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Coexistence of unbounded solutions and periodic solutions of Liénard equations with asymmetric nonlinearities at resonance

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Science china mathematics 2007年第8期50卷 1205-1216页

作者： Zai-hong WANG School of Mathematical Sciences,Capital normal {2.,beijing 100037,china School of Mathematical Sciences Capital Normal University Beijing China

In this paper, we deal with the existence of unbounded orbits of the mapping $$\left\{ \begin{gathered} \theta _1 = \theta + 2.\pi + \frac{1}{\rho }\mu (\theta ) + o(\rho ^{ - 1} ), \hfill \\ \rho _1 = \rho + c - \mu ... 详细信息

In this paper, we deal with the existence of unbounded orbits of the mapping $$\left\{ \begin{gathered} \theta _1 = \theta + 2.\pi + \frac2.{\rho }\mu (\theta ) + o(\rho ^{ - 1} ), \hfill \\ \rho _1 = \rho + c - \mu '(\theta ) + o(1), \rho \to \infty \hfill \\ \end{gathered} \right.$$ , where n is a positive integer, c is a constant and μ(θ) is a 2.-periodic function. We prove that if c > 0 and μ(θ) ≠ 0, θ, ∈ [0, 2.], then every orbit of the given mapping goes to infinity in the future for ρ large enough; if c 2.], then every orbit of the given mapping goes to infinity in the past for ρ large enough. By using this result, we prove that the equation x″+f(x)x′+ax +?bx ?+?(x)=p(t) has unbounded solutions provided that a, b satisfy $1/\sqrt a + 1/\sqrt b = 2.n$ and ?(x) satisfies some limit conditions. At the same time, we obtain the existence of 2.-periodic solutions of this equation.

关键词： Liénard equations unbounded solutions periodic solutions 34C11 34C2.

DESIGN EFFICIENCY FOR MINIMUM PROJECTION UNIFORMITY DESIGNS WITH TWO LEVELS

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Journal of Systems Science & Complexity 2011年第4期24卷 761-768页

作者： hong QIN Na Z0U Shangli ZHANG Department of Statistics Central China Normal University Wuhan 430079 China. Department of mathematics Beijing Jiaotong University Beijing 100044 China.

The objective of this paper is to study the issue of design efficiency for minimum projection uniformity designs. The results show that for orthogonal arrays with strength two, the minimum projection uniformity criter... 详细信息

关键词： Generalized minimum aberration minimum projection uniformity orthogonal array uniform design.

OSCILLATORY SINGULAR INTEGRALS WITH VARIABLE ROUGH KERNEL, Ⅱ

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Analysis in Theory and Applications 2003年第1期19卷 1-13页

作者： Tang Lin and Yang Dachun (beijing normal {2., china) Tang Lin and Yang Dachun Department of mathematics beijing normal university beijing 100875 P. R. china beijing normal {2. Beijing China Department of mathematics Beijing Normal University Beijing 100875 China

Let n≥2. In this paper, the author establishes the L2.(Rx)-boundedness of some oscillatory singular integrals with variable rough kernels by means of some estimates on hyper geometric functions and confluent hyper ge... 详细信息

关键词： oscillatory singular integral variable rough kernel

Cytosolic calcium oscillations in submandibular gland cells

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Acta Pharmacologica Sinica 2006年第7期27卷 843-847页

作者： Li SU Chun-yan MA Yan-dong ZHOU Yan-hong JIA Zong-jie CUI~2.Institute of Cell Biology,beijing {2. university,beijing 100875,china Institute of Cell Biology Beijing Normal University Beijing China

Calcium oscillations can,by default,encode diverse and specific signals by differ-ent modes of *** modulation is illustrated by the activation ofcalcium/calmodulin-dependent protein kinase Ⅱ at unit Hz,and of calcineurin at 10mHz frequencies,*** submandibular gland secretory axis is charac-terized by both potassium and osmolarity gradients from the luminal side of thesecretory *** gradients may play significant physiological roles throughthe feedback modulation of cholinergic *** potassium transformsplateau calcium increases induced by cholinergic stimulation of the submandibu-lar acinar cells into oscillatory calcium *** ductal cells may have simi-lar mechanisms of feedback modulation both by high potassium and by *** feedback mechanisms could modulate the decision-making pro-cess for determining which secretory products are selectively released after nervestimulation.

关键词： submandibular gland secretory axis calcium oscillation

R-matrix for the 8-Dimensional Spin Representation of Uq(so7)

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Acta Mathematica Sinica,English Series 2024年第2期40卷 485-497页

作者： hong Mei HU Nai hong HU School of Mathematical Sciences Suzhou University of Science and TechnologySuzhou 215009P.R.China School of Mathematical Sciences MOE Key Laboratory of Mathematics and Engineering Applications&Shanghai Key Laboratory of PMMPEast China Normal UniversityShanghai 200241P.R.China

The purpose of the paper is to describe the solution to the quantum Yang-Baxter equation associated with the 8-dimensional spin representation Tsp of Uq(so7).The self-duality of Tsp and the symmetry of the corresponding braiding matrix are ***,the minimal polynomial of the braiding R-matrix of Tsp is presented explicitly in an ingenious method by taking advantage of nice features of the spin representation Tsp.

关键词： Braiding R-matrix spin module minimal polynomial

Flooding 1990s along the Yangtze River, has it concern of global warming?

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Journal of Geographical Sciences 2001年第1期11卷 43-52页

作者： GONG Dao-yi1, ZHU Jin-hong2. WANG Shao-wu2.(1. Key Laboratory of Environmental Change and Natural Disaster, Institute of Resources Science, beijing normal university, {2. 100875, china 2. Department of Geophysics, Peking university, {2. 100871, Key Laboratory of Environmental Change and Natural Disaster Institute of Resources Science Beijing Normal University Beijing China Department of Geophysics Peking University Beijing China

There were a series of severe floods along the middle to lower reaches of the Yangtze River (Changjiang River) in china during the 1990s. The extensive summer (June, July and August) precipitation is mostly responsible for the flooding. The summer rainfall in the 1980s and the 1990s is much higher than that in the previous 3 decades. The means for 1990–1999 is +87.62.mm above normal, marked the 1990s the wettest decade since the 1950s. Six stations with a time span of 1880–1999 are selected to establish century-long rainfall series. This series also shows that the 1990s is the wettest decade during the last 12. years. In the wettest 12.years, four occurred in the 1990s (1991, 1996, 1998 and 1999). Both global and china’s temperature show there is a relative lower air temperature during the 1960–1970s, and a rapid warming in the 1980–1990s. Comparisons of rainfall between 1960–1979 and 1980–1999 show there are dramatic changes. In the cold period 1960–1979, the summer rainfall along the Yangtze River is 3.8 % to 4.7 % below the normal, during the warm period 1980–1999, over 8.4 % to 18.2.% of summer rainfall occurs. Over the whole eastern china, the summer rainfall shows opposite spatial patterns from the 1960–1970s to 1980–1990s. The consistent trend toward more rainfall with global warming is also presented by the greenhouse scenario modeling. A millennial Drought/flood Index for the middle to lower reaches of the Yangtze River showed that although the surplus summer rainfall in the 1990s is the severest during the past 150 years, it is not outstanding in the context of past millennium. Power spectra of the Drought/flood Index show significant interdecadal periods at 33.3 and 11.8 years. Thus, both the natural interdecadal variations and the global warming may play important roles in the frequent floods witnessed during the last two decades.

关键词： summer rainfall Yangtze River global warming interdecadal variation

Uniform design over a convex polyhedron

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Chinese Science Bulletin 1999年第2期44卷 112-114页

作者： FANG Kaitai , TIAN Guoliang XIE Minyu hong Kong Baptist university, Kowloon, hong Kong, china Institute of Applied mathematics, Chinese Academy of Sciences, beijing 100080, china Central china normal university, Wuhan 430070, chinaCorresponding author: Present address: Department of Probability and Statistics, Peking university, beijing 100871, china hong Kong Baptist university Hong Kong China Institute of Applied mathematics Chinese Academy of Sciences Beijing China Central china normal {2. Wuhan China

A new method, called the simplex method, is proposed to generate the uniform design over a convex polyhedron in n-dimensional Euclidean

关键词： convex polyhedron experimental design uniform design.

ERGODICITY OF LINEAR SPDE DRIVEN BY LVY NOISE

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Journal of Systems Science & Complexity 2010年第1期23卷 137-152页

作者： Zhao DONG Yingchao XIE Institute of Applied mathematics Academy of Mathematics and Systems Sciences Chinese Academy of Sciences Beijing 100190 China Department of mathematics Xuzhou Normal University Xuzhou 221116 China.

This paper discusses the ergodicity of a linear stochastic partial differential equation driven by Levy noise.

关键词： Ergodicity invariant measure L^vy noise linear SPDE.

The empirical likelihood goodness-of-fit test for regression model

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Science china mathematics 2007年第6期50卷 829-840页

作者： Li-xing ZHU, Yong-song QIN & Wang-li XU Department of mathematics, hong Kong Baptist {2., Kowloon Tong, hong Kong, china School of Mathematical Sciences, Guangxi normal Uinversity, Guilin 541004, china School of Statistics, Renmin {2. of china, beijing 100875, china Department of mathematics Hong Kong Baptist University Kowloon Tong China School of Mathematical Sciences Guangxi Normal Uinversity Guilin China School of Statistics Renmin University of China Beijing China

Goodness-of-fit test for regression modes has received much attention in literature. In this paper, empirical likelihood (EL) goodness-of-fit tests for regression models including classical parametric and autoregressive (AR) time series models are proposed. Unlike the existing locally smoothing and globally smoothing methodologies, the new method has the advantage that the tests are self-scale invariant and that the asymptotic null distribution is chi-squared. Simulations are carried out to illustrate the methodology.

关键词： regression model AR time series models empirical likelihood asymptotic normality goodness-of-fit 62.05 62.2. 62.30