New minimax inequality with applications to existence theorems of equilibrium points

A new minimax inequality is proved on a set which is the union of an increasing sequence of compact convex sets in a topological vector space. As applications, several existence theorems of equilibrium points for different games are obtained.The authors would like to thank the referees for their helpful suggestions.     

A neuro-fuzzy system for X-ray spectra interpretation

A decision scheme for the interpretation of spectra from wavelength dispersive X-ray fluorescence spectrometry is described that encompasses elements from three areas of artificial intelligence: fuzzy logic, rule based expert systems and neural net technology.After transforming the recorded spectra to line spectra by appropriate background correction a reasoning scheme is applied that takes into account not only the observed spectra, but also the recording conditions and prior spectroscopic information regarding the relative emission probabilities and the usefulness of the different lines for the purpose of element identification. The latter is done on the basis of a previously described scheme to compute conditional a posteriori Bayes probabilities for a mean matrix. These different pieces of information are then assembled into a battery of fuzzy rules. The importance of the rules as well as the importance of the X-ray lines is determined in a training process, similar to the one in a feedforward back-propagation network.To further stabilize the results this network is pruned in a second training cycle. This, however, had little effect on the quality of interpretation.The advantages of this approach to the interpretation of X-ray spectra over older ones are numerous: the system adapts itself to better interpret spectra that are of greater importance to a laboratory as these are better represented in the training set; the fuzzy logic is capable of working with incomplete and uncertain knowledge, and the neural network results based on these fuzzy rules is readily interpretable by the X-ray spectroscopist as every rule can be expressed also in natural language as in any classical rule based system.On leave from Silesian University, Katowice, Poland     

Liouville theorems for stable solutions of semilinear elliptic equations with convex nonlinearities

We extend our recent results on the classification of stable solutions of the equation −Δu=f(u)$-\Delta u=f\left(u\right)$ in R^N${\mathbb{R}}^N$, where f≥0$f\ge 0$ is a general convex, non-decreasing function.     

基于云模型的三维土工网防护边坡侵蚀稳定性综合评价

在分析各项影响因素分级标准的基础上,建立了三维土工网护坡侵蚀稳定性的综合评价体系.针对三维土工网边坡侵蚀稳定性分析中不确定性问题,将云模型理论引入到综合评判中,实现了定性与定量的不确定性转换.通过构建前件云发生器和后件云发生器,利用不确定推理,确定各项评价指标的具体分值.借助层次分析法与敏感度分析确定各项评价指标的权重,进而得出综合评价体系的整体得分.工程实例计算结果证实了模型的实用性和有效性,为三维土工网防护边坡侵蚀稳定性的评价提供了一条新的途径.     

一类含有合作的网站竞争模型

在网站动态竞争模型的基础上,建立了含有真正的合作关系的网站竞争模型.随后对二维的特殊情况进行了定性分析,结合给出的数值模拟图,分析了模型中的相关系数对系统的作用,并针对分析的结果讨论了影响网站发展的主要因素.