Construction algorithms for polynomial lattice rules for multivariate integration

We introduce a new construction algorithm for digital nets for integration in certain weighted tensor product Hilbert spaces. The first weighted Hilbert space we consider is based on Walsh functions. Dick and Pillichshammer calculated the worst-case error for integration using digital nets for this space. Here we extend this result to a special construction method for digital nets based on polynomials over finite fields. This result allows us to find polynomials which yield a small worst-case error by computer search. We prove an upper bound on the worst-case error for digital nets obtained by such a search algorithm which shows that the convergence rate is best possible and that strong tractability holds under some condition on the weights.

We extend the results for the weighted Hilbert space based on Walsh functions to weighted Sobolev spaces. In this case we use randomly digitally shifted digital nets. The construction principle is the same as before, only the worst-case error is slightly different. Again digital nets obtained from our search algorithm yield a worst-case error achieving the optimal rate of convergence and as before strong tractability holds under some condition on the weights. These results show that such a construction of digital nets yields the until now best known results of this kind and that our construction methods are comparable to the construction methods known for lattice rules.

We conclude the article with numerical results comparing the expected worst-case error for randomly digitally shifted digital nets with those for randomly shifted lattice rules.

     

Thermal diffusion of envelope solitons on anharmonic atomic chains

We study the motion of envelope solitons on anharmonic atomic chains in the presence of dissipation and thermal fluctuations. We consider the continuum limit of the discrete system and apply an adiabatic perturbation theory which yields a system of stochastic integro-differential equations for the collective variables of the ansatz for the perturbed envelope soliton. We derive the Fokker-Planck equation of this system and search for a statistically equivalent system of Langevin equations, which shares the same Fokker-Planck equation. We undertake an analytical analysis of the Langevin system and derive an expression for the variance of the soliton position Var[x _s ] which predicts a stronger than linear time dependence of Var[x _s ] (superdiffusion). We compare these results with simulations for the discrete system and find they agree well. We refer to recent studies where the diffusion of pulse solitons were found to exhibit a superdiffusive behaviour on longer time scales.Received: 28 June 2004, Published online: 26 November 2004PACS: 05.10.Gg Stochastic analysis methods - 05.45.Yv Solitons - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 05.50. + q Lattice theory and statistics     

级数小于1的亚纯函数的Borel例外值

证明了当超越亚纯函数的级小于1时，其Norel例外值最多只有一个．由于存在任何级的整函数，因此一个例外值总可达到，故所得结果不能再改进。     

Mathematical modelling of the oxidation of nickel titanium alloys

A one-dimensional bulk reaction model for the oxidation of nickeltitanium is formulated, with preferential oxidation of titaniumbeing included. The modelling is directed at the better understandingof the dominant mechanisms involved in the oxidation processand their significance for the biocompatibility of the alloy.Two different regimes for the relative diffusivities of oxygenand the metals are investigated. By assuming fast bulk reactions,different asymptotic structures emerge in different parameterregimes and the resulting models take the form of moving boundaryproblems. Different profiles of nickel concentration are obtained:in particular a nickel-rich layer (observed in practice) ispresent below the oxide/metal interface for the case when oxygenand the metals diffuse at comparable rates.     

Structure and properties of the mesophase of syndiotactic polystyrene. II. Effect of stepwise extraction on the preparation of the mesophase

In this study, a novel stepwise extraction method has been examined. The guest molecules housed between the helices of the clathrate δ form of syndiotactic polystyrene can be removed completely with this method. A systematic study of the preparation of a solvent‐free mesophase (emptied clathrate) membrane, its helical and residual solvent contents, and its structural transformations has been performed. In this first attempt, an enhancement in the TTGG helical content has been observed in the extracted membrane, and a conceptual mechanism is proposed. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 269–273, 2003     

Synthesis and characterization of new bis(1-aryliminomethylenylnaphthalen-2-oxy)nickel complexes and their catalytic behavior for vinyl polymerization of norbornene

The synthesized 1-aryliminomethylenylnaphthalen-2-ol derivatives reacted with nickel chloride to form bis(1-aryliminomethylenylnaphthalen-2-oxy)nickel complexes. All resultant compounds were structurally characterized by elemental analyses, IR and H NMR, and the structures of the formed complexes were elucidated by X-ray crystal structure analysis. The complexes show high catalytic activities for the vinyl polymerization of norbornene in the presence of methylaluminoxane. The catalytic activity variations have been followed by gas chromatography through monitoring the conversion of norbornene.     

具体和抽象统一的原则

学生学习知识,一般来说,是从生动的具体的直观开始的,生动的直观能使学生获得关于事物生动而具体的感性认识。但是,感性认识并没有揭露事物的本质,人们对事物本质的认识要通过一系列的抽象来完成。     

A fast method to measure the thickness of removed layer from etching of SSNTD based on EDXRF

Solid state nuclear track detectors are commonly used for measurements of concentrations of radon gas and/or radon progeny. All these measurements depend critically on the thickness of the removed layer during etching. However, the thickness of removed layer calculated using the etching period does not necessarily provide a sufficiently accurate measure of the thickness. For example, the bulk etch rate depends on the strength of stirring during etching for the LR 115 detector. We propose here to measure the thickness of the removed layer by using energy-dispersive X-ray fluorescence spectrometry. In the present work, a reference silver nitrate pellet is placed beneath the LR 115 detector, and the fluorescence X-ray intensity for silver is then measured. We have found a linear relationship between the X-ray intensity and the thickness of the removed layer for LR 115 detector. This provides a fast method to measure the thickness of removed layer from etching of LR 115 detector. However, this method was found to be inapplicable for the CR-39 detector. Therefore, alternative methods have yet to be explored for the CR-39 detector.