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Split-plot designs with general minimum lower-order confounding

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Science china Mathematics 2010年第4期53卷 939-952页

作者： WEI JiaLin 1,4,YANG JianFeng 1,LI Peng 3 & ZHANG RunChu 1,2,1 school of mathematical sciences and LPMC,nankai university,tianjin 300071,china 2 KLAS and school of Mathematics and Statistics,Northeast Normal university,Changchun 130024,china 3 school of mathematical sciences,Capital Normal university,Beijing 100037,china 4 school of sciences,tianjin university of Commerce,tianjin 300134,china 1. school of mathematical sciences and LPMC Nankai University Tianjin 300071 China4. School of Sciences Tianjin University of Commerce Tianjin 300134 China3. School of Mathematical Sciences Capital Normal University Beijing 100037 China2. KLAS and School of Mathematics and Statistics Northeast Normal University Changchun 130024 China

Split-plot designs have been widely used in industrial *** to now,most methods for choosing this kind of designs are based on the minimum aberration (MA) ***,by introducing a new pattern,called aliased effect-number pattern (AENP),Zhang et *** a general minimum lowerorder confounding (denoted by GMC for short) criterion and established a general minimum confounding (also denoted by GMC for saving notations) *** is proved that,the GMC criterion selects optimal designs in a more elaborate manner than the existing ones,and when an experimenter has a prior about the importance ordering of factors in experiments the GMC designs are better than other optimal *** this paper we extend the GMC criterion to the split-plot design case and give a GMC-FFSP criterion for ranking split-plot *** comparisons of the new criterion with the MA-MSA-FFSP criterion are given,and the optimal 32-run split-plot designs up to 14 factors under the two criteria are tabulated for comparison and application.

关键词： fractional factorial design GMC criterion minimum aberration split-plot

A theorem of Fong's type for graded algebras

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Science china Mathematics 2005年第5期48卷 577-582页

作者： FAN Yun & ZHU Ping school of Mathematics and Statistics, Central china Normal university, Wuhan 430079, china school of mathematical Science, nankai university, tianjin 300071, china 1. school of Mathematics and Statistics Central China Normal University 430079 Wuhan China 2. school of mathematical Science Nankai University 300071 Tianjin China

Let G be a finite p-solvable group and k be an algebraic closed field of characteristic p. It is proved that any projective indecomposable module of a G-graded k-algebra is an induced module of a module of the subalgebra graded by a Hall p′-subgroup. A necessary and sufficient condition for the indecomposability of an induced module from a Hall p′-subgroup is obtained.

关键词： group graded algebra indecomposable induced module primitive idempotent.

Large Deviation for Stochastic Cahn-Hilliard Partial Differential Equations

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Acta Mathematica Sinica,English Series 2009年第7期25卷 1157-1174页

作者： Ke Hua SHI Dan TANG Yong Jin WANGschool of mathematical sciences, nankai university, tianjin 300071, P. R. china school of mathematical sciences Nankai University Tianjin 300071 P. R. China

In this paper, we prove a large deviation principle for a class of stochastic Cahn-Hilliard partial differential equations driven by space-time white noises.

关键词： stochastic Cahn-Hilliard partial differential equations large deviation principle Freidlin Wentzell inequality

Search for B_c (ns) via the B_c (ns) → B_c (ms) π^+ π^- transition at LHCb and Z^0 factory

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Science china(Physics,Mechanics & Astronomy) 2010年第11期53卷 2019-2024页

作者： KE HongWei 1 & LI XueQian 2 1 school of Science,tianjin university,tianjin 300072,china 2 school of Physics,nankai university,tianjin 300071,china 1. school of Science Tianjin University Tianjin 300072 China2. School of Physics Nankai University Tianjin 300071 China

It is interesting to study the characteristics of the whole family of B c which contains two different heavy *** and the proposed Z 0 factory provide an opportunity because a large database of the B c family will be achieved.B c and its excited states can be identified via their decay *** suggested by experimentalists,B-c (ns) → B c +γ is not easy to be clearly measured,instead,the trajectories of π + and π- occurring in the decay of B c (ns) → B c (ms) + π + π( n > m ) can be unambiguously identified,thus the measurement seems easier and more reliable;therefore this mode is more favorable at the early running stage of LHCb and the proposed Z 0 *** this work,we calculate the rate of B c (ns) → B c (ms) + π + π-in terms of the QCD multipole-expansion and the numerical results indicate that the experimental measurements with the luminosity of LHC and Z 0 factory are feasible.

关键词： meson hadronic decay QCD multipole-expansion

COMPUTATIONAL COMPLEXITY IN WORST, STOCHASTIC AND AVERAGE CASE SETTING ON FUNCTIONAL APPROXIMATION PROBLEM OF MULTIVARIATE

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Acta Mathematica Scientia 2005年第3期25卷 439-448页

作者：房艮孙叶培新 school of mathematical sciences Beijing Normal university school of mathematical sciences and LPMC nankai university

The order of computational complexity of all bounded linear functional ap proximation problem is determined for the generalized Sobolev class Wp?（Id）, Nikolskii class H|∞k（Id） in the worst （deterministic）, stochastic and average case setting, from which it is concluded that the bounded linear functional approximation problem for the classes Wp?（Id） and H∞k（Id） is intractable in worst case setting, but is tractable with respect to stochastic and average case setting.

关键词： worst (deterministic) case stochastic case average case setting bounded linear functional error estimate

Discontinuous Galerkin method for elliptic stochastic partial differential equations on two and three dimensional spaces

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Science china Mathematics 2007年第11期50卷 1661-1672页

作者： Rui-ming YAO~(1+) Li-jun BO~(1,2) 1 Department of Mathematics,Xidian university,Xi’an 710071,china 2 school of mathematical sciences,nankai university,tianjin 300071,china Department of Mathematics Xidian University Xi’an 710071 China school of mathematical sciences Nankai University Tianjin 300071 China

In this paper,we study a discontinuous Galerkin numerical scheme for a class of elliptic stochastic partial differential equations (*** SPDEs) driven by space white noises with homogeneous Dirichlet boundary conditions for two and three space *** also establish L2 error estimates for the *** particular,a numerical test for d = 2 is presented at the end of the article.

关键词： discontinuous Galerkin numerical scheme elliptic SPDEs white noises

Optimal error bound of restricted Monte Carlo integration on anisotropic Sobolev classes

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Progress in Natural Science:Materials International 2006年第6期16卷 588-593页

作者： GAO Wenhua, YE Peixin and WANG Hui (College of Mathematics and System sciences, Xinjiang university, Urumqi 830046, china school of mathematical sciences and LPMC, nankai university, tianjin 300071, china Department of Mathematics, Ily Teachers' College, Yining 835000, china College of Science, Hehai university, Nanjing 210098, china) [a]College of Mathematics and System sciences Xinjiang University Urumqi China [b]school of mathematical sciences and LPMC Nankai University Tianjin China [c]Department of Mathematics Ily Teachers College Yining China [d]College of Science Hehai University Nanjing China

We study the restricted Monte Carlo integration error for anisotropic Sobolev classes. Results prove that with O(log2 n) random bits we have the optimal order for the n-th minimal Monte Carlo integration error with ar... 详细信息

关键词： Monte Carlo integration random bits anisotropic Sobolev classes.

QUANTUM COMPLEXITY OF THE APPROXIMATION FOR THE CLASSES B(W_p^r([0,1]~d)) AND B(H_p^r([0,1]~d))

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Acta Mathematica Scientia 2010年第5期30卷 1808-1818页

作者：叶培新胡晓菲 school of mathematical sciences and LPMC Nankai University College of mathematical Syracuse University

We study the approximation of functions from anisotropic Sobolev classes b（WpR（[0, 1]d）） and HSlder-Nikolskii classes B（HPr（[0, 1]d）） in the Lq （[0, 1]d） norm with q 〈 p in the quantum model of computation. We determine the quantum query complexity of this problem up to logarithmic factors. It shows that the quantum algorithms are significantly better than the classical deterministic or randomized algorithms.

关键词： quantum approximation anisotropic classes minimal query error

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