The Effect of Freezing and Discretization to the Asymptotic Stability of Relative Equilibria

In this paper we prove nonlinear stability results for the numerical approximation of relative equilibria of equivariant parabolic partial differential equations in one space dimension. Relative equilibria are solutions which are equilibria in an appropriately comoving frame and occur frequently in systems with underlying symmetry. By transforming the PDE into a corresponding PDAE via a freezing ansatz [2] the relative equilibrium can be analyzed as a stationary solution of the PDAE. The main result is the fact that nonlinear stability properties are inherited by the numerical approximation with finite differences on a finite equidistant grid with appropriate boundary conditions. This is a generalization of the results in [14] and is illustrated by numerical computations for the quintic complex Ginzburg Landau equation.      

梨和苹果糖度在线检测通用数学模型研究

采用可见/近红外光谱技术在线检测水果糖度,每个水果品种要单独建模,模型升级维护耗时费力。探讨建立苹果、梨等薄皮水果可溶性固形物(SSC)在线检测通用数学模型的可行性。利用自行设计的可见/近红外漫透射光谱在线检测系统,在积分时间80 ms、单线速度5个/s的条件下,采集新梨7号、砀山酥梨、玉露香梨和富士苹果四种水果的可见/近红外漫透射光谱。分析了四种水果的可见/近红外漫透射光谱响应特性,采用变异系数法和连续投影算法,筛选通用数学模型建模用光谱变量,并建立了偏最小二乘和最小二乘支持向量机梨与苹果梨通用数学模型。采用新样品评价模型的预测能力,变异系数法筛选光谱波段建立的偏最小二乘通用数学模型预测精度最高,通用模型预测梨和苹果梨模型预测均方根误差分别为0.49%和0.55%,通用模型预测相关系数分别为0.88和0.93;独立模型预测新梨7号、玉露香梨、砀山酥梨和富士苹果的预测相关系数分别为0.93,0.91,0.88和0.95,预测均方根误差分别为0.40%,0.42%,0.41%和0.46%。通用数学模型的预测精度略低于每个品种的独立数学模型,但是通用模型的通用性高于单一模型。实验结果说明采用变异系数法结合偏最小二乘法建立薄皮水果在线检测通用数学模型,实现四种水果糖度在线检测是可行的。     

某型制导武器通用自动测试系统方案设计

针对基于VXI总线的某型制导武器通用自动测试系统存在的测试效率难以提升、通用化和小型化程度不够、测试技术标准化和信息化水平不高等问题,提出基于PXI总线的某新型制导武器通用自动测试系统的总体设计技术方案,通过采用新型高速仪器总线、合成仪器、TPS可移植等技术,以及软硬件平台模块化、专测组件通用化等设计思想,实现了系统组件标准配置、测试信息网络传输、程序软件移植使用、资源扩展方便快捷的设计初衷,使系统形成跨平台通用化与互操作能力,是现阶段精确制导武器通用自动测试系统较为理想的系统平台解决方案,经新研系统实际试用证明,该设计方案切实可行,能大幅提升多型制导武器通用测试效率,提高部队测试保障能力。     

某些数的代数无关性

本文建立了具有不同参数的广义Ｍａｈｌｅｒ级数在代数点上的值的代数无关性．     

Production of neutron-rich isotopes in fission of uranium induced by neutrons of 20 MeV average energy

In the context of a parameter study conducted by several laboratories for future European radioactive beam facilities based on fast-neutron induced fission, in particular for the SPIRAL-II project at GANIL, we have measured the yields of neutron-rich isotopes in the mass range of 88 to 144. These nuclei were obtained as fission products of natural uranium bombarded by neutrons of 20 MeV average energy emitted by a thick carbon target irradiated by 50 MeV deuterons. Yields have been measured using on-line mass separation with the ion-guide method. Compared with proton-induced fission at 25 MeV the magnitude of cross-sections, except for the symmetric region, is similar. Z-distributions of isobars have the same width, 0.7 charge units, but their maxima are shifted by about 0.8 charge units, favouring production of the neutron-richer isobars. Our data allow calculations of absolute cross-sections for fission of natural uranium induced by neutrons of about 20 MeV. Received: 10 July 2000 / Accepted: 27 October 2000     

On coordination and continuous hawk-dove games on small-world networks

It is argued that small-world networks are more suitable than ordinary graphs in modelling the diffusion of a concept (e.g. a technology, a disease, a tradition, ...). The coordination game with two strategies is studied on small-world networks, and it is shown that the time needed for a concept to dominate almost all of the network is of order , where N is the number of vertices. This result is different from regular graphs and from a result obtained by Young. The reason for the difference is explained. Continuous hawk-dove game is defined and a corresponding dynamical system is derived. Its steady state and stability are studied. Replicator dynamics for continuous hawk-dove game is derived without the concept of population. The resulting finite difference equation is studied. Finally continuous hawk-dove is simulated on small-world networks using Nash updating rule. The system is 2-cyclic for all the studied range. Received 8 July 2000 and Received in final form 23 July 2000     

Casimir amplitudes in a quantum spherical model with long-range interaction

A d-dimensional quantum model system confined to a general hypercubical geometry with linear spatial size L and “temporal size” 1/T ( T - temperature of the system) is considered in the spherical approximation under periodic boundary conditions. For a film geometry in different space dimensions , where is a parameter controlling the decay of the long-range interaction, the free energy and the Casimir amplitudes are given. We have proven that, if , the Casimir amplitude of the model, characterizing the leading temperature corrections to its ground state, is . The last implies that the universal constant of the model remains the same for both short, as well as long-range interactions, if one takes the normalization factor for the Gaussian model to be such that . This is a generalization to the case of long-range interaction of the well-known result due to Sachdev. That constant differs from the corresponding one characterizing the leading finite-size corrections at zero temperature which for is . Received 3 June 1999 and Received in final form 16 August 1999     

Nonmonotonic external field dependence of the magnetization in a finite Ising model: Theory and MC simulation

Using field theory and Monte Carlo (MC) simulation we investigate the finite-size effects of the magnetization M for the three-dimensional Ising model in a finite cubic geometry with periodic boundary conditions. The field theory with infinite cutoff gives a scaling form of the equation of state where is the reduced temperature, h is the external field and L is the size of system. Below and at the theory predicts a nonmonotonic dependence of f(x,y) with respect to at fixed and a crossover from nonmonotonic to monotonic behaviour when y is further increased. These results are confirmed by MC simulation. The scaling function f(x,y) obtained from the field theory is in good quantitative agreement with the finite-size MC data. Good agreement is also found for the bulk value at . Received 20 July 1999 and Received in final form 11 November 1999     

Instabilities in population dynamics

Biologists have long known that the smaller the population, the more susceptible it is to extinction from various causes. Biologists define minimum viable population size (MVP), which is the critical population size, below which the population has a very small chance to survive. There are several theoretical models for predicting the probability that a small population will become extinct. But these models either embody unrealistic assumptions or lead to currently unresolved mathematical problems. In other popular models of population dynamics, like the logistic model, MVP does not exist. In this paper we find the existence of such a critical concentration in a simple model of evolution. We solve this model by a mean field theory and show, in one and two dimensions, the existence of the critical adaptation and concentration below which a population dies out. We also show that, like in the logistic model, above the critical value a population reaches its carrying capacity. Moreover, in the two-dimensional case we find - the so common in biological models - periodic solutions and their biffurcations. Received 15 February 2000