Asymptotics of convolution with the semi-regular-variation tail and its application to risk

In this paper, according to a certain criterion, we divide the exponential distribution class into some subclasses. One of them is closely related to the regular-variation-tailed distribution class, and is called the semi-regular-variation-tailed distribution class. The new class possesses several nice properties, although distributions in it are not convolution equivalent. We give the precise tail asymptotic expression of convolutions of these distributions, and prove that the class is closed under convolution. In addition, we do not need to require the corresponding random variables to be identically distributed. Finally, we apply these results to a discrete time risk model with stochastic returns, and obtain the precise asymptotic estimation of the finite time ruin probability.     

Empirical likelihood for median regression model with designed censoring variables

We propose a new and simple estimating equation for the parameters in median regression models with designed censoring variables, and then apply the empirical log likelihood ratio statistic to construct confidence region for the parameters. The empirical log likelihood ratio statistic is shown to have a standard chi-square distribution, which makes this method easy to implement. At the same time, another empirical log likelihood ratio statistic is proposed based on an existing estimating equation and the limiting distribution of the empirical likelihood ratio statistic is shown to be a sum of weighted chi-square distributions. We compare the performance of the empirical likelihood confidence region based on the new estimating equation, with that based on the existing estimating equation and a normal approximation method by simulation studies.     

Hybrid materials covalently incorporated with isophorone-based dyes through sol-gel process for nonlinear optical applications

Two new push-pull type second-order nonlinear optical (NLO) active isophorone-based alkoxysilane dyes with the same acceptor were synthesized and characterized. One silane (ICTES-HEMA) bears a chromophore with a hydroxyethyl methylamino donor and the other silane (ICTES-HMPP) is a bulkier analogue with a hydroxymethyl diphenylamino donor. Transparent, homogeneous films were prepared via the copolymerization of tetraalkoxysilane (TEOS) and different NLO silanes with the ratio of 5:1. The d(33) values obtained for the HEMA and HMPP films are 46.3 and 20.6 pm/V, respectively. Normalized UV-vis spectra reveal that the introduction of a diaryl group would help to prevent unfavorable organization of the chromophores. The reorientation dynamic stabilities of the samples were studied by second-harmonic generation (SHG) measurements, demonstrating that bulkier chromophores incorporated in sol-gel materials would not necessarily lead to higher stabilities over time.     

Observation of two new N* peaks in J/psi-->ppi-n and ppi+n decays

The decay J/psi-->NNpi provides an effective isospin 1/2 filter for the piN system due to isospin conservation. Using 58x10(6) J/psi decays collected with the Beijing Electromagnetic Spectrometer at the Beijing Electron Positron Collider, more than 100 thousand J/psi-->ppi-n+c.c. events are obtained. Besides the two well-known N* peaks at around 1500 MeV/c2 and 1670 MeV/c2, there are two new, clear N* peaks in the ppi invariant mass spectrum around 1360 MeV/c2 and 2030 MeV/c2 with statistical significance of 11sigma and 13sigma, respectively. We identify these as the first direct observation of the N*(1440) peak and a long-sought missing N* peak above 2 GeV/c2 in the piN invariant mass spectrum.     

Small prime solutions of a pair of linear equations in five prime variables

Assume an additional congruent condition on the coefficients. We prove that the pair 5 of linear equations ∑j=1^5 αλjpj = bλ （λ= 1, 2） has solutions in primes pj satisfying pj 〈〈 （｜b1｜＋｜b2｜＋1） maxλ,j ｜αλj｜^2318＋ε. This improves the exponent 79680 without assuming the additional condition of the second author＇s.     

Automorphism group and representation of a twisted multi-loop algebra

Let G be the complexification of the real Lie algebra so（3） and A = C[t1^±1, t2^±1] be the Lau-ent polynomial algebra with commuting variables. Let L：（t1, t2, 1） = G c .A be the twisted multi-loop Lie algebra. Recently we have studied the universal central extension, derivations and its vertex operator representations. In the present paper we study the automorphism group and bosonic representations ofL（t1, t2, 1）.     

On invariant sets in Lagrangian graphs

In this exposition, we show that the Hamiltonian is always constant on a compact invariant connected subset which lies in a Lagrangian graph provided that the Hamiltonian and the graph are sufficiently smooth. We also provide some counterexamples to show that if the Hamiltonian function is not smooth enough, then it may be non-constant on a compact invariant connected subset which lies in a Lagrangian graph.     

拟-Armendariz模

For a right R-module N, we introduce the quasi-Armendariz modules which are a common generalization of the Armendariz modules and the quasi-Armendariz rings, and investigate their properties. Moreover, we prove that NR is quasi-Armendariz if and only if Mm(N)Mm(R) is quasi-Armendariz if and only if Tm(N)Tm(R) is quasi-Armendariz, where Mm(N) and Tm(N) denote the m×m full matrix and the m×m upper triangular matrix over N, respectively. NR is quasi-Armendariz if and only if N[x]R[x] is quasi-Armendariz. It is shown that every quasi-Baer module is quasi-Armendariz module.     

Isochronicity Problem of Higher-Order Singular Point for Polynomial Differential Systems

Due to the difficulty, the isochronicity problems with respect to higher-order singular point (or degenerate singular point) of polynomial differential systems are far from being solved. The calculation of period constants is an effective way to find necessary conditions for isochronicity. In this paper, by means of a homeomorphic transformation, higher-order singular point is transferred into the origin. At the same time, a new recursive algorithm to compute period constants at the origin of the transformed system is deduced which is easy to realize with the computer algebraic system such as MATHEMATICA or MAPLE. Finally, to illustrate the effectiveness of our algorithm, the pseudo-isochronous center conditions of higher-order singular point for a class of septic system are investigated. Our work is new in terms of research about the isochronicity problem of higher-order singular point and consists of the existing results related to the origin as a special case when it is an elementary singular point.     

Inverse Coefficient Problems for Elliptic Hemivariational Inequalities

This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic hemivariational inequalities. The unknown coefficient of elliptic hemivariational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic hemivariational inequalities are uniquely solvable for the given class of coefficients. The result of existence of quasisolutions of the inverse problems is obtained.