Discontinuous bifurcation and coexistence of attractors in a piecewise linear map with a gap

Coexistence of attractors with striking characteristics is observed in this work, where a stable period-5 attractor coexists successively with chaotic band-ll, period-6, chaotic band-12 and band-6 attractors. They are induced by dif- ferent mechanisms due to the interaction between the discontinuity and the non-invertibility. A characteristic boundary collision bifurcation, is observed. The critical conditions are obtained both analytically and numerically.

LINEAR DILATATION OF QUASIREGULAR MAPPINGS IN SPACE

This paper presents an explicit upper bound for the linear dilatation of K- quasiregular (K-qr) mappings, which improves S. Rickman's [6, P.37] corresponding re- sult for K-qr mappings and generalizes P. Seittenranta's [7, Theorem 1.5] result for K- quasiconformal (K-qc) maps.

Noise destroys the coexistence of periodic orbits of a piecewise linear map

The effects of Gaussian white noise and Gaussian colored noise on the periodic orbits of period-5（P-5） and period-6（P-6） in their coexisting domain of a piecewise linear map are investigated numerically.The probability densities of some orbits are calculated.When the noise intensity is D = 0.0001,only the orbits of P-5 exist,and the coexisting phenomenon is destroyed.On the other hand,the self-correlation time τ of the colored noise also affects the coexisting phenomenon.When τc〈τ〈τc,only the orbits of P-5 appear,and the stability of the orbits of P-5 is enhanced.However,when τ〉τc（τc and τc are critical values）,only the orbits of P-6 exist,and the stability of the P-6 orbits is enhanced greatly.When τ〈τc,the orbits of P-5 and P-6 coexist,but the stability of the P-5 orbits is enhanced and that of P-6 is weakened with τ increasing.

Solution of Nonlinear Advection-Diffusion Equations via Linear Fractional Map Type Nonlinear QCA

Linear fractional map type (LFMT) nonlinear QCA (NLQCA), one of the simplest reversible NLQCA is studied analytically as well as numerically. Linear advection equation or Time Dependent Schrödinger Equation (TDSE) is obtained from the continuum limit of linear QCA. Similarly it is found that some nonlinear advection-diffusion equations including inviscid Burgers equation and porous-medium equation are obtained from LFMT NLQCA.

Linear-fitting-based similarity coefficient map for tissue dissimilarity analysis in T2^＊-w magnetic resonance imaging

Similarity coefficient mapping（SCM） aims to improve the morphological evaluation of T＊2weighted magnetic resonance imaging（T＊2-w MRI）. However, how to interpret the generated SCM map is still pending. Moreover, is it probable to extract tissue dissimilarity messages based on the theory behind SCM？ The primary purpose of this paper is to address these two questions. First, the theory of SCM was interpreted from the perspective of linear fitting. Then, a term was embedded for tissue dissimilarity information. Finally, our method was validated with sixteen human brain image series from multiecho T＊2-w MRI. Generated maps were investigated from signal-to-noise ratio（SNR） and perceived visual quality, and then interpreted from intra- and inter-tissue intensity. Experimental results show that both perceptibility of anatomical structures and tissue contrast are improved. More importantly, tissue similarity or dissimilarity can be quantified and cross-validated from pixel intensity analysis. This method benefits image enhancement, tissue classification, malformation detection and morphological evaluation.

Non-linear Invertible Maps that Preserve Staircase Subalgebras

Let g be the general linear Lie algebra consisting of all n x n matrices over a field F and with the usual bracket operation {x, y} =xy - yx. An invertible map φ ： g →g is said to preserve staircase subalgebras if it maps every staircase subalgebra to some staircase subalgebra of the same dimension. In this paper, we devote to giving an explicit description on the invertible maps on g that preserve staircase subalgebras.

Linear Maps Preserving Idempotency of Products of Matrices on Upper Triangular Matrix Algebras

Let Tn be the algebra of all n × n complex upper triangular matrices. We give the concrete forms of linear injective maps on Tn which preserve the nonzero idempotency of either products of two matrices or triple Jordan products of two matrices.

Dissipative Properties of ω-Order Preserving Partial Contraction Mapping in Semigroup of Linear Operator

This paper consists of dissipative properties and results of dissipation on infinitesimal generator of a C0-semigroup of ω-order preserving partial contraction mapping (ω-OCPn) in semigroup of linear operator. The purpose of this paper is to establish some dissipative properties on ω-OCPn which have been obtained in the various theorems (research results) and were proved.

Galois linear maps and their construction

The condition of an algebra to be a Hopf algebra or a Hopf(co)quasigroup can be determined by the properties of Galois linear maps.For a bialgebra H,if it is unital and associative as an algebra and counital coassociative as a coalgebra,then the Galois linear maps T1 and T2 can be defined.For such a bialgebra H,it is a Hopf algebra if and only if T1 is bijective.Moreover,T1^-1 is a right H-module map and a left H-comodule map(similar to T2).On the other hand,for a unital algebra(no need to be associative),and a counital coassociative coalgebra A,if the coproduct and counit are both algebra morphisms,then the sufficient and necessary condition of A to be a Hopf quasigroup is that T1 is bijective,and T1^-1 is left compatible with ΔT1-11^r and right compatible with mT1-1^l at the same time(The properties are similar to T2).Furthermore,as a corollary,the quasigroups case is also considered.

An Automatic Approach for Satisfying Dose-Volume Constraints in Linear Fluence Map Optimization for IMPT

Prescriptions for radiation therapy are given in terms of dose-volume constraints (DVCs). Solving the fluence map optimization (FMO) problem while satisfying DVCs often requires a tedious trial-and-error for selecting appropriate dose control parameters on various organs. In this paper, we propose an iterative approach to satisfy DVCs using a multi-objective linear programming (LP) model for solving beamlet intensities. This algorithm, starting from arbitrary initial parameter values, gradually updates the values through an iterative solution process toward optimal solution. This method finds appropriate parameter values through the trade-off between OAR sparing and target coverage to improve the solution. We compared the plan quality and the satisfaction of the DVCs by the proposed algorithm with two nonlinear approaches: a nonlinear FMO model solved by using the L-BFGS algorithm and another approach solved by a commercial treatment planning system (Eclipse 8.9). We retrospectively selected from our institutional database five patients with lung cancer and one patient with prostate cancer for this study. Numerical results show that our approach successfully improved target coverage to meet the DVCs, while trying to keep corresponding OAR DVCs satisfied. The LBFGS algorithm for solving the nonlinear FMO model successfully satisfied the DVCs in three out of five test cases. However, there is no recourse in the nonlinear FMO model for correcting unsatisfied DVCs other than manually changing some parameter values through trial and error to derive a solution that more closely meets the DVC requirements. The LP-based heuristic algorithm outperformed the current treatment planning system in terms of DVC satisfaction. A major strength of the LP-based heuristic approach is that it is not sensitive to the starting condition.

An Adaptive Non-Linear Map and Its Application

A novel adaptive non-linear mapping （ANLM）, integrating an adaptive mapping error （AME） with a chaosgenetic algorithm （CGA） including chaotic variable, was proposed to overcome the deficiencies of non-linear mapping （NLM）. The value of AME weight factor is determined according to the relative deviation square of distance between the two mapping points and the corresponding original objects distance. The larger the relative deviation square between two distances is, the larger the value of the corresponding weight factor is. Due to chaotic mapping operator, the evolutional process of CGA makes the individuals of subgenerations distributed ergodieally in the defined space and circumvents the premature of the individuals of subgenerations. The comparison results demonstrated that the whole performance of CGA is better than that of traditional genetic algorithm. Furthermore, a typical example of mapping eight-dimenslonal olive oil samples onto two-dimensional plane was employed to verify the effectiveness of ANLM. The results showed that the topology-preserving map obtained by ANLM can well represent the classification of original objects and is much better than that obtained by NLM.

ESTIMATE ON THE BLOCH CONSTANT FOR CERTAIN HARMONIC MAPPINGS UNDER A DIFFERENTIAL OPERATOR

In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.

Non-linear Maps on Borel Subalgebras of Simple Lie Algebras Preserving Abelin Ideals

Let g be a complex simple Lie algebra of rank ι, b the standard Borel subalgebra. An invertible map on Ь is said to preserve abelian ideals if it maps each abelian ideal to some such ideal of the same dimension. In this article, by using some results of Chevalley groups, the theory of root systems and root space decomposition, the author gives an explicit description on such maps of Ь.

Non-Linear Effects in Optical Systems by Lie Algebra and Symplectic Mapping

The use of signals of different frequencies determines the geometrical deviation with respect to the optical axes of a given beam. This angle can be determined by Sympletic Map (SM), a powerful and simple mathematical tool for the characterization and construction of images in Geometrical Optics. The Sympletic Map constitutes a Lie Group, with an algebra associated: the Lie Algebra. In general, the SM can be expressed as an infinite series, where each term corresponds to different contributions produced by the optical devices that constitute the optical system (lenses, apertures, bandwidth cutoff, etc.). The level of correction to be performed on the image to recover the original object is clear and controllable by SM. This formalism can be extended easily to physical optics to describe diffraction and interference phenomena.

Turbo码Log-MAP译码算法的一种改进算法

Log-MAP算法是Turbo码译码算法的一种简化算法,本文针对其所存在的缺点提出了一种改进的算法,即用分段的线性函数对校正函数进行拟合。计算机模拟结果表明,应用此算法后可在不影响性能的情况下,既能简化算法过程,又能使硬件的实现变得更加容易。

ISOMAP-LDA方法用于化工过程故障诊断

针对化工连续生产过程的时序性及非线性等特征,提出一种新的基于数据驱动的化工过程故障诊断方法:ISOMAP-LDA。首先实行流形学习算法ISOMAP,在保持量测数据几何结构特性下完成非线性降维,然后基于提取的嵌入变量张成的低维空间,选用线性判别分析(LDA)构造故障模式类的判别函数,负责各采样个体故障类型的判定。将该方法用于仿真化工Tennessee East man过程的故障诊断,结果表明,ISOMAP-LDA方法不仅拥有较高的故障诊断能力,而且取得采样在低维空间的可视化表示。

UMTS Turbo码的滑动窗-线性-Log-MAP算法及VLSI设计

讨论UMTS中turbo码的设计,提出采用前向状态度量作为初始化精确值的滑动窗方法和改进的Log-MAP(线性Log-MAP)相结合的算法(称为滑动窗-线性-Log-MAP算法),设计出turbo码的VLSI结构,且在归一化处理时,介绍了一种可节约12.5%存储量的方法。FPGA设计结果显示在BER=10-5时,与最优算法Log-MAP相比,性能损失0.2dB,硬件资源节约30%,译码时延小,吞吐量大。

基于改进ISOMAP算法的图像分类

利用基于邻域的图像欧氏距离寻找最近邻,并用直接线性判别分析方法(Direct LDA)取代多维尺度分析法(MDS),提出一种改进的等距特征映射(ISOMAP)算法(KIMD-ISOMAP)进行降维.人脸图像分类试验表明:KIMD-ISOMAP提高了ISOMAP的分类能力,扩展了邻域半径的选取范围,在加高斯噪声和几何形变的情况下,该算法与其他方法相比,表现出较强的鲁棒性.

基于ISOMAP改进算法的人耳识别

针对ISOMAP算法对新增样本泛化能力较差的缺点,通过对LLE算法局部重构思想的深入理解,提出了MRC-ISOMAP(manifold reconstruction-ISOMAP)算法用于样本特征的维数约简。MRC-ISOMAP算法对训练样本采用全局非线性结构保持的思想,利用ISOMAP算法计算训练样本的低维表示;对新增样本利用局部线性的思想,保持局部线性关系不变,从而可以更加快速准确地用低维训练样本重构新增样本的低维表示。USTB3人耳图像库上的实验结果表明,与原始ISOMAP算法相比,MRC-ISOMAP算法可以获得更高的识别率,并在处理新样本时具有更高的效率。

高性能的Max-Log-MAP线性分段算法研究

针对Max-Log-MAP算法存在译码性能比Log-MAP算法差0.5dB,而Log-MAP算法复杂度大的问题。论文提出了用线性分段(piecewise-linear term:PLT)的最大值运算来替代Log-MAP算法中雅克比公式,并通过研究比例因子对译码性能的影响,获得了最佳的优化Turbo译码性能的方法。研究结果证明,用分段项数r等于3,比例因子s为0.7时,获得的Turbo译码性能略优于Log-MAP算法,而算法的计算复杂度比Max-Log-MAP算法仅增加一次乘法、一次加法和求最大值运算。