On the order supergraph of the power graph of a finite group

Ricerche di Matematica - The power graph $${\mathcal {P}}_{G}$$ of a finite group G is the graph whose vertex set is G, two distinct vertices are adjacent if one is a power of the other. The order...     

LaSrBO4型复合氧化物的合成及其CO氧化活性研究

LaSrBO4(B=Cu、Ni、 Co、 Fe、 Mn、 Cr ) was studied with respect to their preparation, characteristics and catalytic oxidation activity by means of XRD, XPS, electric conductivity and activity evaluation. Results showed that the calcination temperature has great influence on the formation of the phases of such samples, and was associated with the radius of B ion. The greater the B ion radius, the higher the calcination temperature required for the formation of the phases. It was also found that the activity and the relative content of adsorptive oxygen and lattice oxygen on the sample surf are, the activation energy of electron conduction and the CO oxidation activity may vary with different B ions, and demonstrate a dual-peak pattern with the increase in the number of 3d electrons of the B ion.     

Parametric modelling of Poisson-Gaussian random matrix ensembles

We analyse a scheme of transition from the Poissonian statistics for quantum levels to the Gaussian one of random matrix ensembles in the framework of level dynamics discussed by Yukawa. We propose a means of connecting these two limiting statistics by showing a result that Yukawa's parameter / of the exponential family can be efficiently replaced by the ratio <E>/<Q> which reflects directly a degree of the eigenvalue correlations of each sample matrix in the ensemble. On this basis, we discuss a correspondence between the level statistics of a generic quantum system and its classical regular/chaotic dynamics in terms of the semiclassical power spectrum and its second moment formulated by Feingold-Peres and Prosen-Robnik. We also discuss some limiting proceduresN (infinite limit of the matrix dimension) pertinent to the Gaussian ensembles, and remark about the possibility offractional power law of Brody's type.     

A Construction of Partial Difference Sets in {\mathbb{Z}}_{p^{2 \times } } {\mathbb{Z}}_{p^{2 \times \cdot \cdot \cdot \times } } {\mathbb{Z}}_{p^2 }

In this paper, we give a construction of partial difference sets in _p ² x _p ² x ... x _p ²using some finite local rings.Dedicated to Hanfried Lenz on the occasion of his 80th birthdayThe work of this paper was done when the authors visited the University of Hong Kong.     

A finiteness theorem for maximal independent sets

Denote bymi(G) the number of maximal independent sets ofG. This paper studies the setS(k) of all graphsG withmi(G) = k and without isolated vertices (exceptG K ₁) or duplicated vertices. We determineS(1), S(2), andS(3) and prove that |V(G)| 2 ^k–1 +k – 2 for anyG inS(k) andk 2; consequently,S(k) is finite for anyk. Supported in part by the National Science Council under grant NSC 83-0208-M009-050