Tests for change—points based on recursive u—statistics

Tests for change—points for the location as well as regression models are often based on cumulative sums of recursive residuals. These recursive residuals are also employed in the sequential detection problem. In the context of general estimable parameters (funtionals of the underlying distribution functions), such recursive residuals may be defined in terms of recursive U—statistics. A class of tests for the change—points based on recursive U—statistics has been considered. Along with some invariance principles for recursive U—statistics, asymptotic properties of the proposed tests are studied.     

关于互易二端口的若干思考

本文首先介绍了当前教材中通行的四种定义互易二端口的方法。作者从互易的含义出发，给出基于端口变量关系的互易二端口定义，并指出这种定义与基于二端口参数的定义是等价的。进而讨论了互易性元件的定义，说明互易定理的实质内容为仅由互易元件构成的二端口一定是互易二端口，并指出这是互易二端口的充分条件。最后还讨论了互易性和无源性之间的...     

光滑Chua系统异宿轨道存在性的证明

本文用待定系数法证明了具有三次多项式光滑Chua系统异宿轨道的存在性.首先,将光滑Chua系统转换为只含有一个变量的非线性微分方程.其次,证明了该非线性微分方程存在一个指数形式的无穷级数展开式表示的异宿轨道.最后,证明了该无穷级数展开式的一致收敛性,结合Shilnikov不等式,论证了该系统存在Smale马蹄,因而是S...     

On the Theory of Two-Temperature Thermoelasticity with Two Phase-Lags

The present paper is concerned with the theory of two temperature thermoelasticity with two phase-lags in which the theory of heat conduction in deformable bodies depends on two distinct temperatures – the conductive temperature and the thermodynamic temperature. A generalized heat conduction law with dual-phase-lag effects was proposed by Tzou (1995) for the purpose of considering the delayed response in times due to the microstructural interactions in the heat transport mechanism. Recently, Quintanilla (2008) has proposed to combine this constitutive equation with a two temperature heat conduction theory and has proved that a dual-phase-lag theory with two temperatures is a well-posed problem. In the present work we consider the basic equations concerning this dual-phase lag theory of two temperature thermoelasticity and make an attempt to establish some important theorems in this context. A uniqueness theorem has been established for a homogeneous and isotropic body. An alternative characterization of mixed boundary initial value problem is formulated and a variational principle as well as reciprocal principle have been established.     

Analysis of multiple cracks in thin coating on orthotropic substrate under mechanical and residual stresses

The analysis addresses a typical failure development pattern in thin films consisting of a system of multiple surface cracks leading to and branching along or near the interface between the film and the base material. The process is driven by thermal residual stresses and/or mechanical loading. Due to the high temperature gradients during the fabrication process, usually a net of surface cracks develops, which gives the appearance of a granular structure of the surface. A periodic array of parallel surface cracks is assumed. A “unit cell” or single cracked segment attached to the substrate is analyzed instead by assuming the channel cracks are spaced more or less uniformly and perfectly aligned in parallel in the transverse direction of the coating. The analysis is specialized to orthotropic and transversally isotropic materials. The problem is solved using FEM combined with the reciprocal theorem. Matched asymptotic procedure [Leguillon D, Sanchez-Palencia E. Computation of singular solutions in elliptic problems and elasticity. Paris: Masson; 1987; Vu-Quoc L, Tran VX. Singularity analysis and fracture energy-release rate for composites: piecewise homogenous-anisotropic materials. Comput Methods Appl Mech Engng 2006;195:5162-97] is used to derive the change of potential energy. Higher-order terms in the asymptotics are considered. The competition between penetration and debond for periodically distributed edge cracks especially near the critical value of the ratio of fracture spacing to the layer thickness is examined.     

Analysis of warp-knitted fabric structure. Part II: theoretical study on initial modulus of warp-knitted fabrics (tricot,locknit, and satin)

In the first part of this series, a 3D straight line model was presented for the geometry of two-guide-bar warp-knitted fabrics. In this part, first, the variation of unit cell geometry under uniaxial tension in the range of elastic deformation is investigated. In the present study, the energy method and Castiglianos's theorem were used to derive the fabric's initial modulus. Energy terms which are considered in this study are extension, bending, and compression energies. Also, the friction phenomenon is taken into account by using frictional energy term. For this purpose, the loop of each bar is divided into eight elements. Free-body diagrams of elements are drawn to show the relative magnitude and direction of all forces acting upon an object in a given situation. After obtaining the force details, strain energy of each element is calculated. Finally, the initial modulus of warp-knitted fabrics is obtained. To verify the model, samples of tricot fabrics were produced and tested. Results showed that the generated model can predict precisely the initial modulus of aforementioned warp-knitted structures.     

泰勒中值定理在不等式证明中的应用

从不等式的特点出发,应用实际范例给出了泰勒公式中展开点选取的几种情况：区间的中点,已知区间的两端点,函数的极值点或最值点,已知区间的任意点。同时对各种情况的运用范围和特点作了说明,以便更好地运用泰勒中值定理证明不等式。     

An Almost Sure Result on Sampling of Bandlimited Random Signals

The Shannon-Nyquist sampling theorem for deterministic signals is a fundamental result in the field of telecommunication and signal processing, and many re- sults on this topic have been obtained. However, very few results on random signals have been published, after Kol- mogorov mentioned the importance of Shannon-formula for stochastic signals in 1956. In this paper, following the almost sure result for bandlimited stochastic processes pro- posed by Seip in 1990, we give an almost sure result of the classical sampling theorem for bandlimited random signals with local average sampling.     

Use of kernel-based Bayesian models to predict late osteolysis after hip replacement

We studied the relationship between osteolysis and polyethylene wear, age at surgery, body mass index and height in 463 subjects (180 osteolysis and 283 controls) after cemented Charnley total hip arthroplasty (THA), in order to develop a kernel-based Bayesian model to quantitate risk of osteolysis. Such tools may be integrated into decision-making algorithms to help personalize clinical decision-making. A predictive model was constructed, and the estimated posterior probability of the implant failure calculated. Annual wear provided the greatest discriminatory information. Age at surgery provided additional predictive information and was added to the model. Body mass index and height did not contain valuable discriminatory information over the range in which observations were densely sampled. The robustness and misclassification rate of the predictive model was evaluated by a five-times cross-validation method. This yielded a 70% correct predictive classification of subjects into osteolysis versus non-osteolysis groups at a mean of 11 years after THA. Finally, the data were divided into male and female subsets to further explore the relationship between wear rate, age at surgery and incidence of osteolysis. The correct classification rate using age and wear rate in the model was approximately 66% for males and 74% for females.     

Throwing Some Light on the Vast Darkness that is Analysis: Niels Henrik Abel's Critical Revision and the Concept of Absolute Convergence

During the first half of the nineteenth century, mathematical analysis underwent a transition from a predominantly formula-centred practice to a more concept-centred one. Central to this development was the reorientation of analysis originating in A ugustin- L ouis C auchy's (1789–1857) treatment of infinite series in his Cours d'analyse . In this work, C auchy set out to rigorize analysis, thereby critically examining and reproving central analytical results. One of C auchy's first and most ardent followers was the Norwegian N iels H enrik A bel (1802–1829) who vowed to shed some light on the vast darkness in analysis.
This paper investigates some important aspects of A bel's contribution to the reorientation in analysis. In particular, it stresses the role for critical revision in the process of rigorization. By critically examining past practice, the new practice sought to explain the relative success of the previous—now outdated—approach. This is illustrated by discussing a number of issues related to A bel's new proof of the binomial theorem (1826) including his reactions to the exception that he encountered to one of the central theorems of C auchy's theory.
Following this discussion, the formation of new concepts as the result of critical revisions is illustrated by analysing the early history of the concept of absolute convergence. Thereby, it is shown how a new concept was distilled, investigated, put to use and eventually superseded.