Stability of Rotation Relations of Three Unitaries with the Flip Action in C*-Algebras*

The authors show that if Θ = (θ_jk) is a 3 × 3 totally irrational real skewsymmetric matrix, where θ_jk ∈ [0, 1) for j, k = 1, 2, 3, then for any ε > 0, there exists δ > 0 satisfying the following: For any unital C^*-algebra A with the cancellation property,strict comparison and nonempty tracial state space, any four unitaries u₁, u₂, u₃, w ∈ A such that (1) u_ku_j - e^{2πiθjk ujukk} < δ, wu_jw^-1 = u^-1_j, w² = 1_A for j, k = 1, 2, 3; (2)τ (aw) = 0 and τ ((u_ku_ju_k^*u_j^* )ⁿ ) = e^2πinθjk for all n ∈ N, all a ∈ C^*(u₁, u₂, u₃), j, k = 1, 2, 3 and all tracial states τ on A, where C^*(u₁, u₂, u₃) is the C^*-subalgebra generated by u₁, u₂ and u₃, there exists a 4-tuple of unitaries u₁, u₂, u₃, w in A such that u_ku_j = e^2πinθjk u_ku_j, w u_j w^-1 = u^-1 _j, w² = 1A and k u_j - u_jk < ε, k w - wk < ε for j, k = 1, 2, 3. The above conclusion is also called that the rotation relations of three unitaries with the flip action is stable under the above conditions.     

Preparation and characterization of novel organosoluble and thermally stable poly(benzimidazole-amide)s bearing phthalimide pendent groups

Novel aromatic poly(benzimidazole-amide)s, PBAs, have been synthesized by direct polycondensation of a new dicarboxylic acid, N-[3,5-bis(5-carboxylic acid-2-benzimidazole) phenyl]phthalimide (1), containing performed benzimidazole rings and a phthalimide pendent group with various aromatic diamines. The dicarboxylic acid was synthesized by reaction of 5-(N-phthalimide)isophthalic acid with 4-methyl-1,2-phenylenediamine in polyphosphoric acid, followed by its oxidation into relative dicarboxylic acid. To study the structure-property relationships of 1,3-bis(5-carboxylic acid-2-benzimidazole)benzene (2, as a reference) this compound was also synthesized. The chemical structure of 1 and 2 were confirmed by the spectroscopic methods and elemental analyses. The characterization of the polymers was performed with inherent viscosity measurements, solubility tests, FT-IR, Ultraviolet and ¹H NMR spectroscopy and thermogravimetry. The polymers were obtained in quantitative yields with inherent viscosities between 0.53 and 0.91 dl g⁻¹. The effects of the phthalimide pendent group on the polymer properties such as solubility and thermal behavior were investigated and compared with those of the corresponding unsubstituted poly(benzimidazole-amide)s. The modified poly(benzimidazole-amide)s showed enhanced solubilities in some solvents, such as m-cresol and pyridine, in comparison to the unmodified analogues. In addition, the incorporation of the pendent phthalimide groups in the poly(benzimidazole-amide)s backbone increased remarkably the thermal stability of the polymer. The glass transition temperature and 10% weight loss temperature of the poly(benzimidazole-amide)s were in range of 291-334 °C and 466-540 °C, respectively, in nitrogen.     

Extracting the mechanisms and kinetic models of complex reactions from atomistic simulation data

Determining reaction mechanisms and kinetic models, which can be used for chemical reaction engineering and design, from atomistic simulation is highly challenging. In this study, we develop a novel methodology to solve this problem. Our approach has three components: (1) a procedure for precisely identifying chemical species and elementary reactions and statistically calculating the reaction rate constants; (2) a reduction method to simplify the complex reaction network into a skeletal network which can be used directly for kinetic modeling; and (3) a deterministic method for validating the derived full and skeletal kinetic models. The methodology is demonstrated by analyzing simulation data of hydrogen combustion. The full reaction network comprises 69 species and 256 reactions, which is reduced into a skeletal network of 9 species and 30 reactions. The kinetic models of both the full and skeletal networks represent the simulation data well. In addition, the essential elementary reactions and their rate constants agree favorably with those obtained experimentally. © 2019 Wiley Periodicals, Inc.     

沿轴线方向匀速直线运动的电偶极子的电场

本文利用相对论变换关系计算了沿轴线方向匀速直线运动的电偶极子的电场。     

Selection Principles and Sierpinski Sets

We show that a set of real numbers is a Sierpinski set if, and only if, it satisfies a selection property similar to the familiar Menger property.     

[Re5(μ-H)4(CO)20]− and [Re5(μ-H)5(CO)20], Two Isolobal Analogues of Cyclopentane

The first five-membered rings of metal atoms connected by M–M or M-H-M bonds only have been obtained by a Re₂+Re₃ condensation in which a polyhydride acts as a bridging bidentate ligand toward a coordinatively unsaturated fragment (see scheme below). In spite of the octahedral coordination of the Re centers, the Re₅ rings display conformations (twisted and envelope) comparable with those observed for organic five-membered rings of tetrahedral carbon atoms.     

Maximally Clustered Elements and Schubert Varieties

We introduce and study a class of “maximally clustered” elements for simply laced Coxeter groups. Such elements include as a special case the freely braided elements of Green and the author, which in turn constitute a superset of the iji-avoiding elements of Fan. We show that any reduced expression for a maximally clustered element is short-braid equivalent to a “contracted” expression, which can be characterized in terms of certain subwords called “braid clusters”. We establish some properties of contracted reduced expressions and apply these to the study of Schubert varieties in the simply laced setting. Specifically, we give a smoothness criterion for Schubert varieties indexed by maximally clustered elements. Received December 30, 2005     

大肠癌与七种元素关系的分析

用原子吸收光谱法测定了38例大肠癌组织及其边缘组织中铬、锰、锌、铁、镁、钙、铜的含量.结果表明,癌组织中锰含量(0.281±0.179)×10-6,镁含量(76.85±17.66)×10-6,高于其边缘组织(P＜0.01).七种元素含量与大肠癌的病理类型及分化程度无关.提示,大肠癌的发生与锰、镁的含量变化有关.     

构元组集损伤断裂模型及其与内聚区模型的比较

结构的响应实质上是材料的响应,宏观结构损伤至断裂的发展过程也是材料性质不断演化的结果.构元组集模型从材料的微观物理变形机制出发,基于对泛函势理论和Cauchy-Born准则,抽象出两种构元:弹簧束构元和体积构元.在微观层次上,结构损伤和断裂的实质都是原子间键合力减弱和丧失的结果,而弹簧束构元是同一方向上的原子键的抽象,因此损伤可以通过弹簧束构元的响应曲线来反映.组集两种构元的响应,建立了材料的弹性损伤本构关系,从而能一致描述材料从弹性到损伤、破坏的发展过程.将构元组集模型的本构关系嵌入ABAQUS的用户材料单元子程序UMAT,实现对结构响应的数值模拟.论文模拟了包含中心预制裂纹三点弯曲梁的裂纹扩展过程,并与内聚区模型比较,给出了内聚区模型所假设的应力-位移关系曲线,并从材料损伤演化的角度对材料裂纹扩展过程做出了物理解释.     

铝-锂合金动态扭转实验研究

利用霍普金森扭杆（Torsional Split-Hopkinson Bar）技术对三种不同成份或状态的铝-锂合金材料的动态应力-应变-应变率关系进行了实验测定。应变率范围由1300s-1到2600s-1,研究表明随着应变率的提高,三种不同成份或状态的铝-锂合金材料的韧性和强度都有不同程度的提高。对剪切带的初步观察发现,随应变率的增加,剪切带有变窄的趋势。