Nodal Solutions of a p-Laplacian Equation

We prove that the p-Laplacian problem –_p u = f(x, u),with u on a bounded domain R^N, with p > 1 arbitrary, has a nodal solution providedthat f : x R R is subcritical, and f(x, t) / |t|^p –² is superlinear. Infinitely many nodal solutions are obtainedif, in addition, f(x, –t) = –f(x, t). 2000 MathematicsSubject Classification 35J20, 35J65, 58E05.     

On the Nature of Functional Differentiation: The Role of Self-Organization with Constraints

The focus of this article is the self-organization of neural systems under constraints. In 2016, we proposed a theory for self-organization with constraints to clarify the neural mechanism of functional differentiation. As a typical application of the theory, we developed evolutionary reservoir computers that exhibit functional differentiation of neurons. Regarding the self-organized structure of neural systems, Warren McCulloch described the neural networks of the brain as being “heterarchical”, rather than hierarchical, in structure. Unlike the fixed boundary conditions in conventional self-organization theory, where stationary phenomena are the target for study, the neural networks of the brain change their functional structure via synaptic learning and neural differentiation to exhibit specific functions, thereby adapting to nonstationary environmental changes. Thus, the neural network structure is altered dynamically among possible network structures. We refer to such changes as a dynamic heterarchy. Through the dynamic changes of the network structure under constraints, such as physical, chemical, and informational factors, which act on the whole system, neural systems realize functional differentiation or functional parcellation. Based on the computation results of our model for functional differentiation, we propose hypotheses on the neuronal mechanism of functional differentiation. Finally, using the Kolmogorov–Arnold–Sprecher superposition theorem, which can be realized by a layered deep neural network, we propose a possible scenario of functional (including cell) differentiation.     

基于全息聚焦机理空间光孤子的相互作用势函数

利用变分法讨论了反向传输的基于全息聚焦机理空间光孤子的相互作用,导出了相干和非相 干相互作用的势函数.当孤子间的相对相位不随传输距离变化或相对相位对传输距离的偏导 数与孤子间距无关时,相干和非相干相互作用势函数都与孤子间的相对相位无关,出现孤子间 反常相互作用,这正好是近期文献的结果. 关键词： 空间光孤子 相互作用 变分原理     

Variational principles for two kinds of extended Korteweg—de Vries equations

Variational principles are constructed using the semi-inverse method for two kinds of extended Korteweg—de Vries (KdV) equations, which can be regarded as simple models of the nonlinear oceanic internal waves and atmospheric long waves, respectively. The obtained variational principles have also been proved to be correct.     

变分原理分析开裂简支箱梁剪力滞效应

变分原理通常应用于箱形截面梁剪力滞效应弹性分析,本文基于换算截面法,运用变分原理推导了预应力混凝土简支箱梁均布荷载作用、钢筋混凝土简支箱梁集中荷载作用的剪力滞系数计算公式,考虑了混凝土开裂对箱梁剪力滞效应的影响,并与试验结果和规范方法进行了对比分析。变分原理分析开裂混凝土箱梁剪力滞效应方法力学概念明确,是其弹性分析适用范围的拓展,亦可推广应用到混凝土连续箱梁开裂后的剪力滞效应分析,具有广阔的应用前景。     

Structure of ^6He in the frame of a cluster model

A microscopic cluster model with a fully correlated Gaussian basis is developed. In the model, the stochastic variational method is used in order to calculate the ground-energy and the mean-square radius conveniently. Based on this model, the ground-energy level and radius of the neutron halo nucleus, ⁶He, are calculated as a α+n+n three-cluster model. The results are in good agreement with the experimental data.     

广义经典力学系统的第一积分与变分方程特解的联系

给出了广义经典力学系统的变分方程,研究了变分方程的解与系统的第一积分之间的联系,并证明可由系统的第一积分求得变分方程的特解. 关键词： 广义经典力学系统 第一积分 变分方程     

厄尔尼诺和南方涛动海气耦合模型中参数估计的变分方法

提出一种基于变分原理估计厄尔尼诺和南方涛动海气耦合模型中未知参数的方法. 首先将所研究的非线性海气耦合动力方程引入到目标泛函中; 接着利用变分方法导出伴随方程和待辨识参数泛函梯度的公式; 然后设计了估计未知参数的算法.数值试验结果表明变分方法是一 种能有效估计海气耦合非线性系统未知参数的方法.     

Hydrogenation of Pd-capped Mg thin films prepared by DC magnetron sputtering

Structural and optical properties of pure Mg thin film coated with Pd have been investigated. Pd-capped Mg thin films had been prepared by DC magnetron sputtering. This work presents an ex situ study on hydrogenation and dehydrogenation kinetics of Pd/Mg films at different conditions using XRD, AFM and optical spectrophotometer. We have succeeded to load thin films of Mg to MgH₂ at normal temperature and normal pressure of hydrogen gas. In hydrogenation, α-MgH₂ phase of magnesium hydride was observed in hydrogenated films at 200 °C and γ-MgH₂ at 250 °C respectively. The desorption kinetics in vacuum also revealed the phase transformation α-MgH₂ to γ-MgH₂. A reflectance change was observed in hydrogenated films in comparison of as deposited thin film. Hydrogenated (H loaded) samples were observed partially transparent in comparison of as deposited.     

Penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions

The penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions is investigated in this paper. Since this class of nonlinear slip boundary conditions include the subdifferential property, the weak variational formulation is a variational inequality problem of the second kind. Using the penalty finite element approximation, we obtain optimal error estimates between the exact solution and the finite element approximation solution. Finally, we show the numerical results which are in full agreement with the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.