关于函数方程的若干进展

本文介绍了单实变量的函数方程的若干新进展，包括迭代根、Ｓｃｈｒｏｄｅｒ方程和多项式型迭代方程的结果。基本内容有：Ｉ．引言：迭代与相关问题；Ⅱ．迭代根：存在性；Ⅲ．迭代根：唯一性、可微性和分枝；Ⅳ．多项式型迭代方程。     

在点估计判据下Euler级数、Euler迭代族以及Hauey迭代族的收敛性

论文证明了,当 S.Smale[1—3]的点估计判据α(f,z)=‖Df(z)~-1f(z)‖·(?)‖Df(z)~(-1)D~nf(z)/n!‖~(1/(n-1))≤3-22~(1/2)时,求 Banach 空间解析映照f零点ζ的 Newton 迭代的两族高阶推广以及ζ的逆级数都收敛,并且对其中每一个极限来说,条件中的常数3-22~(1/2)都是最好可能的.对其中以f在z的[1/k-1]阶 Padé 逼近的零点的算子形式拓广为迭代函数的那一族迭代(k=1,2,…),还给出了误差的准确估计.     

一种新的Bregman迭代方法在信号恢复中的应用

本文结合残量Bregman迭代方法以及不动点迭代方法提出一种新迭代方法,将其应用于信号恢复问题.数值试验表明,新方法避免了Bregman迭代方法产生的停滞现象且较线性Bregman迭代方法更稳定、快速、有效.     

m-增生算子方程解的Mann和Ishikawa迭代逼近

研究了Ｂａｎａｃｈ 空间中具 ｍ＿ 增生算子的方程解的Ｍａｎｎ 和Ｉｓｈｉｋａｗａ 迭代逼近问题·　研究结果改进和发展了一些文献中的最新成果·     

中点牛顿迭代格式的最优性

研究牛顿迭代法的变形格式,在中点迭代格式的基础上,提出了如下形式的一般迭代格式:{P∶zk+1=(xk-f(xk))/(f′(xk)) C∶xk+1=xk-(f(xk))/(f′(μxk+(1-μ)zk+1))并证明了中点迭代格式是这类迭代格式中最优的,收敛阶为3.     

几类微分方程解的迭代增长级数与零点迭代收敛指数

本文研究了几类微分方程解的迭代增长级及零点迭代收敛指数．     

参数d迭代逼近的GM(1,1)模型及其在技术创新中的应用

首先论述了参数d迭代逼近求解的GM(1,1)模型基本思路.其次,给出了此模型的参数估计与算法,即:1)估算出初始a_l,根据GM(1,1)模型a,c,d之间的关系,由a_l求得C_l,d_l;2)迭代d_l→d_(l+1),再计算a_(l+1),c_(l+1)及平均相对误差mape_l,mape_(l+1);3)多次迭代d_l→d_(l+1),直至|mape_(l+1)-mape_l|ε时,可得mape最小时的最优参数a,c,d值.然后,从理论与实证方面,证明模型是无偏的,且在参数d迭代过程中,a总能取到有意义的值.最后将模型应用于企业技术创新领域之中.     

两族选代的不动点和Julia集

This paper proves that, for complex polynomials, all extraneous fixed pointsfor any iteration of Halley iterative family and another relevant iterative family arerepelling. Thus no false convergent phenomenon arises on these iterations.     

关于强增生算子的带误差项的Ishikawa和Mann迭代程序的注记

设Ｘ是实Ｂａｎａｃｈ空间,Ｈ：Ｘ→Ｘ是Ｌｉｐｓｃｈｉｔｚ算子,Ｔ：Ｘ→Ｘ是值域有界且一致连续的算子,Ｈ＋Ｔ是强增生算子,则具有误差项的Ｉｓｈｉｋａｗａ和Ｍａｎｎ迭代序列强收敛到方程Ｈｘ＋Ｔｘ＝ｆ的唯一解,这些结论推广了最新文献中的相应结果。     

非Hermitian正定线性方程组的外推的HSS迭代方法

为了高效地求解大型稀疏非Hermitian正定线性方程组，在白中治、Golub和Ng提出的Hermitian和反Hermitian分裂（HSS）迭代法的基础上，通过引入新的参数并结合迭代法的松弛技术，对HSS迭代方法进行加速，提出了一种新的外推的HSS迭代方法（EHSS），并研究了该方法的收敛性.数值例子表明：通过参数值的选择，新方法比HSS方法具有更快的收敛速度和更少的迭代次数，选择了合适的参数值后，可以提高HSS方法的收敛效率.     

中国煤层气的产业化进程与发展建议

煤层气产业在中国能源建设中具有重要战略地位。中国煤层气勘探开发历经矿井瓦斯抽排利用、现代煤层气理论技术的引进发展与成功应用、商业化开发试验及产业化发展（初期）4个阶段。由于在煤层气地质基础理论、勘探技术方法、开发工艺技术、集输利用与管理制度等方面的发展创新、系统集成,我国已有能力大规模发展煤层气产业,这在我国能源发展战略上是非常难得的历史机遇。当前,为了加快煤层气产业的发展,必须加强统筹规划,发挥多种积极性;加强煤层气地质研究、提高对区域勘探的指导与目标评价水平;开展高效低成本开发工艺技术攻关;发展煤层气产品集输和加工利用;继续跟踪国外煤层气前沿理论技术,加强技术交流与合作研究。     

基于模糊FNN-ELECTRE法的国有商业银行竞争力评价

随着金融业全方位开放,国有商业银行已成为国家经济命脉的核心,其竞争力强弱关系着国家经济的繁荣与衰退。本文基于模糊FNN-ELECTRE方法建立国有商业银行竞争力评价模型,以因素神经网络理论(FNN)与ELECTRE融合方法为基础,以现有商业银行竞争力评价指标为着眼,把国有商业银行竞争力的评价体系从现实竞争力和潜在竞争力两个因素抽取为一级指标,以规模、质量、业务结构、效率、成长性五个因素设为二级指标。从实证的角度对银行A、银行B、银行C、银行D、银行E五大国有银行进行分析验证,对其属性值进行和谐性与非和谐性检验得出,银行B竞争能力最强,银行E竞争能力最弱,五大国有银行均有改进空间。     

共生视角下我国区域创新生态系统发展观测——基于TOPSIS生态位评估投影模型的时空特征分析

为明确我国区域创新生态系统发展现状,以共生为视角,基于共生单元、共生基质、共生平台、共生网络、共生环境五大生态特征建立区域创新生态系统综合评价指标体系,以2007~2015年我国30个省市相关数据为样本,运用TOPSIS生态位评估投影集成模型及二次加权算法,对我国区域创新生态系统整体及各生态特征的发展状况进行静态和动态综合评价,并分析其时空特征、地区差异及关键因素变迁。结果表明:(1)我国区域创新生态系统发展整体呈趋好态势,东部地区发展趋缓且存在极化现象,中西部地区普遍抬升,地区间发展水平差距较大但随时间推移呈缩小趋势;(2)创新生态系统各生态特征均表现出“东高西低”的地区间非均衡现象,但其时空特征具有显著异质性;(3)区域创新生态系统长远发展的助力优先来自于共生平台和共生网络,而共生单元、共生基质和共生环境的重要性程度呈相对弱化态势。     

A 3D modeling of static and forward smoldering combustion in a packed bed of materials

A three-dimensional (3D) model based on the first principles of mass, momentum and energy was developed that numerically simulates the processes of static and forward smoldering in a porous packed bed of plant materials. The packed bed contains cellulose material or tobacco (cigarette) wrapped in a porous paper and surrounded by an ambient air. Other major characteristics of the model are including the effects of buoyancy forces in the flow field, separate treatment of solid and gas in a thermally non-equilibrium environment, and use of multi-precursor kinetic models for the pyrolysis of staring material and oxidation of char. The changes in porosity due to pyrolysis and char oxidation and the effect of porosity on the bed permeability and gas diffusivity are included. The mass, momentum, energy, and species transport equations are solved in a discretized computational domain using a commercially available computational fluid dynamics (CFD) code. The simulation results show that the model reasonably reproduces the major features of a burning cigarette during smoldering and puffing and are in a good agreement with the existing experimental results for cigarettes. Results include the velocity profiles, gas and solid temperatures, coal shape, burn rates, profile and transport of gas and vapor species throughout the packed bed, dilution through the wrapper paper and ventilation in the filter section, and the mass fraction of some pyrolysis and oxidation products in the mainstream and sidestream flows.     

From inequalities involving exponential functions and sums to logarithmically complete monotonicity of ratios of gamma functions

In this paper, the authors review origins, motivations, and generalizations of a series of inequalities involving finitely many exponential functions and sums. They establish three new inequalities involving finitely many exponential functions and sums by finding convexity of a function related to the generating function of the Bernoulli numbers. They also survey the history, backgrounds, generalizations, logarithmically complete monotonicity, and applications of a series of ratios of finitely many gamma functions, present complete monotonicity of a linear combination of finitely many trigamma functions, construct a new ratio of finitely many gamma functions, derive monotonicity, logarithmic convexity, concavity, complete monotonicity, and the Bernstein function property of the newly constructed ratio of finitely many gamma functions. Finally, they suggest two linear combinations of finitely many trigamma functions and two ratios of finitely many gamma functions to be investigated.     

基于关系契约视角的农户与农产品电子商务企业合作机制演化博弈分析

本文基于关系契约的视角,运用演化博弈理论,构建有限理性特性下的农户与农产品电子商务企业合作演化博弈模型,分析双方合作策略的演进过程、稳定策略及其影响因素,并通过Matlab仿真模拟分析影响双方合作策略选择的因素,验证博弈结果正确性。研究结果表明:农户和农产品电子商务企业选择合作策略与合作投入成本、实现的超额收益密切相关,博弈初始状态、再交易成本、单方不合作获得的收益及违约罚金等因素影响系统的演化稳定结果。因此完善农户与农产品电子商务企业的合作机制,需要构建合理的利益分配机制、良好的关系治理机制、有效的监督和惩罚机制和信息共享、沟通与协调机制。     

Financial Risk Modelling and Econometric Inference

In finance, the explicit modelling of uncertainty takes on a particularly important role. The values of financial derivatives increase in the return volatility of the underlying security. This notion requires a concept of volatility and hence uncertainty. In addition, the choice between modelling in discrete and continuous time is not arbitrary, since it corresponds to a distinction between incomplete and complete markets, respectively, and this distinction matters for asset pricing, financial risk modelling, and inference. Risk and volatility are closely connected, and implied volatility, volatility forecasting, volatility in term structure models, stochastic volatility, and portfolio analysis are considered and related to a more general interplay between cross-sectional and dynamic aspects in finance. Stocks, bonds, and options are considered and placed in the context of efficiency and separation in inference.     

基于经销商再制造的闭环供应链政府补贴策略及效果分析

针对制造商负责再制造设计,经销商负责再制造的闭环供应链系统,建立政府无补贴、补贴经销商再制造和补贴制造商再制造设计3种策略下的Stackelberg博弈模型,分析不同补贴策略对供应链成员企业决策的影响。同时,应用数值仿真方法研究相同补贴支出下两种补贴策略的优劣。结果表明:相对于无补贴策略,两种补贴策略均会降低再制品和新产品的销售价格,提高再制品销售量,提升再制造设计水平,并且在再制品需求量小于新产品需求量时均会降低新产品销售量,在再制品和新产品的需求量相等时均会提高新产品销售量;另外,在相同的补贴支出下,当新产品需求量大于再制品需求量时,补贴经销商更能降低两种产品的销售价格和新产品的销售量,提高再制品销售量和制造商与经销商的利润,补贴制造商则更能提升再制造设计水平。     

The strength of Mac Lane set theory

Saunders Mac Lane has drawn attention many times, particularly in his book Mathematics: Form and Function, to the system of set theory of which the axioms are Extensionality, Null Set, Pairing, Union, Infinity, Power Set, Restricted Separation, Foundation, and Choice, to which system, afforced by the principle, , of Transitive Containment, we shall refer as . His system is naturally related to systems derived from topos-theoretic notions concerning the category of sets, and is, as Mac Lane emphasises, one that is adequate for much of mathematics. In this paper we show that the consistency strength of Mac Lane's system is not increased by adding the axioms of Kripke–Platek set theory and even the Axiom of Constructibility to Mac Lane's axioms; our method requires a close study of Axiom H, which was proposed by Mitchell; we digress to apply these methods to subsystems of Zermelo set theory , and obtain an apparently new proof that is not finitely axiomatisable; we study Friedman's strengthening of , and the Forster–Kaye subsystem of , and use forcing over ill-founded models and forcing to establish independence results concerning and ; we show, again using ill-founded models, that proves the consistency of ; turning to systems that are type-theoretic in spirit or in fact, we show by arguments of Coret and Boffa that proves a weak form of Stratified Collection, and that is a conservative extension of for stratified sentences, from which we deduce that proves a strong stratified version of ; we analyse the known equiconsistency of with the simple theory of types and give Lake's proof that an instance of Mathematical Induction is unprovable in Mac Lane's system; we study a simple set theoretic assertion—namely that there exists an infinite set of infinite sets, no two of which have the same cardinal—and use it to establish the failure of the full schema of Stratified Collection in ; and we determine the point of failure of various other schemata in . The paper closes with some philosophical remarks.