New Results on Generalized $c$-Distance Without Continuity in Cone $b$-Metric Spaces over Banach Algebras

In this work, some new fixed point results for generalized Lipschitz mappings on generalized $c$-distance in cone $b$-metric spaces over Banach algebras are obtained, not acquiring the condition that the underlying cone should be normal or the mappings should be continuous. Furthermore, the existence and the uniqueness of the fixed point are proven for such mappings. These results greatly improve and generalize several well-known comparable results in the literature. Moreover, some examples and an application are given to support our new results.     

双一流背景下有机化学精准教学的探究实践*

有机化学课程是本校化学师范和高分子材料与工程2个国家级一流本科专业以及应用化学、制药工程等专业基础必修课程。由于化学师范和非师范专业的培养目标不同,有机化学的精准教学方面也有所差异。主要从理论教学、实验教学和多媒体教学等3个方面对化学师范专业和非师范专业有机化学差异化精准教学进行了探究实践,化学师范专业有机化学的精准教学侧重于培养学生的教学能力,非师范专业有机化学的精准教学侧重于培养学生的应用能力。     

完全非正规Toeplitz算子

In this paper, we show that the hyponormal Toeplitz operator Tφ with trigonometric polynomial symbol φ is either normal or completely non-normal. Moreover, if Tφ is non-normal, then Tφ has a dense set of cyclic vectors. Some general conditions are also considered.     

Scale‐free power‐laws as interaction between progress and diffusion

While scale‐free power‐laws are frequently found in social and technological systems, their authenticity, origin, and gained insights are often questioned, and rightfully so. The article presents a newly found rank‐frequency power‐law that aligns the top‐500 supercomputers according to their performance. Pursuing a cautious approach in a systematic way, we check for authenticity, evaluate several potential generative mechanisms, and ask the “so what” question. We evaluate and finally reject the applicability of well‐known potential generative mechanisms such as preferential attachment, self‐organized criticality, optimization, and random observation. Instead, the microdata suggest that an inverse relationship between exponential technological progress and exponential technology diffusion through social networks results in the identified fat‐tail distribution. This newly identified generative mechanism suggests that the supply and demand of technology (“technology push” and “demand pull”) align in exponential synchronicity, providing predictive insights into the evolution of highly uncertain technology markets. © 2013 Wiley Periodicals, Inc. Complexity 19: 56–65, 2014     

具x/ζ型卷积核的奇异积分方程的求解

讨论了具x/ζ型卷积核的奇异积分方程的求解问题.通过Fourier积分变换,将所讨论的积分方程转化成在一定可解条件下与其同解意义下等价的Riemann边值问题.利用Riemann边值问题理论,分别讨论了在正则和非正则两种情况下的Riemann边值问题,进而得到相对应的x/ζ变量比型卷积核的积分方程一般解及可解条件.     

结构系统可靠性优化设计的神经网络方法

针对具有非正态随机参数的可靠性(优化)设计,提出了随机摄动-Edgeworth级数方法,采用该方法将可靠性概率约束转化为等价的确定型约束,可以迅速准确地获得优化设计信息。针对具有多失效模式的结构系统可靠性优化设计,提出了随机模拟一神经网络方法(MCS—NN),将随机模拟方法与神经网络技术有机结合,为结构系统可靠性优化设计提供了一种新方法。     

Direct and Inverse Problems for a Phase-Field Model with Memory

We consider a semilinear integrodifferential system in non-normal form. Such a system is a generalization of the one that arises in the phase-field theory with memory. We prove an abstract existence and uniqueness theorem and a continuous dependence result for the direct problem. Reformulating the direct problem in a suitable way we prove that the identification problem admits a unique solution.     

对一个统计控制问题的再探讨

本文对利用回归模型进行统计控制的问题进行了进一步研究,发现已有的方法有值得改进之处,并为此提出了一种新的求解控制阈值的方法。模拟和实例研究表明我们的方法适用于一般的误差分布情形,而且在误差分布为非正态时优于已有的方法。     

Whitening as a Tool for Estimating Mutual Information in Spatiotemporal Data Sets

We address the issue of inferring the connectivity structure of spatially extended dynamical systems by estimation of mutual information between pairs of sites. The well-known problems resulting from correlations within and between the time series are addressed by explicit temporal and spatial modelling steps which aim at approximately removing all spatial and temporal correlations, i.e. at whitening the data, such that it is replaced by spatiotemporal innovations; this approach provides a link to the maximum-likelihood method and, for appropriately chosen models, removes the problem of estimating probability distributions of unknown, possibly complicated shape. A parsimonious multivariate autoregressive model based on nearest-neighbour interactions is employed. Mutual information can be reinterpreted in the framework of dynamical model comparison (i.e. likelihood ratio testing), since it is shown to be equivalent to the difference of the log-likelihoods of coupled and uncoupled models for a pair of sites, and a parametric estimator of mutual information can be derived. We also discuss, within the framework of model comparison, the relationship between the coefficient of linear correlation and mutual information. The practical application of this methodology is demonstrated for simulated multivariate time series generated by a stochastic coupled-map lattice. The parsimonious modelling approach is compared to general multivariate autoregressive modelling and to Independent Component Analysis (ICA).     

Approximate maximum likelihood estimation in linear regression

The application of the ML method in linear regression requires a parametric form for the error density. When this is not available, the density may be parameterized by its cumulants ( _i ) and the ML then applied. Results are obtained when the standardized cumulants ( _i ) satisfy _i = _i+2/ ₂ ^(i+2)/2 =O(v ⁱ ) asv 0 fori>0.Research financed in part by the Research Center of the Athens University of Economics and Business.