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Dynamic behavior of micro-diaphragms and its characterized description

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Science China(Physics,Mechanics & Astronomy) 2009年第8期52卷 1345-1356页

作者： GE LiFeng School of Electronic Science and Technology, Anhui University, Hefei 230039, China School of Electronic Science and Technology Anhui University Hefei China

Diaphragm structures with micron scale play a significant role in microtransducers and micro-nano devices, and the performance of these devices depends mainly on the dynamic behaviour of diaphragms. Micro-diaphragms are treated commonly as membranes and in some cases as plates or plates in tension (called TD plates for short), but they also show in many cases the behaviour of plates in tension and supported by air spring (called TDK plates for short). Therefore, it is necessary to perform systematic research on the dynamic behaviour of micro-diaphragms, and establish a characterized mathematical description. This paper focuses on the TDK plates since they possess universality, gives the corresponding basic equations, and then derives analytical solutions of TDK circular plates under clamped and simply supported boundary conditions. This paper also gives a 3D plot representation of characteristic curved surfaces, revealing the transition from the TDK and TD plate to the pure plate or pure membrane behaviour; and further uses the value φ to determine the property of diaphragms. Its two extreme cases, i.e. φ = 0 and φ = ∞ , correspond to pure plate or pure membrane, respectively. Thus, membrane, plate and TD plate can be treated as special cases of TDK plate. In addition, this paper reveals that the presence of air-spring not only enhances the restoring force of diaphragm such that increases its natural frequencies, but also results in the resonance of a dynamic system consisting of diaphragm and air-spring. These analytical and computational results are significant for the understanding of the operation mechanism of capacitive microtransducers and their optimized design.

关键词： micro-diaphragm membrane and plate TD plate and TDK plate dynamic behaviour characterized description

STRONG UNIFORM CONSISTENCY RATES FOR CONDITIONAL FUNCTION ESTIMA TORS WITH ■-MIXING SAMPLE

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Systems Science and Mathematical Sciences 1992年第4期5卷 365-382页

作者： HU Shuhe (Anhui University,Hefei 230039,China) 安徽大学安徽合肥

Strong uniform consistency rates are given for kernel type estimatorsof the conditional function with （?）-mixing sample.Especially,for nonparametricestimators of kernel density,the regression function when Y is bounded,conditionaldf’s,L-smoothing and M-smoothing,we obtain the same rate O(（n/log n）-1/3)as in the i.***.d.sample established by H（?）rdle,Janssen and Serfling.

关键词： Strong uniform consistency rates ■-mixing sample nonparametric kernel estimators density and regression function estimation

Asymptotic profile of solutions to the two-dimensional dissipative quasi-geostrophic equation

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Science China Mathematics 2010年第10期53卷 2733-2748页

作者： DONG BoQing & LIU QingQing School of Mathematical Sciences,Anhui University,Hefei 230039,China School of Mathematical Sciences Anhui University Hefei China

This paper is concerned with the asymptotic behavior of the two-dimensional dissipative quasigeostrophic equation.Based on the spectral decomposition of the Laplacian operator and iterative techniques,we obtain improved L2 decay rates of weak solutions and derive more explicit upper bounds of higher order derivatives of solutions.We also prove the asymptotic stability of the subcritical quasi-geostrophic equation under large initial and external perturbations.

关键词： quasi-geostrophic equation L2 decay asymptotic stability

Development of Multi-Wavelength Spectral-Correction Method

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Chinese Chemical Letters 2000年第10期11卷 893-894页

作者： Hong Wen GAO (School of Chemistry and Chemical Engineering, Anhui University, Hefei 230039) Sch. of Chem. and Chem. Engineering Anhui University Hefei 230039 China

This investigation developed a new method for determining metal complex's property containing the stepwise real absorptivity(epsilon) and stability constant (K-m). The correction equation of the multi-wavelength spectral absorption was established for the simultaneous determination of various complexes to give high accuracy for trace analysis. This method was more acceptable in theory and simpler in operation than the classical methods.

关键词： simultaneous determination multi-wavelength spectral-correction complex property

HORMANDER MULTIPLIER THEOREM ON SU(2)

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Chinese Annals of Mathematics,Series B 1995年第1期16卷 103-108页

作者： FAN DASHAN XU ZENGFU(Department of Mathematics, Auhui Universityt Hefei 230039, China.) AUHUI UNIV DEPT MATHHEFEI 2300039PEOPLES R CHINA

ＨＲＡＮＤＥＲＭＵＬＴＩＰＬＩＥＲＴＨＥＯＲＥＭＯＮＳＵ（２）￥ＦＡＮＤＡＳＨＡＮ；ＸＵＺＥＮＧＦＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｕｈｕｉＵｎｉｖｅｒｓｉｔｙｔＨｅｆｅｉ２３００３９，Ｃｈｉｎａ... 详细信息

ＨＲＡＮＤＥＲＭＵＬＴＩＰＬＩＥＲＴＨＥＯＲＥＭＯＮＳＵ（２）￥ＦＡＮＤＡＳＨＡＮ；ＸＵＺＥＮＧＦＵ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｕｈｕｉＵｎｉｖｅｒｓｉｔｙｔＨｅｆｅｉ２３００３９，Ｃｈｉｎａ．）Ａｂｓｔｒａｃｔ：Ａｂｏｕｎｄ...

关键词：原子成分多项式特殊酉群李群

LOCAL OSCILLATION MODULUS OF THE UNIFORM EMPIRICAL PROCESS

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Systems Science and Mathematical Sciences 1992年第2期5卷 164-179页

作者： HONG Shengyan (Anhui University,Hefei 230039,China) 安徽大学安徽合肥

In this paper,we present a detailed description of the limiting behaviorof local oscillation of the uniform empirical process.As an application,we estab-lish the laws of the iterated logarithm for the“naive”estimator and the nearestneighbor estimator of the density function.When compared to those of Hall andHong,the conditions of the bandwidth imposed here are as weak as possible.

关键词： Uniform empirical process local oscillation modulus naive estimator nearest neighbor estimator law of the iterated logarithm

ASYMPTOTIC PROPERTIES OF L_1-NORM KERNEL ESTIMATOR OF THE CONDITIONAL MEDIAN

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Systems Science and Mathematical Sciences 1992年第1期5卷 55-69页

作者： HONG Shengyan (Anhui University,Hefei 230039,China)

Let（X,Y） be a pair of Rd×R1-valued random variables.In thispaper we investigate the asymptotic properties of the L1-norm kernel estimator ofthe conditional median function of Y on X.Under appropriate regularity condi-tions,asymptotic normality and the optimal rates of convergence n（-1）/（2+d）and(n-1log n)1/（2+d） in the Lq（1（?）q∞-norms restricted to a compactset,respectively,are obtained.Our study shows that this estimator and the well-known Nadaraya-Watson’s kernel estimator of the conditional mean function of Yon X have the same asymptotic properties.

关键词： L1-norm kernel estimator conditional median rate of convergence asymptotic normality

A theoretical model of electrostatic ultrasonic transducers with micro air-gap structure

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Chinese Science Bulletin 1998年第9期43卷 728-731页

作者： GE Lifeng (GE Li-Feng) Department of Physics, Anhui University, Hefei 230039, China Department of Physics Anhui University Hefei China

A new plate-on-air-spring model (or called short tube or DK model) for modelling the behaviour of electrostatic air-coupled ultrasonic transducers is developed and verified by accurate predictions of natural frequenci... 详细信息

关键词： electrostatic ultrasonic transducer micro air-gap structure modelling.

Degenerate Semilinear Eliptic Equations with Critical Exponent

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Communications in Mathematical Research 1999年第1期 76-84页

作者： Hu Maolin (Department of Mathematics, Anhui University, Hefei, Anhui, 230039)

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ，ｗｅａｒｅｉｎｔｅｒｅｓｔｅｄｉｎｔｈｅｅｘｉｓｔｅｎｃｅ，ｎｏｎｅｘｉｓｔｅｎｃｅｏｆｐｏｓｉｔｉｖｅａｎｄｍｕｌｔｉｐｌｅｓｏｌｕｔｉｏｎｓｔｏｔｈｅｐｒｏｂ... 详细信息

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｔｈｉｓｐａｐｅｒ，ｗｅａｒｅｉｎｔｅｒｅｓｔｅｄｉｎｔｈｅｅｘｉｓｔｅｎｃｅ，ｎｏｎｅｘｉｓｔｅｎｃｅｏｆｐｏｓｉｔｉｖｅａｎｄｍｕｌｔｉｐｌｅｓｏｌｕｔｉｏｎｓｔｏｔｈｅｐｒｏｂｌｅｍｏｆｄｅｇｅｎｅｒａｔｅｓｅ...

关键词： Degenerate Equation Critical Exponent Multiplicity of Solutions Positive Solution Nonexistence Result