半群的强可分性

目的研究阿基米德半群,π-正则半群等半群类的强可分性。方法将拓扑学中的可分性引入到一些经典的非正则半群类中,与通过断面研究半群的方法相反,利用半群类的性质来研究一个半群。结果若一个半群在阿基米德半群类或π-正则半群类上是强满逐点可分的,则该半群也为同类半群。结论将Marron DJ,Mcmaster TB和Hhnna AJ的结果推广到了非正则半群类。

关于强可分扩张的注记（英文）

设R和S是环,?:R→S是强可分扩张.本文研究了(Gorenstein)整体维数和表示型在R与S之间的关系.利用同调方法,证明了(1)R与S有相同的左整体维数,左弱整体维数,左Gorenstein整体维数;(2)若R和S是阿丁代数,则R是CM-有限的(CM-自由的,有限表示型)当且仅当S是CM-有限的(CM-自由的,有限表示型),推广了已知的结果.

一类强可分码的构造

强可分码可以有效的打击盗版,从而维护多媒体文件生产商的合法权益.本文提出了一种新的研究强码长为3的强可分码的方法,并利用此方法,得到了一个强可分码码字个数的更紧下界.

有限维张量积空间上的强可分算子

设F是一个域,a∈F^nF^m.若存在h∈F^m,k∈F^m,使得a=hk,则称a是可分的.空间F^nF^m上的线性算子A称为是强可分的,是指x∈F^nF^m,x可分Ax可分.本文证明了F^nF^n上的线性算子A是强可分的当且仅当存在F^n上的线性双射A_1与A_2,使得A=A_1A_2或A=A_1~T A_2;证明了F^nF^m(n≠m)上线性算子A是强可分的当且仅当存在F^n与F^m上的线性双射A_1与A_2,使得A=A_1A_2.最后,给出了可分算子、强可分算子和秩1保持映射之间的关系.

张量积空间上的强可分算子和弱可分算子

引入强可分算子与弱可分算子的概念。称具有形式T=AB的算子T为可分算子;称T为强可分算子,若T可以将所有向量映成可分向量;称可分算子T为弱可分算子,若Tx是可分向量意味着x∈C^n是可分向量。首先给出了当C^nC^n\{0}中可分向量的有限和仍是可分向量时,对应分量组成的向量组秩的刻画。其次分别得到了C^2C^2上的可分算子是强可分的和弱可分的刻画,并分别证明了两个可分算子的和是强可分算子和弱可分算子的充分必要条件。

模消去的Morita Contexts

证明了置换环上n-稳定秩条件关于Morita Context是遗传的;进一步把该结果推广到了强可分环,从而提供了新的具有模消去的置换环。

STOCHASTIC BOUNDARY ELEMENT METHODS FOR 3D PROBLEMS WITH BODY FORCES AND ITS APPLICATION IN RELIABILITY OF TURBINE DISKS

The stochastic boundary element method(SBEM)is developed in this paper for 3D problems with body forces and reliability analysis of engineering structures.The integral equations of SBEM are established by the approach of partial derivation with respect to stochastic variables,considering the yield limit,rotation speeds and material density to be the fundamental stochastic variables.Through analyzing a numerical example and a turbo-disk of an aeroengine,the results show that the method developed is successful.

Reliability Analysis Based on a Direct Ship Hull Strength Assessment

A method of reliability analysis based on a direct strength calculation employing the von Mises stress failure criterion is presented here. The short term strain distributions of ship hull structural components are identified through the statistical analysis of the wave-induced strain history and the long term distributions by the weighted summation of the short term strain distributions. The wave-induced long term strain distribution is combined with the still water strain. The extreme strain distribution of the response strain is obtained by statistical analysis of the combined strains. The limit state function of the reliability analysis is based on the von Mises stress failure criterion, including the related uncertainties due to the quality of the material and model uncertainty. The reliability index is calculated using FORM and sensitivity analysis of each variable that has effects on the reliability is also discussed.

Accurate estimation of soil shear strength parameters

The cost and safety of geotechnical engineering are highly depending on the accuracy of soil shear strength parameters.There are three methods often used to estimate soil shear strength parameters,i.e.,moment method,3-sigma rule and linear regression method.In this study,the accuracy of these three methods is compared.Traditional linear regression method(LRM)can only offer the mean of shear strength parameters.Some engineers misuse the standard error of shear strength indexes as the standard deviations.Such misuse may highly underestimate the uncertainty and induce high risk to the geotechnical design.A modified LRM is proposed to determine both the mean and variance of shear strength parameters.The moment method,three-sigma rule and LRM are used to analyze the tri-axial test data in Xiaolangdi Hydraulic Project and three numerical shear strength tests.The results demonstrate that:1)The modified LRM can offer the most accurate estimation to shear strength parameters;2)A dimensionless formula is much preferred in LRM rather than a dimensional formula.The stress ratio formula is much better than stress relation in the shear strength parameter analysis.The proposed method is applicable to shear strength parameter analysis for tri-axial test data,direct shear test and the un-drained shear strength test of stratified clay.

Reinforcement learning with partitioning function system

The size of state-space is the limiting factor in applying reinforcement learning algorithms to practical cases. A reinforcement learning system with partitioning function (RLWPF) is established, in which state-space is partitioned into several regions. Inside the performance principle of RLWPF is based on a Semi-Markov decision process and has general significance. It can be applied to any reinforcement learning with a large state-space. In RLWPF, the partitioning module dispatches agents into different regions in order to decrease the state-space of each agent. This article proves the convergence of the SARSA algorithm for a Semi-Markov decision process, ensuring the convergence of RLWPF by analyzing the equivalence of two value functions in two Semi-Markov decision processes before and after partitioning. This article can show that the optimal policy learned by RLWPF is consistent with prior domain knowledge. An elevator group system is devised to decrease the average waiting time of passengers. Four agents control four elevator cars respectively. Based on RLWPF, a partitioning module is developed through defining a uniform round trip time as the partitioning criteria, making the wait time of most passengers more or less identical then elevator cars should only answer hall calls in their own region. Compared with ordinary elevator systems and reinforcement learning systems without partitioning module, the performance results show the advantage of RLWPF.

Reliability and sensitivity of bogie frame of high-speed train with strength degradation

High-speed bogie frame is a key mechanical component in a train system. The reliability analysis of the bogie is necessary to the safety of high-speed train. Reliability analysis of a bogie frame was considered. The equivalent load method was employed to account for random repeated loads in structural reliability analysis. Degradation of material strength was regarded as a Gamma process. The probabilistic perturbation method was, then, employed for response moment computation. Example of a high-speed train bogie structure under time-variant load was employed for reliability and sensitivity analyses. Monte-Carlo simulation verifies the accuracy and efficiency of the proposed method in time-variant reliability analysis. The analysis results show that the reliability calculation considering the strength degradation and repeated load is closer to the practicality than the method of considering reliability calculation only. Its decreasing velocity is faster than the traditional reliability. The reliability sensitivity value changes over time. The analysis results provide a variation trend of reliability and sensitivity to design and usage of bogie frame.

Tunable Self-assembled Weak Polyelectrolyte Brushes

The authors have investigated the pH and ionic strength response of self-assembled layers formed by adsorption of amphiphilic weak polyelectrolytes. Using the SFA （Surface Forces Apparatus） the authors measured force-distance profiles of poly （isoprene）-poly （acrylic acid） block copolymers adsorbed on mica. Also by Atomic Force Microscopy the authors captured single polyelectrolyte molecule adsorbed on a surface. The effect of salt concentration （Cs） and pH upon the height of the brush layers was explored mainly by measuring the forces between two adsorbed polyelectrolyte brushes. At pH = 4 our results are in good agreement with the scaling prediction L0 ∝Cs-1/3 Changing the pH from 4 to 10 causes a remarkable swelling of the polymer layer, but only a weak dependence on salt concentration was detected at the higher pH. This can be attributed to the degree of dissociation, which depends on the local pH value. At low pH the polyelectrolyte chains have a low charge density, while on increasing the pH the degree of dissociation rises, and the increased charge density is followed by swelling of the adsorbed layer. The local concentration of ions in the brush is now greater than that of pH = 4 and approximately equivalent to 0.3 M. So the swelling is only weakly dependent on salt concentration in the range 0.01-1.0 M. The results demonstrate the tunable nature of such self-assembled polyelectroiyte brushes whose height and range of interactions, can be systematically controlled by adjusting the pH and ionic strength of the medium.

On the Adjacent Strong Edge Coloring of Outer Plane Graphs

A k-adjacent strong edge coloring of graph G(V, E) is defined as a proper k-edge coloring f of graph G(V, E) such that f[u] ≠ f[v] for every uv ∈ E(G), where f[u] = {f(uw)|uw ∈ E(G)} and f(uw) denotes the color of uw, and the adjacent strong edge chromatic number is defined as x'as(G) = min{k| there is a k-adjacent strong edge coloring of G}. In this paper, it has been proved that △ ≤ x'as(G) ≤ △ + 1 for outer plane graphs with △(G) ≥ 5, and X'as(G) = △ + 1 if and only if there exist adjacent vertices with maximum degree.

LIL behavior for B-valued strong mixing random variables

Given a sequence of mixing random variables {X1,Xn;n≥1} taking values in a separable Banach space B,and Sn denoting the partial sum,a general law of the iterated logarithm is established,that is,we have with probability one,lim supn→∞‖Sn‖/cn = α0 < ∞ for a regular normalizing sequence {cn}1,where α 0 is a precise value.

Wind Turbine Gearbox Reliability Analysis Based on the System Level Stress-Strength Model

In order to estimate the reliability of wind turbine gearbox based on the system level, a generalized stress-strength model is introduced. Considering that the system works properly under a variety of random stresses which affect every component, the total stress on the system is given by a known linear combination of the stresses of all components. Then the strength of the system can be viewed as a linear combination of the strengths of relative components. In this model, stress and strength are independent of each other. Reliability of the system is the probability that strength exceeds stress. Finally, the reliability of wind turbine gearbox is estimated by the multivariable reliability calculation method. The corresponding result is compared with the results of reliability in the extreme cases(completely dependent and completely independent) by the traditional evaluation method.

Similarity invariants of operators on a class of Gowers-Maurey spaces

This paper studies the similarity invariants of operators on a class of Gowers-Maurey spaces, ∑dc spaces, where an infinite dimensional Banach space X is called a ∑dc space if for every bounded linear operator on X the spectrum is disconnected unless it is a singleton. It shows that two strongly irreducible operators T1 and T2 on a ∑dc space are similar if and only if theK0-group of the commutant algebra of the direct sum T1 GT2 is isomorphic to the group of integers Z. On a ∑dc space X, it uses the semigroups of the commutant algebras of operators to give a condition that an operator is similar to some operator in （∑SI）（X）, it further gives a necessary and sufficient condition that two operators in （∑SI）（X） are similar by using the ordered K0-groups. It also proves that every operator in （∑SI）（X） has a unique （SI） decomposition up to similarity on a ∑dc space X, where （∑SI）（X） denotes the class of operators which can be written as a direct sum of finitely many strongly irreducible operators.

Study of the B_c→B_sπ decay with the perturbative QCD approach

The Bc → Bsπ decay is studied with the perturbative QCD approach. Three types of wave functions for Bs meson are considered. The transition form factor F0Bc → Bsπ （0） and the branching ratio IBr（Bc → Bsπ） are sensitive to the model of the Bs meson wave functions. With appropriate inputs, our estimate on 23r（Bc → Bsπ） is comparable with the recent LHCb measurement. A clear signal of Bc → Bsπ decay should be easily observed at the Large Hadron Collider.

Reproducibility in Surface-Enhanced Raman Spectroscopy

Surface-enhanced Raman spectroscopy（SERS） is an intense ongoing hot topic because it is an attractive tool for sensing or detecting molecules in trace amounts. Despite its high specificity and sensitivity, the SERS technique has not been established as a routine analytic method most likely due to the low reproducibility of the SERS signal. This review considers the influence factors to produce the poor reproducibility during the SERS measurement. This review starts with the discussion of calculation of surface-enhanced Raman intensity in order to explain the reason why it is so difficult to achieve a high reproducibility of SERS measurement from the origin of enhancement mechanism. Then we focus on the fabrication of SERS substrates generally including two types：① single particles and ② arrays on substrate that are directly used to detect molecules or other components.In addition, we discuss the molecule factors and optical system for the reproducibility for sample-to-sample or spot-to-spot on a substrate. In the final part of this review, some effects resulting in the irreproducibility of Raman bands＇ position from recent literatures are discussed.