New algebraic structures from Hermitian one-matrix model

Virasoro constraint is the operator algebra version of one-loop equation for a Hermitian one-matrix model, and it plays an important role in solving the model. We construct the realization of the Virasoro constraint from the Conformal Field Theory (CFT) method. From multi-loop equations of the one-matrix model, we get a more general constraint. It can be expressed in terms of the operator algebras, which is the Virasoro subalgebra with extra parameters. In this sense, we named as generalized Virasoro constraint. We enlarge this algebra with central extension, this is a new kind of algebra, and the usual Virasoro algebra is its subalgebra. And we give a bosonic realization of its subalgebra.     

Standard molar enthalpy of formation of [(C12H8N2)2Bi(O2NO)3] and its biological activity on Schizosaccharomyces pombe

The title complex [(C₁₂H₈N₂)₂Bi(O₂NO)₃] was synthesized by reaction of 1,10-phenanthroline (phen) and Bi(NO₃)₃·5H₂O. The structure of the complex was characterized by single-crystal X-ray diffraction, IR spectroscopy, and elemental analysis. An advanced solution-reaction isoperibol microcalorimeter was applied to determine the standard molar enthalpies of formation at 298.15 K of the complex and Bi(NO₃)₃·5H₂O, giving –(798.92 ± 5.99) and –(1986.87 ± 0.20) kJ mol⁻¹, respectively. The biological effect of the complex was evaluated by microcalorimetry on the growth of Schizosaccharomyces pombe (S. pombe). According to thermogenic curves, the corresponding thermokinetics and thermodynamic parameters were derived. The complex had good bioactivity on the growth metabolism of S. pombe, with the value of IC₅₀ being 2.8 × 10⁻⁵ mol L⁻¹.

     

Novel Bi2MoO6 Nanosheets/Vertical TiO2 Nanorods Arrays Heterojunction with Enhanced Photoelectrochemical Performance under Visible Light Irradiation

Novel Bi₂MoO₆/TiO₂ heterojunction was fabricated by growing Bi₂MoO₆ nanosheets arrays on the vertically aligned TiO₂ nanorods arrays via a two-step solvothermal method. The obtained Bi₂MoO₆/TiO₂ hierarchical heterojunction showed excellent visible light photoelectrochemical performance. Compared with the pure TiO₂ and Bi₂MoO₆, the photocurrent density of the heterojunction was increased 57 and 29 times, respectively. Furthermore, the hydrogen generation rate of the Bi₂MoO₆/TiO₂ for photoelectrocatalytic water-splitting was about 6 times higher than that of the pure Bi₂MoO₆. The improved performance can be attributed to the synergistic effects of enhanced absorption of visible light, increase of migration rate and separation efficiency of photo-induced carriers.     

Gradient estimates for solutions to quasilinear elliptic equations with critical sobolev growth and hardy potential

This note is a continuation of the work[17].We study the following quasilinear elliptic equations(■)where 1 p N,0 ≤μ ((N-p)/p)~p and Q ∈ L~∞(R~N).Optimal asymptotic estimates on the gradient of solutions are obtained both at the origin and at the infinity.     

Invariants of finite groups generated by generalized transvections in the modular case

We investigate the invariant rings of two classes of finite groups G ≤ GL(n, F _q) which are generated by a number of generalized transvections with an invariant subspace H over a finite field F _q in the modular case. We name these groups generalized transvection groups. One class is concerned with a given invariant subspace which involves roots of unity. Constructing quotient groups and tensors, we deduce the invariant rings and study their Cohen-Macaulay and Gorenstein properties. The other is concerned with different invariant subspaces which have the same dimension. We provide a explicit classification of these groups and calculate their invariant rings.     

New model and heuristic solution approach for one-dimensional cutting stock problem with usable leftovers

In the one-dimensional cutting stock problem with usable leftovers (1DCSPUL), items of the current order are cut from stock bars to minimize material cost. Here, stock bars include both standard ones bought commercially and old leftovers generated in processing previous orders, and cutting patterns often include new leftovers that are usable in processing subsequent orders. Leftovers of the same length are considered to be of the same type. The number of types of leftovers should be limited to simplify the cutting process and reduce the storage area. This paper presents an integer programming model for the 1DCSPUL with limited leftover types and describes a heuristic algorithm based on a column-generation procedure to solve it. Computational results show that the proposed approach is more effective than several published algorithms in reducing trim loss, especially when the number of types of leftovers is limited.     

考虑底部隆起的浅埋隧道围岩压力计算分析

针对浅埋隧道开挖后底部隆起变形现象,应用极限分析上限法构造了考虑底部隆起变形的围岩压力计算模型,结合线性Mohr-Coulomb准则等推导出极限围岩压力的理论表达式。通过约束条件将围岩压力的计算转化为数学中的最优化问题,编制程序进行了优化计算。将计算结果与工程实测数据及文献计算结果进行了对比,验证了当前方法的可靠性。同时,指出在运用极限分析法处理浅埋隧道围岩压力问题过程中应将隧道底部一同考虑,对隧道底部支护会对整个围岩压力产生影响,有助于隧道结构的整体稳定。研究可以为浅埋隧道的开挖、支护提供一定的理论指导.     

Experiments on crack identification in cantilever beams

In this paper we present an experimental investigation of the identification of crack location and size. By providing the first three natural frequencies through vibration measurements, curves of crack equivalent stiffness versus crack location are plotted, and the intersection of the three curves predicts the crack location and size. In the experiments, the cracked specimens were made using a wire-cut electrical discharge machine, and the cantilever beams were excited next to the free end by means of an impulse force hammer. In order to obtain the accurate natural frequencies from the transient signal measured, the method of zoom fast Fourier transform is adopted to improve frequency resolution. From experimental results, it is observed that the identification errors of crack location and size are less than 2% and 4%, respectively. The effectiveness of crack identification through vibration measurements is verified.     

基于神经网络与光纤传感阵列的结构状态监测方法

以探测机敏复合材料与结构内应变、应力及损伤等物理状态的位置信息为目的．提出了一种新颖的可内埋于材料与结构内作为结构状态监测用的强度调制型光纤传感阵列网络，并采用人工神经网络来处理传感阵列输出的并行分布式传感信号，阐述了适用的Ｋｏｈｏｎｅｎ网模型及其变化形式，给出了仿真实验结果