Finite Zeitübersetzung mit Extrapolation in der nichtlinearen Strukturdynamik

Übersicht Die Simulation steifer Differentialgleichungssysteme sehr hoher Ordnung durch implizite Runge-Kutta-Verfahren (gelegentlich auch nach Padé benannt) ist global weitgehend theoretisch geklärt. Bei der konkreten Behandlung von Aufgaben der nichtlinearen Strukturdynamik ist man jedoch zu vielfältigen Zusatzüberlegungen genötigt, um zu vertretbaren Rechenzeiten zu gelangen. Anknüpfend an die bewährte gleichgradige quadratische Padé-Entwicklung oder auch kubische Interpolation am System 1. Ordnung wird die Konvergenzbeschleunigung durch Extrapolation der Nichtlinearitäten belegt. Weiterhin werden Phänomene der modalen Reduktion beim Zusammenwirken verschiedener Steifigkeiten aufgezeigt.

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Finite elements in time with extrapolation in nonlinear structural dynamics

Summary Today the theory of integrating stiff differential equations of high order by implicit Runge-Kutta methods (sometimes called Padé approximations) is developed very well especially concerning global properties. Nevertheless, additional considerations must be done in order to minimize the numerical effort when special problems from nonlinear structural dynamics are to be solved. Using a quadratic Padé-approximation or a cubic interpolation for the first-order-system it is shown that the rate of convergence profits from extrapolating the nonlinearities. Some observations and comments on modal reduction for problems characterized by multiple stiffnesses are added.

     

带风险指数的金融均衡的存在性定理及其结构特征(下)

本文主要论证了在不完全市场条件下带风险指数的金融均衡的存在性，并揭示其均衡结构的特征．本文中建立的模型是一、二期货币投入产出金融经济且具有可微的资产结构，这一模型包括了许多具有特殊资产结构的均衡模型，如实资产结构、虚资产结构、恒秩资产结构的均衡模型．因此本文的这一模型具有广泛的应用前景和实用价值．接着给出了本文的金融均衡的存在性定理，再借助微分拓扑给出它的证明过程，这一证明过程较之以前证明均衡存在性的经典方法（如Duffie，D＆W．Shfer（1985）的方法）要简便得多．同时也应注意到本文的这一结论既适用于资产市场下会随机风险因素的情形，也适用于商品空间为无限维的情形，除此之外，还给出了怎样判别资产结构是否属于T类的判别法，为检验均衡存在性提供了更为便利的途径．最后，本文论证了在金融市场里，尽管由于稀缺性的存在，从而导致均衡分配的多样化，然而均衡分配集却形成了一光滑子流，但该流形的维数与稀缺性有关．换句话说，尽管市场是不完全的，但均市分配不确定性的反却是可比的．如此使得人们对均衡资产结构的认识更进一步．     

On Two Measures of Problem Instance Complexity and their Correlation with the Performance of SeDuMi on Second-Order Cone Problems

We evaluate the practical relevance of two measures of conic convex problem complexity as applied to second-order cone problems solved using the homogeneous self-dual (HSD) embedding model in the software SeDuMi. The first measure we evaluate is Renegar's data-based condition measure C(d), and the second measure is a combined measure of the optimal solution size and the initial infeasibility/optimality residuals denoted by S (where the solution size is measured in a norm that is naturally associated with the HSD model). We constructed a set of 144 second-order cone test problems with widely distributed values of C(d) and S and solved these problems using SeDuMi. For each problem instance in the test set, we also computed estimates of C(d) (using Peña’s method) and computed S directly. Our computational experience indicates that SeDuMi iteration counts and log (C(d)) are fairly highly correlated (sample correlation R = 0.675), whereas SeDuMi iteration counts are not quite as highly correlated with S (R = 0.600). Furthermore, the experimental evidence indicates that the average rate of convergence of SeDuMi iterations is affected by the condition number C(d) of the problem instance, a phenomenon that makes some intuitive sense yet is not directly implied by existing theory.     

Enantioseparation of Dencichine and D-Isomer on L-Cysteine Derivative Phase by Ligand-exchange Chromatography

Dencichine (β-N-oxalyl-L-α, β-diaminopropionic acid, L-ODAP), a nonprotein amino acid, is a haemostatic agent present in important Chinese medicinal herbs such as Panax notoginseng, as well as other Panax species1. It was first isolated from the seeds …     

完全可分的三元系TS(v,4)的支撑集

§ 1　 IntroductionA triple system of order v and indexλ,denoted by TS(v,λ) ,is a collection of3- ele-mentsubsets Aof a v- set X,so thatevery 2 - subsetof X appears in preciselyλ subsets of A.L etλ≥ 2 and (X,A) be a TS(v,λ) .If Acan be partitioned into t(≥ 2 ) parts A1,A2 ,...,Atsuch that each (X,Ai) is a TS(v,λi) for 1≤ i≤ t,then (X,A) is called de-composable.Otherwise it is indecomposable.If t=λ,λi=1for 1≤ i≤ t,the TS(v,λ) (X,A) is called completely decomposable.It …     

基于TMS320C5410EVM板的IIR数字滤波器的设计

本文研究DSP中的IIR数字滤波器的原理和用MATLAB在TMS320C5410EVM中设计IIR数字滤波器的过程和设计方法以及程序的调试方法。     

三维Minkowski空间中的曲面及其可积性

利用可积系统的思想,借助三维Minkowski空间L3的矩阵模型,研究了L3中具有调和逆平均曲率的类空曲面和洛伦兹调和逆平均曲率类时曲面的可积性及其形变.     

Enumeration on Nonseparable Planar Maps

This paper provides some functional equations satisfied by the generating functions for nonseparable rooted planar maps with the valency of root-vertex, the number of edges and the valency of root-faces of the maps as three parameters. But the solutions of these equations can only be obtained indirectly by considering some relations between nonseparable and general rooted planar maps. One of them is an answer to the open problem 6.1 in Liu (1983, Comb. Optim. CORR83-26, University of Waterloo).     

基于偶联反应新极谱法测定痕量亚硝酸根的研究——Ⅱ.以苯酚为偶联试剂

本文研究了苯酚在氨性缓冲溶液中与NO_2~--磺胺重氮盐偶联反应的实验条件,建立了一个灵敏快速测定痕量NO_2~-的新方法。NO_2~-离子浓度在1.0×10~(-10)～4.8×10~(-7)g/ml范围内,与峰高呈良好的线性关系.4000倍量NO_3~-存在不干扰.