Sum of Element Orders of Maximal Subgroups of the Symmetric Group

For a finite group G, let ψ(G) denote the sum of element orders of G. The aim of this article is to show that ψ(H) < ψ(A _n ) for every proper subgroup H of the symmetric group of degree n, which is different from the alternating group A _n .     

The Roberts characterization of proper and unit interval graphs

In this note, a constructive proof that the classes of proper interval graphs and unit interval graphs coincide is given, a result originally established by Fred S. Roberts. Additionally, the proof yields a linear-time and space algorithm to compute a unit interval representation, given a proper interval graph as input.     

Essential norm of products of multiplication composition and differentiation operators on weighted Bergman spaces

Let ψ be a holomorphic function on the open unit disk D and φ a holomorphic self-map of D. Let C_φ,M_ψ and D denote the composition, multiplication and differentiation operator, respectively. We find an asymptotic expression for the essential norm of products of these operators on weighted Bergman spaces on the unit disk. This paper is a continuation of our recent paper concerning the boundedness of these operators on weighted Bergman spaces.     

A fast low-pressure transport route to large black phosphorus single crystals

Black phosphorus, a promising candidate for lithium battery electrodes, can be prepared by a low-pressure transport reaction route representing the first effective and scalable access to this element modification. Crystal sizes larger than 1 cm were obtained at low-pressure conditions in silica ampoules. X-ray phase analyses, EDX, ICP-MS and optical microscopy were applied to characterize the resulting black phosphorus. The present method drastically improves the traditional preparation ways like mercury catalysis, bismuth-flux or high-pressure techniques and represents an easy, non-toxic, fast and highly efficient method to achieve black phosphorus. In contrast to a previously reported low-pressure route the present transport reaction allows an up-scaling to higher masses of starting materials, a larger black phosphorus yield and faster reaction time under retention of the high product crystallinity.     

Testing for cointegration using induced-order statistics

In this paper we explore the usefulness of induced-order statistics in the characterization of integrated series and of cointegration relationships. We propose a non-parametric test statistic for testing the null hypothesis of two independent random walks against wide cointegrating alternatives including monotonic nonlinearities and certain types of level shifts in the cointegration relationship. We call our testing device the induced-order Kolmogorov–Smirnov cointegration test (KS), since it is constructed from the induced-order statistics of the series, and we derive its limiting distribution. This non-parametric statistic endows the test with a number of desirable properties: invariance to monotonic transformations of the series, and robustness for the presence of important parameter shifts. By Monte Carlo simulations we analyze the small sample properties of this test. Our simulation results show the robustness of the induced order cointegration test against departures from linear and constant parameter models. This paper is an extension of the work of Aparicio and Granger (1995) and Aparicio and Escribano (1998).     

Functional convergence of stochastic integrals with application to statistical inference

Assuming that {(U_n,V_n)} is a sequence of càdlàg processes converging in distribution to (U,V) in the Skorohod topology, conditions are given under which {?f_n(β,u,v)dU_ndV_n} converges weakly to ?f(β,x,y)dUdV in the space C(R), where f_n(β,u,v) is a sequence of “smooth” functions converging to f(β,u,v). Integrals of this form arise as the objective function for inference about a parameter β in a stochastic model. Convergence of these integrals play a key role in describing the asymptotics of the estimator of β which optimizes the objective function. We illustrate this with a moving average process.     

Boundedness of admissible area function on nonisotropic Lipschitz space

Let be the unit ball in , let be the unit sphere, and let be the admissible area function. In this paper, we show that if , then and there exists a constant such that .

     

一类六参数非协调任意凸四边形单元

本文构造了一类六参数非协调四边形单元,证明由此产生的有限元对任意四边形网格通过Irons分片检查,其收敛效果同Wilson元相当且形状函数的选择不依赖于单元本身。类Wilson元及改进的Wilson任意四边形单元是其中的特例。     

About measures and nodal systems for which the Hermite interpolants uniformly converge to continuous functions on the circle and interval

We obtain the Laurent polynomial of Hermite interpolation on the unit circle for nodal systems more general than those formed by the n-roots of complex numbers with modulus one. Under suitable assumptions for the nodal system, that is, when it is constituted by the zeros of para-orthogonal polynomials with respect to appropriate measures or when it satisfies certain properties, we prove the convergence of the polynomial of Hermite-Fejér interpolation for continuous functions. Moreover, we also study the general Hermite interpolation problem on the unit circle and we obtain a sufficient condition on the interpolation conditions for the derivatives, in order to have uniform convergence for continuous functions.Finally, we obtain some improvements on the Hermite interpolation problems on the interval and for the Hermite trigonometric interpolation.     

非负整数格上元素的性质及其在刻画@-Fuzzy关系方程解集中的作用

首先讨论了非负整数格上元素的性质. 从而完全地刻画了非负整数格上@-Fuzzy关系方程(其中@表示inf-α合成)的解集.