Fourier Analysis of Serial Dependence Measures

Classical spectral analysis is based on the discrete Fourier transform of the autocovariances. In this article we investigate the asymptotic properties of new frequency‐domain methods where the autocovariances in the spectral density are replaced by alternative dependence measures that can be estimated by U‐statistics. An interesting example is given by Kendall's τ, for which the limiting variance exhibits a surprising behavior.     

新疆西准噶尔哈图岩体地球化学特征及其地质意义

哈图岩体侵位于西准噶尔南部早—中泥盆世海相火山-沉积地层中,主要岩性为二长花岗岩、正长花岗岩及少量碱长花岗岩,是研究西准噶尔晚石炭世构造环境的理想对象。哈图岩体花岗岩中SiO₂含量(质量分数,下同)为72.06%～76.53%,全碱(Na₂O+K₂O)为7.80%～8.57%,CaO为0.20%～1.58%,MgO为0.07%～0.42%,明显具有高Si、富碱、贫Ca、低Mg的特征; 这些花岗岩的Al₂O₃含量为12.55%～14.06%,A/CNK值为1.06～1.15,A/NK值为1.15～1.36,显示其为弱过铝质—强过铝质花岗岩。此外,哈图岩体具有较低的稀土元素总含量((88.14～139.53)×10^-6)和高的轻、重稀土元素比值((La/Yb)_N值为3.04～6.50),在球粒陨石标准化稀土元素配分模式中显示为典型的右倾“V”字形且具有强烈的负Eu异常,表明源区可能有斜长石残留或出现斜长石的分离结晶作用; 在原始地幔标准化微量元素蛛网图中,这些花岗岩明显富集Rb、Th、U、K、Pb等大离子亲石元素,相对富集Zr、Hf,强烈亏损Sr、Ti、P,相对亏损Ba、Nb。以上特征及主量、微量元素特征和图解表明,哈图岩体为典型的弱过铝质—强过铝质A₂型花岗岩,其形成于造山后伸展阶段,是由洋壳和岛弧组成的新生地壳受上涌的幔源物质加热,在浅部低压条件下发生部分熔融,再经分离结晶作用的产物。     

An inverse problem for non-selfadjoint Sturm–Liouville operator with discontinuity conditions inside a finite interval

This paper is concerned with the inverse problem for non-selfadjoint Sturm–Liouville operator with discontinuity conditions inside a finite interval. Firstly, we give the definitions of generalized weight numbers for this operator which may have the multiple spectrum and then investigate the connections between the generalized weight numbers and other spectral characteristics. Secondly, we obtain the generalized spectral data, which consists of the generalized weight numbers and the spectrum. Then the operator is determined uniquely by the method of spectral mappings. Finally, we give an algorithm for reconstructing the potential function and the coefficients of the boundary conditions and the coefficients of the discontinuity conditions.     

The special‐linear update: An application of differential manifold theory to the update of isochoric plasticity flow rules

The evolution of plastic deformations in metals, governed by incompressible flow rules, has been traditionally solved using the exponential mapping. However, the accurate calculation of the exponential mapping and its tangents may result in computationally demanding schemes in some cases, while common low‐order approximations may lead to poor behavior of the constitutive update because of violation of the incompressibility condition. Here, we introduce the special‐linear (SL) update for isochoric plasticity, a flow‐rule integration scheme based on differential manifolds concepts. The proposed update exactly enforces the plastic incompressibility condition while being first‐order accurate and consistent with the flow rule, thus bearing all the desirable properties of the now standard exponential mapping update. In contrast to the exponential‐mapping update, we demonstrate that the SL update can drastically reduce the computing time, reaching one order of magnitude speed‐ups in the calculation of the update tangents. We demonstrate the applicability of the update by way of simulation of single‐crystal plasticity uniaxial loading tests. We anticipate that the SL update will open the way to efficient constitutive updates for the solution of complex multiscale material models, thus making it a very promising tool for large‐scale simulations. Copyright © 2013 John Wiley & Sons, Ltd.     

M-矩阵性质的注记

首先利用M-矩阵的基本性质,讨论了M-矩阵乘积及凸组合特性,获得关于M-矩阵乘积及凸组合的相关结论;随后通过比较矩阵及非负矩阵的性质,探讨了矩阵的逆及行列式性质,推导出了M-矩阵的不等式关系.     

Common fixed points of a countable family of multivalued quasi-nonexpansive mappings in uniformly convex Banach spaces

In this paper, we introduce a one-step iterative scheme for finding a common fixed point of a countable family of multivalued quasi-nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems of the proposed iterative scheme under some control conditions.     

Function evaluation with feedforward neural networks

Much effort has previously been spent in investigating the decision making/object identification capabilities of feedforward neural networks. In the present work we examine the less frequently investigated abilities of such networks to implement computationally useful operations in arithmetic and function evaluation. The approach taken is to employ standard training methods, such as backpropagation, to teach simple three-level networks to perform selected operations ranging from one-to-one mappings to many-to-many mappings. Examples considered cover a wide range, such as performing reciprocal arithmetic on real valued inputs, implementing particle identifier functions for identification of nuclear isotopes in scattering experiments, and locating the coordinates of a charged particle moving on a surface. All mappings are required to interpolate and extrapolate from a small sample of taught exemplars to the general continuous domain of possible inputs. A unifying principle is proposed that looks upon all such function constructions as expansions in terms of basis functions, each of which is associated with a hidden node and is parameterized by such techniques as gradient descent methods.     

数字化车间多源异构质量数据集成方案研究

针对数字化制造中多源异构质量数据信息量大且缺乏统一、规范和标准化数据管理的问题,提出一种基于面向对象技术和基于映像的数据抽取、转换和加载(Extract-Transform-Load,ETL)技术的异构数据集成方案,该方案简单实用,具有很高的通用性,可提高异构数据的提取精度,有效地解决多源异构质量数据集成问题。     

La(1−x)SrxCo1−yFeyO3 perovskites prepared by sol–gel method: Characterization and relationships with catalytic properties for total oxidation of toluene

La_(1−x)Sr_xCo_(1−y)Fe_yO₃ samples have been prepared by sol–gel method using EDTA and citric acid as complexing agents. For the first time, Raman mappings were achieved on this type of samples especially to look for traces of Co₃O₄ that can be present as additional phase and not detect by XRD. The prepared samples were pure perovskites with good structural homogeneity. All these perovskites were very active for total oxidation of toluene above 200 °C. The ageing procedure used indicated good thermal stability of the samples. A strong improvement of catalytic properties was obtained substituting 30% of La³⁺ by Sr²⁺ cations and a slight additional improvement was observed substituting 20% of cobalt by iron. Hence, the optimized composition was La_0.7Sr_0.3Co_0.8Fe_0.2O₃. The samples were also characterized by BET measurements, SEM and XRD techniques. Iron oxidation states were determined by Mössbauer spectroscopy. Cobalt oxidation states and the amount of O⁻ electrophilic species were analyzed from XPS achieved after treatment without re-exposition to ambient air. Textural characterization revealed a strong increase in the specific surface area and a complete change of the shape of primary particles substituting La³⁺ by Sr²⁺. The strong lowering of the temperature at conversion 20% for the La_0.7Sr_0.3Co_(1−y)Fe_yO₃ samples can be explained by these changes. X photoelectron spectra obtained with our procedure evidenced very high amount of O⁻ electrophilic species for the La_0.7Sr_0.3Co_(1−y)Fe_yO₃ samples. These species able to activate hydrocarbons could be the active sites. The partial substitution of cobalt by iron has only a limited effect on the textural properties and the amount of O⁻ species. However, Raman spectroscopy revealed a strong dynamic structural distortion by Jahn–Teller effect and Mössbauer spectroscopy evidenced the presence of Fe⁴⁺ cations in the iron containing samples. These structural modifications could improve the reactivity of the active sites explaining the better specific activity rate of the La_0.7Sr_0.3Co_0.8Fe_0.2O₃ sample. Finally, an additional improvement of catalytic properties was obtained by the addition of 5% of cobalt cations in the solution of preparation. As evidenced by Raman mappings and TEM images, this method of preparation allowed to well-dispersed small Co₃O₄ particles that are very efficient for total oxidation of toluene with good thermal stability contrary to bulk Co₃O₄.