Transitive sets for quasi-periodically forced monotone maps

There has been considerable interest in recent years in quasi-periodically forced systems, partly due to the fact that these commonly exhibit strange non-chaotic attractors. Relatively little is known rigorously about such systems. In this paper we concentrate on investigating the structure of the simplest possible invariant sets for a particular class of quasi-periodically forced maps, namely those that are monotone in each fibre. Due to the quasi-periodic nature of the forcing, periodic orbits cannot occur, and their role is played by various types of invariant graph. Any compact invariant set is bounded by two invariant graphs, which are respectively upper and lower semi-continuous. If the set is minimal, these two graphs intersect on a residual set, on which both are continuous. Any transitive set Ω contains either one or two minimal sets, which must be the closure of one or the other of the boundaries of Ω. If Ω contains only one minimal set, then again its upper and lower boundaries intersect on a residual set. This case contains the original example of Grebogi et al. and its generalizations by Keller and by Glendinning. If Ω contains two minimal sets, then its upper and lower boundaries cannot intersect, though as far as we are aware, there is no known example where the existence of such a transitive set has been proven rigorously.     

Discretizing randomly perturbed circle maps

Let f be a C² expanding map of the circle and = d m be the absolutely continuous invariant measure for this system. We formulate a model for a discrete approximation for by perturbing the measure and then discretizing it. We show that whenever the distance between lattice points of the discretization decays polynomially (but not linearly) in the perturbation parameter , then as tends to 0, the discretized density converges to in a suitable Hölder norm. Namely, if < ^1+c for some c > 0, then || , ||(c) 0 as 0, where , is the discretized density. We also show that the rate of convergence is + c. This strengthens the work of Kifer, who shows (in a more general setting), weak convergence of the discretized perturbed measure to .     

Irregular dynamics of a chain of circle maps with quasiperiodic excitation

An analysis is made of the spatial evolution of quasiperiodic regimes in a chain of coupled circle maps. Mechanisms for the appearance of strange nonchaotic dynamics and the properties of irregular attractors are analyzed. Pis’ma Zh. Tekh. Fiz. 23, 73–79 (April 12, 1997)     

Vibro-impact forced oscillations of a heavy mass particle along a rough circle excited by a single-frequency force

The first part of the article presents a motion analysis of a vibro-impact system based on an oscillator moving along a rough circle line in a vertical plane, under the action of an external single-frequency force. Non-ideality of the bond originates of sliding Coulomb’s type friction force with coefficient μ = tg α ₀. The oscillator consists of one heavy mass particle whose forced motion is limited by one stabile angular elongation limiter. The differential equation of motion of the analyzed vibro-impact system cannot be solved explicitly (in closed form). For its approximately solving, the software package WOLFRAM Mathematica 7 is used. The results are checked by using the software package MATLAB R2008a. The combination of the analytical–numerical results for the defined parameters of the analyzed vibro-impact system, is base for the motion analysis visualization, as a first part of this analytic research. In the second part, the influence of parameters (amplitude and circle frequency) of the external single-frequency force to the system motion, based on real geometry and kinetic parameters of the analyzed vibro-impact system, is investigated. As a result of this study in the second part of this article, there is a conclusion that the motion of the analyzed vibro-impact system in or out of the resonant area can be influenced, and this is significant for engineering practice.     

On performance measures for multistate monotone systems

This paper gives an overview of relevant performance measures for a multistate monotone system, observed in a time interval J. Flow network systems are an important class of these systems. The computation of these measures are discussed. Some easily computed approximation formulae are established. The accuracy of these formulae are studied by making comparisons with results obtained by Monte Carlo simulation.     

一种改进的随机圆检测算法

提出了一种用于圆检测的改进随机算法。首先利用4-邻接优先的八方向跟踪方法对边缘图像中的边缘像素进行跟踪形成一系列边缘链,然后从每段边缘中随机选取3个边缘像素并通过定义一个距离准则来判定这三个点能否确定一个候选圆。确定候选圆后,利用证据积累的方法进一步判断该候选圆是否为真正的圆。在证据积累过程中,无需对候选圆外接正方形之外的像素进行平方运算,只需进行简单的比较运算。通过对真实图像进行了圆检测实验,结果表明,该算法具有准确率高、速度快的优点。     

Safety criteria for aperiodically forced systems

The theory of uniform hyperbolicity is used to obtain sets of forcing functions for which the response of a dynamical system remains in a prescribed 'safe' region. The resulting safety criteria are asymptotically optimal as the size of the safe region goes to zero.     

Real-time rolling circle amplification for protein detection

Real-time nucleic acid amplification methods can be extremely useful for the identification and quantitation of nucleic acid analytes, but are more difficult to adapt to protein or other analytes. To facilitate the development of real-time rolling circle amplification (RCA) for protein targets, we have developed a novel type of conformation-switching aptamer that can be circularized upon interaction with its protein target, the platelet-derived growth factor (PDGF). Using the structure-switching aptamer, real-time RCA can be used to specifically quantitate PDGF down to the low-nanomolar range (limit of detection, 0.4 nM), even against a background of cellular lysate. The aptamer can also be adapted to RCA on surfaces, although quantitation proved to be more difficult. One of the great advantages of the method described herein is that it can be immediately adapted to almost any aptamer and does not require two or more affinity reagents as do sandwich or proximity assays.     

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.     

Deformation mechanism maps for ceramics

Deformation mechanism maps may be constructed for either a constant grain size or a constant temperature. A simple method is described for constructing maps at constant temperature, and maps are presented for two representative oxides, a carbide, and three alkali halides. A method is also described for superimposing a set of similar deformation mechanism maps.     

Failure-mechanism maps for engineering polymers

This paper reports on progress in assembling experimental data and simplified theoretical models for the deformation and fracture of engineering polymers into diagrams which summarize their inelastic response to stress. A number of regimes are identified: brittle fracture initiated by crazing or shear-banding; plasticity terminated by ductile fracture; cold-drawing; rubbery and viscous flow; a regime in which deformation is purely elastic; and one in which adiabatic heating influences deformation. Data for a number of commercial polymers (polymethylmethacrylate, polystyrene, polycarbonate, polyisobutylene and an epoxy resin) are fitted to simplified constitutive equations for each regime. The equations are then used to construct diagrams, one for tension and one for compression, which relate strength to temperatureT and strain rate , over a wide range of these variables.     

Structure maps for crystal engineering

The ordering of A and B atoms of compounds A_xB_y on the different positions of a lattice is analyzed by the numbers T₁ T₂ T₃; r of nearest, next-nearest and third neighbors of the same kind and the ratio r=y/x. The T₁, T₂ or T₁, T₂, T₃ structure maps containing all possible structures select the structures with maximum attractive or repulsive interactions which are stabilized by enthalpy. These structures at the borders of the structure maps are assembled from different structural units with different physical properties. The square net, body-centered cubic and diamond lattices containing surface structures, ordered alloys or semiconducting adamantanes are closely related. A periodic variation of crystal structures and interactions is suggested for the low-temperature modifications of the elements.     

基于最大方差旋转的因子分析算法

为探索因子分析中因子旋转的性能和提升因子分析计算的效率,研究因子分析的原理并提出基于最大方差旋转的因子分析算法．从线性表示的角度分析,因子分析模型与稀疏表示情况下的独立分量分析相似,独立分量分析模型是忽略了噪声因子的因子分析模型．目标函数关系分析表明,传统的因子旋转方法,如最大方差方法和一般直交法,与独立分量分析的峭度估计方法条件等价,但并不再适用于源信号中既包括超高斯源又包括次高斯源的情况．基于以上分析,提出了一种基于最大方差旋转的因子分析算法,其中的源信号可以是混合类型,而不限定单纯的次高斯源或者超高斯源．此外,这种算法还可以作为Fastica算法的简单模式并适用于高阶统计分析．仿真结果表明,在混合矩阵为稀疏的情况下,所提出的基于最大方差旋转的因子分析算法具有简易高效等优异性能．和独立分量分析的Fastica算法比较,新算法的估计精度相近,平均值达到0．9753,但是效率高得多,时耗仅占25％．