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THE JOINT DISTRIBUTIONS OF SOME ACTUARIAL DIAGNOSTICS FOR THE JUMP-DIFFUSION RISK PROCESS

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Acta Mathematica Scientia 2010年第3期30卷 664-676页

作者：吕玉华吴荣徐润 department of mathematics Qufu Normal University School of mathematics Sciences and LPMC Nankai University

In this article, the joint distributions of several actuarial diagnostics which are important to insurers＇ running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus process leaving zero ultimately （simply, the ultimately leaving-time）, the surplus immediately prior to ruin, the supreme profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. The explicit expressions for their distributions are obtained mainly by the various properties of Levy process, such as the homogeneous strong Markov property and the spatial homogeneity property etc, moveover, the many properties for Brownian motion.

关键词： Jump-diffusion risk process Brownian motion time of ruin ultimately leaving-time homogeneous strong Markov property

Highest weight representations of a Lie algebra of Block type

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Science china mathematics 2007年第4期50卷 549-560页

作者： Yue-zhu wu & Yu-cai SU department of mathematics, Shanghai Jiaotong university, Shanghai 200240, china department of mathematics, Qufu normal university, Qufu 273165, china department of mathematics, university of Science and Technology of china, Hefei 230026, china department of mathematics Shanghai Jiaotong University Shanghai China department of mathematics Qufu Normal University Qufu China department of mathematics University of Science and Technology of China Hefei China

For a field $\mathbb{F}$ of characteristic zero and an additive subgroup G of $\mathbb{F}$ , a Lie algebra B(G) of the Block type is defined with the basis {L α,i , c | α ∈ G ?1 ≤ i ∈ ?} and the relations [L α,i , L β,j ] = ((i + 1)β ? (j + 1)α)L α+β,i+j + αδ α, ?β δ i+j,?2 c, [c, L α,i ] = 0. Given a total order ? on G compatible with its group structure, and any Λ ∈ B(G) 0 * , a Verma B(G)-module M(Λ, ?) is defined, and the irreducibility of M(Λ, ?) is completely determined. Furthermore, it is proved that an irreducible highest weight B(?)-module is quasifinite if and only if it is a proper quotient of a Verma module.

关键词： Verma modules Lie algebras of Block type irreducibility 17B10 17B65 17B68

STUDY ON SPATIAL LANDSCAPE PATTERN OF YANTAI CITY BASED ON RS AND GIS

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Chinese Geographical Science 2003年第3期13卷 254-258页

作者： wu Quan-yuan (department of Geography, shandong normal university, Jinan 250014, P. R. china) department of Geography Shandong Normal University Jinan P. R. China

Influenced by artificial factors, landscape pattern of Yantai City, shandong Province changes continuously. Revealing its landscape pattern and its changing process has a practical significance for the urban development and layout. Zhifu District, Development Zone, Laishan District and Fushan District in Yantai City were selected to study the landscape pattern. Remote sensing technology was used to obtain landscape information of different periods. Under the support of Geographic Information System (GIS), the spatial landscape pattern of Yantai City was analyzed and simulated by using various special quantitative analysis models. The analysis shows that built-up area lies in the center of Yantai City, the outside is vegetable land, irrigated land, dry land, garden land and woodland.

关键词： landscape remote sensing geographic information system yantai city

Commuting Involutions with Fixed Point Set of Constant Codimension

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Acta Mathematica Sinica,English Series 1999年第2期15卷 181-186页

作者： Yanying Wang Zhende wu Yanhong Ding, department of mathematics, Hebei normal university, Shijiazhuang 050016, P. R. china department of mathematics Hebei Normal University Shijiazhuang P. R. China

Special generators of the unoriented cobordism ring MO* are constructed to determine the groups Jn,kτ of n-dimensional cobordism classes in MOn containing a representative Mn admitting a （Z2）k -action with fixed po... 详细信息

关键词： Cobordism class Fixed point set Projective space bundle (Z2)k-action

K-uniformly rotund spaces and k-uniformly smooth spaces

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Chinese Science Bulletin 1998年第2期43卷 92-95页

作者： Suyalatu 1 and wu Congxin 2 1. department of mathematics,Inner Mongolia normal university, Huhhot 010022, china 2. department of mathematics, Harbin Institute of Technology, Harbin 150006, china department of mathematics Inner Mongolia Normal University Huhhot China department of mathematics Harbin Institute of Technology Harbin China

The conception of k_uniform smoothness (KUS) is introduced. It is the extension of the conception of uniform smoothness. It is proved that the k_uniform smoothness and Sullivan’s K_uniform rotundity (KUR) are the daul notions. X+* is a KUR space if and only if X is a KUS space, X+* is a KUS space if and only if X is a KUR space. If X is a KUS space, then X is a (K+1)US space. It is also proved that the KUS space includes the Nan’s k_strongly smooth space.

关键词： K_uniform smoothness K_uniform convexity.

Estimates for eigenvalues of Laplacian operator with any order

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Science china mathematics 2007年第8期50卷 1078-1086页

作者： Fa-en wu~(1+) Lin-fen CAO~2 1 department of mathematics,Beijing Jiaotong university,Beijing 100044,china 2 department of mathematics,Henan normal university,Xinxiang 453007,china department of mathematics Beijing Jiaotong University Beijing China department of mathematics Henan Normal University Xinxiang China

Let D be a bounded domain in an n-dimensional Euclidean space ? n . Assume that $$0 < \lambda _1 \leqslant \lambda _2 \leqslant \cdots \leqslant \lambda _k \leqslant \cdots $$ are the eigenvalues of the Dirichlet Laplacian operator with any order l: $$\left\{ \begin{gathered} ( - \vartriangle )^l u = \lambda u, in D \hfill \\ u = \frac{{\partial u}}{{\partial \vec n}} = \cdots = \frac{{\partial ^{l - 1} u}}{{\partial \vec n^{l - 1} }} = 0, on \partial D \hfill \\ \end{gathered} \right.$$ . Then we obtain an upper bound of the (k+1)-th eigenvalue λ k+1 in terms of the first k eigenvalues. $$\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )} \leqslant \frac{1}{n}[4l(n + 2l - 2)]^{\tfrac{1}{2}} \left\{ {\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{{l - 1}}{l}} \sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{1}{l}} } } } \right\}^{\tfrac{1}{2}} $$ . This ineguality is independent of the domain D. Furthermore, for any l ? 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang.

关键词： Dirichlet problem eigenvalue estimate Laplacian operator 35P15 58G25

SELF-INTERSECTIONS OF BROWNIAN MOTIONON THE SIERPRISKI GASKET

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Acta Mathematica Scientia 1997年第3期17卷 353-360页

作者：魏文展吴军 department of mathematics Guangxi Normal College Nanning 530001 China department of mathematics Wuhan University Wuhan 430072 China

Let {X(t),t greater than or equal to 0} be Brownian motion on the Sierpinski gasket, E is a compact subset of [0,+infinity). In this paper, we determine when X(E) has k-multiple points and when not. We also obtain the... 详细信息

关键词： Brownian motion on the Sierpinski gasket k-multiple points k-multiple times

ROW-ACTION METHODS FOR CONVEX QUADRATIC PROGRAMMING

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Systems Science and Mathematical Sciences 1994年第4期7卷 352-361页

作者： GUO Tiande(mathematics department of Qufu normal university, Qufu, shandong 273165, china)wu Shiquan(Institute of Applied mathematics, Academia Sinica, Beijing 100080, china)

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关键词： Convex quadratic programming linear programming least-norm solution SOR algorithm gradient algorithm conjugate direction algorithm

Difference discrete connection and curvature on cubic lattice

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Science china mathematics 2006年第11期49卷 1458-1476页

作者： wu Ke, ZHAO Weizhong & GUO Hanying department of mathematics, Capital normal university, Beijing 100037, china Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100080, china department of mathematics Capital Normal University Beijing China Institute of Theoretical Physics Chinese Academy of Sciences Beijing China

In a way similar to the continuous case formally, we define in different but equivalent manners the difference discrete connection and curvature on discrete vector bundle over the regular lattice as base space. We deal with the difference operators as the discrete counterparts of the derivatives based upon the differential calculus on the lattice. One of the definitions can be extended to the case over the random lattice. We also discuss the relation between our approach and the lattice gauge theory and apply to the discrete integrable systems.

关键词： discrete connection, discrete curvature, noncommutative calculus, lattice gauge theory, discrete Lax pair.