构造二次函数解决一元二次方程问题

有些难以直接求解的一元二次方程的问题,通过构造法,转化为二次函数的形式,再利用二次函数的性质进行求解,可收到事半功倍之效.下面举例加以说明,供参考.     

基于投人产出分析的中国能源消费分行业碳排放系数因素分解

采用投入产出分析法,结合部门能源消费数据,从最终需求的角度评估和计算了中国1997年、2002年和2007年的碳排放量、碳排放系数、直接碳排放系数和完全碳排放系数.研究结果表明,金属冶炼及压延加工业、燃气生产和供应业、非金属矿物制品业、电力、热力的生产和供应业、水的生产和供应业以及煤炭开采和洗选业的直接碳排放系数历年均是最高的,能源强度是影响这些行业直接碳排放系数变化的主要因素;金属冶炼及压延加工业、非金属矿物制品业、金属制品业、化学工业、电力、热力的生产和供应业、水的生产和供应业以及煤炭开采和洗选业的完全碳排放系数历年均居前列,中间产品投入和能源强度是影响完全碳排放系数变化的主要因素.针对实证结果,现阶段我国节能减排的重点方向在于调控金属冶炼及压延加工业、化学工业等高碳排放行业,并通过提高能源效率、调整产业结构及优化能源结构来达到降低碳排放系数的目的.     

Bazilevic函数相邻两系数模之差的估计

本文研究单叶函数相邻系数模之差的增长问题,设f(z)∈S, 0<λ<1．当f为Bazilevic函数时,得到||Dn+1|-|Dn||的准确的阶的估计．     

AN IMPROVED SEARCH-EXTENTION METHOD FOR SOLVING SEMILINEAR PDES

This article will combine the finite element method, the interpolated coefftcient finite element method, the eigenfunction expansion method, and the search-extension method to obtain the multiple solutions for semilinear elliptic equations. This strategy not only grently reduces the expensive computation, but also is successfully implemented to obtain multiple solutions for a class of semilinear elliptic boundary value problems with non-odd nonlinearity on some convex or nonconvex domains. Numerical solutions illustrated by their graphics for visualization will show the efficiency of the approach.     

三系数有限元向量尺度函数的构造

The aim of this paper is to present construction of finite element multiscaling function with three coefficients. In order to illuminate the result, two examples are given finally.     

Hilbert Space of Probability Density Functions Based on Aitchison Geometry

The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison＇s ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.     

高薪养廉的效用模型分析

针对我国近年来提出的"高薪养廉"观点,采用VNM效用函数建立了相应的数学模型.通过分析,找到了一个满足一定约束的均衡点(y_1~*,y_2~*),此点即达到了高薪养廉的目的.但在进一步的讨论中,发现均衡点(y_1~*,y_2~*)有很大的局限性,且模型显示出加强监督与惩罚力度的重要性.     

带有限反馈下层的二层规划问题的部分合作模型

对下层最优反馈为离散有限多个的二层规划问题的部分合作模型进行探讨. 当下层的合作程度依赖于上层的决策变量时, 给出一个确定合作系数函数的一般方法, 进而得到一个新的部分合作模型. 在适当地假设下, 可保证所给的部分合作模型一定可以找到比悲观解要好的解, 并结合新的部分合作模型对原不适定问题进行分析, 得到了一些有益的结论. 最后以实际算例说明了所给部分合作模型的可行性.