Global attractor for a nonlinear viscoelastic model

In this paper we establish the existence of global attractors of a semiflow and a semigroup for a nonlinear 1-d viscoelasticity in two frameworks. We exploit the properties of the analytic semigroup to show the compactness for the semiflow and semigroup generated by the weak global solutions.     

On the perturbations of spectra of upper triangular operator matrices

In this paper we investigate perturbations of the regular spectrum of an upper triangular operator matrix such as eight="22" border="0" style="vertical-align:bottom" width="71" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X08004939-si1.gif"> acting on a Hilbert space <em>Hem>⊕<em>Kem>.     

Abel's method on summation by parts and theta hypergeometric series

Abel's lemma on summation by parts is reformulated to investigate systematically terminating theta hypergeometric series. Most of the known identities are reviewed and several new transformation and summation formulae are established. The authors are convinced by the exhibited examples that the iterating machinery based on the modified Abel lemma is powerful and a natural choice for dealing with terminating theta hypergeometric series.     

A distance-labelling problem for hypercubes

Let <em>iem>₁&ge;<em>iem>₂&ge;<em>iem>₃&ge;1 be integers. An <em>Lem>(<em>iem>₁,<em>iem>₂,<em>iem>₃)-labelling of a graph <em>Gem>=(<em>Vem>,<em>Eem>) is a mapping <em>?em>:<em>Vem>→{0,1,2,&hellip;} such that |<em>?em>(<em>uem>)−<em>?em>(<em>vem>)|&ge;<em>iem>_<em>tem> for any <em>uem>,<em>vem>∈<em>Vem> with <em>dem>(<em>uem>,<em>vem>)=<em>tem>, <em>tem>=1,2,3, where <em>dem>(<em>uem>,<em>vem>) is the distance in <em>Gem> between <em>uem> and <em>vem>. The integer <em>?em>(<em>vem>) is called the label assigned to <em>vem> under <em>?em>, and the difference between the largest and the smallest labels is called the span of <em>?em>. The problem of finding the minimum span, <em>λem>_{<em>iem>1,<em>iem>2,<em>iem>3}(<em>Gem>), over all <em>Lem>(<em>iem>₁,<em>iem>₂,<em>iem>₃)-labellings of <em>Gem> arose from channel assignment in cellular communication systems, and the related problem of finding the minimum number of labels used in an <em>Lem>(<em>iem>₁,<em>iem>₂,<em>iem>₃)-labelling was originated from recent studies on the scalability of optical networks. In this paper we study the <em>Lem>(<em>iem>₁,<em>iem>₂,<em>iem>₃)-labelling problem for hypercubes <em>Qem>_<em>dem> (<em>dem>&ge;3) and obtain upper and lower bounds on <em>λem>_{<em>iem>1,<em>iem>2,<em>iem>3}(<em>Qem>_<em>dem>) for any (<em>iem>₁,<em>iem>₂,<em>iem>₃).     

On multicolour noncomplete Ramsey graphs of star graphs

Given graphs eight="12" border="0" style="vertical-align:bottom" width="82" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0166218X07004842-si1.gif">, where <em>kem>&ge;2, the notation

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Existence and subharmonicity of solutions for nonlinear non-smooth periodic systems with a -Laplacian

In the present paper, we consider the nonlinear periodic systems driven by a vectorial p-Laplacian with a locally Lipschitz nonlinearity. Some existence, multiplicity and subharmonic results are obtained by using non-smooth critical point theory.     

On the convergence in capacity on compact Kahler manifolds and its applications

The main aim of the present note is to study the convergence in ega }$"> on a compact Kahler mainfold . The obtained results are used to study global extremal functions and describe the ega $">-pluripolar hull of an ega $">-pluripolar subset in .

     

An extension of the Wang transform derived from Bühlmann’s economic premium principle for insurance risk

It is well known that the Wang transform [Wang, S.S., 2002. A universal framework for pricing financial and insurance risks. Astin Bull. 32, 213–234] for the pricing of financial and insurance risks is derived from Bühlmann’s economic premium principle [Bühlmann, H., 1980. An economic premium principle. Astin Bull. 11, 52–60]. The transform is extended to the multivariate setting by [Kijima M., 2006. A multivariate extension of equilibrium pricing transforms: The multivariate Esscher and Wang transforms for pricing financial and insurance risks, Astin Bull. 36, 269–283]. This paper further extends the results to derive a class of probability transforms that are consistent with Bühlmann’s pricing formula. The class of transforms is extended to the multivariate setting by using a Gaussian copula, while the multiperiod extension is also possible within the equilibrium pricing framework.     

弱化限制等距性的稀疏信号恢复

众所周知,传统的信号压缩和重建遵循香农一耐奎斯特采样定律,即采样率必须至少为信号最高频率的两倍,才能保证在重建时不产生失真,这无疑将给信号采样,传输和存储过程带来越来越大的压力.随着科技的飞速发展,特别是近年来传感器技术获取数据能力提高,物联网等促使人类社会的数据规模遽增,大数据时代正式到来.大数据的规模效应给数据存储,传输,管理以及数据分析带来了极大的挑战.压缩采样应运而生.限制等距性(Restricted Isometry Property,RIP)在压缩传感中起着关键的作用.只有满足限制等距条件的压缩矩阵才能平稳恢复原始信号.RIP作为衡量矩阵是否能作为测量矩阵得到了认可,但是此理论的缺陷在于对任一矩阵,很难有通用,快速的算法来验证其是否满足RIP条件.很多学者尝试弱化RIP条件以找到测量矩阵构造的突破口.首先构造了新的限制等距条件δ_(1.5k)+θ_(k,1.5k)≤1,然后证明在这个条件下无噪声稀疏信号能被精确的恢复,并且噪声稀疏信号能被平稳的估计.最后,通过比较表明δ_(1.5k)+θ_(k,1.5k)≤1优于现存的条件.