New aspects in the reaction of azomethines with cyclic CH-acidic compounds

Summary Treatment of substituted benzylidene anilines1 a – df with cyclic CH-acidic compounds2a–m in ethanol at room temperature yields in additon/elimination reactions the corresponding arylidene derivatives4 and the 2:1 adducts5. The addition products3, which are formed as intermediates, could not be isolated in any case. The donor/acceptor effect of the substituents on the benzylidene moiety influences to a significant extent the reactivity towards the azomethine carbon.

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Neue Aspekte der Reaktion von Azomethinen mit cyclischen CH-aciden Verbindungen

Zusammenfassung Bei der Umsetzung der substituierten Benzylidenaniline1 a – f mit den cyclischen CH-aciden Verbindungen2 a – m in Ethanol bei Raumtemperatur erhält man in Additions/Eliminierungsreaktionen die Arylidenderivate4 und die 2:1-Addukte5. Die als Intermediat gebildeten Additionsprodukte3 konnten in keinem Fall isoliert werden. Die Donor-bzw. Acceptorwirkung der Substituenten am Benzylidenrest beeinflußt maßgebend die Reaktivität am Azomethinkohlenstoff.

     

Human Group IIA Phospholipase A2—Three Decades on from Its Discovery

Phospholipase A₂ (PLA₂) enzymes were first recognized as an enzyme activity class in 1961. The secreted (sPLA₂) enzymes were the first of the five major classes of human PLA₂s to be identified and now number nine catalytically-active structurally homologous proteins. The best-studied of these, group IIA sPLA₂, has a clear role in the physiological response to infection and minor injury and acts as an amplifier of pathological inflammation. The enzyme has been a target for anti-inflammatory drug development in multiple disorders where chronic inflammation is a driver of pathology since its cloning in 1989. Despite intensive effort, no clinically approved medicines targeting the enzyme activity have yet been developed. This review catalogues the major discoveries in the human group IIA sPLA₂ field, focusing on features of enzyme function that may explain this lack of success and discusses future research that may assist in realizing the potential benefit of targeting this enzyme. Functionally-selective inhibitors together with isoform-selective inhibitors are necessary to limit the apparent toxicity of previous drugs. There is also a need to define the relevance of the catalytic function of hGIIA to human inflammatory pathology relative to its recently-discovered catalysis-independent function.     

The small quantum cohomology of a weighted projective space, a mirror D-module and their classical limits

We first describe a mirror partner (B-model) of the small quantum orbifold cohomology of weighted projective spaces (A-model) in the framework of differential equations: we attach to the A-model (resp. B-model) a quantum differential system (that is a trivial bundle equipped with a suitable flat meromorphic connection and a flat bilinear form) and we give an explicit isomorphism between these two quantum differential systems. On the A-side (resp. on the B-side), the quantum differential system alluded to is naturally produced by the small quantum cohomology (resp. a solution of the Birkhoff problem for the Brieskorn lattice of a Landau–Ginzburg model). Then we study the degenerations of these quantum differential systems and we apply our results to the construction of (classical, limit, logarithmic) Frobenius manifolds.     

分数阶模糊时滞神经网络模型解的存在唯一性和有限时间稳定性

本文介绍了一类分数阶模糊时滞神经网络模型.利用压缩映射原理,讨论了带时滞的分数阶神经网络模型解的存在性和唯一性,并根据Gronwall不等式结合分数阶微分方程的性质,证明了分数阶神经网络模型平衡点的有限时间稳定性,给出了有限时间稳定性的判断准则.最后,给出数值仿真说明了理论结果的正确性.     

The co-degrees of irreducible characters

LetG be a finite group. The co-degree of an irreducible character χ ofG is defined to be the number |G|/χ(1). The set of all prime divisors of all the co-degrees of the nonlinear irreducible characters ofG is denoted by Σ(G). First we show that Σ(G)=π(G) (the set of all prime divisors of |G|) unlessG is nilpotent-by-abelian. Then we make Σ(G) a graph by adjoining two elements of Σ(G) if and only if their product divides a co-degree of some nonlinear character ofG. We show that the graph Σ(G) is connected and has diameter at most 2. Additional information on the graph is given. These results are analogs to theorems obtained for the graph corresponding to the character degrees (by Manz, Staszewski, Willems and Wolf) and for the graph corresponding to the class sizes (by Bertram, Herzog and Mann). Finally, we investigate groups with some restriction on the co-degrees. Among other results we show that ifG has a co-degree which is ap-power for some primep, then the corresponding character is monomial andO _p (G)≠1. Also we describe groups in which each co-degree of a nonlinear character is divisible by at most two primes. These results generalize results of Chillag and Herzog. Other results are proved as well. The paper was written during this author’s visit at the Technion and the University of Tel Aviv. He would like to thank the departments of mathematics at the Technion and the University of Tel Aviv for their hospitality and support.     

How Do Cultural Classes Emerge from Assimilation and Distinction? An Extension of the Cucker-Smale Flocking Model

When cultural tastes are not neutral but hierarchically matched to social status, people assimilate themselves to higher status by consuming cultural goods while distinguishing themselves from lower status by developing new tastes. Extending the Cucker-Smale model for mutual influence among agents, we examine when and how many cultural classes emerge from continuous distributions of tastes and what conditions those classes satisfy, through the assimilation-distinction mechanism. We simulate the models with different initial distributions of tastes (uniform, normal, and chi-square), given various ranges of 2 parameters: (a) the strength and (b) the range of distinction relative to assimilation. Tastes are flocking and cultural classes emerge when the range of assimilation is much larger than that of distinction. The number of classes increases with the strength of distinction, whereas the distance between classes equals the range of distinction. Some properties of emergent classes are mathematically proved. First, in a two-class system, the stronger distinction, the larger the upper class. Second, in a three-class system, the middle class is necessarily larger than the lower class and likely larger than the upper class. Third, a 3-class system cannot emerge if distinction is weaker than assimilation. These properties are universal and do not depend on the initial distribution of cultural tastes. This independence predicts homogeneous cultural classes emerging across different social conditions. Also, the cultural middle class as the largest group may explain why subjective class consciousness is often higher than objective position. Unless assimilating efforts can reach an infinite range, there emerges a cultural outcast at the lowest end of the cultural hierarchy.     

不确定信息处理及在归纳学习中的应用

信息的不确定性是由于模糊性、随机性、不完全性、不精确性等因素造成的,不确定性信息在现实世界中广泛存在.关于这方面的研究主要集中在模糊性这种不确定性上.我们课题组在此领域的研究已经持续20余年,概括起来讲,早期的研究兴趣在于模糊(非可加)测度与积分的理论建立,主要研究了传统的可加测度与积分理论到非可加情况的推广;尔后的兴趣转向为如何用数值方法确定非可加测度;近期的研究兴趣在于从已有数据中获取模糊控制规则以及具有模糊表示的归纳学习问题.近10年的研究曾得到了多项基金项目资助,出版专著3部,发表学术论文100余篇,30余篇被SCI收录,20余篇被EI收录,省级以上奖励3项.以下是我们近期研究工作的一个总结,主要包括模糊决策树归纳;基于模糊信息的决策表简化;产生模糊规则的扩张矩阵算法;模糊归纳学习在其他领域中的应用;基于示例学习的模糊控制等.