并行最优路径算法及K优路径算法研究

最优路径问题是计算机科学、运筹学、工程设计等领域很多问题的基础。它的应用包括网络路由、电路设计、交通运输、机器人运动规划、事务调度中关键路径的计算以及VLSI设计等。同时，它也为很多最优化问题提供了解决框架，如背包问题、分子生物学中的序列比对、内接多边形的构造和长度受限的霍夫曼编码等都可以转化成最优路径问题进行求解。 求解网络中最优路径的方法可以分为两大类。一种是标号设定算法（label setting ,LS）,另一种是标号改变算法（label correcting ,LC）。由于网络路径算法的应用越来越强调动态性和及时性，使得高效求解最优路径问题变得越来越重要。在这里，我们利用一种高效的网络划分方法，实现了基于网络划分的LS/LC并行算法。实验结果表明，基于这种网络划分的并行算法对于求解最优路径有很好的加速比和扩展比。 在许多更加复杂的应用中，不仅要求计算出最优路径，而且要求给出前K优路径。K优路径是长期研究的泛化最优路径问题，即不但要求得到最优路径，还要得到次短、再次短等路径。 节点s到节点t的K优路径问题可以分为两大类：一类是求解K优非简单路径，即得到的路径可以包含环路；另一类是求解K优简单路径，即路径是简单通路，不包含环路。经过大量学者的研究，求解K优非简单路径相对容易。Fox 于1975年提出了复杂度为O(m+nlogn) 的求解K优非简单路径的算法，最近， Eppstein于1998年给出了一种优化的求解K优非简单路径的算法，时间复杂度达到了O(m+nlogn+k) ，基本上达到了理论下限。 在2000年对E 的算法进行并行化，时间复杂度为 。求解K优简单路径已被证明是更为具有挑战性，这个问题最先由Hofman和Pavley 在1957年进行开始研究，但几乎所有试图解决该问题的算法时间复杂度都达到指数时间。众所周知，Yen提出了一结果比较好的算法，利用现代的数据结构达到O(kn(n+nlogn)) 时间复杂度。John Hershberger于2007年给出了一个新的求K优路径的算法，该算法基于有效率的替代路径算法,相对于以前的替代路径算法，其加速比可达到O(n) 。在本文中，我们基于John Hershberger给出的K优路径算法，尝试给出其并行的方法，并在SMP的高性能计算机上进行了测试。 关键词 并行算法、最优路径、K优路径、网络划分

Cinnamate-Functionalized Poly(ester-carbonate): Synthesis and Its UV Irradiation-Induced Photo-Crosslinking

A functionalized. cyclic carbonate monomer containing a cinnamate moiety, 5-methyl-5-cinnamoyloxymethyl-1,3-dioxan-2-one (MC), was prepared for the first time with 1,1,1-tri(hydroxymethyl) ethane as a starting material. Subsequent polymerization of the new cyclic carbonate and its copolymerization with L-lactide (LA) were successfully performed with diethyl zinc (ZnEt2) as initiator/catalyst. NMR was used for microstructure identification of the obtained monomer and copolymers. Differential scanning calorimetry (DSC) was used to characterize the functionalized poly(ester-carbonate). The results indicated that the copolymers displayed a single glass transition temperature (T-g) and the T, decreased with increasing carbonate content and followed the Fox equation, indicative of a random microstructure of the copolymer. The photo-crosslinking of the cinnamate-carrying copolymer was also demonstrated.

Thermal and crystalline properties of random copolymer of CL and DTC prepared by La(OAr)(3)

Thermal and crystalline properties of random copolymer of epsilon-caprolactone (CL) and 2,2-dimethyl trimethylene carbonate (DTC) prepared by lanthanum tris(2,6-di-tert-butyl-4-methylphenolate) (La(OAr)(3)) have been investigated by differential scanning calorimetry (DSC), thermogravimetric analysis (TG) and wide-angle X-ray diffraction (WAXD). Fox equation interprets the relationship between glass transition temperature (T-g) and copolymer compositions. T-g decreases from PDTC (16.7degreesC) to PCL (-65.1degreesC), reflecting the internal plasticizing effect of CL units on DTC units in the copolymers. The introduction of CL units to PDTC can effectively improve its heat resistance. Small amount of DTC (5% molar) in PCL chain improves the mechanical properties of the polymer, which had elongation of 1000, much higher than that of PCL (8.8).

Pressure-dependent glass-transition temperatures of poly(methyl methacrylate)/poly(styrene-co-acrylonitrile) blends

The pressure-dependent glass-transition temperatures (T-g's) of poly(methyl methacrylate) (PMMA)/poly(styrene-co-acrylonitrile) (SAN) blends were determined by pressure-volume-temperature (PVT) dilatometry via an isobaric cooling procedure. The Gordon-Taylor and Fox equations were used to evaluate the relationships between the T-g's and compositions of the PMMA/SAN system at different pressures. The relationships were well fitted by the Gordon-Taylor equation, and the experimental data for T-g positively deviated from the values calculated with the Fox equation. Also, the influence of the cooling rate (during the PVT measurements) on T-g was examined.

Chain conformation of a high-performance polyimide in organic solution

An organo-soluble polyimide based on 1,4-bis(3,4-dicarboxyphenoxy) benzene dianhydride (HQDPA) and 2,2'dimethyl-4,4'-methylene dianiline (DMMDA), was synthesized via two-step polycondensation accompanied by chemical imidization. Five fractions were prepared by fractionation. The dilute solutions of the fractions were studied by LLS (Laser Light Scattering) and the intrinsic viscosities of the fractions were measured. The unperturbed dimension was determined by the intrinsic viscosity with the Stockmayer-Fox equation. The results indicate that the polyimide in this study has a flexible chain conformation in chloroform and N,N-dimethyl acetamide (DMAc). However, the degree of chain expansion differs in different solvents. (C) 1998 Published by Elsevier Science Ltd. All rights reserved.

Effects of molecular weight and interaction parameter on the glass transition temperature of polystyrene mixtures and its blends with polystyrene/poly(2,6-dimethyl-p-phenylene oxide)

The glass transition temperature (T-g) of mixtures of polystyrene (PS) with different molecular weight and of blends of poly(2,6-dimethyl-p-phenylene oxide) (PPO) and polystyrene with different molecular weight (DMWPS) was studied by a DSC method. For the whole range of composition, the curves of T-g vs composition obtained by experiment were compared with predictions from the Fox, Gordon-Taylor, Couchman and Lu-Weiss, equations. It was found that the experimental results were not in agreement with those from the Fox, Gordon-TayIor and Couchman equations for the binary mixtures of DMWPS, where the interaction parameter chi was approximately zero. However, for the blends PPO/DMWPS (chi < 0), with an increase of molecular weight of PS, it was shown that the experimental results fitted well with those obtained from the Couchman, Gordon-Taylor and Fox equations, respectively. Furthermore, the Gordon-Taylor equation was nearly identical to the Lu-Weiss equation when \chi\ was not very large. Further, the dependence of the change of heat capacity associated with the glass transition (Delta C-p) on the molecular weight of PS was investigated and an empirical equation was presented. (C) 1997 Elsevier Science Ltd.

Study on the structure and miscibility of PBPI-E/PTI-E blends

The crystallization, miscibility and structure of polyimide PBPI-E/PTI-E blends were studied by DSC, DMA, NMR and fluorescence techniques, where PBPI-E is a biphenyldianhydride-based polyimide, and PTI-E is a polyimide from 4,4'-thiodiphthalic anhydride and 4,4'-oxydianiline. The results obtained show that PBPI-E/PTI-E blends are miscible at a molecular level for all the compositions studied. However, the glass transition temperature of the blends is well below the value predicted by the Fox equation, and the blends are not stable at high temperature, i.e. phase separation will occur when the blends are annealed about T-g. Moreover, the melting point T-m, differential enthalpy Delta H and spin-lattice relaxation time T-l(c) of the blends increase with the annealing time. (C) 1997 Elsevier Science Ltd. All rights reserved.

GLASS-TRANSITION TEMPERATURE AND MOLECULAR-PARAMETERS OF POLYMER

A new relationship, which correlates the glass transition temperature (T(g)) with other molecular parameters, is developed by using Flory's lattice statistics of polymer chain and taking the dynamic segment as the basic statistical unit. The dependences of T(g) on the chain stiffness factor (sigma-2), dynamic stiffness factor (beta = -d ln-sigma-2/dT) and molecular weight of polymer are discussed in detail based on the theory. The theory is compared with experimental data for many linear polymers and good agreement is obtained. It is shown that T(g) is essentially governed by the chain stiffness factor at T(g). Moreover, a simple correlation between the parameter K(g) of the Fox-Flory equation (T(g) = T(g)infinity - K(g)/M(n)) and other molecular parameters is deduced. The agreement between theoretical predictions and experimental measurements of K(g) has been found to be satisfactory for many polymers.

聚环氧乙烷(PE0)与聚双酚A羟基醚(PBHE)共混体系的研究

用偏光显微镜(PLM)、扭辫(TBA)、IR及WAXD对PEO/PBHE共混体系结晶形态进行了研究。结果表明,PEO含量在50％以上的共混体系,几乎完全被PEO球晶充满,非晶态PBHE作为微区分散在大球晶之间或球晶之中。PEO含量为40％和30％的照片上呈现树枝晶。PEO含量为20％以下时照片中不再看到结晶出现,PEO与PBHE形成单一非晶相。PEO/PBHE共混体系的组分之间存在着氢键相互作用,这种作用强于PBHE分子间的氢键作用。共混体系的结晶度及T_g随PBHE组分含量的增加,前者减小后者增加并符合FOX方程揭示的规律。PEO与PBHE具有很好的相容性。

Reproduction and behavior of plateau pikas (Ochotona curzoniae Hodgson) under predation risk: A field experiment

The mixture of the feces and urine of the red fox (Vulpes vulpes Linnaeus) was used to increase the perception of predation risk of plateau pikas (Ochotona curzoniae Hodgson) in the field. The influence of the predation risk on the reproduction and behavior of plateau pikas was examined through comparing reproductive characteristics and five different kinds of behavior between treatment and control plots. The results showed that 1) the body weight of the pikas was not significantly different between treatment and control plots. 2) The reproductive period of the pikas extended from March to later August in both treatment and control plots. The pregnant ratio, developed testes ratio, reproductive success and sex ratio of the pikas were not significantly different between the treatment and control plots. 3) The pikas increased their observing and calling frequencies and decreased their moving and feeding frequencies when exposed to red fox's feces and urine. 4) The increased red fox's feces and urine had no influence on the behavior of the pikas when the number of their natural enemies increased; the pikas obviously increased the observing frequencies and sharply decreased the calling frequency so as to decrease the direct predation risk. 5) There were no significantly behavioral differences between males and females as well as between adults and young. 6) The results reject the hypothesis 1 that the red fox's feces and urine as indirect predation risk suppresses the reproduction of the pikas and support the hypothesis 2 that the pikas can make decision by changing behavior to avoid the predation risk they encountered whenever.