Computational methods for delay parabolic and time‐fractional partial differential equations

This article is concerned with ?‐methods for delay parabolic partial differential equations. The methodology is extended to time‐fractional‐order parabolic partial differential equations in the sense of Caputo. The fully implicit scheme preserves delay‐independent asymptotic stability and the solution continuously depends on the time‐fractional order. Several numerical examples of interest are included to demonstrate the effectiveness of the method. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Fitted modifications of classical Runge‐Kutta pairs of orders 5(4)

Runge‐Kutta pairs sharing orders 5 and 4 are among the most celebrated methods for solving initial value problems. Here, after considering the phase lag as a function of frequency v, we derive a modification of a particular pair. Namely, we present a zero dissipative pair with vanished phase error and its first derivative. After extended numerical tests in various oscillatory problems, it seems that this modified pair outperforms existing methods in the literature.     

Trigonometric fitted,eighth‐order explicit Numerov‐type methods

We consider the integration of the special second‐order initial value problem of the form . A recently introduced family of 7 stages, eighth‐order methods, sharing constant coefficients, is used as base. This family is properly modified to derive phase fitted and zero dissipative methods (ie, trigonometric fitted) that are best suited for integrating oscillatory problems. Numerical tests over a set of problems shows enhanced performance when the purely linear part of the problems is rather large in comparison with the rest of nonlinear parts. An appendix implementing a MATLAB listing with the coefficients of the new method is also given.     

The influence of capital market laws and initial public offering (IPO) process on venture capital

This paper is concerned with the influence of capital market laws and initial public offering (IPO) process on venture capital. It discusses the impact of US federal state laws and Securities and Exchange Commission (SEC) regulations to the venture capital markets, arguing if the rules and regulatories are burdensome to entrepreneurs and new-growth businesses. The impact of Sarbanes-Oxley Act and the future Investment Act on venture capital funds and entrepreneurial companies going public are also discussed. The paper proposes the model of venture capital financing describing the process from fund raising to investment exits, the linkages of the venture capital market to the financial/capital markets and the related capital market laws. The policy implications on SEC regulations essential to the development of venture capital industry are suggested.     

Use of experiment and an inverse method to study interface heat transfer during solidification in the investment casting process

A technique to determine the thermal boundary conditions existing during the solidification of metallic alloys in the investment casting process is presented. Quantitative information about these conditions is needed so that numerical models of heat transfer in this process produce accurate results. In particular, the variation of the boundary conditions both spatially and temporally must be known. The method used involves the application of a new inverse heat conduction method to thermal data recorded during laboratory experiments of aluminium alloy solidification in investment casting shell moulds. The resultant heat transfer coefficient for the alloy/mould interface is calculated. An experimental programme to determine requisite mould thermal properties was also undertaken. It was observed that there is significant variation of the alloy/mould heat transfer coefficient during solidification. It is found to be highly dependent on the alloy type and on the vertical position below the initial free surface of the liquid metal. The aluminium casting alloys used in this study were 413, A356, 319 (Aluminum Association designations), and commercially pure aluminium. These alloys have significantly different freezing ranges. In particular, it was found that alloys with a high freezing range solidify with rates of heat transfer to the mould which are very sensitive to metallostatic head.     

投资与融资优化决策模型研究综述分析

本文对投资与融资优化模型及研究思路进行了分析,并对各类模型的改进或拓宽做了进一步讨论,为更深入研究组合投资和资本结构总体优化问题作准备。     

变高度简支箱梁剪力滞半解析解

基于结构动力学中的Ritz向量叠加法基本原理,建立了求解静力学中变高度简支箱梁剪力滞效应半解析解的分析方法．该方法以相同跨度、相同边界条件等截面Euler梁的振动模态及其导数为Ritz基函数,将箱梁的竖向挠度在模态空间线性展开,将剪切转角的最大差值在模态导数的空间线性展开,从而将变系数剪力滞效应微分方程组转变为线性代数方程组进行求解．随后分别进行截面高度为常量、线性衰减和抛物线变化箱梁的剪力滞计算．计算结果表明,截面高度变化越小,Ritz法收敛越快;随着参与计算模态阶数的增加,Ritz法的计算结果逐步收敛到解析解;采用10阶以上模态进行箱梁剪力滞系数的计算,计算误差小于5 %．     

Characterization of the transport properties of membranes of uncertain macroscopic structural homogeneity

The present paper confirms and extends previous applications of an original method of time-lag analysis to (concentration-independent) gas permeation through porous pellets produced by uniaxial compaction of fine graphite powder. It is shown that this approach to the study of membrane permeability enables one to (i) detect unambiguously a macroscopic structural inhomogeneity affecting transport across the membrane (often present as an unsuspected artifact of the membrane fabrication process); (ii) determine appropriate average values of the resulting space-dependent diffusion, D(x), and sorption, S(x), coefficients (without recourse to equililibrium sorption measurements); (iii) secure substantial information about the functional form, as well as the degree, of variability of D(x) and S(x); and ultimately (iv) link this information to the underlying membrane structural inhomogeneity. In the present context, the salient underlying structural feature is nonuniform porosity across the membrane, represented by (x), and the link between D(x), S(x) and (x) is provided by the simple dual-mode (intrapore gas-phase + adsorbed-phase) model of sorption and transport in porous media. The effect of increasing overall pellet porosity (_obs) by reducing applied compacting pressure, was specifically studied and found to entail marked enhancement of the degree of structural inhomogeneity without material changes in the functional form of D(x), S(x) and hence of (x). The conclusions drawn from time-lag analysis were shown to be consistent with the observed behavior of apparent diffusion coefficients derived from transient-state sorption or permeation measurements and with the results of dual-mode steady-state permeation analysis. The latter results showed additionally that, for a more complete interpretation of observed transport behavior, the variability across the pellet of the orientation of graphite particles should also be taken into account.     

高层束筒建筑板块法理论

本文给出了正交异性板在多种平面应力边界条件下的应力分布解析表达式，由此提出了多筒高层框筒（或剪力墙筒体）内力与位移计算的正变异性板板块法理论．该方法是基于力法体系及形变协调条件的半解析法，可方便地应用于多筒筒体或多室梯形箱梁等折板结构分析。