激光大气闪烁的分形分析

 采用分形理论分析了激光大气闪烁的统计特征。研究结果表明：在弱起伏条件下，激光大气闪烁的分形维和奇异性随光强起伏的增强而增大，而其长期相关性则减小；不同Fresnel尺度下具有相同闪烁指数的激光大气闪烁的分形特征存在着明显的差别；在强起伏条件下，有限的数据中尚未发现分形维有饱和现象，因此可以用来描述激光大气闪烁的强度。     

考虑情感的三策略囚徒困境博弈模型与合作演化

基于社会比较情境下强者和弱者之间产生的同情、欺凌、漠然、尊敬、嫉妒和畏惧等6种情感,建立个体情感特征的定量表达方法。考虑情感驱动的三策略囚徒困境博弈模型,设计了6种情感与合作、背叛及孤独3个博弈策略之间的对应关系和定量表达机制。采用二维格子网络、随机网络和无标度网络等三种网络模型进行演化博弈仿真分析。结果显示:较大的背叛成功诱惑促进了采取背叛策略的情感类型发展演化和繁荣稳定,系统的最终演化状态都体现出程度不同的负性情感特征;空间网络结构对情感类型和合作行为的演化存在重要影响,无标度网络结构能够导致具有一定良性特征的情感类型演化稳定,并带来较高的合作水平;从社会比较及由此产生的对比效应和同化效应的角度,对三种网络下不同的情感演化状态进行了相应阐释。     

ANALYSIS OF THE CHAOTIC DYNAMICS OF A HIGH-FLUX CFB RISER USING SOLIDS CONCENTRATION MEASUREMENTS

A high-flux circulating fluidized bed （CFB） riser （0.076-m I.D. and 10-m high） was operated in a wide range of operating conditions to study its chaotic dynamics, using FCC catalyst particles （dp= 67μm, ρp = 1500 kg·m^-3）. Local solids concentration fluctuations measured using a reflective-type fiber optic probe were processed to determine chaotic invariants （Kolmogorov entropy and correlation dimension）, Radial and axial profiles of the chaotic invariants at different operating conditions show that the core region exhibits higher values of the chaotic invariants than the wall region. Both invariants vary strongly with local mean solids concentration. The transition section of the riser exhibits more complex dynamics while the bottom and top sections exhibit a more uniform macroscopic and less-complex microscopic flow structure. Increasing gas velocity leads to more complex and less predictable solids concentration fluctuations, while increasing solids flux generally lowers complexity and increases predictability. Very high solids flux, however, was observed to increase the entropy.     

A construction of a robust family of exponential attractors

Given a dissipative strongly continuous semigroup depending on some parameters, we construct a family of exponential attractors which is robust, in the sense of the symmetric Hausdorff distance, with respect to (even singular) perturbations.

     

Bi-Lipschitz homogeneous curves in are quasicircles

We show that a bi-Lipschitz homogeneous curve in the plane must satisfy the bounded turning condition, and that this is false in higher dimensions. Combined with results of Herron and Mayer this gives several characterizations of such curves in the plane.

     

Benzoxazolyl-and benzothiazolyl-guanidines in three-component reactions

The previously unknown three component condensation of hetarylguanidines, orthoesters, and active methylene carbonyl compounds has been studied. Depending on the nature of the latter products of both linear combination and subsequent cyclizationl leading to pyrimidine or tetrahydroquinazoline structures were obtained. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, 1080–1088, July, 2006.     

Asymptotic order of quantization for Cantor distributions in terms of Euler characteristic, Hausdorff and Packing measure

For homogeneous one-dimensional Cantor sets, which are not necessarily self-similar, we show under some restrictions that the Euler exponent equals the quantization dimension of the uniform distribution on these Cantor sets. Moreover for a special sub-class of these sets we present a linkage between the Hausdorff and the Packing measure of these sets and the high-rate asymptotics of the quantization error.     

On the Koszul Modules of Exterior Algebras

We prove that the Koszul modules over an exterior algebra can be filtered by the cyclic Koszul modules. We also introduce the cyclic dimension vector as invariants for studying the Koszul modules over an exterior algebra.     

Fractal Dimensions for Repellers of Maps with Holes

In this work we study the Hausdorff dimension and limit capacity for repellers of certain non-uniformly expanding maps f defined on a subset of a manifold. This subset is covered by a finite number of compact domains with pairwise disjoint interiors (the complement of the union of these domains is called hole) each of which is mapped smoothly to the union of some of the domains with a subset of the hole. The maps are not assumed to be hyperbolic nor conformal. We provide conditions to ensure that the limit capacity of the repeller is less than the dimension of the ambient manifold. We also prove continuity of these fractal invariants when the volume of the hole tends to zero.