Error Analysis of Chebyshev-Legendre Pseudo-spectral Method for a Class of Nonclassical Parabolic Equation

Many physical phenomena are modeled by nonclassical parabolic initial boundary value problems which involve a nonclassical term u _xxt in the governed equation. Combining with the Crank-Nicolson/leapfrog scheme in time discretization, Chebyshev-Legendre pseudo-spectral method is applied to space discretization for numerically solving the nonclassical parabolic equation. The proposed approach is based on Legendre Galerkin formulation while the Chebyshev-Gauss-Lobatto (CGL) nodes are used in the computation. By using the proposed method, the computational complexity is reduced and both accuracy and efficiency are achieved. The stability and convergence are rigorously set up. The convergence rate shows ??spectral accuracy??. Numerical experiments are presented to demonstrate the effectiveness of the method and to confirm the theoretical results.     

Identification of Breast Cancer Prognosis Markers via Integrative Analysis

In breast cancer research, it is of great interest to identify genomic markers associated with prognosis. Multiple gene profiling studies have been conducted for such a purpose. Genomic markers identified from the analysis of single datasets often do not have satisfactory reproducibility. Among the multiple possible reasons, the most important one is the small sample sizes of individual studies. A cost-effective solution is to pool data from multiple comparable studies and conduct integrative analysis. In this study, we collect four breast cancer prognosis studies with gene expression measurements. We describe the relationship between prognosis and gene expressions using the accelerated failure time (AFT) models. We adopt a 2-norm group bridge penalization approach for marker identification. This integrative analysis approach can effectively identify markers with consistent effects across multiple datasets and naturally accommodate the heterogeneity among studies. Statistical and simulation studies demonstrate satisfactory performance of this approach. Breast cancer prognosis markers identified using this approach have sound biological implications and satisfactory prediction performance.     

Extended Gaussian Kriging for computer experiments in engineering design

Metamodeling or surrogate modeling is becoming increasingly popular for product design optimization in manufacture industries. In this paper, an extended Gaussian Kriging method is proposed to improve the prediction performance of widely used ordinary Kriging in engineering design. Unlike the forgoing approaches, the proposed method places a variance-varying Gaussian prior on the unknown regression coefficients in the mean model of Kriging and makes prediction at untried design points based on the principle of Bayesian maximum a posterior. The achieved regression mean model is adaptive, therefore capable of capturing more effectively the overall trend of computer responses and leading to a more accurate metamodel. Particularly, the regression coefficients in the mean model are estimated by a fast numerical algorithm, making extended Gaussian Kriging implemented roughly as efficient as ordinary Kriging. Experiment results on several examples are presented, showing remarkable improvement in prediction using extended Gaussian Kriging over ordinary Kriging and several other metamodeling methods.     

A new view of fuzzy ideals in \Upgamma-rings

By means of a kind of new idea, we redefine fuzzy ideals and fuzzy interior ideals in a $\Upgamma$ -ring and investigate some of their related properties. In particular, we show that the regular and semisimple $\Upgamma$ -rings can be described by using these kinds of generalized fuzzy ideals.     

Synthesis of neural tree models by improved breeder genetic programming

Neural tree model has been successfully applied to solving a variety of interesting problems. In most previous studies, optimization of the neural tree model was divided into two steps: first structure optimization, then parameter optimization. One major problem in the evolution of structure without parameter information was noisy fitness evaluation. In this paper, an improved breeder genetic programming algorithm is proposed to the synthesis of neural tree model. The effectiveness and performance of the method are evaluated on time series prediction problems and compared with those of related methods. Simulation results show that the proposed algorithm is a potential method with better performance and effectiveness.     

地震属性对云质岩储层识别的探讨

由于油气预探阶段钻井相对较少,地震属性分析技术能弥补此阶段钻、测井资料不足的劣势,其在储集性能评价和含油气性评价中起了重要作用。本文应用地震属性分析技术对新疆某地区风城组云质岩储层进行识别,并通过已钻井进行对比分析,从而确定研究工作的可靠性,对该地区储层预测工作具有指导意义和应用价值。     

370 m跨径X形提篮拱结构有限元模拟研究

渝黔铁路是国家“八纵八横铁路网”中“包柳铁路大通道”的重要组成部分.以渝黔铁路线中X形提篮拱桥为依托工程,为确保施工工程质量与安全,采用Midas/Civil2010有限元软件对该拱桥成桥后主拱圈应力、运营阶段稳定性与位移验算等进行了计算和分析,结果表明该提篮拱桥拱脚处最大压应力为14 MPa满足混凝土规范要求设计值,结构运营阶段稳定系数为32.2,满足现行规范限值,结构在横纵向自振周期分别为1.473 s与1.389 s均满足规范限值.     

最短路问题在旅游线路优化中的应用

本文利用Floyd算法探究了最短路问题,经过Matlab实现后将其应用到旅游线路优化设计中。选取了甘肃及周边地区13个旅游景点,求得从任意景点出发到任意目的景点的最短路,以及途中必须给定两个景点的最短路问题。     

江西经济发展走势对运输需求的分析与预测

区域经济的发展是运输需求的源泉。新世纪以来,江西经济进入了持续稳定发展的快车道,极大地促进了运输需求的持续增长,运输线路长度不断延长,全社会运输量不断增加。随着江西经济社会快速发展,城镇化进程的加快,资源环境约束压力的加大,运输需求结构提升,对运输需求提出了更高的要求,运输需求多样化、个性化、机动化、快速化和网络化的趋势更加显著。     

Weighted progressive interpolation of Loop subdivision surfaces

This paper proposes a weighted progressive method for constructing a Loop subdivision surface interpolating a given mesh. The convergent rate of the weighted progressive interpolation can be controlled by adjusting the weight of the iteration. For different weights in the available range, the limit meshes are the same as that of the reverse solution by directly solving a linear system. The theoretical value for the optimal weight is given based on the smallest eigenvalue of the collocation matrix. An appropriate value of the weight is assigned based on both theoretical analysis and numerical experiments.