Sparse generalized Fourier transforms

Block-diagonalization of sparse equivariant discretization matrices is studied. Such matrices typically arise when partial differential equations that evolve in symmetric geometries are discretized via the finite element method or via finite differences. By considering sparse equivariant matrices as equivariant graphs, we identify a condition for when block-diagonalization via a sparse variant of a generalized Fourier transform (GFT) becomes particularly simple and fast. Characterizations for finite element triangulations of a symmetric domain are given, and formulas for assembling the block-diagonalized matrix directly are presented. It is emphasized that the GFT preserves symmetric (Hermitian) properties of an equivariant matrix. By simulating the heat equation at the surface of a sphere discretized by an icosahedral grid, it is demonstrated that the block-diagonalization is beneficial. The gain is significant for a direct method, and modest for an iterative method. A comparison with a block-diagonalization approach based upon the continuous formulation is made. It is found that the sparse GFT method is an appropriate way to discretize the resulting continuous subsystems, since the spectrum and the symmetry are preserved. AMS subject classification (2000)  43A30, 65T99, 20B25     

在Triton X—100存在下,用2-(5-溴-2-吡啶偶氮)-5-二乙胺基苯酚(5-Br-PADAP)分光光度测定方钍石中的钍

方钍石是钍来源的重要含钍矿物。目前测定钍的含量的方法较多,虽有用5-Br-PADAP测定钍的方法的报导,但未见有在triton X-100存在下,用5-Br-PADAP直接测定方钍石中钍的含量的报导。Triton X-100的存在,使测定的酸度增加,从而增加干扰元素的干扰比;并且增加了络合物的稳定时间。本文采用5-Br-PADAP作显色剂,在氯乙酸-氯乙酸钠缓冲体系中用triton X-100表面活性剂胶束增溶分光光度测定方钍石(人工样品)中钍的含量,获得较满意的结果。在25毫升中,钍的比耳定律范围在0～20微克,摩尔吸光系数为5.2×10~4升·摩尔~(-1)·厘米~(-1),Sandell灵敏度为0.0045微克钍(IV)/厘米~2。我们对两种含量的方钍石人工样品进行了测试,结果良好,回收率在97.3～101.4％之间,此方法可靠,精密度较高,误差符合微量组分的测定要求,我们对样品测定结果表示满意。     

Generalized Physical and SRB Measures for Hyperbolic Diffeomorphisms

In this paper we introduce the notion of generalized physical and SRB measures. These measures naturally generalize classical physical and SRB measures to measures which are supported on invariant sets that are not necessarily attractors. We then perform a detailed case study of these measures for hyperbolic Hènon maps. For this class of systems we are able to develop a complete theory about the existence, uniqueness, finiteness, and properties of these natural measures. Moreover, we derive a classification for the existence of a measure of full dimension. We also consider general hyperbolic surface diffeomorphisms and discuss possible extensions of, as well as the differences to, the results for Hènon maps. Finally, we study the regular dependence of the dimension of the generalized physical/SRB measure on the diffeomorphism. For the proofs we apply various techniques from smooth ergodic theory including the thermodynamic formalism. 2000 Mathematics Subject Classification. Primary: 37C45, 37D20, 37D35, Secondary: 37A35, 37E30     

正丁基苝四羧酸二酰亚胺的晶型和性能研究

文章合成了N,N'-二正丁基苝四羧酸二酰亚胺,并纯化、调晶,进行了IR、元素分析、X射线等测定.分析该化合物在DMF中的紫外光谱(最大吸收波长524.80 nm)、荧光光谱(最大发射波长539.0 nm)、Stokes位移(数值15 nm)等光谱性质.在400～700 nm范围内,α晶型薄膜紫外-可见吸收出现很强的吸收峰,且由β型变为α型,最大吸收波长有明显的红移(545 nm变为580 nm).X射线粉末衍射也反映出α晶型的2θ在26.0°处衍射峰CPS为2 508,β型在25.2°为1 891.α,β晶型作为电荷产生材料制得的功能分离型有机光导体,在光源滤波波长λ=532 nm曝光下,测得含α,β感光体达到饱和电位的时间分别为46,93.98 s,光衰电位(5.3千伏电压负充电电晕,1～2 s后的表面电位)分别为727和525 V,半衰曝光量分别为4.32,4.34μJ·cm-2,残余电位分别为30和45 V等光导性能数值.     

Beyond Cartesian limits: Leibniz's passage from algebraic to “transcendental” mathematics

This article deals with Leibniz's reception of Descartes' “geometry.” Leibnizian mathematics was based on five fundamental notions: calculus, characteristic, art of invention, method, and freedom. On the basis of methodological considerations Leibniz criticized Descartes' restriction of geometry to objects that could be given in terms of algebraic (i.e., finite) equations: “Descartes's mind was the limit of science.” The failure of algebra to solve equations of higher degree led Leibniz to develop linear algebra, and the failure of algebra to deal with transcendental problems led him to conceive of a science of the infinite. Hence Leibniz reconstructed the mathematical corpus, created new (transcendental) notions, and redefined known notions (equality, exactness, construction), thus establishing “a veritable complement of algebra for the transcendentals”: infinite equations, i.e., infinite series, became inestimable tools of mathematical research.     

基于改善空间关联性的混沌控制

基于混沌信号的统计特性，提出了一种通过改善混沌信号的空间关联性实现混沌控制的方法.以Hénon离散混沌系统和四阶Chua's电路超混沌连续系统为例进行了数值研究，验证了这种控制方法的有效性.结果表明， 通过改善混沌信号之间的空间关联性， 混沌系统能以较快的速度收敛到它的平衡点或多种周期轨道. 关键词： 混沌控制 空间关联性 Hénon系统 四阶Chua's电路     

Numerical simulation and experimental validation of heat transfer within rotating flows for three‐dimensional non‐axisymmetric,turbulent conditions

A control volume type numerical methodology for the analysis of steady three‐dimensional rotating flows with heat transfer, in both laminar and turbulent conditions, is implemented and experimentally tested. Non‐axisymmetric momentum and heat transfer phenomena are allowed for. Turbulent transport is alternatively represented through three existing versions of the k–ε model that were adjusted to take into account the turbulence anisotropy promoted by rotation, streamline curvature and thermal buoyancy. Their relative performance is evaluated by comparison of calculated local and global heat balances with those obtained through measurements in a laboratory device. A modified version of the Lam and Bremhorst, low Reynolds number model is seen to give the best results. A preliminary analysis focused on the flow structure and the transfer of heat is reported. Copyright © 2002 John Wiley & Sons, Ltd.     

Lagrangean heuristics combined with reoptimization for the 0-1 bidimensional knapsack problem

First, this paper deals with lagrangean heuristics for the 0-1 bidimensional knapsack problem. A projected subgradient algorithm is performed for solving a lagrangean dual of the problem, to improve the convergence of the classical subgradient algorithm. Secondly, a local search is introduced to improve the lower bound on the value of the biknapsack produced by lagrangean heuristics. Thirdly, a variable fixing phase is embedded in the process. Finally, the sequence of 0-1 one-dimensional knapsack instances obtained from the algorithm are solved by using reoptimization techniques in order to reduce the total computational time effort. Computational results are presented.     

不同方法制备的CO2-3替换磷灰石固溶体晶体化学的FTIR研究

采用不同方法制备了CO2-3替换的磷灰石固溶体,利用FTIR结合XRD对其进行了晶体化学研究,结果表明均相沉淀法制备的碳羟磷灰石(CHAP)属B型替换且替换方式是[CO3·OH]四面体替换[PO4]四面体;固相离子交换法制备的CHAP属A型替换且替换方式是[CO3]三角形配位体替换通道位置的OH-;固相反应法制备的碳氟磷灰石(CFAP)属B型替换,其替换方式是[CO3·F]四面体替换[PO4]四面体;sol-gel法制备的CHAP属AB混合型替换,其Ψ3分裂为Ψ3-1,Ψ3F,Ψ3-4.高斯函数法拟合表明Ψ3F峰是A型替换的Ψ3-2与B型替换的Ψ3-3的叠合.当WCO2-3＜3.34%时,随CO2-3含量增加,A型替换量增大,且当WCO2-3=3.34%时达最大值,当3.34%＜WCO2-3＜7.52%时,随CO2-3含量增加,B型替换量增大,且当WCO2-3= 7.52%时亦到饱和.     

The Role of a Specific Response of Media in the Vavilov-Cherenkov Effect

It is shown that the condition υ > υ_p (ω), which is necessary in order to trigger the Vavilov-Cherenkov effect, determines the interval of radiated frequencies and it alone cannot establish a strong restriction to the velocity of the particle. It is exhibited that it is possible to define a general lower bound for the velocity of the particle, which does not depend on the frequency when both, a specific response of the medium is taken into account and the mentioned condition is considered. The minimum value of the phase velocity of light in the medium determines the existence of such general lower bound.