On spanning tree problems with multiple objectives

We investigate two versions of multiple objective minimum spanning tree problems defined on a network with vectorial weights. First, we want to minimize the maximum ofQ linear objective functions taken over the set of all spanning trees (max-linear spanning tree problem, ML-ST). Secondly, we look for efficient spanning trees (multi-criteria spanning tree problem, MC-ST).Problem ML-ST is shown to be NP-complete. An exact algorithm which is based on ranking is presented. The procedure can also be used as an approximation scheme. For solving the bicriterion MC-ST, which in the worst case may have an exponential number of efficient trees, a two-phase procedure is presented. Based on the computation of extremal efficient spanning trees we use neighbourhood search to determine a sequence of solutions with the property that the distance between two consecutive solutions is less than a given accuracy.Partially supported by Deutsche Forschungsgemeinschaft and HCº Contract no. ERBCHRXCT 930087.Partially supported by Alexander von Humboldt-Stiftung.     

认购证发行总数的估计

利用发行的认购证有编号１，２，……，Ｎ，，本文通过随机抽取的几个认购证号码，给出了认购证发行总数的最大似然估计，一致最小方差无偏估计和Ｂａｙｅｓ估计。     

Calculus of variations as a basic tool for modelling of reaction paths and localisation of stationary points on potential energy surfaces

ABSTRACT

The theory of calculus of variations is a mathematical tool which is widely used in different scientific areas in particular in physics and chemistry. This theory is strongly related with optimisation. In fact the former seeks to optimise an integral related with some physical magnitude over some space to an extremum by varying a function of the coordinates. On the other hand, reaction paths and potential energy surfaces, in particular their stationary points, are the basis of many chemical theories, in particular reactions rate theories. We present a review where it is gathered together the variational nature of many types of reaction paths: steepest descent, Newton trajectories, artificial force induced reaction (AFIR) paths, gradient extremals, and gentlest ascent dynamics (GAD) curves. The variational basis permits to select the best optimisation technique in order to locate important theoretical objects on a potential energy surface.     

Properties of the skeleton of aggregates grown on a Cayley tree

We discuss and analyze a family of trees grown on a Cayley tree, that allows for a variable exponent in the expression for the mass as a function of chemical distance, M(l)l ^dl . For the suggested model, the corresponding exponent for the mass of the skeleton,d _l ^s , can be expressed in terms ofd _l asd _l ^s = 1,d _l d _l ^c = 2;d _l ^s = d _l –1,d ₁ d _l ^c = 2, which implies that the tree is finitely ramified ford _l 2 and infinitely ramified whend _l 2. Our results are derived using a recursion relation that takes advantage of the one-dimensional nature of the problem. We also present results for the diffusion exponents and probability of return to the origin of a random walk on these trees.     

热质的运动和传递-最低热质能耗散原理和热质运动方程

过增元基于质能方程提出了热质的概念.在非平衡热力学中,存在最低能量耗散原理,根据该原理可以导出热传导,扩散及粘性流动等不可逆输运过程的方程式.当采用热质模型对传热现象进行描述时,发现热质的运动也满足最小作用量原理:最低热质能耗散原理,根据该原理可以推导得出热质运动的动量守恒方程。     

Phase diagrams of Ising models on Husimi trees II. Pair Wand multisite interaction systems

We continue an earlier study of multisite interaction Ising spin models on Husimi trees. In particular, attention is given to systems with both a nearestneighbor pair interaction and three-site interactions. We use our calculations of the phase diagrams of the systems on Husimi trees as approximations of systems with the same interactions but on a regular lattice, e.g., the triangle lattice. Specific models where exact results are available are used as test cases. All of the work involves computation of quantities, such as the magnetization, by iterative processes. Hence we are dealing with a discrete map and for certain values of the interaction strengths we obtain for the magnetization diagram results involving period doubling, chaos, period-three windows, etc., all phenomena of recent interest in connection with dynamical systems and now associated with certain Ising spin systems.     

基于最小电压法的超声换能器谐振频率自动跟踪*

首先分析了最大电流法跟踪超声换能器谐振频率的原理及应用范围。研究了基于由串联电感和并联电容匹配电路下,不同频率时换能器两端电压电流的变化规律。研究表明在串联电感和并联电容匹配电路下发生谐振时,换能器两端的电压最小而电流并非最大。由此形成了采用最小电压法跟踪谐振频率的自动跟踪策略,并给出了该方法的具体实施步骤。论文研究结果为换能器谐振频率的自动跟踪方法提供了新的选择。     

介质膜滤波器色散特性的研究

采用信号处理的方法,对介质膜滤波器的滤波特性进行了详细的研究。介质膜滤波器是最小相位滤波器,它的幅度响应与相位响应之间存在希尔伯特变换规律,因此可以通过它的幅度响应重构它的相位响应,进而可以得到它的色散特性。为了验证理论分析,设计了射频调制法测试介质膜滤波器群速度延时的实验装置。实验测试了一个100GHz33信道的介质膜滤波器的群速度延迟。通过对实验结果与理论计算结果的对比分析,发现实验数据与理论分析吻合得比较好。最后,对介质膜滤波器的色散的特点进行了分析。     

直视型微光夜视系统最小可分辨对比度模型

从信号检测和人眼视觉角度出发,研究了直视微光夜视系统综合性能评估理论,推导出直视型微光成像系统的MRC（最小可分辨对比度）模型。该模型将光学传递特性与系统信噪比结合,建立了系统直视微光夜视MRC与目标特性、直视微光夜视仪以及人眼各部分参数之间的数学关系。验证结果表明,由该模型得到的系统极限分辨率相较于系统实际测出的分辨率相对误差为3.08%。     

Establishment of hybrid-derived offspring populations in the Ohomopterus ground beetles through unidirectional hybridization

An approach to deduce the mechanism of stabilization of the hybrid-derived populations in the Ohomopterus ground beetles has been made by comparative studies on the phylogenetic trees of the mitochondrial and nuclear DNA. A phylogenetic tree based on the internal transcribed spacer (ITS) of nuclear ribosomal gene roughly reflects the relations of morphological species group, while mitochondrial NADH dehydrogenase subunit 5 (ND5) gene shows a considerable different topology on the tree; there exist several geographically-linked lineages, most of which consist of more than one species. These results suggest that the replacement of mitochondria has occurred widely in the Ohomopterus species. In most cases, hybridization is unidirectional, i.e., the species A (♂) hybridized with another species B (♀) and not vice versa, with accompanied replacement of mitochondria of A by those of B. The results also suggest that partial or complete occupation of the distribution territory by a hybrid-derived morphological species. The morphological appearance of the resultant hybrid-derivatives are recognized as that of the original species A. Emergence of a morphological new species from a hybrid-derived population has been exemplified.