正四面体套中心构型的存在唯一性

Two cases of the nested configurations in R^3 consisting of two regular quadrilaterals are discussed. One case of them do not form central configuration, the other case can be central configuration. In the second case the existence and uniqueness of the central configuration are studied. If the configuration is a central configuration, then all masses of outside layer are equivalent, similar to the masses of inside layer. At the same time the following relation between r(the ratio of the sizes) and mass ratio b = m/m must be satisfied b=24(3的立方根)（3r^2 2r 3）^-3/2-8（1-r）|1-r|^-3-3(6r的立方根)/24(3的立方根)（3 r）（3r^2 2r 3）^-3/2-8r（1-r）|1-r|^-3-3(6r^-2的立方根)in which the masses at outside layer are not less than the masses at inside layer, and the solution of this kind of central configuration is unique for the given ratio (b) of masses.     

Global weak solutions for a viscous liquid–gas model with transition to single-phase gas flow and vacuum

This work deals with a viscous two-phase liquid–gas model relevant to the flow in wells and pipelines. The liquid is treated as an incompressible fluid whereas the gas is assumed to be polytropic. The model is rewritten in terms of Lagrangian coordinates and is studied in a free boundary setting where the liquid and gas masses are of compact support initially, and continuous at the boundary. Consequently, the initial masses involve a transition to single-phase gas flow and vacuum at the boundary. An appropriate balance between pressure and viscous forces is identified which allows obtaining pointwise upper and lower estimates of masses. These estimates rely on the assumption of a certain relation between the rate of degeneracy of the viscosity coefficient and the rate that determines how fast the initial masses are vanishing at the boundary. By combining these estimates with basic energy type of estimates, higher order regularity estimates are obtained. The existence of global weak solutions is then proved by showing compactness for a class of semi-discrete approximations.     

The inverse scattering transform: Tools for the nonlinear fourier analysis and filtering of ocean surface waves

Surface wave data from the Adriatic Sea are analysed in the light of new data analysis techniques which may be viewed as a nonlinear generalization of the ordinary Fourier transform. Nonlinear Fourier analysis as applied herein arises from the exact spectral solution to large classes of nonlinear wave equations which are integrable by the inverse scattering transform (IST). Numerical methods are discussed which allow for implementation of the approach as a tool for the time series analysis of oceanic wave data. The case for unidirectional propagation in shallow water, where integrable nonlinear wave motion is governed by the Korteweg-deVries (KdV) equation with periodic/quasi-periodic boundary conditions, is considered. Numerical procedures given herein can be used to compute a nonlinear Fourier representation for a given measured time series. The nonlinear oscillation modes (the IST ‘basis functions’) of KdV obey a linear superposition law, just as do the sine waves of a linear Fourier series. However, the KdV basis functions themselves are highly nonlinear, undergo nonlinear interactions with each other and are distinctly non-sinusoidal. Numerical IST is used to analyse Adriatic Sea data and the concept of nonlinear filtering is applied to improve understanding of the dominant nonlinear interactions in the measured wavetrains.     

柔性头颅模型撞击弹性板的动态响应分析

将柔性接触撞击过程处理为一个振动系统响应,采用机械网络图和求机械阻抗的方法解决了这一动态响应问题。柔性接触撞击模型考虑了头部的实际结构,把头部简化成撞击部位的头皮和头骨的质量、头部其它部分的头骨和脑液的质量、头部的刚度、头皮和脑液的阻尼系数组成的振动模型,弹性板也同样简化成由质量、刚度和阻尼构成的振动模型。采用求激振点速度阻抗的方法,得到了系统的动态撞击力、头部所受到的撞击加速度值,以及板的弹性变形、系统的固有频率等动态响应。实验数据与计算数据符合较好,证明方法是计算撞击作用下系统动态响应的实用方法,从而为头部撞击保护设计提供参考。     

Elastic Oscillations of a Half-Space Excited by Free Oscillations of a Heavy Fluid on Its Surface

An approximate mathematical model is constructed to account for the presence of long-period elastic deformations of the Earth's surface as a result of free oscillations of closed, bounded bodies of water (inland seas). The model provides a basis (ignoring the Earth's rotation) for calculating the frequencies and corresponding waveforms of free oscillations of the Black Sea and the Sea of Azov, which are treated as isolated basins of shallow, variable depth. The theoretical amplitudes of the components of the strain tensor and other elastic characteristics of the medium are calculated at a given point of the Earth's surface (recording instrument station).     

基于海空协同的群岛救援方案优化模型及算法

针对边远群岛的物资供给受突发事件影响可能出现中断,需要开展紧急救援的实际情况,以中心岛屿为救援出发地,采用海空协同运输方式,以选择救援路线和分配救援物资批量为优化内容,对中心岛屿周边各岛救援用时最短为目标,建立了考虑海空协同的群岛应急救援模型。根据所建模型的特点,对基于运输点划分的遗传算法(PB-GA)进行进一步的改进,提出一种能够同时考虑两种运输方式、多批次运输的双层搜索遗传算法进行求解。最后,以南海群岛开展紧急救援为算例进行了优化分析。采用不同算法分别进行比较后显示,本文算法在优化结果、运算时间等方面均更优,从而验证了所建模型和算法的合理性与有效性。本文研究为制定群岛海空联合救援的应急预案提供了分析方法。     

On an Isoperimetric Problem with a Competing Nonlocal Term II: The General Case

This paper is the continuation of a previous paper (H. Knüpfer and C. B. Muratov, Comm. Pure Appl. Math. 66 (2013), 1129–1162). We investigate the classical isoperimetric problem modified by an addition of a nonlocal repulsive term generated by a kernel given by an inverse power of the distance. In this work, we treat the case of a general space dimension. We obtain basic existence results for minimizers with sufficiently small masses. For certain ranges of the exponent in the kernel, we also obtain nonexistence results for sufficiently large masses, as well as a characterization of minimizers as balls for sufficiently small masses and low spatial dimensionality. The physically important special case of three space dimensions and Coulombic repulsion is included in all the results mentioned above. In particular, our work yields a negative answer to the question if stable atomic nuclei at arbitrarily high atomic numbers can exist in the framework of the classical liquid drop model of nuclear matter. In all cases the minimal energy scales linearly with mass for large masses, even if the infimum of energy cannot be attained. © 2014 Wiley Periodicals, Inc.     

Stability of the Optimal Solution to a Problem of Variational Assimilation with Error Covariance Matrices of Observational Data for a Sea Thermodynamics Model

A mathematical model of sea thermodynamics developed at the Institute of Numerical Mathematics of the Russian Academy of Sciences is considered. A problem of variational assimilation of daily-averaged sea surface temperature (SST) data with observational error covariance matrices is formulated and investigated. On the basis of variational assimilation of satellite observation data, an inverse problem of restoring the heat flux on the sea surface is solved. The stability of the optimal solution to the problem of variational data assimilation is studied, and the results of numerical experiments with the model for Baltic Sea dynamics are presented.     

On the 2D critical and supercritical dissipative quasi-geostrophic equation in Besov spaces

We prove the local smoothing effect of the 2D critical and supercritical dissipative quasi-geostrophic equations in critical Besov spaces. As an application, a global well-posedness result is established by adapting a method in Kiselev, Nazarov, and Volberg (2007) [16] and an idea in Dong and Du (2008) [15] with suitable modifications. Moreover, we show that the unique solution obtained in Chen, Miao, and Zhang (2007) [11] is a classical solution. These generalize some previous results in Dong (2010) [13], Dong and Du (2008) [15]. The main ingredients of the proofs are two commutator estimates and the preservation of suitable modulus of continuity of the solutions.     

Ultra-low frequency passive vertical vibration isolation system

An ultra-low frequency passive vertical vibration isolator is constructed by mounting a couple of additional masses on the crank-arms of the torsion spring. The theoretical analysis and experimental results show that the system with additional masses can achieve better vertical vibration isolation and longer resonant period. Measured displacement response of the test mass under seismic excitation reaches 3 x 10^{-12 m/√ Hz} around 10 Hz, and the isolation ratio comes to about 60 dB attenuation at 6 Hz, which is about 30 dB lower than that of the system without additional masses. Project supported by the National Natural Science Foundation of China (Grant Nos. 19425008, 49674246 and 59678032).     

Ultra-low frequency passive vertical vibration isolation system

An ultra-low frequency passive vertical vibration isolator is constructed by mounting a couple of additional masses on the crank-arms of the torsion spring. The theoretical analysis and experimental results show that the system with additional masses can achieve better vertical vibration isolation and longer resonant period. Measured displacement response of the test mass under seismic excitation reaches 3 x 10^{-12 m/√ Hz} around 10 Hz, and the isolation ratio comes to about 60 dB attenuation at 6 Hz, which is about 30 dB lower than that of the system without additional masses.     

Chaotic dynamic and control for micro-electro-mechanical systems of massive storage with harmonic base excitation

This paper explores chaotic behaviour and control of micro-electro-mechanical systems (MEMS), which consist of thousands of small read/write probe tips that access gigabytes of data stored in a non-volatile magnetic surface. The model of the system is formed by two masses connected by a nonlinear spring and a viscous damping. The paper shows that, by means of an adequate feedback law, the masses can behave as two coupled Duffing’s oscillators, which may reach chaotic behaviour when harmonic forces are applied. The chaotic motion is destroyed by applying the following control strategies: (i) static output feedback control law with constant forces and (ii) geometric nonlinear control. The aim is to drive the masses to a set point even with harmonic base excitation, by using chaotic dynamics and nonlinear control. The paper shows that it is possible to obtain a positioning time around a few ms with sub-nanometre accuracy, velocities, accelerations and forces, as it appears in the design of present MEMS devices. Numerical simulations are used to verify the mathematical discussions.     

非重复析因试验数据分析的两个方法

本文介绍了非重复析因试验数据分析的两个比较实用的方法 :Lenth方法和Dong方法 ,并对这两个方法进行了比较全面的比较     

Nonlinear behavior of the renormalization group flow and standard model parameters

The standard model for high-energy physics (SM) describes fundamental interactions between subatomic particles down to a distance scale on the order of 10⁻¹⁸ m. Despite its widespread acceptance, a consistent and comprehensive understanding of SM parameters is missing. Starting from a less conventional standpoint, our work suggests that the spectrum of particle masses, gauge couplings and fermion mixing angles may be derived from the chaotic regime of the renormalization group flow. In particular, we argue that the observed hierarchies of standard model parameters amount to a series of scaling ratios depending on the Feigenbaum constant. Leading order predictions are shown to agree well with experimental data.     

Homogenization of a model spectral problem for the Laplace operator in a domain with many closely located “ heavy” and “intermediate heavy” concentrated masses

We study the asymptotic behavior of eigenelements of boundary value problems in a domain Ω ⊂ ℝ^d, d ⩾ 3, with rapidly alternating type of boundary conditions. The density is equal to 1 outside tiny domains and is equal to ε^−m inside them, where ε is a small parameter. These domains (concentrated masses) of diameter εa are located on the boundary at a positive distance of order O(ε) from each other, where a = const. The Dirichlet boundary condition is on parts of ∂Ω that are tangent to concentrated masses, and the Neumann boundary condition is stated outside concentrated masses. We construct the limit (homogenized) operator, prove the convergence of eigenelements of the original problem to the eigenelements of the limit (homogenized) problem in the case m ⩾ 2, and estimate the difference between the eigenelements. Bibliography: 79 titles. Illustrations: 4 figures. __________ Translated from Problemy Matematicheskogo Analiza, No. 32, 2006, pp. 45–75.     

南极中山站周边水环境冰情监测系统的设计与研究

系统实现对南极中山站周边冰、水环境的长期连续实时监测,可以为分析南极环境变化是否对全球气候异常变化造成影响提供最基本的科学数据.利用空气,冰与水介质的电导率不同的原理用微控制器控制冰情检测传感器来实现冰水环境的自动化监测,设计了可以实现冰厚度、水深度、温度的定点连续冰情监测系统,监测数据可以存储在系统内嵌的SD存储卡中,方便观测人员进行调用.通过卫星实现数据无线传输.     

Well-Posedness of A Compressible Gas-Liquid Model for Deepwater Oil Well Operations

The main purpose of this paper is two-fold: (i) to generalize an existence result for a compressible gas-liquid model with a friction term recently published by Friis and Evje [SIAM J. Appl. Math., 71 (2011), pp. 2014–2047]; (ii) to derive a uniqueness result for the same model. A main ingredient in the existence part is the observation that we can consider weaker assumptions on the initial liquid and gas mass, and still obtain an existence result. Compared to the above mentioned work, we rely on a more refined application of the estimates provided by the basic energy estimate. Concerning the uniqueness result, we borrow ideas from Fang and Zhang [Nonlinear Anal. TMA, 58 (2004), pp. 719–731] and derive a stability result under appropriate constraints on parameters that determine rate of decay toward zero at the boundary for gas and liquid masses, and growth rate of masses associated with the friction term and viscous coefficient.     

北京市用水结构预测分析

城市化进程给城市用水量与用水结构带来了显著的改变,通过研究北京市用水结构的发展趋势,为区域水资源的科学管理与合理配置提供依据.用水结构主要包括农业用水、工业用水、生活用水和生态用水四类,可将历年用水量作为一系列按照时间顺序排列的成分数据,运用球坐标变换的成分数据预测方法,研究了北京市用水量结构的动态规律,并对未来两年的用水量结构作出预测.     

Earth Vision 2000: Examining Students' Representations of Complex Data Sets

Graphic representations are powerful tools used by scientists and other professionals to help them understand multifaceted natural phenomena. They can also serve teachers and students as they attempt to understand complex data sets. This study examines pencil‐and‐paper graphs produced by students at the beginning of a 1‐week summer teacher/student institute, as well as computer‐based graphs produced by the same students at the end of the institute. Initial problems with managing the data set and producing meaningful graphs disappeared quickly as students used a process of “building up” to handle the complexity of web‐based data on water quality. This process is examined, as are findings from the institute related to (a) barriers to accessing web‐based data, (b) students' problem‐solving processes, and (c) the promise of this approach for learning about environmental science issues.     

两个垂直圆柱在水波中的水动力相互作用

基于线性势流理论研究了两个垂直圆柱在水波中的水动力相互作用．两个圆柱中的一个固定在底部，另一个铰接在底部且可以在入射波方向以小振幅振动．本文研究了绕射波和辐射波，运用加法定理得到了每个圆柱表面速度势的简单的解析表达式，用级数形式显式表示了圆柱上的波浪激励力和力矩及振动圆柱的附加质量和辐射阻尼系数．级数的系数由代数方程组的解决定．给出了一些数值例子以说明诸如间距、圆柱的相对大小、入射角等各种参数对一阶力、定常二阶力、附加质量和辐射阻尼系数以及振动圆柱的响应等的影响．