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关键词： 水平井   产能计算   数学分析   解析模型  

摘要： 自20世纪40年代起,国内外对水平井产能作了大量的研究,提出了一系列的产能公式,其间经过学者不断的研究与改进,水平井产能公式越来越接近于油田生产实际。本文从水平井产能研究的方法,水平井产能公式等方面进行综合的阐述,指出了不同产能公式的不同适用范围,分析了水平井产能的影响因素以及其不足之处。

关键词： population dynamics   non-linear integral equations   eigenvalues and eigenvectors  

摘要： In this paper, we establish the existence of travelling wave solution to an intrinsically non-linear differential-integral equation formed as a result of mathematical modelling of the evolution of an asexual population in a changing environment. This equation is first converted to a non-linear integral equation. The discretization and manipulation of the corresponding eigenvalue problem allows us to use the theory of positive matrices to get some very useful estimates and then to confirm the existence of solution. We also exhibit numerical simulation results and explain the biological meaning of the results. (C) 2007 Elsevier Inc. All rights reserved.

关键词： STIRLING engines   FLUID dynamics   BIOMASS   MATHEMATICAL analysis   HEAT engines   ENGINES -- Design & construction   FLUID mechanics   THERMODYNAMICS   HEAT engineering  

摘要： The article presents a summary of the article entitled 'Design Improvements to a Biomass Stirling Engine Using Mathematical Analysis and 3D CFD Modeling' and discusses the issues and answers arising from it. It states that the authors of the paper believe that soundness of the original design was eradicated during the transformation into the stirling engine. In addition, the original engine presented several problems involving the heater tubes, the engine itself and the regenerator. The issue on the constant changing of nomenclature is also discussed.

关键词： reaction-diffusion   partial differential equations   elliptic eigenvalue problem   habitat fragmentation   habitat shape   optimisation   edge effects   boundary effects   periodic environment  

摘要： We study a reaction-diffusion model in a binary environment made of habitat and non-habitat regions. Environmental heterogeneity is expressed through the species intrinsic growth rate coefficient. It was known that, for a fixed habitat abundance, species survival depends on habitat arrangements. Our goal is to describe the spatial configurations of habitat that maximise the chances of survival. Through numerical computations, we find that they are of two main types - ball-shaped or stripe-shaped. We formally prove that these optimal shapes depend on the habitat abundance and on the amplitude of the growth rate coefficient. We deduce from these observations that the optimal shape of the habitat realises a compromise between reducing the detrimental habitat edge effects and taking advantage of the domain boundary effects. In the case of an infinite-periodic environment, we prove that the optimal habitat shapes can be deduced from those in the case of a bounded domain. (c) 2007 Elsevier Inc. All rights reserved.

关键词： diffusion   dissolution   precipitation   kinetics   finite volume method  

摘要： Modeling the kinetics of a precipitation dissolution reaction occurring in a porous medium where diffusion also takes place leads to a system of two parabolic equations and one ordinary differential equation coupled with a stiff reaction term. This system is discretized by a finite volume scheme which is suitable for the approximation of the discontinuous reaction term of unknown sign. Discrete solutions are shown to exist and converge towards a weak solution of the continuous problem. Uniqueness is proved under a Lipschitz condition on the equilibrium gap function. Numerical tests are shown which prove the efficiency of the scheme.

关键词： MATHEMATICAL analysis   CURVATURE   GAMMA functions   BOUNDARY value problems  

摘要： The mechanical model for the rectangular cantilever beam proposed by Zhang et al is solved analytically by the series solution with mathematical properties investigated in detail. The derived series solution is proved convergent, and restrained only by the small deflection presumed by the Euler - Bernoulli beam theorem, and is applicable for calculating the deflection and curvature for any value of the exerted axial stress. The formulae estimating the accuracy of the coefficients and the series solution are developed from Stirling's approximation for the gamma function. The condition on the axial stress is developed, by which the genuinely nonlinear curvature can be approximated by a linear function and the deflection can be calculated from the boundary condition by a cubic polynomial. The additional redundant boundary condition used in Zhang's work is discussed, which should be removed since it fails to fit the model by inducing errors for calculating the deflection and the curvature. The present series solution approach provides formal deflection - stress and curvature - stress relations for the design of a MEMS micro-cantilever system as a bio-detection device. For self-assembly applications, the adsorbing material can be identified by solving the exerted axial stress from the series solution.

摘要： Purpose: With brighter stimuli, the photopic ERG b-wave increases to a maximal value and then decreases to a plateau, a feature known as the Photopic Hill (PH). Recently, a mathematical model combining a Gaussian (GF) and a Logistic Growth (LGF) functions was developed to fit the PH (Hamilton et al., Vision Research, in press). We examined if this equation could help us sort out selected retinopathies. Methods: We compared PHs (background: 30 cd.m-2; intensities: -0.8 to 2.84 log ***.m-2) obtained from normals (N=40) and patients (N=20) affected with Congenital Stationary Night Blindness (CSNB), Congenital Postreceptoral Cone Pathway Anomaly (CPCPA) and Retinitis Pigmentosa (RP) with the GL ratio [GL= Gb / (Gb+Vbmax)] were Gb and Vbmax represent the amplitude of the Gaussian and logistic (Vbmax) functions respectively. Results: The normal GL ratio is 0.60 ± 0.08 (mean ± 1SD) compared to ≈1.0 in CSNB (almost pure GF) and 0.32±0.08 in CPCP [reduced GF (p<.05) and normal LF (p>.05)] patients. Six of the 8 RP patients had a GL ratio above 0.5 (mean GL= 0.70 ± 0.19) and 2 below (0.28 and 0.41). Of interest, while in some retinopathies, a decline in Gb and Vbmax occurred with disease progression (longitudinal and transversal comparisons), it did not always modify the GL ratio. Conclusions: Human PH can be dissected into two distinct and concomitant phenomena each represented by its own equation. Altghough the retinal origin of the GF and LGF awaits to be confirmed, use of this mathematical approach appears to add valuable information that will further refine the diagnosis of retinal disorders affecting the photopic (cone) pathway. Supported by CIHR and Réseau Vision.

关键词： 盲孔法   焊接残余应力   应变释放系数   模糊模型   隶属函数  

摘要： 在分析一些引起盲孔法检测焊接残余应力测量误差的不确定因素的基础上,引入模糊数学方法对应变释放系数进行评价。在允许常规模型中的有关参数在一定范围内变动、用隶属函数表示其取值分布情况的前提下,建立应变释放系数的模糊数学模型。将应变释放系数评价模型中的有关参数考虑为正态分布模糊数,利用水平截集概念转化为普通集问题进行求解。以921A钢板焊接的残余应力测量为例,计算出不同置信水平的应变释放系数A和B的数值。结果表明,基于模糊集的应变释放系数评价模型能适当屏蔽一些不确定因素,更准确地反映实际情况。

关键词： 极限理论   循序渐进   抽象思维  

摘要： 论述数学分析课程极限理论一步走的教学方式中,如何循序渐进,螺旋发展,突出重点,分散难点,加强直观理解,使绝大多数学生接受,并学好微积分,初步形成动态抽象思维。

关键词： 数学分析选讲   必要性   实践   认识  

摘要： 通过开设《数学分析选讲》课程,在教学内容、教学方法等方面进行了有益的探索,编写出符合大专优秀学生实际的《数学分析同步辅导》讲义,优化了数学分析内容,改进了传统的教学方法,在培养学生的思堆能力和应用能力等方面,取得了较好的效果。