Least Squares Convex-Concave Data Smoothing

We consider n noisy measurements of a smooth (unknown) function, which suggest that the graph of the function consists of one convex and one concave section. Due to the noise the sequence of the second divided differences of the data exhibits more sign changes than those expected in the second derivative of the underlying function. We address the problem of smoothing the data so as to minimize the sum of squares of residuals subject to the condition that the sequence of successive second divided differences of the smoothed values changes sign at most once. It is a nonlinear problem, since the position of the sign change is also an unknown of the optimization process. We state a characterization theorem, which shows that the smoothed values can be derived by at most 2n – 2 quadratic programming calculations to subranges of data. Then, we develop an algorithm that solves the problem in about O(n ²) computer operations by employing several techniques, including B-splines, the use of active sets, quadratic programming and updating methods. A Fortran program has been written and some of its numerical results are presented. Applications of the smoothing technique may be found in scientific, economic and engineering calculations, when a potential shape for the underlying function is an S-curve. Generally, the smoothing calculation may arise from processes that show initially increasing and then decreasing rates of change.     

A Class of Combined Iterative Methods for Solving Variational Inequalities

A general approach to constructing iterative methods that solve variational inequalities is proposed. It is based on combining, modifying, and extending ideas contained in various Newton-like methods. Various algorithms can be obtained with this approach. Their convergence is proved under weak assumptions. In particular, the main mapping need not be monotone. Some rates of convergence are also given.     

Fracture of a rectangular piezoelectromagnetic body

The singular stress, electric fields and magnetic fields in a rectangular piezoelectromagnetic body containing a center Griffith crack under longitudinal shear are obtained. Fourier transforms and Fourier sine series are used to reduce the mixed boundary value problems of the crack, which is assumed to be impermeable, to dual integral equations. The solution of the dual integral equations is then expressed in terms of Fredholm integral equations of the second kind. Expressions for stresses, electric displacements and magnetic inductions in the vicinity of the crack tip are derived. Also obtained are the field intensity factors and the energy release rates. Numerical results obtained show that the geometry of the rectangular body have significant influence on the field intensity factors and the energy release rates.     

SHPB试验中粘弹性材料的应力均匀性分析

采用特征线解法，对满足ZWT方程的粘弹性材料在高应变率SHPB试验中的应力均匀性进行了数值研究。着重分析了不同的材料本构粘性(松弛时间)、瞬态波阻抗比和入射波升时对于试样中应力均匀性、应变均匀性和平均应变率等的影响。为今后动态试验的试样设计提供了一定的理论依据。     

Structural first failure times under non-Gaussian stochastic behavior

An analytical moment-based method for calculating structural first failure times under non-Gaussian stochastic behavior is proposed.In the method,a power series that constants can be obtained from response moments (skewness,kurtosis,etc.) is used firstly to map a non-Gaussian structural response into a standard Gaussian process,then mean up-crossing rates,mean clump size and the initial passage probability of a critical barrier level by the original structural response are estimated,and finally,the formula for calculating first failure times is established on the assumption that corrected up-crossing rates are independent.An analysis of a nonlinear single-degree-of-freedom dynamical system excited by a Gaussian model of load not only demonstrates the usage of the proposed method but also shows the accuracy and efficiency of the proposed method by comparisons between the present method and other methods such as Monte Carlo simulation and the traditional Ganssian model.     

Clarifying and illustrating the electronic energy transfer pathways in trimeric and hexameric aggregation state of cyanobacteria allophycocyanin within the framework of Förster theory

Within the framework of the Förster theory, the electronic excitation energy transfer pathways in the cyanobacteria allophycocyanin (APC) trimer and hexamer were studied. The associated physical quantities (i.e., excitation energy, oscillator strength, and transition dipole moments) of the phycocyanobilins (PCBs) located in APC were calculated at time‐dependent density functional theory (TDDFT) level of theory. To estimate the influence of protein environment on the preceding calculated physical quantities, the long‐range interactions were approximately considered with the polarizable continuum model at the TDDFT level of theory, and the short‐range interaction caused by surrounding aspartate residue of PCBs were taken into account as well. The shortest energy transfer time calculated in the framework of the Förster model at TDDFT/B3LYP/6–31+G* level of theory are about 0.10 ps in the APC trimer and about 170 ps in the APC monomer, which are in qualitative agreement with the experimental finding that a very fast lifetime of 0.43–0.44 ps in APC trimers, whereas its monomers lacked any corresponding lifetime. These results suggest that the lifetime of 0.43–0.44 ps in the APC trimers determined by Sharkov et al. was most likely attributed to the energy transfer of α¹‐84 ? β³‐84 (0.23 ps), β¹‐84 ? α²‐84 (0.11 ps) or β²‐84 ? α³‐84 (0.10 ps). So far, no experimental or theoretical energy transfer rates between two APC trimmers were reported, our calculations predict that the predominate energy transfer pathway between APC trimers is likely to occur from α³‐84 in one trimer to α⁵‐84 in an adjacent trimer with a rate of 32.51 ps. © 2014 Wiley Periodicals, Inc.     

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In this paper, the empirical Bayes (EB) two-sided test for parameter of Cox models is investigated under square loss functions. At first by using recursive kernel estimation of probability function the empirical Bayes two-sided test rule is constructed. It proves that the proposed empirical Bayes test rule is asymptotic optimal and convergence rates are obtained under suitable conditions. Finally an example of satisfying theorem conditions is given.     

Asymptotic behavior of solutions to the compressible nematic liquid crystal system in ℝ3

In this paper, we study a nematic liquid crystals system in three-dimensional whole space ?³ and obtain the time decay rates of the higher-order spatial derivatives of the solution by the method of spectral analysis and energy estimates if the initial data belongs to L¹?³ additionally.     

伸缩张量率的抽象表示

本文用“主轴内蕴法”给出右-左伸缩张量 U 和 V 的时间导数 U 和 V 的抽象表示。文中引进所谓“分离技巧”,使能有效地应用张量函数的标准表示。V 的表达式是新的。还给出U 和 V 的两个新关系式。     

Velocity and Strain-Rate Characteristics of Opposed Isothermal Flows

Velocity measurements in the isothermal flows created by an opposed nozzle configuration are reported with emphasis on the axis, stagnation plane and the distributions of mean and instantaneous strain rates. The instrumentation comprised particle image velocimetry (PIV) with silicon oil droplets added to the flows upstream of both nozzles with the laser sheet passing through the axis between the nozzles. The results identify the regions of high strain rates and quantify the development of the mean and turbulent components of the flow from the nozzle exits as a function of bulk velocities from 3 to 8.2 m/s and nozzle separations from 0.4 to 1.0 diameters. Results show, for example, the rise in the values of axial and radial normal stress towards the stagnation plane with values increasing by up to 300% and 160% respectively. The maximum mean strain rate occurred just over one nozzle radius from the axis at the smallest separation and with values that increased from 450 to 950 s⁻¹ with decreasing separation at a bulk velocity of 3.0 m/s. Probability density functions were near Gaussian and hence much larger instantaneous strain rates were observed. The PIV image size had the advantage that it allowed the entire flow field to be viewed in terms of velocity vectors and derived quantities include mean strain rates. Small asymmetry of the flow and the higher strain rates at finite distances from the nominal impingement plane were observed. The experimental results permitted the domain of applicability of different modelling approaches to be defined more accurately and calculations were performed with different turbulence models. The results showed that two-equation turbulence models did not represent turbulence intensities close to impingement and that Reynolds stress closures produce superior agreement. It was further shown that ad hoc modifications to the dissipation equation, such as those based on the ratio of the turbulent to mean strain time scale, can improve results at the expense of generality. It is also shown that mean flows are well reproduced by a Reynolds stress closure for all nozzle separations. Comments are included on the implications of the results for investigations of reacting flows and extinction.