Fractal measures for meromorphic functions of finite order

We prove several essential fractal properties, such as positivity, finiteness or local infinity, of Hausdorff and packing measures of radial Julia sets for large subclasses of entire and meromorphic functions considered in our previous work: çGeometric thermodynamical formalism and real analyticity for meromorphic functions of finite order'. Most of the results proven are shown to be optimal.     

利用n维参数L系统构造超复数空间广义M-J集

利用n维参数L系统描述了超复数空间广义Mandelbrot集和Julia集,给出了描述算法和实验所得图形,并对四元数广义M-J集的动力学特征进行了理论上的分析和探讨.经过实验发现,四元数广义M-J集在保留了复平面M-J集特征的基础上,还有一些特殊的性质,如广义M集在三维虚轴截面上的拓扑结构等同于球体,四元数Julia集在参数c同模同实部的情况下保持着结构的一致性.实验结果表明,n维参数L系统字母表较为简洁,包含信息量大,可以有效的描述诸如广义M-J集和四元数广义M-J集的分形集.     

二阶Carotid-Kundalini函数Julia分形集的特征

Julia分形图是研究复动力系统的一种有力工具.本文研究了由二阶Carotid-Kundalini函数f(z)=cos(Nz2arccos(z))+c生成的Julia分形图的性质:当c为实数和N为实数或纯虚数时,分形图具有对称性;当N为实数,c=0时,图形具有5主瓣和4个从主瓣上发出的触角,且触角无界.     

On the relative power of polynomials with real, rational, and integer coefficients in proofs of termination of rewriting

In the seventies, Manna and Ness, Lankford, and Dershowitz pionneered the use of polynomial interpretations with integer and real coefficients in proofs of termination of rewriting. More than twenty five years after these works were published, however, the absence of true examples in the literature has given rise to some doubts about the possible benefits of using polynomials with real or rational coefficients. In this paper we prove that there are, in fact, rewriting systems that can be proved polynomially terminating by using polynomial interpretations with (algebraic) real coefficients; however, the proof cannot be achieved if polynomials only contain rational coefficients. We prove a similar statement with respect to the use of rational coefficients versus integer coefficients. Tel.: +34 96 387 7007 (ext. 73531)     

Julia集和Mandelbrot集的反演变换

论文讨论了居里叶集与曼德尔布罗特集的反演变换问题,通过扩充复平面上关于任意定点的反演变换,获得了两类共轭函数。使得这两类共轭函数的居里叶集与曼德尔布罗特集,恰好是原居里叶集与曼德尔布罗特集关于定点的反演变换,并运用逃逸时间算法绘制居里叶集和曼德尔布罗特集的反演图。     

Regularity for steady periodic capillary water waves with vorticity

In the following, we prove new regularity results for two-dimensional steady periodic capillary water waves with vorticity, in the absence of stagnation points. Firstly, we prove that if the vorticity function has a H?lder-continuous first derivative, then the free surface is a smooth curve and the streamlines beneath the surface will be real analytic. Furthermore, once we assume that the vorticity function is real analytic, it will follow that the wave surface profile is itself also analytic. A particular case of this result includes irrotational fluid flow where the vorticity is zero. The property of the streamlines being analytic allows us to gain physical insight into small-amplitude waves by justifying a power-series approach.     

Complex analytic dynamics phenomena in a system of coupled nonautonomous oscillators with alternative excitation

A model system of two coupled nonautonomous oscillators is proposed, in which the phenomena of complex analytic dynamics (Mandelbrot and Julia sets, etc.) characteristic of complex logistic maps are realized. The idea underlying the model is based on the mechanism of alternative excitation transfer from one subsystem to another and on the method (well known in the theory of oscillations) of slowly varying complex amplitudes.     

Simultaneously non-dense orbits under different expanding maps

Given a point and an expanding map on the unit interval, we consider the set of points for which the forward orbit under this map is bounded away from the given point. It is well-known that in many cases such sets have full Hausdorff dimension. We prove that such sets have a large intersection property, i.e. countable intersections of such sets also have full Hausdorff dimension. This result applies to a class of maps including multiplication by integers modulo 1 and x ? 1/x modulo 1. We prove that the same properties hold for multiplication modulo 1 by a dense set of non-integer numbers between 1 and 2.     

Pseudorandom numbers for conformal measures

We propose a new algorithm for generating pseudorandom (pseudo-generic) numbers of conformal measures of a continuous map T acting on a compact space X and for a Hölder continuous potential φ : X → ?. In particular, we show that this algorithm provides good approximations to generic points for hyperbolic rational functions of degree two and the potential ?h log |T′|, where h denotes the Hausdorff dimension of the Julia set of T.     

Analytic Equations of State for the Generalized Lennard-Jones Fluid Based on the Ross Variational Perturbation Theory and the Percus-Yevick Radial Distribution Function of Hard Spheres

Analytic expressions for the equation of state and thermodynamic properties have been derived for a generalized Lennard-Jones fluid, based on the Ross variational perturbation theory and the analytic Percus-Yevick (PY) expression for the radial distribution function of hard spheres. It is shown that the variational procedure is absolutely convergent and the calculations are convenient and fast. Numerical calculations have been made within wide temperature and density ranges. The results show that the precision is equivalent to the non-analytic modified Weeks-Chandler- Anderson (mWCA) and complete analytic mean spherical approximation (MSA) theories as compared with computer simulation results. It is concluded that the analytic theory can be applied to research practical fluids within wide temperature and density ranges.     

一类递归集的Hausdorff维数

对由自相似压缩映射生成的递归集，引入了一种网测度α（Ｅ），证明了它与Ｈａｕｓｄｏｒｆｆ测度最多在一点上不相等．由此给出了这类递归集的Ｈａｕｓｄｏｒｆｆ维数。简化了部分分形集维数的计算，并以例子说明．     

Locating a straight crack in an infinite elastic medium by using complex path-independent integrals

Summary The Cauchy integral theorem and the relevant formula (or, equivalently, complex path-independent integrals) have been used in a long series of papers for the determination of zeros and poles of analytic and meromorphic functions. Here this approach is generalized to become applicable to the problem of location of a straight crack inside an infinite plane isotropic elastic medium. The complex path-independent integrals used here contain the first complex potential (z) of Kolosov-Muskhelishvili, which can be obtained experimentally. The present method can be modified to apply to a variety of problems where discontinuity intervals of analytic (or, rather, sectionally analytic) functions are sought.     

Conformal iterated function systems with overlaps

For a conformal iterated function system satisfying the bounded distortion property and the weak separation condition, we prove a formula for the Hausdorff dimension of the attractor, and establish the equality between the Hausdorff dimension and the growth dimension. Furthermore, a relation between the open set condition and the weak separation condition is given.     

Self-similarity in piecewise isometric systems

This paper deals with piecewise isometries and their scaling properties. We aim to present a general framework in which piecewise isometric dynamical systems can be fully or partially renormalized. We precisely describe the dynamics on fractal invariant sets by means of a conjugacy with substitution dynamical systems and Bratteli diagrams. We describe their geometrical properties in terms of graph-directed constructions and we compute their Hausdorff dimension. We also present an example of application to a continuous family of piecewise rotations.     

复杂三维曲梁结构的无闭锁等几何分析算法研究

梁结构在工程中应用广泛,梁结构的仿真分析是计算力学的一个重要研究内容。该文研究了复杂三维曲梁结构的等几何分析方法,首次应用拟协调有限元中的多套函数技术,使用降阶基函数逼近梁内应变项,解决复杂三维曲梁结构仿真中的闭锁问题。利用全局坐标系列式方法,避免了单元刚度阵组装时的复杂坐标变换过程,提高计算效率。使用多片NURBS （非均匀有理B样条）数据表示复杂三维梁结构,可精确描述曲梁结构的几何形状,与有限元方法等仿真技术相比避免了网格生成过程,减少了几何误差。数值结果表明该文算法可有效解决闭锁问题,适于复杂三维曲梁结构的仿真分析。     

Dimension results for inhomogeneous Moran set constructions

We compute the Hausdorff upper box and packing dimensions for certain inhomogeneous Moran set constructions. These constructions are beyond the classical theory of iterated function systems, as different nonlinear contraction transformations are applied at each step. Moreover, we also allow the contractions to be weakly conformal and consider situations where the contraction rates have an infimum of zero. In addition, the basic sets of the construction are allowed to have a complicated topology such as having fractal boundaries. Using techniques from thermodynamic formalism, we calculate the fractal dimension of the limit set of the construction. As a main application we consider dimension results for stochastic inhomogeneous Moran set constructions, where chaotic dynamical systems are used to control the contraction factors at each step of the construction.     

时域稳定的基础频响连续有理近似参数识别方法EI北大核心CSCD

采用连续有理近似函数描述基础时域动力模型是土-结动力相互作用时程分析的重要方法。该近似函数的稳定性和精度决定了土-结相互作用系统时域分析的稳定性和精度。目前,连续时间有理近似函数的参数识别方法无法同时确保精度、稳定性和计算效率。该文基于线性系统控制理论,将有理近似函数分解为一系列一阶和二阶子系统的组合,并通过各子系统的稳定条件提出了被识别参数的理论稳定边界。基于此,利用遗传算法和序列二次规划算法建立了时域稳定的连续有理函数参数识别方法。不同基础频响函数数值仿真结果表明:对于简单函数,该文方法与既有方法均可保持高精度,但该文方法在确保稳定性的同时可以提高近35%的计算效率。对于复杂函数,采用高阶有理函数时,该文方法用时仅为既有方法的25%,同时精度大于95%。证明了该方法可以在保证函数稳定性与拟合精度的同时提高了计算效率,从而使得连续有理近似函数适用性更好。     

Probability density function for frequency response function measurements using periodic signals

Frequency response function (FRF) measurements are often used to characterize linear dynamic systems. Today, uncertainty bounds on FRF measurements still are based on linear approximations, which are valid for sufficiently large input signal-to-noise-ratios (SNR) only. In this paper, exact uncertainty bounds are calculated, which are valid for any input SNR. These bounds are obtained via an analytic expression of the probability density function (pdf) of the FRF measurements. The results are valid for open- and closed-loop measurements, and the theory is illustrated on a real measurement example.     

Fitting Spheres to Range Data From 3-D Imaging Systems

Two error functions used for nonlinear least squares (LS) fitting of spheres to range data from 3-D imaging systems are discussed: the orthogonal error function and the directional error function. Both functions allow unrestricted gradient-based minimization and were tested on more than 40 data sets collected under different experimental conditions (e.g., different sphere diameters, instruments, data density, and data noise). It was found that the orthogonal error function results in two local minima and that the outcome of the optimization depends on the choice of starting point. The centroid of the data points is commonly used as the starting point for the nonlinear LS solution, but the choice of starting point is sensitive to data segmentation and, for some sparse and noisy data sets, can lead to a spurious minimum that does not correspond to the center of a real sphere. The directional error function has only one minimum; therefore, it is not sensitive to the starting point and is more suitable for applications that require fully automated sphere fitting.