A tensor product of the Steinberg module and a certain simple kG(pr)-module

Let G be a connected, semisimple, and simply connected algebraic group defined and split over the finite field of order p, and let G(q) be the corresponding finite Chevalley or twisted group, where q = p^r. Recently, Anwar determines the direct sum decomposition of the tensor product of the rth Steinberg module and a simple G-module with a (p,r)-minuscule highest weight λ. In this paper, we determine that of the tensor product regarded as a module for G(q) under some weak assumptions for λ.     

On the complexity of the word problem for automaton semigroups and automaton groups

In this paper, we study the word problem for automaton semigroups and automaton groups from a complexity point of view. As an intermediate concept between automaton semigroups and automaton groups, we introduce automaton-inverse semigroups, which are generated by partial, yet invertible automata. We show that there is an automaton-inverse semigroup and, thus, an automaton semigroup with a PSpace-complete word problem. We also show that there is an automaton group for which the word problem with a single rational constraint is PSpace-complete. Additionally, we provide simpler constructions for the uniform word problems of these classes. For the uniform word problem for automaton groups (without rational constraints), we show NL-hardness. Finally, we investigate a question asked by Cain about a better upper bound for the length of a word on which two distinct elements of an automaton semigroup must act differently.A detailed listing of the contributions of this paper can be found at the end of this paper.     

所有极大子群都为SMSN-群的有限群

若有限群G的每个2-极大子群在G中次正规,则称G为SMSN-群.本文研究了有限群G的每个真子群是SMSN-群但G本身不是SMSN-群的结构,利用局部分析的方法,获得了这类群的完整分类,推广了有限群结构理论的一些成果.     

半监督度量学习内蕴最速下降算法的收敛性分析

主要研究对称正定矩阵群上的内蕴最速下降算法的收敛性问题.首先针对一个可转化为对称正定矩阵群上无约束优化问题的半监督度量学习模型,提出对称正定矩阵群上一种自适应变步长的内蕴最速下降算法.然后利用李群上的光滑函数在任意一点处带积分余项的泰勒展开式,证明所提算法在对称正定矩阵群上是线性收敛的.最后通过在分类问题中的数值实验说明算法的有效性.     

On the Chow groups of certain cubic fourfolds

This note is about the Chow groups of a certain family of smooth cubic fourfolds. This family is characterized by the property that each cubic fourfold X in the family has an involution such that the induced involution on the Fano variety F of lines in X is symplectic and has a K3 surface S in the fixed locus. The main result establishes a relation between X and S on the level of Chow motives. As a consequence, we can prove finite-dimensionality of the motive of certain members of the family.     

Exploring the Role of Surface States in Emissive Carbon Nanodots: Analysis at Single-Particle Level

Fluorescent carbon nanodots (CDs) have been highlighted as promising semiconducting materials due to their outstanding chemical and optical properties. However, the intrinsic heterogeneity of CDs has impeded a clear understanding of the mechanisms behind their photophysical properties. In this study, as-prepared CDs are fractionated via chromatography to reduce their structural and chemical heterogeneity and analyzed through ensemble and single-particle spectroscopies. Many single particles reveal fluorescence intensity fluctuations between two or more discrete levels with bi-exponential decays. While the intrinsic τ₁ components are uniform among single particles, the τ₂ components from molecule-like emissions spans a wider range of lifetimes, reflecting the inhomogeneity of the surface states. Furthermore, it is concluded that the relative population and chemical states of surface functional groups in CDs have a significant impact on emissive states, brightness, blinking, stability, and lifetime distribution of photoluminescence.     

Adsorption of Volatile Organic Compounds (VOCs) on Oxygen-rich Porous Carbon Materials Obtained from Glucose/Potassium Oxalate

To investigate the effects of oxygen-containing functional groups on the adsorption of volatile organic compounds (VOCs) with different polarity, oxygen-rich porous carbon materials (OPCs) were synthesized by heat treatment of glucose/potassium oxalate material. The carbon material had a large specific surface area (1697 m² g⁻¹) and a high oxygen content (18.95 at.%). OPC exhibited high adsorption capacity of toluene (309 mg g⁻¹) and methanol (447 mg g⁻¹). The specific surface area and total pore volume determined the adsorption capacity of toluene and methanol at the high-pressure range, while the oxygen-containing groups became the main factor affecting the methanol adsorption at the low-pressure range due to the hydrogen bond interaction through the density functional theory (DFT) calculations. This study provides an important hint for developing a novel O-doped adsorbent for the VOCs adsorption applications and analyzing the role of oxygen-containing groups in the VOCs adsorption under the low-pressure range.     

Simulating periodic trends in the structure and catalytic activity of coinage metal nanoribbons

We present a systematic density functional theory (DFT) study of the structure and catalytic activity of group 10 (Ni, Pd, Pt) and group 11 (Cu, Ag, Au) coinage metal nanoribbons. These infinite, periodic, quasi‐one‐dimensional structures are conceptually important as intermediates between small metal clusters and close‐packed metal surfaces, and have been shown experimentally to be practical catalysts. We find that nanoribbons have significantly higher predicted H₂ dissociation activity than close‐packed metal surfaces consistent with their lower coordination numbers. Computed periodic trends are reasonable, with late transition states and low barriers for H₂ dissociation over late group 10 nanoribbons, suggesting their promise as practical catalysts. These trends are consistent with the isolated nanoribbons' computed molecular electrostatic potentials. Calculations also predict nearly linear Brønsted–Evans–Polanyi relationships between the nanoribbons' H₂ dissociation energies and dissociation barriers. We also test new meta‐generalized gradient approximation (GGA) and hybrid DFT approximations for H₂ dissociation over these nanoribbons. These new functionals increase the (generally underestimated) dissociation barriers predicted by standard GGAs, motivating their continued application in surface chemistry. © 2015 Wiley Periodicals, Inc.