树与色树

给出了色树的两种性质；（１）色树相关联的两个顶点对应的串是色分划的不同色组对应的串；（２）色树顶点的对应串所含链的上等。并应用构造方法证明了任意树都是以树，从而解决了遗留问题。     

New general guidance method in constrained optimal control,part 2: Application to space shuttle guidance

The application and the performance of the neighboring optimal feedback scheme presented in Part 1 of this paper is demonstrated for the heating-constrained cross-range maximization problem of a space-shuttle-orbiter-type vehicle. This problem contains five state variables, two control variables, and a state variable inequality constraint of order zero.This research was supported in part by the Deutsche Forschungsgemeinschaft under the Schwerpunktprogramm Anwendungsbezogene Optimierung und Steuerung.The authors wish to express their sincere and grateful appreciation to Professor Roland Bulirsch who encouraged this work.     

Tree-gel and loop-gel conversions in nonlinear polymerization

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Optimum gas chromatographic conditions in wall-coated capillary columns. Extended and simplified forms of the Golay-equation

Band broadening in capillary columns is satisfactorily described by the Golay-equation extended to situations of appreciable pressure drop by Giddings. In practice, however, several simplifications are often made. The effect of these simplifications on the calculated values of the minimum plate height and optimum carrier gas velocity are treated systematically.     

二组分混合物的最小流化特性 Ⅰ.混合/分离状态与最小流化空隙率

分析了二组分混合物的３种混合／分离状态及在完全混合时发生连续相转变的极限组成。提出一个判别非等密度体系混合／分离状态的法则与确定混合物空隙率简易可行的随意松散堆积方法。     

Equilibrium polymerization in a solvent: Solution on the Bethe lattice

The lattice model for equilibrium polymerization in a solvent proposed by Wheeler and Pfeuty is solved exactly on a Bethe lattice (core of a Caylay tree) with general coordination numberq. Earlier mean-field results are reobtained in the limitq, but the phase diagrams show deviations from them for finiteq. Whenq=2, our results turn into the solution of the one-dimensional problem. Although the model is solved directly, without the use of the correspondence between the equilibrium polymerization model and the diluten0 model, we verified that the latter model may also be solved on the Bethe lattice, its solution being identical to the direct solution in all parameter space. As observed in earlier studies of the puren0 vector model, the free energy is not always convex. We obtain the region of negative susceptibility for our solution and compare this result with mean field and renormalization group (-expansion) calculations.     

Properties of a genetic algorithm extended by a random self-learning operator and asymmetric mutations: A convergence study for a task of powder-pattern indexing

Genetic algorithms represent a powerful global-optimisation tool applicable in solving tasks of high complexity in science, technology, medicine, communication, etc. The usual genetic-algorithm calculation scheme is extended here by introduction of a quadratic self-learning operator, which performs a partial local search for randomly selected representatives of the population. This operator is aimed as a minor deterministic contribution to the (stochastic) genetic search. The population representing the trial solutions is split into two equal subpopulations allowed to exhibit different mutation rates (so called asymmetric mutation). The convergence is studied in detail exploiting a crystallographic-test example of indexing of powder diffraction data of orthorhombic lithium copper oxide, varying such parameters as mutation rates and the learning rate. It is shown through the averaged (over the subpopulation) fitness behaviour, how the genetic diversity in the population depends on the mutation rate of the given subpopulation. Conditions and algorithm parameter values favourable for convergence in the framework of proposed approach are discussed using the results for the mentioned example. Further data are studied with a somewhat modified algorithm using periodically varying mutation rates and a problem-specific operator. The chance of finding the global optimum and the convergence speed are observed to be strongly influenced by the effective mutation level and on the self-learning level. The optimal values of these two parameters are about 6 and 5%, respectively. The periodic changes of mutation rate are found to improve the explorative abilities of the algorithm. The results of the study confirm that the applied methodology leads to improvement of the classical genetic algorithm and, therefore, it is expected to be helpful in constructing of algorithms permitting to solve similar tasks of higher complexity.     

On the Randić Index of Acyclic Conjugated Molecules

The Randić index of an organic molecule whose molecular graph is G is the sum of the weights (d(u)d(v))^−1/2 of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G. We give a sharp lower bound on the Randić index of conjugated trees (trees with a perfect matching) in terms of the number of vertices. A sharp lower bound on the Randić index of trees with a given size of matching is also given Mei Lu: Partially supported by NNSFC (No. 60172005) Lian-zhu Zhang: Partially supported by NNSFC (No. 10271105) Feng Tian: Partially supported by NNSFC (No. 10431020)     

Fast folding and comparison of RNA secondary structures

Summary Computer codes for computation and comparison of RNA secondary structures, the Vienna RNA package, are presented, that are based on dynamic programming algorithms and aim at predictions of structures with minimum free energies as well as at computations of the equilibrium partition functions and base pairing probabilities.An efficient heuristic for the inverse folding problem of RNA is introduced. In addition we present compact and efficient programs for the comparison of RNA secondary structures based on tree editing and alignment.All computer codes are written in ANSI C. They include implementations of modified algorithms on parallel computers with distributed memory. Performance analysis carried out on an Intel Hypercube shows that parallel computing becomes gradually more and more efficient the longer the sequences are.

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Schnelle Faltung und Vergleich von Sekundärstrukturen von RNA

Zusammenfassung Die im Vienna RNA package enthaltenen Computer Programme für die Berechnung und den Vergleich von RNA Sekundärstrukturen werden präsentiert. Ihren Kern bilden Algorithmen zur Vorhersage von Strukturen minimaler Energie sowie zur Berechnung von Zustandssumme und Basenpaarungswahrscheinlichkeiten mittels dynamischer Programmierung.Ein effizienter heuristischer Algorithmus für das inverse Faltungsproblem wird vorgestellt. Darüberhinaus präsentieren wir kompakte und effiziente Programme zum Vergleich von RNA Sekundärstrukturen durch Baum-Editierung und Alignierung.Alle Programme sind in ANSI C geschrieben, darunter auch eine Implementation des Faltungs-algorithmus für Parallelrechner mit verteiltem Speicher. Wie Tests auf einem Intel Hypercube zeigen, wird das Parallelrechnen umso effizienter je länger die Sequenzen sind.

     

结构方程模型在兴安落叶松林生长中的应用

【目的】通过结构方程模型,确定气候、土壤和海拔对兴安落叶松林生长指标的影响以及路径关系。【方法】选取年平均气温、年平均降水量、太阳辐射、土壤全氮含量、土壤有机碳密度和海拔作为影响因素,探究兴安落叶松地上生物量、地下生物量、树高与这些影响因素的关系,并利用AMOS 21.0软件构建衡量兴安落叶松生长的3个指标与气候、土壤和海拔的结构方程模型。【结果】兴安落叶松的地上生物量、地下生物量随着海拔、年平均降水量的增大呈现先增大后减少的趋势,树高随着海拔的增加而增加。地上和地下生物量随着土壤有机碳密度的增加而增加。海拔对兴安落叶松生长的总效应系数为0.200且是正向效应,海拔对兴安落叶松生长的直接效应(0.224)大于间接效应(-0.024);气候因子对兴安落叶松林生长的总影响系数为-0.771且是负向效应;土壤因子对兴安落叶松生长的总影响系数为-0.216,其对兴安落叶松林生长起到一定的抑制作用。【结论】根据结构方程模型的路径系数,气候因子的总影响系数绝对值最大,其次是土壤和海拔,兴安落叶松林静态生长主要受到气候因子的制约。