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△-tame quasi-hereditary algebras

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Science china Mathematics 2007年第2期50卷 240-252页

作者： Yun-ge XU & Ying-bo ZHANG Faculty of Mathematics and Computer Science, Hubei university, Wuhan 430062, china school of Mathematics Sciences, beijing Normal university, beijing 100875, china Faculty of Mathematics and Computer Science Hubei University Wuhan China school of Mathematics Sciences Beijing Normal University Beijing China

Let (K, M,H) be an upper triangular bimodule problem. Briistle and Hille showed that the opposite algebra A of the endomorphism algebra of a projective generator P of the matrices category of (K., M, H) is quasi-hereditary, and there is an equivalence between the category of△-good modules of A and Mat(K, M). In this note, based on the tame theorem for bimodule problems, we show that if the algebra A associated with an upper triangular bimodule problem is of△-tame representation type, then the category F(△) has the homogeneous property, i.e. almost all modules in F(△) are isomorphic to their Auslander-Reiten translations. Moreover, if (K, M,H)is an upper triangular bipartite bimodule problem, then A is of△-tame representation type if and only if F(△) is homogeneous.

关键词： bimodule problem quasi-hereditary algebra △-tameness homogeneity.

Exact n-width on the class of analytic functions in the space of continuous functions

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Progress in Natural Science:Materials International 2005年第8期15卷 761-764页

作者： FANG Gensun* and LI Xuehua(school of Mathematical Sciences, beijing Normal university, beijing 100875, china) school of Mathematical Sciences Beijing Normal University Beijing 100875 China

Let ω(·) be a given concave modulus of continuity and ω(g,·) be the modulus of continuity of a function g∈C, where C is the space of 2π-periodic, continuous functions on with norm ‖f‖_C∶= maxt∈|f(t)|, r,ω__ ∞,β(r=0,1,2,…) denotes those 2π-periodic, real-valued functions f on that are analytic in the strip S_β∶=｛z∈:|Imz|0, and satisfy the restriction condition: ω(f (r),·)≤ω(·). In this paper, the exact n-width of the class of functions r,ω__ ∞,β in the space C is determined.

关键词： analytic function concave modulus of continuity n-width.

A NOTE ON THE CONSISTENCY OF LS ESTIMATES IN LINEAR MODELS

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Chinese Annals of Mathematics,Series B 2001年第4期22卷 471-474页

作者： CHEN XIRU The Graduate school at beijing, university of Science and Technology of china, beijing 100039, china. The Graduate school at beijing University of Science and Technology of China Beijing 100039 China

It is well known that when the random errors are iid. with finite variance, the week and the strong consiStency of LS estimate of multiple regression coefficients are equivalent. This note, by constructing a counter-example, shows that this equivalence no longer holds true in case that the random errors possess only the r-th moment with 1≤5 T ＜ 2.

关键词： Linear regression model Consistency LS estimate

Recycling of Spent Nickel-Cadmium Batteries

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International Journal of Minerals,Metallurgy and Materials 2000年第2期14卷 126-131页

作者： Xanghua Kong Pingnan Wu(Metallurgy school, university of Science and Technology beijing, beijing 100083, china) Metallurgy school University of Science and Technology Beijing Beijing 100083 China

A technique for recycling spent nickel-cadmium batteries, which makes separaion of cadmium and nickel possible, is developed by laboratory-scale experiments. NH3-H2CO3 aqueous solution was used in this leaching technique. Since neutralization and/or solvent extraction were not required in the separation procedure of nickel and cadmium, the closed systemizaion of the process becomespossible. Experimental results show that, (1) if the NH3 concentraion of leaching solution is sufficiently high and the ratio of H2CO3 toNH3 is properly adjusted, both Ni(OH)2 and Cd(OH)2 react with NH, and quickly dissolve into leaching solution, and (2) Ni(OH)2 can beconverted into insoluble NiO by calcination at 500℃, and CdO from Cd(OH)2 by calcination maintains good solubility in NH3-H2CO3aqueous solution. As a conclusion, the recycling technique characterized by two step leaching can be developed based on such changesin dissolution behavior by calcination. Meanwhile, the yields of 99.8% for nickel and 97.6% for cadmium are obtained, and the puritiesof Recycling of Spent Nickel-Cadmium BatterieRecycling of Spent Nickel-Cadmium Batteries Recycling of Spent Nickel-Cadmium Batteriesrecovered nickel and cadmium are 99.9% and 98.6%, respectively.

关键词： nickel-cadmium batteries recycling, ammonia leaching closed system environmental protection

Asymptotic distributions in the projection pursuit based canonical correlation analysis

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Science china Mathematics 2010年第2期53卷 485-498页

作者： JIN Jiao & CUI HengJian Department of statistics and Financial Mathematics, school of Mathematical Sciences, beijing Normal university, Laboratory of Mathematics and Complex Systems (beijing Normal university), Ministry of Education, beijing 100875, china 1. Department of statistics and Financial Mathematics School of Mathematical Sciences Beijing Normal University Beijing 100875 China2. Ministry of Education Laboratory of Mathematics and Complex Systems (Beijing Normal University) Beijing 100875 China

In this paper, associations between two sets of random variables based on the projection pursuit (PP) method are studied. The asymptotic normal distributions of estimators of the PP based canonical correlations and we... 详细信息

关键词： asymptotic distribution canonical correlation analysis influence function robust statistics

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.

Nonlinear Doob-Meyer Decomposition for General Filtration

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Acta Mathematicae Applicatae Sinica 2002年第4期18卷 619-624页

作者： Qing-quan Linchina Financial Policy Research Center, school of Finace, renmin university of china, beijing 100872. china china Financial Policy Research Center School of Finace Renmin University of China Beijing 100872 China

The comparison theorem for generalized backward stochastic differential equations is discussed. Some topics related to equations of this type are also investigated.

关键词： Generalized backward stochastic differential equation Doob-Meyer decomposition theorem,g-supermartingale g-supersolution

Approximation for a scheduling problem with application in wireless networks

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Science china Mathematics 2010年第6期53卷 1643-1655页

作者： ZHU QingHua & LI DeYing Key Laboratory of Data Engineering and Knowledge Engineering,MOE,school of Information,renmin university of china,beijing 100872,china 1. Key Laboratory of Data Engineering and Knowledge Engineering MOE School of Information Renmin University of China Beijing 100872 China

A network of many sensors and a base station that are deployed over a region is *** sensor has a transmission range,an interference range and a carrier sensing range,which are r,αr and βr,*** this paper,we study the minimum latency conflict-aware many-to-one data aggregation scheduling problem:Given locations of sensors along with a base station,a subset of all sensors,and parameters r,α and β,to find a schedule in which the data of each sensor in the subset can be transmitted to the base station with no conflicts,such that the latency is *** designe an algorithm based on maximal independent sets,which has a latency bound of(a+19b)R + Δb-a + 5 time slots,where a and b are two constant integers relying on α and β,Δ is the maximum degree of network topology,and R is the trivial lower bound of *** Δ contributes to an additive factor instead of a multiplicative one,thus our algorithm is nearly a constant(a+19b)-ratio.

关键词： approximation algorithm conflict-aware many-to-one data aggregation latency wireless sensor network

Adaptive control for autonomous rendezvous of spacecraft on elliptical orbit

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Acta Mechanica Sinica 2009年第4期25卷 539-545页

作者： Shan Lu Shijie Xu school of Astronautics, Beihang university,100191 beijing, china school of Astronautics Beihang University 100191 Beijing China

A strategy for spacecraft autonomous rendezvous on an elliptical orbit in situation of no orbit information is developed. Lawden equation is used to describe relative motion of two spacecraft. Then an adaptive gain factor is introduced, and an adaptive control law for auton- omous rendezvous on the elliptical orbit is designed using Lyapunov approach. The relative motion is proved to be ultimately bounded under this control law, and the final relative position error can achieve the expected magnitude. Simulation results indicate that the adaptive control law can realize autonomous rendezvous on the elliptical orbit with relative state information only.

关键词： Autonomous rendezvous Elliptical orbit Lyapunov approach Adaptive control Gain factor