一种奇异临界椭圆方程的非平凡解

该文研究了一类带有Sobolev-Hardy临界指数的半线性椭圆方程,运用变分理论中的环绕定理证明了方程非平凡解的存在性     

Interactive Visualization of Hierarchically Structured Data

We introduce methods for visualization of data structured along trees, especially hierarchically structured collections of time series. To this end, we identify questions that often emerge when working with hierarchical data and provide an R package to simplify their investigation. Our key contribution is the adaptation of the visualization principles of focus-plus-context and linking to the study of tree-structured data. Our motivating application is to the analysis of bacterial time series, where an evolutionary tree relating bacteria is available a priori. However, we have identified common problem types where, if a tree is not directly available, it can be constructed from data and then studied using our techniques. We perform detailed case studies to describe the alternative use cases, interpretations, and utility of the proposed visualization methods.     

Existence of solutions for a class of noncooperative elliptic systems

We establish the existence of a nontrivial solution for a class of noncooperative elliptic systems with nonlinearities of superlinear growth. Moreover, if there is resonance, we also find at least a solution. All results are obtained by the minimax methods in critical point theory.     

一类拟线性椭圆方程的非平凡解

运用环绕理论和对称型山路理论对一类具有次临界多项式增长和次临界指数增长的$p$-Laplacian方程建立一个非平凡解(无穷多个非平凡解)的存在性结果.     

Linking solutions for p-Laplace equations with nonlinearity at critical growth

Under a suitable condition on n and p, the quasilinear equation at critical growth −Δpu=λ|u|^p−2u+|u|^p∗−2u is shown to admit a nontrivial weak solution for any λ?λ₁. Nonstandard linking structures, for the associated functional, are recognized.     

带跳跃非线性边界的p-Laplacian问题(英文)

利用Fadell与Rabinowitz提出的同调指标理论,研究了一类带不定权非线性边界的p-Laplacian特征值问题;更进一步,利用环绕定理,证明了一类带跳跃非线性边界的p-Laplacian问题非平凡解的存在性.     

Causal relations via linking in twistor space

We investigate the relationship between two different notions on linking, one homological and one holomorphic, in a twistorial context. The two notions turn out to be supprisingly closely related.     

电镜联机图象处理与分析系统的研制

设计了一个慢扫描图象结口与通用微机联接。不用帧存贮器，实现了扫描电镜图象采集、数字处理和返回电镜拍照，图象空间分辨率达到１０２４×７６８，图象灰度分辩率达到２５６级；除了图象处理和分析测量功能具有新的特色外，还将目前非常活跃的分形分析方法融入其中；采用浮雕式全汉化菜单（也可用西文），弹出式提示和问答窗口；菜单和图象同屏幕显示，结构紧凑。     

Periodic solutions of second order discrete Hamiltonian systems with potential indefinite in sign

In this paper, an existence theorem is obtained for the periodic solutions of second-order discrete Hamiltonian systems with potential indefinite in sign by Linking theorem in the critical point theory.     

Existence theorems for second-order discrete boundary value problems

This article is concerned with the existence of solutions of boundary value problems for nonlinear second-order difference equations of the type , where δ>0 is the ratio of odd positive integers, {p_n} and {q_n} are real sequences. The authors apply the Linking Theorem and the Mountain Pass Lemma in the critical point theory and give some new results for the existence of solutions.