Numerical proof of stability of roll waves in the small-amplitude limit for inclined thin film flow

We present a rigorous numerical proof based on interval arithmetic computations categorizing the linearized and nonlinear stability of periodic viscous roll waves of the KdV–KS equation modeling weakly unstable flow of a thin fluid film on an incline in the small-amplitude KdV limit. The argument proceeds by verification of a stability condition derived by Bar–Nepomnyashchy and Johnson–Noble–Rodrigues–Zumbrun involving inner products of various elliptic functions arising through the KdV equation. One key point in the analysis is a bootstrap argument balancing the extremely poor sup norm bounds for these functions against the extremely good convergence properties for analytic interpolation in order to obtain a feasible computation time. Another is the way of handling analytic interpolation in several variables by a two-step process carving up the parameter space into manageable pieces for rigorous evaluation. These and other general aspects of the analysis should serve as blueprints for more general analyses of spectral stability.     

MATHEMATICAL STUDY OF A PEST CONTROL MODEL INCORPORATING STERILE INSECT TECHNIQUE

The menace of insect pests is a topic of major concern throughout the world. Chemical pesticides are conventionally used to control these insect pests. However, the adverse effects of these synthetic pesticides, such as high toxicity from residues in food, contamination of water and the environment resulting in human health hazard and resistance of the pest to the pesticides have necessitated development of some nonconventional approaches of biological pest control. In this research, we have focused on a mathematical model of biological pest control using the sterile insect release technique. Unlike most of the existing modeling studies in this field that mainly deal with the pest population only, we have incorporated the crop population as a distinct dynamical equation together with the fertile and sterile insect pests. Local stability analysis is performed around the crop and fertile insect free axial equilibrium, the fertile‐insect‐free boundary equilibrium, the crop‐free boundary equilibrium and the equilibrium point of coexistence. From the study we have derived a number of thresholds for the SIRR (the main parameter for our study) that cause existence and or extinction of the crop population as well as the fertile insect pests. A global study of the model system using comparison arguments revealed existence of a global attractor for the system. Numerical simulations are done to support and augment analytical results.     

关于判断矩阵一致性检验与调整的一个注记

首先分析了判断矩阵不一致形成的原因,认为一个判断矩阵中的不一致是由强矛盾判断,弱矛盾判断,标度离散性,标度有限性共同作用的结果,并通过两个例子指出现有一致性检验与调整方法中存在的问题,最后在已有研究基础上给出了判断矩阵一致性调整的新步骤.     

天然气消费量的偏最小二乘支持向量机预测

结合偏最小二乘法和支持向量机的优缺点,提出基于偏最小二乘支持向量机的天然气消费量预测模型。首先,利用偏最小二乘法确定影响天然气消费量的新综合变量,建立以新综合变量为输入,天然气消费量为输出的支持向量机模型,对天然气消费量进行了预测;然后,与多元回归、偏最小二乘回归、普通支持向量机做误差检验比较,验证该方法的可行性与正确性。结果表明,此天然气消费量预测模型具有较高的精确度和应用价值。     

On the Properties of the Solution of a Strongly Degenerate Parabolic Equation

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由连续半鞅驱动的倒向随机微分方程解的比较定理

彭实戈[1]首先建立了一维倒向随机微分方程的比较定理,本文在Lipschitz条件下研究由连续半鞅驱动的倒向随机微分方程,我们将比较定理推广到此类倒向随机微分方程,并且证明方法比彭实戈[1]的更加直接和简单.     

Simulation of oscillatory flow in an aortic bifurcation using FVM and FEM: A comparative study of implementation strategies

Cardiovascular diseases are one of the major causes of long‐term morbidity and mortality in human beings. The nearly epidemic increase in prevalence of such diseases poses a serious threat to public health and calls for efficient methods of diagnosis and treatment. Non‐invasive diagnostic procedures such as MRI are often used in this context; however, these are limited in terms of spatial and temporal resolution and do not provide information on time‐dependent pressures and wall shear stresses—key quantities considered to be partially responsible for the formation and development of related pathologies. The present study is concerned with the numerical simulation of oscillatory flow through the abdominal aortic bifurcation. Computational fluid dynamics simulation of oscillatory flow in a branched geometry at high Reynolds numbers poses considerable challenges. The present study reports a detailed comparison of simulations performed with a finite volume and a finite element method, two approaches with significant differences in their discretization strategy, treatment of boundary conditions and other numerical aspects. Both solvers were parallelized, using loop parallelization of the BiCGStab linear solver for the finite volume and domain decomposition based on the Schur complement method for the finite element technique. The experience gained with these two approaches for the solution of flow in a bifurcation forms the focus of this study. Although similar results were obtained for both methods, the computation time required for convergence was found to be significantly smaller for the finite element approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Theoretical investigation of histidine-tryptophan preferential interactions

Several histidine-tryptophan complexes (either stacked or T-shaped), derived from the crystal structures available in the Brookhaven Protein Data Bank, have been examined with molecular mechanics (MM), using the Tripos force field with Gasteiger-Hückel charges, whose trend was found to be analogous to the AMBER or CHARMM ones. The MM results were compared to the ab initio MP2 results, with and without counterpoise (CP) correction, previously obtained using extended basis sets on 5-methylimidazole and indole as model systems. MM seems to underestimate the interaction energy between the two monomers when compared to the uncorrected MP2 results, while the agreement is much better after including the CP correction at the MP2 level in all cases. MM was thus used to qualitatively analyse the dependence of the stacking energy on the ring rotation at a variable distance and ring centroid displacement for these systems, while keeping the rings in parallel planes. An analogous study was carried out for a T-shaped adduct. Received: 24 March 1998 / Accepted: 3 September 1998 / Published online: 1 February 1999     

微分方程解的存在区间的确定

从六个方面说明了确定一阶微分方程解的存在区间的方法.