Finite Dimensional Behavior for Weakly Damped Generalized KdV-Burgers Equations

ＦｉｎｉｔｅＤｉｍｅｎｓｉｏｎａｌＢｅｈａｖｉｏｒｆｏｒＷｅａｋｌｙＤａｍｐｅｄＧｅｎｅｒａｌｉｚｅｄＫｄＶ－Ｂｕｒｇｅｒｓ　ＥｑｕａｔｉｏｎｓＧｕｏＢｏｌｉｎｇ（郭柏灵）（ＣｅｎｔｒｅｆｏｒＮｏｎｌｉｎｅａｒＳｔｕｄｉｅｓ，ＩｎｓｔｉｔｕｔｅｏｆＡ...     

WELL-BEHAVED BASIS AND LR ARRAYS

ＷＥＬＬ－ＢＥＨＡＶＥＤＢＡＳＩＳＡＮＤＬＲＡＲＲＡＹＳＬＩＮＤＯＮＧＤＡＩ（林东岱）（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅ，Ｂｅｉｊｉｎｇ１０００８０，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ...     

ThePropertiesofConcentrationsinaPolymerBlend1

ＴｈｅＰｒｏｐｅｒｔｉｅｓｏｆＣｏｎｃｅｎｔｒａｔｉｏｎｓｉｎａＰｏｌｙｍｅｒＢｌｅｎｄ１ＹｕｎＨＵＡＮＧ，ＤｅｌｕＺＨＡＯ（ＤｅｐａｒｔｍｅｎｔｏｆＰｈｙｓｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ１００８７１，Ｃｈｉｎａ）（Ｉｎｓｔ...     

Bounds for Determinants of Quaternion Matrices

ＢｏｕｎｄｓｆｏｒＤｅｔｅｒｍｉｎａｎｔｓｏｆＱｕａｔｅｒｎｉｏｎＭａｔｒｉｃｅｓＨｕａｎｇＬｉｐｉｎｇ（黄礼平）（Ｄｅｐｔ．ｏｆＢａｓｉｃＳｃｉｅｎｃｅｓ，ＸｉａｎｇｔａｎＭｉｎｉｎｇＩｎｓｔｉｔｕｔｅ，Ｘｉａｎｇｔａｎ，４１１２０１）ＣａｉＹｏｎ...     

The Existence of the Complete and Completely Distributive Lattices

ＴｈｅＥｘｉｓｔｅｎｃｅｏｆｔｈｅＣｏｍｐｌｅｔｅａｎｄＣｏｍｐｌｅｔｅｌｙＤｉｓｔｒｉｂｕｔｉｖｅＬａｔｔｉｃｅｓＢａｔＲｕｉｐｕ（白瑞蒲）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｅｂｅｉＵｎｉｖｅｒｓｉｔｙ，Ｂａｏｄｉｎｇ，０７１００...     

A BRANCH BOUND METHOD FOR SUBSET SUM PROBLEM

ＡＢＲＡＮＣＨＢＯＵＮＤＭＥＴＨＯＤＦＯＲＳＵＢＳＥＴＳＵＭＰＲＯＢＬＥＭＷＵＳＨＩＱＵＡＮ（吴士泉）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１０００８０，Ｃ...     

三角形一个重要公式及其应用

在三角形中，我们把角的顶点与其对边上一点的连线称作这个角的分角线．下面给出分角线长的一种公式．定理　如图１，Ｄ是△ＡＢＣ的边ＢＣ上一点，设ＡＢ、ＡＣ分别为ｃ、ｂ，∠ＢＡＤ＝α，∠ＣＡＤ＝β，图１则　　　　ＡＤ＝ｂｃｓｉｎ（α＋β）ｃｓｉｎα＋ｂｓｉｎβ．（１）当ＡＤ是∠Ａ的平分线时，　　　ＡＤ＝２ｂｃｃｏｓＡ２ｂ＋ｃ；（２）当ＡＤ是中线时，　　ＡＤ＝ｂｓｉｎ（α＋β）２ｓｉｎα＝ｃｓｉｎ（α＋β）２ｓｉｎβ；（３）当ＡＤ是高线时，　　　ＡＤ＝ｃｃｏｓα＝ｂｃｏｓβ＝ｂｃｓｉｎＡａ．（４）证明　在…     

A THEOREM ON EMBEDDING W~(s,p) INTO L(np/n-sp).p

ＡＴＨＥＯＲＥＭＯＮＥＭＢＥＤＤＩＮＧＷ~（ｓ，ｐ）ＩＮＴＯＬ(np/n-sp).pＪｉａｎｇＭｉｎｇ（姜明）（Ｄｅｐｔ．Ａｐｐｌ．Ｍａｔｈ．ＢｅｉｊｉｎｇＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇｙ，Ｂｅｉｊｉｎｇ１０００８１，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：Ｉｔ...     

数学问题解答

20 0 1年 1 1月号问题解答(解答由问题提供人给出 )1 3 4 1　锐角三角形ＡＢＣ中有内接△ＤＥＦ ,且ＦＤ⊥ＢＣ于Ｄ ,ＤＥ ⊥ＡＣ于Ｅ ,ＥＦ ⊥ＡＢ于Ｆ ,求证 :Ｓ△ＡＢＣ ≥ 3Ｓ△ＤＥＦ.(武汉华中理工大学西十四舍 5号　黄元兵　 43 0 0 74)证　△ＡＢＣ三边分别与△ＤＥＦ三边垂直 ,又△ＡＢＣ为锐角三角形 ,有∠Ａ =∠ＤＥＦ ,∠Ｂ =∠ＥＦＤ ,∠Ｃ =∠ＦＤＥ即有△ＡＢＣ ∽△ＤＥＦ .又公比ｑ=ＢＣＤＦ =ＢＤＤＦ ＣＤＤＦ=ｃｏｔＢ ＤＥＤＦｓｉｎＣ=ｃｏｔＢ ｓｉｎＢｓｉｎＡｓｉｎＣ =ｃｏｔＢ ｓｉｎ(Ａ Ｃ)ｓｉｎＡｓｉｎＣ=…     

Completely Positive Definite Maps Over Topological^＊—algebras

ＣｏｍｐｌｅｔｅｌｙＰｏｓｉｔｉｖｅＤｅｆｉｎｉｔｅＭａｐｓＯｖｅｒＴｏｐｏｌｏｇｉｃａｌ－ａｌｇｅｂｒａｓＸｕＴｉａｎｚｈｏｕ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＢｅｉｊｉｎｇＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｆｏｇｙ，...     

Towards the Exact Minimization of BDDs—An Elitism-Based Distributed Evolutionary Algorithm

Binary Decision Diagrams (BDDs) are the state-of-the-art data structure for representation and manipulation of Boolean functions. In general, exact BDD minimization is NP-complete. For BDD-based technology, a small improvement in the number of nodes often simplifies the follow-up problem tremendously. This paper proposes an elitism-based evolutionary algorithm (EBEA) for BDD minimization. It can efficiently find the optimal orderings of variables for all LGSynth91 benchmark circuits with a known minimum size. Moreover, we develop a distributed model of EBEA, DEBEA, which obtains the best-ever variable orders for almost all benchmarks in the LGSynth91. Experimental results show that DEBEA is able to achieve super-linear performance compared to EBEA for some hard benchmarks.     

Performance assessment and reliability analysis of dependable and distributed computing systems based on BDD and recursive merge

System reliability evaluation, sensitivity analysis, failure frequency analysis, importance measures, and optimal design are important issues that have become research topics for distributed dependable computing. Finding all of the Minimal File Spanning Trees (MFST) and avoiding repeatedly computing the redundant MFSTs have been key techniques for evaluating the reliability of a distributed computing system (DCS) in previous works. However, identifying all of the disjointed MFSTs is difficult and time consuming for large-scale networks. Although existing algorithms have been demonstrated to work well on medium-scale networks, they have two inherent drawbacks. First, they do not support efficient manipulation of Boolean algebra. The sum-of-disjoint-products method used by these algorithms is inefficient when dealing with large Boolean functions. Second, the tree-based partitioning algorithm does not merge isomorphic sub-problems, and therefore, redundant computations cannot be avoided. In this paper, we propose a new efficient algorithm for the reliability evaluation of a DCS based on the recursive merge and the binary decision diagram (BDD). Using the BDD substitution method, we can easily apply our algorithm to a network with imperfect nodes. The experimental results show a significant improvement in the execution time compared to previous works.     

On robust identification in the square and king grids

Fault diagnosis of multiprocessor systems gives the motivation for robust identifying codes. We provide robust identifying codes for the square and king grids. Often we are able to find optimal such codes.     

FTA法和重要度分析在某系统可靠性中的应用

应用失效树分析（Fault Tree Analysis）法（简称FTA法）,对某型火炮遥控系统进行了可靠性分析,建立了该系统的失效树,并在此基础上计算了该系统的可靠性参数,讨论了部件的概率重要度和相对比重要度,并把部件的概率重要度和相对比重要度推广到了分系统,结合所建的失效树给出了相应的结果。通过重要度分析,找到了提高系统可靠性中的途径。     

高强度锚具可靠性分析及夹片曲线概率优化研究

本文用失效树分析法,对现有锚具进行失效分析,计算出失效概率.同时,对锚具主要零件夹片的夹口曲线进行概率优化,使优化后的曲线对在公差范围内合格钢筋的拟合概率最大,从而设计出新的锚具及夹片.夹口曲线的求法也为其它类型锚具夹片的设计提供了一种新的方法.     

An n log n Algorithm for Online BDD Refinement

Binary decision diagrams are in widespread use in verification systems for the canonical representation of finite functions. Here we consider multivalued BDDs, which represent functions of the form : ^ν →  , where is a finite set of leaves. We study a rather natural online BDD refinement problem: a partition of the leaves of several shared BDDs is gradually refined, and the equivalence of the BDDs under the current partition must be maintained in a discriminator table. We show that it can be solved in O(n log n) time if n bounds both the size of the BDDs and the total size of update operations. Our algorithm is based on an understanding of BDDs as the fixed points of an operator that in each step splits and gathers nodes. We apply our algorithm to show that automata BDD-represented transition functions can be minimized in time O(n · log n), where n is the total number of BDD nodes representing the automaton. This result is not an instance of Hopcroft's classical minimization algorithm, which breaks down for BDD-represented automata because of the BDD path compression property.     

Modeling,analysis and performance evaluation for fault diagnosis and Fault Tolerant Control in bottle-filling plant modeled using Hybrid Petri nets

In this paper, an approach to achieve fault diagnosis and Fault Tolerant Control in a typical bottle-filling plant using event based techniques is discussed. For this purpose, the plant is modeled using Hybrid Petri nets which enable study and analysis with regard to the working of the plant. Once effective modeling is done based on two different case studies considered, new algorithms are proposed to achieve fault diagnosis and Fault Tolerant Control on the models developed. Finally, performance measures with regard to the models proposed are evaluated to check the correctness of the models developed. Both analytical and numerical results are obtained which are highly useful to understand plant behavior.     

BDD-based optimization for the quadratic stable set problem

The quadratic stable set problem (QSSP) is a natural extension of the well-known maximum stable set problem. The QSSP is NP-hard and can be formulated as a binary quadratic program, which makes it an interesting case study to be tackled from different optimization paradigms. In this paper, we propose a novel representation for the QSSP through binary decision diagrams (BDDs) and adapt a hybrid optimization approach which integrates BDDs and mixed-integer programming (MIP) for solving the QSSP. The exact framework highlights the modeling flexibility offered through decision diagrams to handle nonlinear problems. In addition, the hybrid approach leverages two different representations by exploring, in a complementary way, the solution space with BDD and MIP technologies. Machine learning then becomes a valuable component within the method to guide the search mechanisms. In the numerical experiments, the hybrid approach shows to be superior, by at least one order of magnitude, than two leading commercial MIP solvers with quadratic programming capabilities and a semidefinite-based branch-and-bound solver.     

Synthesis and analysis of temporal fault trees with PANDORA: The time of Priority AND gates

Classical Fault Tree Analysis (FTA) can determine the effects of combinations of failure events on a system but cannot capture the significance of the temporal order of events, which may be critical. In this paper, we propose an extension based on formal definition and use of Priority AND gates that enables representation of event sequences and analysis of temporal relationships in FTA. In addition, we show how this type of temporal analysis can be used in conjunction with a recently proposed method for automated fault tree synthesis to allow accurate failure analyses of system models to be carried out efficiently. The approach is demonstrated on a generic system with a shared backup component. The paper tentatively concludes that this type of temporal FTA can provide a more precise and ultimately more correct insight into the failure behaviour of a system.