稀土硫化物的研究进展

稀土硫化物是一类结构复杂、性能丰富、应用广泛的功能材料,在无机颜料、热电材料、光学材料及磁性材料等领域有着独特的优势和广阔的应用前景,是近些年来国际上的研究热点之一.本文总结了稀土硫化物的制备方法及其应用研究进展,对稀土硫化物制备的一些常见方法进行了总结和评述,对稀土硫化物的应用研究进行了总结,重点介绍了γ-稀土倍半硫化物的结构、性能特点以及相应的应用,尤其是它在环保颜料、高温热电材料以及纳米材料等领域中应用;此外,本文对稀土硫化物研究中还存在的一些问题进行了评述,并对未来的相关研究进行了展望.     

Structures and magnetic properties of several novel lanthanide coordination polymers based on thiophene-2,5-dicarboxylic acid

Eight novel lanthanide complexes: {Ln(TDA)1.5(H2O)2}n (Ln = Pr(1a), Nd(2a)) and {Ln(TDA)(Ac)(H2O)}n (Ln = Pr(1), Nd(2), Eu(3), Gd(4), Tb(5), Dy(6); TDA = Thiophene-2,5-dicarboxylic acid anion) have been constructed by hydrothermal reaction. Structural analyses reveal that complexes 1a and 2a belong to the space group C2/c, exhibiting three-dimensional (3D) frameworks. Complexes 1-6 with P21/c space group were prepared in the presence of excessive ammonium acetate, giving rise to interesting 3D frameworks different from those of 1a and 2a. Magnetic property studies of 4-6 reveal the weak antiferromagnetic interaction exists between adjacent Gd3+ in 4. The complex 6 displays rather rare slow magnetization relaxation behavior in 3D frameworks.     

The Arnold cat map, the Ulam method and time reversal

We study the properties of the Arnold cat map on a torus with several periodic sections using the Ulam method. This approach generates a Markov chain with the Ulam matrix approximant. We study numerically the spectrum and eigenstates of this matrix showing their relation with the Fokker-Planck relaxation and the Kolmogorov-Sinai entropy. We show that, in the frame of the Ulam method, the time reversal property of the map is preserved only on a short Ulam time which grows only logarithmically with the matrix size. Parallels with the evolution in a regime of quantum chaos are also discussed.     

关于渐近循环马氏链泛函的强大数定律

研究了一类非齐次马氏链———渐近循环马氏链泛函的强大数定律,首先引出了渐近循环马氏链的概念,然后给出了若干引理.利用了渐近循环马氏链关于状态序偶出现频率的强大数定理给出并证明了关于渐近循环马氏链泛函的强大数定律,所得定理作为推论可得到已有的结果.     

Extremal first passage times for trees

For random walks associated with trees with probability zero of staying at any vertex, we develop explicit graph theoretic formulas for the mean first passage times between states, we give lower and upper bounds for the entries of the mean first passage matrix E, and we characterize the cases of equality in these bounds. We also consider the variance of the first return time to a state and we find those trees which maximize the variance and those trees which minimize the variance. As may be expected, the trees which provide extremal behavior are given by paths and stars.     

树上路径过程的随机路径条件概率的极限性质

本文研究了树上路径过程的极限性质.利用构造鞅的方法得到了树上路径过程的条件概率调和平均的极限性质.所得结果推广了树上非齐次马氏链随机转移概率和任意随机变量序列随机条件概率的调和平均极限性质.     

The infection time of graphs

Consider k particles, 1 red and k-1 white, chasing each other on the nodes of a graph G. If the red one catches one of the white, it “infects” it with its color. The newly red particles are now available to infect more white ones. When is it the case that all white will become red? It turns out that this simple question is an instance of information propagation between random walks and has important applications to mobile computing where a set of mobile hosts acts as an intermediary for the spread of information.In this paper we model this problem by k concurrent random walks, one corresponding to the red particle and k-1 to the white ones. The infection timeT_k of infecting all the white particles with red color is then a random variable that depends on k, the initial position of the particles, the number of nodes and edges of the graph, as well as on the structure of the graph.In this work we develop a set of probabilistic tools that we use to obtain upper bounds on the (worst case w.r.t. initial positions of particles) expected value of T_k for general graphs and important special cases. We easily get that an upper bound on the expected value of T_k is the worst case (over all initial positions) expected meeting timem^* of two random walks multiplied by . We demonstrate that this is, indeed, a tight bound; i.e. there is a graph G (a special case of the “lollipop” graph), a range of values k<n (such that ) and an initial position of particles achieving this bound.When G is a clique or has nice expansion properties, we prove much smaller bounds for T_k. We have evaluated and validated all our results by large scale experiments which we also present and discuss here. In particular, the experiments demonstrate that our analytical results for these expander graphs are tight.