Chain Conditions on Essetial Subacts

Let S be a semigroup with zero and an S-act be a centered left S-act. This paper is devoted to the study of chain conditions on PS-acts. We prove that a PS-act having finite decomposition has ACC （DCC） on all subacts if it has ACC （DCC） on essential subacts. Moreover, a PS-act with ACC （DCC） on essential subacts has ACC （DCC） on all subacts if and only if it has finite decomposition. We characterize the structure of a PS-act and generalize some results of the Goldie dimension and semisimple S-acts.

Weight hierarchies of linear codes satisfying the almost chain condition

The weight hierarchy of a linear [n, k;q] code C over GF(q) is the sequence (d1,d2,..., dk) where dr is the size of the smallest support of an r-dimensional subcode of C. An [n,k;q] code satisfies the chain condition if there exists subcodes D1 D2 … Dk = C of C such that Dr has dimension r and support of size dr for all r. Further, C satisfies the almost chain condition if it does not satisfy the chain condition, but there exist subcodes Dr of dimension r and support of size dr for all r such that D2 D3 Dk = C and D1 D3. A simple necessary condition for a sequence to be the weight hierarchy of a code satisfying the almost chain condition is given. Further, explicit constructions of such codes are given, showing that in almost all cases, the necessary conditions are also sufficient.

Chain Condition on Annihilators and Strongly Hopfian Property in Hurwitz Series Ring

In this paper we study some properties of the Hurwitz series ring HA over a commutative ring A, such as the nilradical of HA and the chain condition on its an- nihilators. We provide an example showing that the last property does not pass from A to HA. A strongly Hopfian ring is a ring satisfying the chain condition on some type of annihilators. We give a large class of strongly Hopfian rings A such that HA are not strongly Hopfian.

Generalised Chain Conditions,Prime Ideals,and Classes of Locally Finite Lie Algebras

A Noetherian(Artinian)Lie algebra satisfies the maximal(minimal)condition for ideals.Generalisations include quasi-Noetherian and quasi-Artinian Lie algebras.We study conditions on prime ideals relating these properties.We prove that the radical of any ideal of a quasi-Artinian Lie algebra is the intersection of finitely many prime ideals,and an ideally finite Lie algebra is quasi-Noetherian if and only if it is quasi-Artinian.Both properties are equivalent to soluble-by-finite.We also prove a structure theorem for serially finite Artinian Lie algebras.

PROPER CONDITIONS OF MESHING FOR Hy-Vo SILENT CHAIN AND SPROCKET

Proper meshing of Hy-Vo silent chain and sprocket is important for realizing the transmission of the silent chain with more efficiency and less noise. Based on the study of the meshing theory of the Hy-Vo silent chain with the sprocket and the roll cutting machining principle of the sprocket with the hob, the proper conditions of the meshing for the Hy-Vo silent chain and the sprocket are put forward with the variable pitch characteristic of the Hy-Vo silent chain taken into consideration, and the proper meshing design method on the condition that the value of the link tooth pressure angle is unequal to the value of the sprocket tooth pressure angle is studied. Experiments show that this new design method is feasible. In addition, the design of the pitch, the sprocket tooth pressure angle and the fillet radius of the sprocket addendum circle are studied. It is crucial for guiding the design of the hob which cuts the Hy-Vo silent chain sprocket.

Matching Boundary Conditions for a Heterogeneous Atomic Chain

We propose accurate boundary treatments for a heterogeneous atomic chain, in terms of matching boundary conditions （MBCs）. The main challenge lies in reproducing the physical reflection across the boundary to a correct amount. With reflection coefficients we demonstrate that the accuracy is improved when more atoms are used under the boundary condition. The inclusion of an atom in the embedded sublattice B may considerably enhance the performance. Numerical testing illustrates the effectiveness of the proposed MBCs.

两支路自动循环调配系统的可靠性研究

两支路自动循环调配系统广泛应用于空调等电气系统的温、湿度自动调节,即当温、湿度等控制参数达到某一设定阈值时,调配系统自动切换至另一支路进行工作以达到参数调控的目的。针对部件寿命服从指数分布的情况,分析了转换开关失效对系统可靠性的影响模式,构建了两支路自动循环调配系统的物理模型,应用Markov链理论求出冷贮备条件下系统不同状态间的转移概率及其转移率矩阵,再通过Laplace变换得到在不同条件下两支路自动调配冷贮备系统的可靠性预测公式。空调系统的应用研究验证了可靠性预测模型的有效性。

一类被有限非齐次马氏链控制的条件独立的随机变量序列的强极限定理

设Ｅ＝｛１，２，…，Ｎ｝，｛（Ｋｋ，Ｙｋ），ｋ≥１｝是在Ｅ×Ｅ中取值的随机向量序列，其中｛Ｙｋ，ｋ≥１｝是非齐次马氏链，对于任意的ｎ≥２，（Ｘ１，…，Ｘｎ）在给定（Ｙ１，…，Ｙｎ）的情况下条件独立，且Ｘｉ的条件分布仅依赖于Ｙｉ的值．设ｉ∈Ｅ，Ｓｎ（ｉ），Ｑｎ（ｉ）分别表示序列Ｘｉ，…，Ｘｎ与Ｙｎ，…，Ｙｎ中的ｉ的个数．本文用分析方法研究关于Ｓｎ（ｉ）与Ｑｎ（ｉ）的强极限定理．

A Simple Proof of ACC for Minimal Log Discrepancies for Surfaces

Following Shokurov's idea,we give a simple proof of the ACC conjecture for minimal log discrepancies for surfaces.

Geodesic metrics on fractals and applications to heat kernel estimates

It is well known that for a Brownian motion, if we change the medium to be inhomogeneous by a measure μ, then the new motion(the time-changed process) will diffuse according to a different metric D(·, ·).In 2009, Kigami initiated a general scheme to construct such metrics through some self-similar weight functions g on the symbolic space. In order to provide concrete models to Kigami’s theoretical construction, in this paper,we give a thorough study of his metric on two classes of fractals of primary importance: the nested fractals and the generalized Sierpinski carpets;we further assume that the weight functions g := ga are generated by“symmetric” weights a. Let M be the domain of a such that Dgadefines a metric, and let S be the boundary of M. One of our main results is that the metrics from ga satisfy the metric chain condition if and only if a ∈ S.To determine M and S, we provide a recursive weight transfer construction on the nested fractals, and a basic symmetric argument on the Sierpinski carpet. As an application, we use the metric chain condition to obtain the lower estimate of the sub-Gaussian heat kernel. This together with the upper estimate obtained by Kigami allows us to have a concrete class of metrics for the time change, and the two-sided sub-Gaussian heat kernel estimate on the fundamental fractals.

Finite Projective Geometries and Classification of the Weight Hierarchies of Codes(Ⅰ)

The weight hierarchy of a binary linear [n, k] code C is the sequence (d 1, d 2, . . . , d k ), where d r is the smallest support of an r-dimensional subcode of C. The codes of dimension 4 are collected in classes and the possible weight hierarchies in each class is determined by finite projective geometries. The possible weight hierarchies in class A, B, C, D are determined in Part (I). The possible weight hierarchies in class E, F, G, H, I are determined in Part (II).