基于云模型的定性运算理论与方法

将定性值像定量值一样参与运算和推导,是定性理论走向真正实际应用必须解决的极为关键的研究问题.相关研究提出的方法在此方面均有一定的局限性.本文提出了一种基于云模型的定性运算理论与方法.首先在云模型基本运算的基础上提出了基于云模型的定性关系演算方法,其次提出了基于云模型的一元一次定性方程的求解方法.理论和方法能比较科学合理地计算出定性值,且具有定性与定量相互融合的特点.为定性演算和推导在系统分析和仿真等领域中进一步应用提供了重要的借鉴方法.     

OWA算子赋权新方法

对于如何对决策数据给出合理的权重,介绍基于OWA算子理论的两种赋权的方法.提出两种赋权的方法.由于组合数和整数联系相关的,提出一种新颖的基于组合数给出OWA算子权重的方法;由于正态分布的良好性质,从已知的OWA算子赋权方法出发,提出一种与决策数据关联紧密的赋权的方法,也给出这两种方法的简单分析.最后通过算例对该法进行说明和分析.     

基于Vague集的群决策方法研究

首先介绍了Vague集的基本概念,将直觉模糊集的一些运算规则重新在Vague集上作了定义,提出用Vague值表示的九级语言术语集.接着指出衡量Vague集(值)相似度要考虑的三个因素,提出了新的度量方法.在同时考虑专家决策结果的一致性和专家权重的基础上,提出了汇总各专家Vague意见的方法.最后以一个案例说明了所提出的方法.     

基于条件分布函数的高维回归模型的变量选择方法

高维回归分析的变量选择问题是目前统计学研究的一个热点和难点问题.提出了一个基于条件分布函数的相关性度量准则,并在此基础上提出三种变量选择方法.与现有的方法相比,提出的方法不依赖于统计模型,可以适用于线性模型和非参数可加模型.数值模拟结果表明,即使协变量之间存在一定的相关性,方法也有较为满意的表现.     

加热下分数阶广义二阶流体的Rayleigh-Stokes问题的一种有效数值方法

考虑加热下分数阶广义二阶流体的Rayleigh-Stokes问题(RSP-HGSGF),提出了一种逼近有界区域内RSP-HGSGF的有效数值方法.并且讨论了所提出方法的稳定性和收敛性.最后,利用数值例子体现数值方法的有效性.     

变系数空间自相关模型的Bayesian-INLA估计

文章提出了一类变系数空间自相关模型(VCSAM)新的Bayesian-INLA估计方法.在这个模型中,响应变量具有空间自相关性,且包含变系数的非参数部分.尽管已有的工作对该模型已经进行了大量研究,但很少有研究使用贝叶斯方法提出高效求解模型的方法.因此基于上述动机,文章提出了基于B ayesian-INLA技术的方法,以寻求在VCSAM框架内代替MCMC方法的有效解决方案.变系数部分使用B-样条基函数的线性组合进行逼近,空间自相关系数采用M-H算法进行估计,并应用Bayesian-INLA技术来估计变系数函数和相关系数的后验分布.通过模拟研究,展示了文章提出的估计方法在同时处理空间依赖效应和空间非平稳性时的优势.此外,通过对波士顿房价数据的实证分析,展示了文章提出的估计方法优越的性能.     

建立在割线条件上的新Liu-Storey型共轭梯度法的全局收敛性(英文)

我们基于拟牛顿法的割线条件提出两种LS型共轭梯度法.有趣的是,我们提出的方法中对于βk的计算公式与戴和廖[3]提出的有相似的结构.但是,新方法能够在合理的假设下保证充分下降性,这一点是戴-廖方法所不具备的.在强Wolfe线搜索下,给出了新方法的全局收敛结果.数值结果论证了该方法的有效性.     

线性混合效应模型的正交经验似然推断

基于经验似然方法和QR分解技术, 对线性混合效应模型提出了一个基于正交经验似然的估计方法. 在一些正则条件下, 证明了所提出的经验对数似然比函数渐近服从卡方分布, 进而给出了模型固定效应的置信区间估计. 所提出估计过程不受模型随机效应的影响, 进而保证了所给出的估计是比较有效的. 一些数值模拟和实例分析进一步表明了所提出的估计方法是行之有效的.     

常微分方程数值计算的新方法—偏差分方法的理论与分析

提出了一种新的常微分方程数值计算的方法,构建了一些新的计算公式.提出的新方法计算公式繁多,是一种值得研究的常微分方程数值计算方法.     

一种半参数ROC曲面估计方法

ROC曲面是诊断医学统计学里评估有多类诊断结果的诊断测试方法准确性的一个重要工具,也是近年来的一个研究热点.本文提出一种半参数的ROC曲面估计方法.该方法可以借助于许多统计软件里的逻辑斯蒂回归程序进行计算,所以它的实施较为方便.相关统计模拟显示,本文提出的方法与传统的非参数方法相比,有效性得到了显著提高.而与参数方法相比,当参数模型假设是正确时仍比参数方法有略高的有效性；而当参数模型假设不正确时,本文提出的半参数方法明显优于参数方法.     

Zero-dimensional subschemes of ruled varieties

Here we study zero-dimensional subschemes of ruled varieties, mainly Hirzebruch surfaces and rational normal scrolls, by applying the Horace method and the Terracini method This research is part of the T.A.S.C.A. project of I.N.d.A.M., supported by P.A.T. (Trento) and M.I.U.R. (Italy)     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.     

On the weakening of the convergence of Newton’s method using recurrent functions

We use Newton’s method to approximate a locally unique solution of an equation in a Banach space setting. We introduce recurrent functions to provide a weaker semilocal convergence analysis for Newton’s method than before [J. Appell, E. De Pascale, J.V. Lysenko, P.P. Zabrejko, New results on Newton–Kantorovich approximations with applications to nonlinear integral equations, Numer. Funct. Anal. Optim. 18 (1997) 1–17; I.K. Argyros, The theory and application of abstract polynomial equations, in: Mathematics Series, St. Lucie/CRC/Lewis Publ., Boca Raton, Florida, USA, 1998; I.K. Argyros, Concerning the “terra incognita” between convergence regions of two Newton methods, Nonlinear Anal. 62 (2005) 179–194; I.K. Argyros, Convergence and Applications of Newton-Type Iterations, Springer-Verlag Publ., New York, 2008; S. Chandrasekhar, Radiative Transfer, Dover Publ., New York, 1960; F. Cianciaruso, E. De Pascale, Newton–Kantorovich approximations when the derivative is Hölderian: Old and new results, Numer. Funct. Anal. Optim. 24 (2003) 713–723; N.T. Demidovich, P.P. Zabrejko, Ju.V. Lysenko, Some remarks on the Newton–Kantorovich method for nonlinear equations with Hölder continuous linearizations, Izv. Akad. Nauk Belorus 3 (1993) 22–26. (in Russian); E. De Pascale, P.P. Zabrejko, Convergence of the Newton–Kantorovich method under Vertgeim conditions: A new improvement, Z. Anal. Anwendvugen 17 (1998) 271–280; L.V. Kantorovich, G.P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982; J.V. Lysenko, Conditions for the convergence of the Newton–Kantorovich method for nonlinear equations with Hölder linearizations, Dokl. Akad. Nauk BSSR 38 (1994) 20–24. (in Russian); B.A. Vertgeim, On conditions for the applicability of Newton’s method, (Russian), Dokl. Akad. Nauk., SSSR 110 (1956) 719–722; B.A. Vertgeim, On some methods for the approximate solution of nonlinear functional equations in Banach spaces, Uspekhi Mat. Nauk 12 (1957) 166–169. (in Russian); English transl.:; Amer. Math. Soc. Transl. 16 (1960) 378–382] provided that the Fréchet-derivative of the operator involved is p$p$-Hölder continuous (p∈(0,1]$p\in (0,1]$).     

Comments on generalized Heron polynomials and Robbins’ conjectures

Heron’s formula for a triangle gives a polynomial for the square of its area in terms of the lengths of its three sides. There is a very similar formula, due to Brahmagupta, for the area of a cyclic quadrilateral in terms of the lengths of its four sides. (A polygon is cyclic if its vertices lie on a circle.) In both cases if A is the area of the polygon, (4A)² is a polynomial function of the square in the lengths of its edges. David Robbins in [D.P. Robbins, Areas of polygons inscribed in a circle, Discrete Comput. Geom. 12 (2) (1994) 223-236. MR 95g:51027; David P. Robbins, Areas of polygons inscribed in a circle, Amer. Math. Monthly 102 (6) (1995) 523-530. MR 96k:51024] showed that for any cyclic polygon with n edges, (4A)² satisfies a polynomial whose coefficients are themselves polynomials in the edge lengths, and he calculated this polynomial for n=5 and n=6. He conjectured the degree of this polynomial for all n, and recently Igor Pak and Maksym Fedorchuk [Maksym Fedorchuk, Igor Pak, Rigidity and polynomial invariants of convex polytopes, Duke Math. J. 129 (2) (2005) 371-404. MR 2006f:52015] have shown that this conjecture of Robbins is true. Robbins also conjectured that his polynomial is monic, and that was shown in [V.V. Varfolomeev, Inscribed polygons and Heron polynomials (Russian. Russian summary), Mat. Sb. 194 (3) (2003) 3-24. MR 2004d:51014]. A short independent proof will be shown here.     

Transverse compression of PPTA fibers

Results of single transverse compression testing of PPTA and PIPD fibers, using a novel test device, are presented and discussed. In the tests, short lengths of single fibers are compressed between two parallel, stiff platens. The fiber elastic deformation is analyzed as a Hertzian contact problem. The inelastic deformation is analyzed by elastic-plastic FE simulation and by laser-scanning confocal microscopy of the compressed fibers ex post facto. The results obtained are compared to those in the literature and to the theoretical predictions of PPTA fiber transverse elasticity based on PPTA crystal elasticity.Presented at the 11th International Conference on Mechanics of Composite Materials (Riga, June 11–15, 2000).3TEX, Inc. 109, MacKenan Drive, Cary, North Carolina 27511, USA. Published in Mekhanika Kompozitnykh Materialov, Vol. 36, No. 4, pp. 533–544, March–April, 2000.     

Effectivity functions and simple games

The rather new notion of effectivity function is related to the notion of simple game. Every effectivity function is associated with a simple game. So theory about simple games may be applicable to effectivity functions. E.g. if the effectivity function is additive, then the associated simple game is weighted. Via a characterization of weighted simple games it is possible to characterize maximal additive effectivity functions.Finally we characterize additive effectivity functions and their associated simple games.I thank G.J. Otten for useful comments and stimulating conversations.     

Iterated function systems, Ruelle operators, and invariant projective measures

We introduce a Fourier-based harmonic analysis for a class of discrete dynamical systems which arise from Iterated Function Systems. Our starting point is the following pair of special features of these systems. (1) We assume that a measurable space comes with a finite-to-one endomorphism which is onto but not one-to-one. (2) In the case of affine Iterated Function Systems (IFSs) in , this harmonic analysis arises naturally as a spectral duality defined from a given pair of finite subsets in of the same cardinality which generate complex Hadamard matrices.

Our harmonic analysis for these iterated function systems (IFS) is based on a Markov process on certain paths. The probabilities are determined by a weight function on . From we define a transition operator acting on functions on , and a corresponding class of continuous -harmonic functions. The properties of the functions in are analyzed, and they determine the spectral theory of . For affine IFSs we establish orthogonal bases in . These bases are generated by paths with infinite repetition of finite words. We use this in the last section to analyze tiles in .

     

Dynamic assessment of reinforced concrete beams repaired with externally bonded FRP sheets

This research deals with RC beams strengthened with FRP. An experimental research is presented which is aimed at evaluating the capability of an experimental modal analysis to assess the stiffness decrease due to damage, as well as the stiffness recovery due to strengthening. Ten beams were tested. All of them were subjected to loading cycles with increasing load levels in order to induce cracking of different severity in them. The beams were then retrofitted by externally bonded FRP sheets. Three types of composites were used. The number of layers was varied, too. Modal tests were carried out after each loading-unloading cycle. The modal frequencies and damping ratios were determined for the first four vibration modes. The results obtained indicate that an experimental modal analysis can give useful information on the severity of damage and the effectiveness of strengthening. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 3–20, January–February, 2006.     

Imbeddings of free actions on handlebodies

Fix a free, orientation-preserving action of a finite group on a -dimensional handlebody . Whenever acts freely preserving orientation on a connected -manifold , there is a -equivariant imbedding of into . There are choices of closed and Seifert-fibered for which the image of is a handlebody of a Heegaard splitting of . Provided that the genus of is at least , there are similar choices with closed and hyperbolic.

     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.