THE ''HYBRID'' TECHNIQUE FOR RISK ANALYSIS OF SOME DISEASES

51. IntroductionSince the theory of fuszy set was introduced by Lotfi A. Zadeh in 1965, fuzzy techniquehas developed rapidly and has been successfully aPplied into many fields.In receat yeaJrs3 a new and promising way of using the fuzzy technique is combinedwith other deterministic and statistica1 methods. The so-called 'hybrid' technique has beenaPplied to insurance business and achieved positive results (see [1, 2], etc.).Based on the data obtained from a survey recelltly made in a commun…     

Existence of Canards under Non-generic Conditions

The canard phenomenon occurring in planar fast-slow systems under nongeneric conditions is investigated. When the critical manifold has a non-generic fold point by using the method of asymptotic analysis combined with the recently developed blow-up technique, the existence of a canard is established and the asymptotic expansion of the parameter for which a canard exists is obtained.     

On the Error Estimate of the Harmonic B_z Algorithm in MREIT from Noisy Magnetic Flux Field

Magnetic resonance electrical impedance tomography(MREIT, for short) is a new medical imaging technique developed recently to visualize the cross-section conductivity of biologic tissues. A new MREIT image reconstruction method called harmonic Bz algorithm was proposed in 2002 with the measurement of Bz that is a single component of an induced magnetic flux density subject to an injection current. The key idea is to solve a nonlinear integral equation by some iteration process. This paper deals with the convergence analysis as well as the error estimate for noisy input data Bz, which is the practical situation for MREIT. By analyzing the iteration process containing the Laplacian operation on the input magnetic field rigorously, the authors give the error estimate for the iterative solution in terms of the noisy level δ and the regularizing scheme for determiningΔBz approximately from the noisy input data. The regularizing scheme for computing the Laplacian from noisy input data is proposed with error analysis. Our results provide both the theoretical basis and the implementable scheme for evaluating the reconstruction accuracy using harmonic Bz algorithm with practical measurement data containing noise.     

A new method of moving asymptotes for large-scale linearly equality-constrained minimization

A new method of moving asymptotes for large-scale minimization subject to linear equality constraints is discussed.In this method,linear equality constraints are deleted with null space technique and the descending direction is obtained by solving a convex separable subproblem of moving asymptotes in each iteration. New rules for controlling the asymptotes parameters are designed and the global convergence of the method under some reasonable conditions is established and proved.The numerical results show that the new method may be capable of processing some large scale problems.     

The spectrum sequences of periodic frame multiresolution analysis

The periodic multiresolution analysis （PMRA） and the periodic frame multiresolution analysis （PFMRA） provide a general recipe for the construction of periodic wavelets and periodic wavelet frames, respectively. This paper addresses PFMRAs by the introduction of the notion of spectrum sequence. In terms of spectrum sequences, the scaling function sequences generating a normalized PFMRA are characterized; a characterization of the spectrum sequences of PFMRAs is obtained, which provides a method to construct PFMRAs since its proof is constructive; a necessary and sufficient condition for a PFMRA to admit a single wavelet frame sequence is obtained; a necessary and sufficient condition for a PFMRA to be contained in a given PMRA is also obtained. What is more, it is proved that an arbitrary PFMRA must be contained in some PMRA. In the meanwhile, some examples are provided to illustrate the general theory.     

求解无约束非线性规划问题的一个新的重开始共轭梯度算法的收敛性

Conjugate gradient optimization algorithms depend on the search directions.with different choices for the parameters in the search directions.In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991),a class of new restarting conjugate gradient methods is presented.Global convergences of the new method with two kinds of common line searches,are proved .Firstly,it is shown that,using reverse modulus of continuity funciton and forcing function,the new method for solving unconstrained optimization can work for a continously differentiable function with Curry-Altman‘s step size rule and a bounded level set .Secondly,by using comparing technique,some general convergence propecties of the new method with other kind of step size rule are established,Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method.     

A Spectral Method for the Electrohydrodynamic Flow in a Circular Cylindrical Conduit

This paper presents a combination of the hybrid spectral collocation technique and the spectral homotopy analysis method(SHAM for short) for solving the nonlinear boundary value problem(BVP for short) for the electrohydrodynamic flow of a fluid in an ion drag configuration in a circular cylindrical conduit. The accuracy of the present solution is found to be in excellent agreement with the previously published solution. The authors use an averaged residual error to find the optimal convergence-control parameters. Comparisons are made between SHAM generated results, results from literature and Matlab ode45 generated results, and good agreement is observed.     

A Fixed Point Approach to the Fuzzy Stability of a Mixed Typ e Functional Equation

Through the paper, a general solution of a mixed type functional equation in fuzzy Banach space is obtained and by using the fixed point method a generalized Hyers-Ulam-Rassias stability of the mixed type functional equation in fuzzy Banach space is proved.     

数学年刊第35卷B辑第3期(2014)目次和提要

<正>On the Error Estimate of the Harmonic B_z Algorithm in MREIT from Noisy Magnetic Flux Field Qun CHEN Jijun LIUMagnetic resonance electrical impedance tomography(MREIT,for short)is a new medical imaging technique developed recently to visualize the cross-section conductivity of biologic tissues.A new MREIT image reconstruction method called harmonic B_z algorithm was proposed in 2002with the measurement of B_z that is a single component of an induced magnetic flux density subject to an injection current.The key idea is to solve a nonlinear integral equation by some iteration     

LOCAL GAUSSIAN-COLLOCATION SCHEME TO APPROXIMATE THE SOLUTION OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS USING VOLTERRA INTEGRAL EQUATIONS

This work describes an accurate and effective method for numerically solving a class of nonlinear fractional differential equations.To start the method,we equivalently convert these types of differential equations to nonlinear fractional Volterra integral equations of the second kind by integrating from both sides of them.Afterward,the solution of the mentioned Volterra integral equations can be estimated using the collocation method based on locally supported Gaussian functions.The local Gaussian-collocation scheme estimates the unknown function utilizing a small set of data instead of all points in the solution domain,so the proposed method uses much less computer memory and volume computing in comparison with global cases.We apply the composite non-uniform Gauss-Legendre quadrature formula to estimate singular-fractional integrals in the method.Because of the fact that the proposed scheme requires no cell structures on the domain,it is a meshless method.Furthermore,we obtain the error analysis of the proposed method and demon-strate that the convergence rate of the approach is arbitrarily high.Illustrative examples clearly show the reliability and efficiency of the new technique and confirm the theoretical error estimates.     

毕达哥拉斯群决策方法及其在绿色供应商选取中的应用

针对专家权重未知且属性值为毕达哥拉斯模糊数的多属性群决策问题,基于证据理论和混合加权毕达哥拉斯MSM算子,提出了一种群决策方法。 首先,由决策信息矩阵获取专家的模糊测度,并赋予其相应的权重;其次,基于新构造的混合加权毕达哥拉斯MSM算子对专家所提供的属性信息分别进行集结,得到各个专家的综合评价信息;再次,利用证据合成方法,对专家综合评价信息进行融合,获得候选方案的综合证据信息,进而可知备选方案的信任区间,并据此对候选方案进行优选决策;最后,绿色供应商选取案例的分析与对比验证了方法的可行性与合理性。     

应急管理关键因素的混合型识别方法研究

如何细致识别出自然灾害下应急管理的关键因素,对于开展科学有效的应急管理具有重要的现实意义。本文提出一种新的应急管理关键因素的混合型识别方法,该方法通过构建三角模糊数为基本语言集、三角区间模糊数为补充语言集的评价尺度集,建立混合型初始直接关联矩阵并将之转化为区间数直接关联矩阵,进而实现中心度和原因度的综合排序,从而据此有效的识别出应急管理的关键因素,为制订高效科学的应急管理政策提供良好的方法论支持。同时,通过一个算例表明了本方法具有良好的识别效果。本混合型识别方法突破了已有研究单一性模糊评价尺度集的局限性,具有方法论创新价值,并在关键因素识别领域具有较好的应用普适性。     

模糊影响图评价算法在供应链金融信用风险评估中的应用

传统的银行信贷模式风险评价专注于个体企业的财务数据.供应链金融新融资模式下的信用风险评价不同于传统的融资模式风险评价,它的评价范围更宽,不确定性因素更加复杂.在分析供应链金融模式的信用风险评价体系的基础上,结合模糊集和影响图理论建立了模糊影响图评价模型,对评估中难以量化的问题进行模糊处理,对变量之间的模糊影响关系进行分析,最后计算出信用风险概率分布.方法定性与定量相结合,为供应链金融新模式下的风险评估提供了一种新思路.     

西部地区高技术产业自主创新能力组合评价研究

为了提高综合评价的全面性、科学性和合理性,分别运用模糊综合评价法和灰色关联投影法对西部7省(区)1市高技术产业自主创新能力进行评价,在此基础上,利用模糊Borda法对两种单一方法的评价结果进行组合,得出组合评价结果.与单一方法相比,组合评价结果具有较高的可信度,可作为全面提升西部地区高技术产业自主创新能力的决策依据.     

评价指标体系的设计方法研究——基于产业集群竞争力

产业集群竞争力评价是一个复杂的多属性决策问题,论文探讨了整个评价环节中的指标遴选问题。通过对相关评价指标的综合,借助于Delphi问卷获取了指标筛选的基础数据,并借助模糊隶属度、差异性分析、相关性分析、信度与效度检验、稳定性与贴近度等技术指标得到了较为合理的评价指标体系。这一方法的提出,为评价系统中指标体系的遴选提供了一种新的思路和方法。     

基于改进模糊综合评价法的小微企业

本文结合小微企业的具体环境及实际情况构建小微企业信用评价指标体系,通过对比分析国内外信用评价方法,提出一种基于信息熵与层次分析法(AHP)结合的改进综合评价法,该方法利用信息熵计算客观权重,运用层次分析法计算主观权重,并对主客观权重进行拟合得出综合权重,分析得到小微企业信用评价等级,实现对小微企业金融风险的分析。实验结果表明,基于改进模糊评价法的小微企业金融风险分析模型可操作性较强,评估结果相对准确合理。     

应用模糊综合评判和灰色关联度分析评价水平井多级压裂效果

水平井多级压裂是低渗透和非常规油气田开发的有效技术手段,其压后产能评价问题已成为相关研究的热点和难点.水平井多级压裂压后产能的各项影响因素之间关系复杂,通过常规理论分析量化研究困难,压裂效果很难准确预测.本文提出应用模糊综合评判和灰色关联度分析相结合的方法,对多级压裂水平井的压裂效果进行评价.首先运用灰色理论分析影响压裂效果的各因素之间的灰色关联度,计算各影响因素在综合评判中的权重值,再结合模糊综合评判方法,对多级压裂井压后效果进行预测评价.通过目的区块24口多级压裂水平井压后效果评价与实际生产情况对比,表明模型计算准确率达到95.8%,评价结果准确可靠.     

A New Method for the Assessment of Noise Pollution in Urban Agglomerations

This work introduces a new method for the assessment of sound pollution in urban agglomeration. The method is based on fuzzy technique, which is a not used method until at this time for the pollution evaluation, but it will prove to be particularly useful and competitiveness. Starting from the classics design of the crowd and element of a crowd, shall be determined characteristics called degrees of belonging. The work presents the theoretical appropriateness for the application of fuzzy technique, the steps necessary to apply it, the program for the application of this technique, but also the computerized results obtained by application of the new methods, for the assessment of sound pollution by fuzzy technique. Concrete Implementation of a study from municipal area, with the implementation of the evaluation system based on fuzzy crowd is a rapid method, non-invasive, and has been obtained from the indicator of the impact on an intense inhabited road and powerful intense polluted from the movement of motor vehicles. Results of the study obtained from the application of technique fuzzy, compared with the measurement results in the same places, have proved viable and thus fuzzy technique becomes a useful tool, quick and non -destructive test for the assessment noise pollution in urban agglomerations. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)