Universal deformation rings and self-injective Nakayama algebras

Let k be a field and let Λ be an indecomposable finite dimensional k-algebra such that there is a stable equivalence of Morita type between Λ and a self-injective split basic Nakayama algebra over k. We show that every indecomposable finitely generated Λ-module V has a universal deformation ring $R(\mathrm{\Lambda },V)$ and we describe $R(\mathrm{\Lambda },V)$ explicitly as a quotient ring of a power series ring over k in finitely many variables. This result applies in particular to Brauer tree algebras, and hence to p-modular blocks of finite groups with cyclic defect groups.     

Coleman automorphisms of finite groups and their minimal normal subgroups

In this paper, we show that all Coleman automorphisms of a finite group with self-central minimal non-trivial characteristic subgroup are inner; therefore the normalizer property holds for these groups. Using our methods we show that the holomorph and wreath product of finite simple groups, among others, have no non-inner Coleman automorphisms. As a further application of our theorems, we provide partial answers to questions raised by M. Hertweck and W. Kimmerle. Furthermore, we characterize the Coleman automorphisms of extensions of a finite nilpotent group by a cyclic p-group. Finally, we note that class-preserving Coleman automorphisms of p-power order of some nilpotent-by-nilpotent groups are inner, extending a result by J. Hai and J. Ge, where p is a prime number.     

On images of locally finite derivations and E-derivations

Some cases of the LFED Conjecture, proposed by the second author [15], for certain integral domains are proved. In particular, the LFED Conjecture is completely established for the field of fractions $k(x)$ of the polynomial algebra $k[x]$, the formal power series algebra $k[[x]]$ and the Laurent formal power series algebra $k[[x]][x^{?1}]$, where $x=(x_1,x_2,\dots ,x_n)$ denotes n commutative free variables and k a field of characteristic zero. Furthermore, the relation between the LFED Conjecture and the Duistermaat–van der Kallen Theorem [3] is also discussed and emphasized.     

Indecomposable involutive set-theoretic solutions of the Yang–Baxter equation

We describe the indecomposable involutive non-degenerate set-theoretic solutions of the Yang–Baxter equation as dynamical extensions of non-degenerate left cycle sets. Moreover we characterize the indecomposable dynamical extensions and we produce several examples. As an application we construct a family of finite indecomposable solutions whose structure groups have not the unique product property.     

A variational approach for a generalized emden-fowler equation

Existence of positive solutions of singular boundary value problems related to Emden-Fowler equation is proved. A general minimization theorem in Sobolev spaces is applied.     

基于假设脱钩区间模型的省际节能减排压力测算以辽宁省为例

参照资源消耗及废物排放与经济增长的定量表达式-IGT方程和IGTX方程,分别推导出资源脱钩指数和二氧化碳排放指数方程.根据脱钩指数,将二氧化碳排放与GDP脱钩程度分为绝对脱钩、相对脱钩和未脱钩三种程度,并构建了假设相对脱钩和假设绝对脱钩区间.以辽宁省1995-2012年间二氧化碳排放量和GDP增长量为对象,分析了二者的脱钩关系.研究发现,除了1997和1999年二者处于相对脱钩状态,其余年份均未脱钩.运用假设脱钩区间模型,分别计算达到相对脱钩和绝对脱钩状态的二氧化碳年排放理想值,并与现值进行比较,得到各年节能减排的压力值.研究结果表明:相对脱钩的压力相对较小,减排压力在0-1671万t之间,占基准年碳排放量的0%-12.23%;绝对脱钩的压力较大,减排压力在320.77-4899.84万t,占基准年碳排放量的2.35%-23.94%.     

Enveloping algebras that are principal ideal rings

Let L be a restricted Lie algebra over a field of positive characteristic. We prove that the restricted enveloping algebra of L is a principal ideal ring if and only if L is an extension of a finite-dimensional torus by a cyclic restricted Lie algebra.     

Tungsten doped mesoporous SBA‐16 as novel heterogeneous catalysts for oxidation of cyclopentene to glutaric acid

Novel heterogeneous tungsten species in mesoporous silica SBA‐16 catalysts based on ship‐in‐a‐bottle methodology are originally reported for oxidizing cyclopentene (CPE) to glutaric acid (GAC) using hydrogen peroxide (H₂O₂). For all W‐SBA‐16 catalysts, isolated tungsten species and octahedrally coordinated tungsten oxide species are observed while WO₃ crystallites are detected for the W‐SBA‐16 catalysts with Si/ W = 5, 10, and 20. The specific surface areas and the corresponding total pore volumes decrease significantly as increasing amounts of tungsten incorporated into the pores of SBA‐16. Using tungsten‐substituted mesoporous SBA‐16 heterogeneous catalysts, high yield of GAC (55%) is achieved with low tungsten loading (for Si/W = 30, ~13 wt%) for oxidation of CPE. The W‐SBA‐16 catalysts with Si/W = 30 can be reused five times without dramatic deactivation. In fact, low catalytic activity provided by bulk WO₃ implies that the highly distributed tungsten species in SBA‐16 and the steric confinement effect of SBA‐16 are key elements for the outstanding catalytic performance.