一类具无穷时滞泛函微分方程的周期解

讨论具有无穷时滞中立型泛函微分方程$ \frac{\rm d}{{\rm d}t}\left(x(t)-\int_{-\infty}^{0}g(s,x(t+s)){\rm d}s\right) =A(t,x(t))x(t)+f(t,x_t)$的周期解问题,利用重合度理论中的延拓定理得到了周期解的存在性和唯一性条件;特别地,当$g(s,x)\equiv 0, A(t,x)=A(t)$时, 给出了存在唯一稳定周期解的条件.     

Multiple nontrivial solutions for nonlinear periodic problems with the p-Laplacian

We consider a nonlinear periodic problem driven by the scalar p-Laplacian with a nonsmooth potential (hemivariational inequality). Using the degree theory for multivalued perturbations of (S)₊-operators and the spectrum of a class of weighted eigenvalue problems for the scalar p-Laplacian, we prove the existence of at least three distinct nontrivial solutions, two of which have constant sign.     

Coupling leads to chaos

The main goal of this paper is to prove analytically the existence of strange attractors in a family of vector fields consisting of two Brusselators linearly coupled by diffusion. We will show that such a family contains a generic unfolding of a 4-dimensional nilpotent singularity of codimension 4. On the other hand, we will prove that in any generic unfolding Xμ of an n-dimensional nilpotent singularity of codimension n there are bifurcation curves of (n−1)-dimensional nilpotent singularities of codimension n−1 which are in turn generically unfolded by Xμ. Arguments conclude recalling that any generic unfolding of the 3-dimensional nilpotent singularity of codimension 3 exhibits strange attractors.     

琼脂凝胶中形成铬酸铅周期性沉淀的机理研究

选择硝酸铅和铬酸钾作为相互扩散的反应物以形成铬酸铅在琼脂凝胶中的周期性沉淀．分别在光照和黑暗中对六种不同浓度的硝酸铅溶液进行了实验．根据实验现象对周期性沉淀的形成提出了可能的机理．认为光辐射可使铬酸铅部分电离，从而减慢了胶核成长速率，有利于汇聚成带．     

Estimation of diffusion coefficient of Ba++ ions in silica gel from periodic precipitation of BaMoO4

Formation of Liesegang rings on the growth of BaMoO₄ crystals in silica gel by single diffusion is discussed. The rhythmic precipitation is found to be influenced profoundly by (a) the molarity of inner and outerelectrolytes (b) the age of gel and (c) the pH of the gel medium. The time law, spacing law and the law relating diffusion depth and width are verified. A method to estimate the diffusion coefficient of the outer electrolyte in the gel medium is developed and calculated for Ba⁺⁺ions.     

Qualitative properties of pulsating fronts for reaction–advection–diffusion equations in periodic excitable media

In this paper, we study the pulsating fronts of reaction–advection-diffusion equations with two types of nonlinear term in periodic excitable media. Firstly, for the case with combustion nonlinearity, the unique front is proved to decay exponentially when it approaches the unstable limiting state. Secondly, for the degenerate monostable type nonlinearity, it is shown that the front with critical speed is unique, monotone and decays exponentially at negative end, while the fronts of noncritical speeds decay to zero non-exponentially.     

Relativistic calculations on the ground and excited states of AgH and AuH in cylindrical harmonic confinement

The relativistic ground and low-lying excited state potential energy curves of AgH and AuH in the presence of a cylindrical harmonic confining potential were calculated using the multi-state multi-reference perturbation theory with the spin-free no-pair Hamiltonian obtained via the third-order Douglas–Kroll transformation, incorporated with the full two-electron Breit–Pauli spin–orbit operator. The spectroscopic parameters were obtained for both the scalar- and quasi-relativistic potentials. The spin–orbit coupling constants were calculated for several strengths of the confining potential, and the effects of the applied potential on the coupling constants were analyzed using configuration interaction. This paper is dedicated to Serafín Fraga—colleague, mentor, and friend.     

Bifurcation phenomena near homoclinic systems: A two-parameter analysis

The bifurcations of periodic orbits in a class of autonomous three-variable, nonlinear-differential-equation systems possessing a homoclinic orbit associated with a saddle focus with eigenvalues ( ±i,), where ¦/¦ < 1 (Sil'nikov's condition), are studied in a two-parameter space. The perturbed homoclinic systems undergo a countable set of tangent bifurcations followed by period-doubling bifurcations leading to periodic orbits which may be attractors if ¦/¦ < 1/2. The accumulation rate of the critical parameter values at the homoclinic system is exp(-2¦/¦). A global mechanism for the onset of homoclinicity in strongly contractive flows is analyzed. Cusp bifurcations with bistability and hysteresis phenomena exist locally near the onset of homoclinicity. A countable set of these cusp bifurcations with scaling properties related to the eigenvalues±i of the stationary state are shown to occur in infinitely contractive flows. In the two-parameter space, the periodic orbit attractor domain exhibits a spiral structure globally, around the set of homoclinic systems, in which all the different periodic orbits are continuously connected.     

ADSORPTION OF 2,4-D ON MODIFIED HYPERCROSSLINKED POLYSTYRENE （NDA-99） AND XAD-4 RESIN

The adsorption behavior of pesticide 2,4-dichlorophenoxyacetic acid (2,4-D) in aqueous solution has been investigated using a hypercrosslinked polystyrene adsorbent (NDA-99) modified by dimethylamine group as well as a nonionic macroporous adsorbent (XAD-4). The Langmuir and Freundlich isotherm models were employed to fit the experimental data to describe adsorption mechanism. It shows that NDA-99 resin exhibits an adsorption affinity for 2,4-D higher than XAD-4 resin owing to its exceptional micropore structure and the amine group of the hypercrosslinked matrix.Further studies indicate that the hydrogen bonding interaction and the stronger π-π conjugation play a significant role in the course of the adsorption of 2,4-D on NDA-99 resin, which is in agreement with the IR spectroscopic results and the △E values of HOMO (the highest occupied molecular orbit) of adsorbent and LUMO (the lowest unoccupied molecular orbit) of adsorbate calculated from the MINDO/3 model.     

8,10-二炔廿五碳酸LB膜的周期结构

合成了8,10-二炔廿五碳酸,在玻璃片、石英片和镀金片上沉积了它的LB膜,X-射线衍射研究了LB膜的周期结构和聚合对它的影响。在2θ=1°—15°范围内观察到了多达7个布拉格衍射峰。由此计算了等同周期和分子在基片上的倾斜角。用分子模型计算了衍射峰强度,得到了与实验结果相符合的衍射峰强度奇偶起伏现象。