静止水滴真空闪蒸模型及实验研究

本文建立了描述真空制取二元冰过程中静止水滴的传热传质模型,研究冰晶形成过程的结晶成核与生长现象及其影响因素。设计并建立了一种可视化的真空制冰系统,清晰地展示了静态水滴成核结冰时液态蒸发、伴随气泡生长的蒸发、稳态蒸发结冰、伴随气泡生长的结冰、外部结冰内部气泡逸出最终爆裂的五种形态;利用所设计的二元冰真空制备装置进行冰晶的生成实验研究,分析讨论各种因素对二元冰真空制备的影响,并通过实验对照比较来证明模型的可靠性。     

空间微小碎片累积撞击损伤效应加速模拟研究

利用等离子体驱动微小碎片加速器对太阳同步轨道上太阳电池在轨10年遭遇微小碎片超高速撞击的累积损伤效应进行了加速模拟, 获得了电池性能参数的损伤结果, 并与所建立的损伤评估模型的预测结果进行了分析比较, 二者基本一致.     

冰的熔解热实验中冰水质量比的探讨

冰与温水质量比对冰的熔解热实验的成败起着关键作用。文章对冰水质量比进行测量和分析,得出了冰的熔解热实验中最适合的冰水质量比的范围约为1／12-1／5。     

Strong embeddings of minimum genus

A “folklore conjecture, probably due to Tutte” (as described in [P.D. Seymour, Sums of circuits, in: Graph Theory and Related Topics (Proc. Conf., Univ. Waterloo, 1977), Academic Press, 1979, pp. 341-355]) asserts that every bridgeless cubic graph can be embedded on a surface of its own genus in such a way that the face boundaries are cycles of the graph. Sporadic counterexamples to this conjecture have been known since the late 1970s. In this paper we consider closed 2-cell embeddings of graphs and show that certain (cubic) graphs (of any fixed genus) have closed 2-cell embedding only in surfaces whose genus is very large (proportional to the order of these graphs), thus providing a plethora of strong counterexamples to the above conjecture. The main result yielding such counterexamples may be of independent interest.     

Regular path decompositions of odd regular graphs

Kotzig asked in 1979 what are necessary and sufficient conditions for a d‐regular simple graph to admit a decomposition into paths of length d for odd d>3. For cubic graphs, the existence of a 1‐factor is both necessary and sufficient. Even more, each 1‐factor is extendable to a decomposition of the graph into paths of length 3 where the middle edges of the paths coincide with the 1‐factor. We conjecture that existence of a 1‐factor is indeed a sufficient condition for Kotzig's problem. For general odd regular graphs, most 1‐factors appear to be extendable and we show that for the family of simple 5‐regular graphs with no cycles of length 4, all 1‐factors are extendable. However, for d>3 we found infinite families of d‐regular simple graphs with non‐extendable 1‐factors. Few authors have studied the decompositions of general regular graphs. We present examples and open problems; in particular, we conjecture that in planar 5‐regular graphs all 1‐factors are extendable. © 2009 Wiley Periodicals, Inc. J Graph Theory 63: 114–128, 2010     

Crown reductions for the Minimum Weighted Vertex Cover problem

The paper studies crown reductions for the Minimum Weighted Vertex Cover problem introduced recently in the unweighted case by Fellows et al. [Blow-Ups, Win/Win's and crown rules: some new directions in FPT, in: Proceedings of the 29th International Workshop on Graph Theoretic Concepts in Computer Science (WG’03), Lecture notes in computer science, vol. 2880, 2003, pp. 1-12, Kernelization algorithms for the vertex cover problem: theory and experiments, in: Proceedings of the Workshop on Algorithm Engineering and Experiments (ALENEX), New Orleans, Louisiana, January 2004, pp. 62-69]. We describe in detail a close relation of crown reductions to Nemhauser and Trotter reductions that are based on the linear programming relaxation of the problem. We introduce and study the so-called strong crown reductions, suitable for finding (or counting) all minimum vertex covers, or finding a minimum vertex cover under some additional constraints. It is described how crown decompositions and strong crown decompositions suitable for such problems can be computed in polynomial time. For weighted König-Egerváry graphs (G,w) we observe that the set of vertices belonging to all minimum vertex covers, and the set of vertices belonging to no minimum vertex covers, can be efficiently computed.Further, for some specific classes of graphs, simple algorithms for the MIN-VC problem with a constant approximation factor r<2 are provided. On the other hand, we conclude that for the regular graphs, or for the Hamiltonian connected graphs, the problem is as hard to approximate as for general graphs.It is demonstrated how the results about strong crown reductions can be used to achieve a linear size problem kernel for some related vertex cover problems.     

The structure of matrices with a maximum multiplicity eigenvalue

There is remarkable and distinctive structure among Hermitian matrices, whose graph is a given tree T and that have an eigenvalue of multiplicity that is a maximum for T. Among such structure, we give several new results: (1) no vertex of T may be “neutral”; (2) neutral vertices may occur if the largest multiplicity is less than the maximum; (3) every Parter vertex has at least two downer branches; (4) removal of a Parter vertex changes the status of no other vertex; and (5) every set of Parter vertices forms a Parter set. Statements (3), (4) and (5) are also not generally true when the multiplicity is less than the maximum. Some of our results are used to give further insights into prior results, and both the review of necessary background and the development of new structural lemmas may be of independent interest.     

Fuzzy minimum weight edge covering problem

Minimum weight edge covering problem, known as a classic problem in graph theory, is employed in many scientific and engineering applications. In the applications, the weight may denote cost, time, or opponent’s payoff, which can be vague in practice. This paper considers the edge covering problem under fuzzy environment, and formulates three models which are expected minimum weight edge cover model, α-minimum weight edge cover model, and the most minimum weight edge cover model. As an extension for the models, we respectively introduce the crisp equivalent of each model in the case that the weights are independent trapezoidal fuzzy variables. Due to the complexity of the problem, a hybrid intelligent algorithm is employed to solve the models, which can deal with the problem with any type of fuzzy weights. At last, some numerical experiments are given to show the application of the models and the robustness of the algorithm.     

Universal abelian covers of superisolated singularities

We give explicit examples of Gorenstein surface singularities with integral homology sphere link, which are not complete intersections. Their existence was shown by Luengo–Velasco, Melle–Hernández and Némethi, thereby providing counterexamples to the universal abelian covering conjecture of Neumann and Wahl (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Valid inequalities for the single-item capacitated lot sizing problem with step-wise costs

This paper presents a new class of valid inequalities for the single-item capacitated lot sizing problem with step-wise production costs (LS-SW). Constant sized batch production is carried out with a limited production capacity in order to satisfy the customer demand over a finite horizon. A new class of valid inequalities we call mixed flow cover, is derived from the existing integer flow cover inequalities by a lifting procedure. The lifting coefficients are sequence independent when the batch sizes (V) and the production capacities (P) are constant and when V divides P. When the restriction of the divisibility is removed, the lifting coefficients are shown to be sequence independent. We identify some cases where the mixed flow cover inequalities are facet defining. We propose a cutting plane algorithm for different classes of valid inequalities introduced in the paper. The exact separation algorithm proposed for the constant capacitated case runs in polynomial time. Computational results show the efficiency of the new class mixed flow cover compared to the existing methods.