数学建模是开启数学大门的金钥匙

作为大学《数学建模》课程的导言,对什么是数学建模,以及数学建模在推动数学学科发展及培养创新型人才方面的重要性,作充分的阐述.同时,针对数学建模的特点,对数学建模课程的教学,提出一些必要的建议.     

质量评价的属性数学模型和模糊数学模型

本文提出了质量评价的属性数学模型。该模型由三部分组成：单指标属性测度分析，多指标综合属性测度分析，属性识别分析。我们分析了属性数学模型和模糊数学模型的差异。应用例子表明属性数学模型是更合理的     

数学建模思维方法论

数学建模过程是一个复杂的思维过程,全国大学生数学建模竞赛又加以竞赛的形式,有其特殊性,其中如何研究问题、如何做出成果、如何争取获奖,本文探讨其思维规律、方法技巧.     

Interior point solutions for boundary integral equation axisymmetric stress analysis

Owing to the complexities of the equations involved, the evaluation of stresses for interior point solutions for boundary integral equations (BIE) axisymmetric analysis is difficult. Equations and corresponding expressions for such solutions are presented explicitly for easy implementation into BIE computer codes.     

A deficient spline function approximation to systems of first order differential equations

The stability of the vector-valued spline function approximations S(x) of degree m deficiency 3, i.e., S∈C^m?3, to systems of first order differential equations are investigated. The method will be shown to be A-stable for m=4, unstable and hence divergent for m?6. The method is stable form=5.     

关于Logistic模型的倍周期收敛现象

运用实验和归纳的方法 ,讨论了如何利用 Mathematic数学软件观察 Logistic模型的倍周期收敛现象以及对初值的依赖性 ,并从理论上解释了倍周期收敛现象     

局部武装冲突中战时航空技术装备使用模型的建立

高技术局部战争已成为未来战争的重要作战样式,为了应对千变万化的战场形势,需要对战时航空技术装备使用做出科学合理的规划.在用马尔科夫随机过程对航空技术装备使用的实际过程进行分析的基础上,建立了局部武装冲突中战时航空技术装备的使用模型,并对航空技术装备的准备和战斗利用情况进行了分析,增强了战时航空技术装备使用的计划性和针对性,有利于更大限度地发挥各种航空技术装备的整体优势,为保障和作战预案的制定以及指挥决策提供更加科学有力的理论支持.     

几种电梯运行模式的比较及应用

通过对上班高峰时段的电梯运行情况进行分析,以"最后被运送的乘客的等待时间最短"的"最大最小"原则作为其评价指标,以"电梯运行周期与运行总时间之比等于电梯在一个周期内运送的乘客数与乘客总数之比"的"比例"原则为依据,对高层楼宇中人员流动高峰时段的几种电梯运行方案建立了数学模型进行描述与比较,找到了电梯停靠楼层的最佳方案,并对北京大学第三医院外科楼的运行方案做出定量的数学证明.     

A deficient spline function approximation to systems of first-order differential equations: part 2

The problem of stability was discussed in part 1 of this paper (Appl. Math. Modelling 1983, 7, 380). This part looks at the convergence of the spline approximation of deficiency 3 to systems of first-order differential equations. Convergence is shown for m = 4 and 5. In addition, global error bounds of the form: ∥S⁽ⁱ⁾(x) ? y⁽ⁱ⁾(x)∥∞ = 0(h^m+1?i), i = 0(1)m are presented, together with a computational example which illustrates the convergence of the proposed method.     

Optimization of a minimal-storage strategy for cloud amount data

A strategy is proposed which reduces the storage requirements for cloud amount information by up to 50%. Archiving only the mean cloud amount, μ, is recommended. Retrieval of most of the original data is possible if observations are made at high resolution ( 1 km) and the processing system gives rise to predominantly binary (i.e. cloud or no-cloud) information. The strategy is applicable to cloud amount at any level and to total cloud cover. One year's global cloud data can be stored on 2.5 computer magnetic tapes in contrast to the 13 tapes suggested by GARP/JOC (1980) and ISCCP (1982). The resultant new cloud archive will have the advantage of being equally useful for all scientific users (e.g. remote sensing and climate modelling groups) and each group's post-processing time will be greatly reduced.     

The extrapolation of Padé approximants in the closed-loop simulation of human thermoregulation

This paper presents a mathematical model of the human thermoregulatory system which has been developed to simulate the reaction of the human body to instantaneous changes in the temperature of the environment. The model combines two widely accepted approaches: the expression of heat flow within and from the human body in the form of partial differential equations, and the use of control theory. The closed-loop simulation is generated by introducing physical phenomena such as sweating, shivering, vasodilation and vasoconstriction, thus transforming the model equations into a system of nonlinear partial differential equations. The central difference operator is used to approximate spatial partial derivatives at a large number of mesh points, thus achieving high accuracy in the space dimension, and the problem is reduced to that of solving a nonlinear system of ordinary differential equations. A novel extrapolation algorithm, which copes well with the discontinuities between initial and boundary conditions caused by instantaneous environmental changes, is used to produce a high accuracy approximation in the time domain, and generate a solution to the problem. The model is used to simulate several important physical problems.     

Embodied and disembodied technical change and the constant elasticity of substitution production function

This study examines the empirical basis for the suggestion that both disembodied technical progress and embodied technical progress in the capital stock and in labour have been important in the United States in the period 1947–1980. The results obtained by using a constant elasticity of substitution production function suggest that disembodied technical progress has been about 3% per year, embodied technical progress in the capital stock is in the neighbourhood of 3 to 4% annually and educational attainment significantly enhances labour productivity. Finally, when the structural stability of the underlying production relationship is examined, the period 1971–1980 gives rise to some inconsistency.     

反映生物系统平衡点稳定性的数学模型

本文利用 Logistic模型 ,建立了反映生物系统竞争和排斥的数学模型 ,并且讨论了模型的平衡点的稳定性 .     

Remarks on the paper ‘Exact bounds on average granular pressures in a general bin model’

In the paper referred to in the title to this communication, Shahinpoor argued that increased density due to material consolidation of a bulk material in a vertical bin reduces the stresses the bulk material exerts on the bin wall below those that would be present if the material were unconsolidated. In this paper it is shown that increased density due to material consolidation actually increases rather than reduces these stresses. Shahinpoor's conclusions are incorrect because he misinterprets his analytical results.     

Prediction,measurement and comparison of fluid-structure interaction using mathematical and experimental models

Without presenting all the associated mathematics this paper considers the combined use of theoretical and experimental methods in the investigation of the fluid structure interaction of rigid and articulated structures. The structures considered are the rigid body form of the Lancaster Flexible Bag (LFB) and an articulated Cockerell raft system.In the case of the LFB the Salvesen-Tuck-Faltinsen strip theory is shown to predict vertical and horizontal bending moments which are generally consistent with measured trends (almost) irrespective of whether 2D-based or 3D-based calculated hydrodynamic active and reactive coefficients are used. The non-repeatability of some of the measured results used in the comparison caused some concern and the additional required model testing is discussed.In direct comparison application difficulties were encountered when using theoretical analyses to assist with the organization of the experiments to investigate the hydrodynamic loading of articulated systems. The finite element program PAFEC 75 was used to predict the vibration frequencies of the framework used to support the Cockerell raft model and the actuator system used to force oscillate the model. The 3D diffraction programme MATTHEW provided predictions of pressure distributions over the raft to assist with sensible positioning of the pressure transducers on the physical model. The difficulties encountered in applying these prediction tools are discussed, also the current research programme is reported.     

基于灰色系统的逻辑斯蒂模型的建模方法

给出了基于灰色系统的逻辑斯蒂(logisitic)模型的建模方法.用实例验证了基于灰色系统的逻辑斯蒂(logisitic)模型的建模过程简便适用,拟合精度较高.     

An infinite element theory

A technique for solution of plane problems in mathematical physics or mechanics is presented. The method was developed initially for elastic plate problems with transverse load concentrations but is here extended to other two-dimensional problems. Draw-down problems with a number of wells in a porous medium, heat-flow problems in a plate with a distributed source, and with discrete sinks, or membrane displacements under concentrated forces, are considered in particular.The technique is to treat the two-dimensional medium as infinite: each source or sink is treated separately and equilibrated by an auxiliary source function. Superposition allows the effects of the separate sources and sinks to be added. The residual effect of the auxiliary source, after superposition, is negligible so that the summed effects of the individual sources and sinks gives the required solution. The method is approximate but the error may be made arbitrarily small. It is simple and well suited to the class of problems above, and to either manual or computer based analyses. Examples of its use are given.     

理想化抽象在数学建模中的作用

理想化抽象是以抽象的理想形态表现研究对象的性质,以理想实验和理想模型为表现形式,是数学研究中采用的重要抽象方法,特别是在建立数学理论模型和数学应用模型时起到重要的作用。     

Optimal observation network in geostatistics and underground hydrology

Mathematical models and algorithms for the optimal design of data collection for regionalized variables are presented. The topics considered subsume as a special case optimal drilling strategies in hydrology, the mining industries and other geostatistical applications. In these disciplines an optimal design is a critical consideration since data, can only be obtained through an expensive drilling process.The methods given here are based on the theory of regionalized variables and of kriging. The basis of the methods for locating a single additional data point, and for locating multiple points, is the theory of minimizing uncertainty in parameter estimation. That is, the possible locations of additional points must be determined on the basis of surface analysis with respect to the projected costs of obtaining this data.After a summary of basic kriging techniques, four models are discussed. The first deals with the optimal location problem for a single experimental point, and the second, third and fourth models pertain to the case of multiple additional points. (Unfortunately the repeated application of the single-point model leads only to approximations of the global optima, since the global optima are usually unobtainable as a simple sum of the partial optima.) In the second model, an optimal regular observation network is to be designed to minimize the uncertainty of the estimation process subject to either the given number of additional data, or an upper bound for the cost of the additional data. In the fourth model, the number or cost of additional points is minimized subject to bounded uncertainty conditions. Finally, a numerical example will be used to illustrate the models and algorithms.