The asymptotic estimate for the sum of two correlated classes of discounted aggregate claims with heavy tails

Consider a risk model with two correlated classes of insurance business and a constant force of interest. We assume that the correlation comes from a common shock and that the claim-size distribution is heavy-tailed. Under this setting, we investigate the tail behavior of the sum of the two correlated classes of discounted aggregate claims. We obtain the uniform asymptotic formulas for some subclass of subexponential distributions.     

近似良紧空间的相对可乘性

文[2]江守礼、李进金定义了相对乘积空间，使不同的LF空间可以进行乘积运算．本文利用广义Zadeh型函数讨论近似良紧空间的相对可乘性，使得文[5]和[6]的一些结论是本文的推论．     

时变观测算子族的无限时容许性

对Hilbert空间中的无界时变观测算子族引入无限时容许性概念,并利用发展半群理论,给出无界时变观测算子族的无限时容许性刻画.最后,对一类具混合边界条件的非自治系统,构造了一类无限时容许观测算子族.     

Strong approximation for the general Kesten-Spitzer random walk in independent random scenery

This paper is to prove that, if a one-dimensional random wa lkcan be approximated by a Brownian motion, then the related random walk in a g eneral independent scenery can be approximated by a Brownian motion in Brownian scenery.     

A hybrid two-stage transportation and batch scheduling problem

We study the coordinated scheduling problem of hybrid batch production on a single batching machine and two-stage transportation connecting the production, where there is a crane available in the first-stage transportation that transports jobs from the warehouse to the machine and there is a vehicle available in the second-stage transportation to deliver jobs from the machine to the customer. As the job to be carried out is big and heavy in the steel industry, it is reasonable assumed that both the crane and the vehicle have unit capacity. The batching machine processes a batch of jobs simultaneously. Each batch occur a setup cost. The objective is to minimize the sum of the makespan and the total setup cost. We prove that this problem is strongly NP-hard. A polynomial time algorithm is proposed for a case where the job transportation times are identical on the crane or the vehicle. An efficient heuristic algorithm for the general problem is constructed and its tight worst-case bound is analyzed. In order to further verify the performance of the proposed heuristics, we develop a lower bound on the optimal objective function. Computational experiments show that the heuristic algorithm performs well on randomly generated problem instances.     

Self‐Assembly and Structural Evolvement of Polyoxometalate‐Anchored Dendron Complexes

A cationic dendritic molecule that has alkyl chains has been synthesized and employed to encapsulate anionic polyoxometalates through electrostatic interactions. The prepared surfactant‐encapsulated polyoxometalate (SEP) complexes were used as building blocks to fabricate self‐assemblies in solution and the solid state. Monodispersion, lamellar, and columnar assemblies of SEP complexes have been characterized in detail. With increasing the number of peripheral cationic dendrons on inorganic clusters, the SEPs undergo changes from globular assemblies to monodispersions in solution and from lamellar assemblies to hexagonal columnar structures in the solid state, depending on the amounts of cationic dendrons in the complexes. The structural evolvement was simulated through consideration of the size and shape of the cationic dendron and polyanionic clusters, and the experimental results are in good agreement with the interpretation of the simulations. The present research demonstrates a new kind of dendritic complex and provides a route for controlling their assembling states by simply alternating the number of cationic dendrons in the complexes.     

Thermo‐ and Acid‐Responsive Photochromic Spironaphthoxazine‐Containing Organogelators

A series of photochromic spironaphthoxazine derivatives has been designed, synthesized, and characterized by using ¹H NMR spectroscopy, FAB mass spectrometry, and elemental analysis. Their photophysical and photochromic behavior have been investigated. Two of the compounds (G¹²‐en‐SA‐SO and G¹⁶‐en‐SA‐SO) have been shown to be capable of forming stable thermoreversible organogels in organic solvents, tested by the “stable‐to‐inversion of a test tube” method. Addition of p‐toluenesulfonic acid was found to induce the formation of stable organogels at concentrations below that of the critical gelation concentration (c.g.c.), with a concomitant change in color from colorless to purple. Transmission electron microscopy and scanning electron microscopy of the xerogels showed typical fibrous structures in the micrometer scale. The activation parameters for the bleaching reaction of G⁸‐en‐SA‐SO in the solution state and G¹⁶‐en‐SA‐SO in the gel state have been determined in ethanol through kinetic studies at various temperatures. The results showed that the rate of the bleaching reaction in the gel state was much slower than that in the solution state.     

新型室温酯化法接枝聚合物改性SiO_2纳米微粒

提出了一种在室温、大气环境等温和条件下通过酯化反应将端羧基聚合物链接枝到纳米SiO2微球表面从而制备有机/无机复合纳米微粒的新方法.该方法通过以下两个步骤得以实现,即第一,用3-环氧丙基三甲氧基硅烷对纳米SiO2微球表面进行改性处理,接着将引入到纳米SiO2表面的环氧基团转化为烷羟基基团;第二,通过引入到纳米SiO2微球表面的烷羟基与聚合物中的端羧基在室温下发生酯化反应,从而将聚合物接枝到纳米SiO2表面制得复合微球.利用XPS、FTIR、TEM和TGA等测试手段对纳米SiO2的改性过程以及聚合物接枝后得到的复合微球进行了表征.研究结果表明,该室温酯化接枝方法具有较高的接枝率,接枝到无机纳米微粒表面的聚合物占复合微球质量的55wt%～70wt%;接枝聚合物后,纳米SiO2微球的粒径从40nm增加到64～75nm,从而得到了以SiO2为核、以聚合物为壳的有机-无机复合微球.     

高功率全固态绿光激光技术研究进展

 报道了高功率全固态腔内和腔外倍频两种绿光激光器研究进展。腔内倍频绿光激光器采用L型腔双棒串接结构,在重复频率10 kHz时,用三硼酸锂晶体倍频获得绿光功率186 W,光-光效率达15.8%。腔外倍频绿光激光器采用主振荡和功率放大器,在重复频率400 Hz时,获得基频激光单脉冲能量1.2 J,采用Ⅱ类相位匹配KTP晶体腔外倍频,获得525 mJ的绿光输出,倍频效率为43.7%。采用偏振合成技术获得了单脉冲能量大于1 J的绿光输出。在该激光放大器实验装置上,进行了双模块热效应补偿技术和受激布里渊散射相位共轭技术实验研究,改善了激光光束质量。     

Littlewood–Paley and Spectral Multipliers on Weighted L p Spaces

Let L be a non-negative self-adjoint operator acting on L ²(X), where X is a space of homogeneous type. Assume that L generates a holomorphic semigroup e ^?tL whose kernel p _t (x,y) has a Gaussian upper bound but there is no assumption on the regularity in variables x and y. In this article we study weighted L ^p -norm inequalities for spectral multipliers of L. We show that a weighted Hörmander-type spectral multiplier theorem follows from weighted L ^p -norm inequalities for the Lusin and Littlewood–Paley functions, Gaussian heat kernel bounds, and appropriate L ² estimates of the kernels of the spectral multipliers.