THEOREMS OF PEANO'S TYPE FOR BIVARIATE FUNCTIONS AND OPTIMAL RECOVERY OF LINEAR FUNCTIONALS

The best recovery of a linear functional Lf, f=f(x,y), on the basis of given linear functionals L jf,j=1,2,...,N in a sense of Sard has been investigated, using analogy of Peano's theorem. The best recovery of a bivariate function by given scattered data has been obtained in a simple analytical form as a special case.

ORTHOGONAL MATRIX POLYNOMIALS WITH RESPECT TO LINEAR MATRIX MOMENT FUNCTION ALS:THEORY AND APPLICATIONS

In this paper orthogonal matrix polynomials with respect to a right matrix moment functional an introduced. Basic results, important examples and applications to the approximation of matrix integrals are studied. Error bounds for the proposed matrix quadrature rules are given.

Some inequalities for the generalized linear distortion function

In this paper, we establish several inequalities for the the generalized linear distortion function λ（a, K） by using the monotonicity and convexity of certain combinations λ（a, K）.

A new chaotic Hopfield network with piecewise linear activation function

This paper presents a new chaotic Hopfield network with a piecewise linear activation function. The dynamic of the network is studied by virtue of the bifurcation diagram, Lyapunov exponents spectrum and power spectrum. Numerical simulations show that the network displays chaotic behaviours for some well selected parameters.

A self-adaptive linear evolutionary algorithm for solving constrained optimization problems

In many real-world applications of evolutionary algorithms,the fitness of an individual requires a quantitative measure.This paper proposes a self-adaptive linear evolutionary algorithm （ALEA） in which we introduce a novel strategy for evaluating individual＇s relative strengths and weaknesses.Based on this strategy,searching space of constrained optimization problems with high dimensions for design variables is compressed into two-dimensional performance space in which it is possible to quickly identify ＇good＇ individuals of the performance for a multiobjective optimization application,regardless of original space complexity.This is considered as our main contribution.In addition,the proposed new evolutionary algorithm combines two basic operators with modification in reproduction phase,namely,crossover and mutation.Simulation results over a comprehensive set of benchmark functions show that the proposed strategy is feasible and effective,and provides good performance in terms of uniformity and diversity of solutions.

Rheological Behaviour for Polymer Melts and Concentrated Solutions Part Ⅲ: A New Multiple Entanglement Model to Predict the Dependence of Linear Viscoelastic Function (η_0, Ψ_(10)~0,η_(ext)~0) on the Ranges of Primary Molecular Weights and th

It is shown theoretically that the viscoelasticity of polymer melts is determined by three combining factorst they are the primary molecular weight and its distribution, the number of entanglement sites on polymer chain and the sequence distribution of constituent chains in entanglement spacings. A unified quantity for the three combing factors is the average constrained dimensional number of constituent chains in the long entanglement spacings (v). A new relation of v to the primary molecular weight and the number of testing polymers were derived from the multiple entanglement and reptation model, and a new method for determining v was proposed. The dependences of linear viscoelastic functions on the primary molecular weight and its distribution were derived by the statistical method. When Mn=6Me to 18 Me, the values of (v) can range from 3.33 to 3.70. Their values are in a good agreement with the experiment data, and it can slightjy vary with the different species of polymers and the different ranges of molecular weight of polymers

A Cell-Based Linear Smoothed Finite Element Method for Polygonal Topology Optimization

The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM.This improves the accuracy and yields an optimal convergence rate.The gradients are smoothed over each smoothing domain,then used to compute the stiffness matrix.Within the proposed scheme,an optimum topology procedure is conducted over the smoothing domains.Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain.Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence,efficiency and accuracy.

On Characterization of Poised Nodes for a Space of Bivariate Functions

There are several examples of spaces of univariate functions for which we have a characterization of all sets of knots which are poised for the interpolation problem. For the standard spaces of univariate polynomials, or spline functions the mentioned results are well-known. In contrast with this, there are no such results in the bivariate case. As an exception, one may consider only the Pascal classic theorem, in the interpolation theory interpretation. In this paper, we consider a space of bivariate piecewise linear functions, for which we can readily find out whether the given node set is poised or not. The main tool we use for this purpose is the reduction by a basic subproblem, introduced in this paper.

Testing Linearity in Functional Partially Linear Models

For the functional partially linear models including flexible nonparametric part and functional linear part,the estimators of the nonlinear function and the slope function have been studied in existing literature.How to test the correlation between response and explanatory variables,however,still seems to be missing.Therefore,a test procedure for testing the linearity in the functional partially linear models will be proposed in this paper.A test statistic is constructed based on the existing estimators of the nonlinear and the slope functions.Further,we prove that the approximately asymptotic distribution of the proposed statistic is a chi-squared distribution under some regularity conditions.Finally,some simulation studies and a real data application are presented to demonstrate the performance of the proposed test statistic.

Derivation of Plastic Work Rate Done per Unit Volume for Mean Yield Criterion and Its Application

In Haigh Westergaard stress space linear combination of twin shear stress and Tresca yield functions is called the mean yield （MY） criterion. The mathematical relationship of the criterion and its plastic work rate done per unit volume were derived. A generalized worked example of slab forging was analyzed by the criterion and its corresponding plastic work rate done per unit volume. Then, the precision of the solution was compared with those by Mises and Twin shear stress yield criterions, respectively. It turned out that the calculated results by MY criterion were in good agreement with those by Mises criterion.

COMPUTATIONAL COMPLEXITY IN WORST, STOCHASTIC AND AVERAGE CASE SETTING ON FUNCTIONAL APPROXIMATION PROBLEM OF MULTIVARIATE

The order of computational complexity of all bounded linear functional ap proximation problem is determined for the generalized Sobolev class Wp?（Id）, Nikolskii class H|∞k（Id） in the worst （deterministic）, stochastic and average case setting, from which it is concluded that the bounded linear functional approximation problem for the classes Wp?（Id） and H∞k（Id） is intractable in worst case setting, but is tractable with respect to stochastic and average case setting.

ORTHOGONAL POLYNOMIALS AND DETERMINANT FORMULAS OF FUNCTION-VALUED PADE-TYPE APPROXIMATION USING FOR SOLUTION OF INTEGRAL EQUATIONS

To solve Fredholm integral equations of the second kind, a generalized linear functional is introduced and a new function-valued Padé-type approximation is defined. By means of the power series expansion of the solution, this method can construct an approximate solution to solve the given integral equation. On the basis of the orthogonal polynomials, two useful determinant expressions of the numerator polynomial and the denominator polynomial for Padé-type approximation are explicitly given.

NUAT T-splines of odd bi-degree and local refinement

This paper presents a new kind of spline surfaces, named non-uniform algebraic- trigonometric T-spline surfaces （NUAT T-splines for short） of odd hi-degree. The NUAT T- spline surfaces are defined by applying the T-spline framework to the non-uniform algebraic- trigonometric B-spline surfaces （NUAT B-spline surfaces）. Based on the knot insertion algorithm of the NUAT B-splines, a local refinement algorithm for the NUAT T-splines is given. This algorithm guarantees that the resulting control grid is a T-mesh as the original one. Finally, we prove that, for any NUAT T-spline of odd hi-degree, the linear independence of its blending functions can be determined by computing the rank of the NUAT T-spline-to-NUAT B-spline transformation matrix.

AN OPTIMAL FUZZY APPROXIMATOR

In a dot productspace with the reproducing kernel (r.k.S.) ,a fuzzy system with the estimation approximation errors is proposed,which overcomes the defect thatthe existing fuzzy control system is difficult to estimate the errors of approximation for a desired function,and keeps the characteristics of fuzzy system as an inference approach.The structure of the new fuzzy approximator benefits a course got by other means

An overview of a unified theory of dynamics of vehicle–pavement interaction under moving and stochastic load

This article lays out a unified theory for dynamics of vehicle-pavement interaction under moving and stochastic loads. It covers three major aspects of the subject： pavement surface, tire-pavement contact forces, and response of continuum media under moving and stochastic vehicular loads. Under the subject of pavement surface, the spectrum of thermal joints is analyzed using Fourier analysis of periodic function. One-dimensional and two-dimensional random field models of pavement surface are discussed given three different assumptions. Under the subject of tire-pavement contact forces, a vehicle is modeled as a linear system. At a constant speed of travel, random field of pavement surface serves as a stationary stochastic process exciting vehicle vibration, which, in turn, generates contact force at the interface of tire and pavement. The contact forces are analyzed in the time domain and the frequency domains using random vibration theory. It is shown that the contact force can be treated as a nonzero mean stationary process with a normal distribution. Power spectral density of the contact force of a vehicle with walking-beam suspension is simulated as an illustration. Under the subject of response of continuum media under moving and stochastic vehicular loads, both time-domain and frequency-domain analyses are presented for analytic treatment of moving load problem. It is shown that stochastic response of linear continuum media subject to a moving stationary load is a nonstationary process. Such a nonstationary stochastic process can be converted to a stationary stochastic process in a follow-up moving coordinate.

Studies on the Quantitative Structure-activity Relationship of Toxicity of Chlorophenol Serial Compounds in the ab initio Methods and Substitutive Position of Chlorine Atom (N_(PCS))

20 Quantum chemical parameters of chlorophenol compounds were fully optimized by using B3LYP method on both 6-31G^＊ and 6-311G^＊ basis sets. These structural parameters are taken as theoretical descriptors, and the experimental data of 20 compounds＇ aquatic photogen toxicity（-lgEC50） are used to perform stepwise regression in order to obtain two predicted -lgEC50 correlation models whose correlation coefficients R^2 are respectively 0.9186 and 0.9567. In addition, parameters of chlorine atom＇s substitutive positions and their correlations （NPCs） are taken as descriptors to obtain another predicted -lgEC50 model with the correlation coefficient R2 of 0.9444. Correlation degree of each independent variable in the three models is verified by using variance inflation factors （VIF） and t value. In the cross-validation method, cross-validation coefficients q^2 of 3 models are respectively 0.8748, 0.9119 and 0.8993, which indicates that the relativity and prediction ability of this model are superior to those of the model obtained by topological and BLYP methods.

估计第二类Fredholm积分方程特征值的函数值部分Padé-型逼近方法(英文)

Abstract A new function-valued partial Padé-type approximation was introduced in the polynomial space, and an explicit determinant formula was derived by means of some orthogonal polynomials. This method can be applied to estimating surplus eigenvalues of the Fredholm integral equation of the second kind when its partial eigenvalues have been known, and at the same time, it can be applied to solving the approximating solution of the given equation.

Some Properties of Conditioned Superdiffusion

Some properties of a conditioned superdiffusion are investigated. By a basic property we obtain for it, a class of linear additive functionals, so-called weighted occupation time, is studied. At last, we get an interesting result about its extinctive property.

Edge method for measuring source spot-size and its principle

The edge method is used to measure the source spot-size. In this paper, the measuring principle and applying range are discussed. It is shown that the method can directly be used to measure the spot-size of either light source, or low-energy x-ray source, or x-ray source with an energy higher than 250 keV.

Backward Dijkstra Algorithms for Finding the Departure Time Based on the Specified Arrival Time for Real-Life Time-Dependent Networks

A practical transportation problem for finding the “departure” time at “all source nodes” in order to arrive at “some destination nodes” at specified time for both FIFO (i.e., First In First Out) and Non-FIFO “Dynamic ” Networks is considered in this study. Although shortest path (SP) for dynamic networks have been studied/documented by various researchers, contributions from this present work consists of a sparse matrix storage scheme for efficiently storing large scale sparse network’s connectivity, a concept of Time Delay Factor (TDF) combining with a “general piece- wise linear function” to describe the link cost as a function of time for Non-FIFO links’ costs, and Backward Dijkstra SP Algorithm with simple heuristic rules for rejecting unwanted solutions during the backward search algorithm. Both small-scale (academic) networks as well as large- scale (real-life) networks are investigated in this work to explain and validate the proposed dynamic algorithms. Numerical results obtained from this research work have indicated that the newly proposed dynamic algorithm is reliable, and efficient. Based on the numerical results, the calculated departure time at the source node(s), for a given/specified arrival time at the destination node(s), can be non-unique, for some Non-FIFO networks’ connectivity.