every Hausdorff function h, the paper gives a constructionof a compact metric space of infinite diameter-based h-packingmeasure which has no subsets of positive finite measure. Itthen indicates how such a construction can be modified to providethe same result for a radius-based packing measure in the caseof certain Hausdorff functions which do not satisfy a doublingcondition. This is in surprising contrast to another resultwhich shows that for a particular radius-based definition ofpacking measure no such example can be found.     

S-Noetherian Rings of the Forms 𝒜[X] and 𝒜[[X]]

Let 𝒜 = (A _n ) _n≥0 be an ascending chain of commutative rings with identity, S ? A ₀ a multiplicative set of A ₀, and let 𝒜[X] (respectively, 𝒜[[X]]) be the ring of polynomials (respectively, power series) with coefficient of degree i in A _i for each i ∈ ?. In this paper, we give necessary and sufficient conditions for the rings 𝒜[X] and 𝒜[[X]] to be S ? Noetherian.     

Universal Central Extensions of the Matrix Leibniz Superalgebras 𝔰𝔩(m,n, 𝒜)

The universal central extensions and their extension kernels of the smatrix Lie superalgebra 𝔰𝔩(m, n, 𝒜), the Steinberg Lie superalgebra 𝔰𝔩(m, n, 𝒜) in category SLeib of Leibniz superalgebras are determined under a weak assumption (compared with Mikhalev and Pinchuk, 2000 Mikhalev , A. V. , Pinchuk , I. A. ( 2000 ). Universal central extension of the matrix Lie superalgebras sl(m, n, A) . Contemp. Math. 264 : 111 – 126 . [Google Scholar]) using the first Hochschild homology and the first cyclic homology group.     

α-Stable characterization of Banach spaces (1 < α < 2)

This work characterizes some subclasses of α-stable (0 < α < 1) Banach spaces in terms of the extendibility to Radon laws of certain α-stable cylinder measures. These result extend the work of S. Chobanian and V. Tarieladze (J. Multivar. Anal.7, 183–203 (1977)). For these spaces it is shown that every Radon stable measure is the continuous image of a stable measure on a suitable L_β space with β = α(1 − α)⁻¹. The latter result extends some work of Garling (Ann. Probab.4, 600–611 (1976)) and Jain (Proceedings, Symposia in Pure Math. XXXI, p. 55–65, Amer. Math. Soc., Providence, R.I.).     

Weak Hausdorff Gaps and the 𝔭 ≤ t Problem

We find topological characterizations of the pseudointersection number ?? and the tower number t of the real line and we show that ?? < t iff there exists a compact separable T₂ space X of π-weight < ?? that can be covered by < t nowhere dense sets iff there exists a weak Hausdorff gap of size K < t, i. e., a pair ({A : i ≠ k}, {B_J : j ε K}) C [W]^W X [U]W such that A = {A_i : i ε K} is a decreasing tower, B = {B_j : j ε K) is a family of pseudointersections of A, and there is no pseudointersection S of A meeting each member of B in an infinite set.     

On the 𝔉‐hypercentre of a finite group

The main objective of this paper is to study and describe the hypercentre of a finite group associated with saturated formations, in terms of some subgroup embedding properties related to permutability. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The constructive completion of the space 𝒟(ℝ)

We prove in the framework of Bishop's constructive mathematics that the sequential completion $ \tilde {\cal D} $(?) of the space ??(?) is filter‐complete. Then it follows as a corollary that the filter‐completeness of ??(?) is equivalent to the principle BD‐?, which can be proved in classical mathematics, Brouwer's intuitionistic mathematics and constructive recursive mathematics of Markov's school, but does not in Bishop's constructive mathematics. We also show that $ \tilde {\cal D} $(?) is identical with the filter‐completion which was provided by Bishop. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On complements of 𝔉-residuals of finite groups

A formation 𝔉 of finite groups has the generalized Wielandt property for residuals, or 𝔉 is a GWP-formation, if the 𝔉-residual of a group generated by two 𝔉-subnormal subgroups is the subgroup generated by their 𝔉-residuals. The main aim of the paper is to determine some su?cient conditions for a finite group to split over its 𝔉-residual.     

Fixed points of (α,ψ)‐contractions in Hausdorff partial metric spaces

The concept of (α,ψ)‐contractions was introduced by Samet et al. in this paper, we introduce (α,ψ)‐generalized contractions in a Hausdorff partial metric space. We discuss its significance and obtain some common fixed point theorems for a pair of self‐mappings. Some examples are given to support the theory.     

Finding Δ(Σ) for a surface σ of characteristic χ(Σ) = −5

For each surface Σ, we define Δ(Σ) = max{Δ(G)|Gis a class two graph of maximum degree Δ(G) that can be embedded in Σ}. Hence, Vizing's Planar Graph Conjecture can be restated as Δ(Σ) = 5 if Σ is a plane. In this paper, we show that Δ(Σ) = 9 if Σ is a surface of characteristic χ(Σ) = ?5. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:148‐168, 2011     

Simple modules of the quantum double of the Nichols algebra of unidentified diagonal type 𝔲𝔣𝔬(7)

The finite-dimensional simple modules over the Drinfeld double of the bosonization of the Nichols algebra 𝔲𝔣𝔬(7) are classified.     

Foxby equivalences associated to Gorenstein categories 𝒢(𝒳,𝒴,𝒵)

In this paper, we establish some new Foxby equivalences between some Gorenstein subcategories in the Auslander class 𝒜_C(R) and that in the Bass class ?_C(S) in a general setting. Our results provide a unification and generalization of some known results and generate some new Foxby equivalences of categories.     

Canonical bases for the quantum supergroup U(𝔤𝔩3|1)

Based on the works of Du and Gu, the canonical bases of U(𝔤𝔩_3|1) are completely determined in this paper.     

Strong Cardinals and Sets of Reals in Lω1(ℝ)

We generalize results of [3] and [1] to hyperprojective sets of reals, viz. to more than finitely many strong cardinals being involved. We show, for example, that if every set of reals in L_ω (?) is weakly homogeneously Souslin, then there is an inner model with an inaccessible limit of strong cardinals.