Heteroclinic Cycles in a Class of 3-Dimensional Piecewise Affine Systems

This paper explores the existence of heteroclinic cycles and corresponding chaotic dynamics in a class of 3-dimensional two-zone piecewise affine systems. Moreover, the heteroclinic cycles connect two saddle foci and intersect the switching manifold at two points and the switching manifold is composed of two perpendicular planes.

A Note on Sharp Affine Poincaré-Sobolev Inequalities and Exact in Minimization of Zhang’s Energy on Bounded Variation and Exactness

As for the affine energy, Edir Junior and Ferreira Leite establish the existence of minimizers for particular restricted subcritical and critical variational issues on BV(Ω). Similar functionals exhibit deeper weak* topological traits including lower semicontinuity and affine compactness, and their geometry is non-coercive. Our work also proves the result that extremal functions exist for certain affine Poincaré-Sobolev inequalities.

CONFORMALLY FLAT AFFINE HYPERSURFACES WITH SEMI-PARALLEL CUBIC FORM

In this paper,we study locally strongly convex affine hypersurfaces with the vanishing Weyl curvature tensor and semi-parallel cubic form relative to the Levi-Civita connection of the affine metric.As a main result,we classify these hypersurfaces as not being of a flat affine metric.In particular,2 and 3-dimensional locally strongly convex affine hypersurfaces with semi-parallel cubic forms are completely determined.

基于Affine强度的一般Poisson损失动态模型

首先介绍了GPL动态模型,然后引入Affine过程的概念,讨论随机强度是Affine过程时的GPL模型,并进一步讨论了如何求出随机过程的损失密度,从而得出CDO债券的价格.

Solving Fully Fuzzy Nonlinear Eigenvalue Problems of Damped Spring-Mass Structural Systems Using Novel Fuzzy-Affine Approach

The dynamic analysis of damped structural system by using finite element method leads to nonlinear eigenvalue problem(NEP)(particularly,quadratic eigenvalue problem).In general,the parameters of NEP are considered as exact values.But in actual practice because of different errors and incomplete information,the parameters may have uncertain or vague values and such uncertain values may be considered in terms of fuzzy numbers.This article proposes an efficient fuzzy-affine approach to solve fully fuzzy nonlinear eigenvalue problems(FNEPs)where involved parameters are fuzzy numbers viz.triangular and trapezoidal.Based on the parametric form,fuzzy numbers have been transformed into family of standard intervals.Further due to the presence of interval overestimation problem in standard interval arithmetic,affine arithmetic based approach has been implemented.In the proposed method,the FNEP has been linearized into a generalized eigenvalue problem and further solved by using the fuzzy-affine approach.Several application problems of structures and also general NEPs with fuzzy parameters are investigated based on the proposed procedure.Lastly,fuzzy eigenvalue bounds are illustrated with fuzzy plots with respect to its membership function.Few comparisons are also demonstrated to show the reliability and efficacy of the present approach.

Inhibition of Xanthine Oxidase Activity by Gnaphalium Affine Extract

Objective To evaluate the inhibitory effect of Gnaphalium affine extracts on xanthine oxidase(XO) activity in vitro and to analyze the mechanism of this effect. Methods In this in vitro study, Kinetic measurements were performed in 4 different inhibitor concentrations and 5 different xanthine concentrations(60, 100, 200, 300, 400 μmol/L). Dixon and Lineweaver-Burk plot analysis were used to determine Ki values and the inhibition mode for the compounds isolated from Gnaphalium affine extract. Results Four potent xanthine oxidase inhibitors were found in 95% ethanolic(v/v) Gnaphalium affine extract. Among them, the f lavone Eupatilin exhibited the strongest inhibitory effect on XO with a inhibition constant(Ki) of 0.37 μmol/L, lower than the Ki of allopurinol(4.56 mol/L), a known synthetic XO inhibitor. Apigenin(Ki of 0.56 μmol/L, a proportion of 0.0053‰ in Gnaphalium affine), luteolin(Ki of 2.63 μmol/L, 0.0032‰ in Gnaphalium affine) and 5-hydroxy-6,7,3',4'-tetramethoxyflavone(Ki of 3.15 μmol/L, 0.0043‰ in Gnaphalium affine) also contributed to the inhibitory effect of Gnaphalium affine extract on XO activity. Conclusions These results suggest that the use of Gnaphalium affine in the treatment of gout could be attributed to its inhibitory effect on XO. This study provides a rational basis for the traditional use of Gnaphalium affine against gout.

A Correntropy-based Affine Iterative Closest Point Algorithm for Robust Point Set Registration

The iterative closest point(ICP)algorithm has the advantages of high accuracy and fast speed for point set registration,but it performs poorly when the point set has a large number of noisy outliers.To solve this problem,we propose a new affine registration algorithm based on correntropy which works well in the affine registration of point sets with outliers.Firstly,we substitute the traditional measure of least squares with a maximum correntropy criterion to build a new registration model,which can avoid the influence of outliers.To maximize the objective function,we then propose a robust affine ICP algorithm.At each iteration of this new algorithm,we set up the index mapping of two point sets according to the known transformation,and then compute the closed-form solution of the new transformation according to the known index mapping.Similar to the traditional ICP algorithm,our algorithm converges to a local maximum monotonously for any given initial value.Finally,the robustness and high efficiency of affine ICP algorithm based on correntropy are demonstrated by 2D and 3D point set registration experiments.

High-frequency acoustic backscattering characteristics for acoustic detection of the red tide species Akashiwo sanguinea and Alexandrium affine

Harmful algal blooms (HABs), caused by the overgrowth of certain phytoplankton species, have negative effects on marine environments and coastal fisheries. In addition to cell-counting methods using phytoplankton nets, a hydroacoustic technique based on acoustic backscattering has been proposed for the detection of phytoplankton blooms. However, little is known of the acoustic properties of HAB species. In this study, as essential data to support this technique, we measured the acoustic properties of two HAB species, Akashiwo sanguinea and Alexandrium affine, which occur in the South Sea off the coast of Korea. Due to the small size of the target, we used ultrasound for the measurements. Experiments were conducted under laboratory and field conditions. In the laboratory experiment, the acoustic signal received from each species was directly proportional to the cell abundance. We derived a relationship between the cell abundance and acoustic signal received for each species. The measured signals were compared to predictions of a fluid sphere scattering model. When A. sanguinea blooms appeared at an abundance greater than 3 500 cells/mL, the acoustic signals varied with cell abundance, showing a good correlation. These results confirm that acoustic measurements can be used to detect HAB species.

Constrained sliding mode control of nonlinear fractional order input affine systems

Asymptotic stability of nonlinear fractional order affine systems with bounded inputs is dealt.The main contribution is to design a new bounded fractional order chattering free sliding mode controller in which the system states converge to the sliding surface at a determined finite time.To eliminate the chattering in the sliding mode and make the input controller bounded,hyperbolic tangent is used for designing the proposed fractional order sliding surface.Finally,the stability of the closed loop system using this bounded sliding mode controller is guaranteed by Lyapunov theory.A comparison with the integer order case is then presented and fractional order nonlinear polynomial systems are also studied as the special case.Finally,simulation results are provided to show the effectiveness of the designed controller.

Image-Moment Based Affine Invariant Watermarking Scheme Utilizing Neural Networks

A new image watermarking scheme is proposed to resist rotation, scaling and translation (RST) attacks. Six combined low order image moments are utilized to represent image information on rotation, scaling and translation. Affine transform parameters are registered by feedforward neural networks. Watermark is adaptively embedded in discrete wavelet transform (DWT) domain while watermark extraction is carried out without original image after attacked watermarked image has been synchronized by making inverse transform through parameters learned by neural networks. Experimental results show that the proposed scheme can effectively register affine transform parameters, embed watermark more robustly and resist geometric attacks as well as JPEG2000 compression.

Global Practical Stabilization of Discrete-Time Switched Affine Systems via a General Quadratic Lyapunov Function and a Decentralized Ellipsoid

This paper addresses the problem of global practical stabilization of discrete-time switched affine systems via statedependent switching rules.Several attempts have been made to solve this problem via different types of a common quadratic Lyapunov function and an ellipsoid.These classical results require either the quadratic Lyapunov function or the employed ellipsoid to be of the centralized type.In some cases,the ellipsoids are defined dependently as the level sets of a decentralized Lyapunov function.In this paper,we extend the existing results by the simultaneous use of a general decentralized Lyapunov function and a decentralized ellipsoid parameterized independently.The proposed conditions provide less conservative results than existing works in the sense of the ultimate invariant set of attraction size.Two different approaches are proposed to extract the ultimate invariant set of attraction with a minimum size,i.e.,a purely numerical method and a numerical-analytical one.In the former,both invariant and attractiveness conditions are imposed to extract the final set of matrix inequalities.The latter is established on a principle that the attractiveness of a set implies its invariance.Thus,the stability conditions are derived based on only the attractiveness property as a set of matrix inequalities with a smaller dimension.Illustrative examples are presented to prove the satisfactory operation of the proposed stabilization methods.

Using Affine Quantization to Analyze Non-Renormalizable Scalar Fields and the Quantization of Einstein’s Gravity

Affine quantization is a parallel procedure to canonical quantization, which is ideally suited to deal with non-renormalizable scalar models as well as quantum gravity. The basic applications of this approach lead to the common goals of any quantization, such as Schroedinger’s representation and Schroedinger’s equation. Careful attention is paid toward seeking favored classical variables, which are those that should be promoted to the principal quantum operators. This effort leads toward classical variables that have a constant positive, zero, or negative curvature, which typically characterize such favored variables. This focus leans heavily toward affine variables with a constant negative curvature, which leads to a surprisingly accommodating analysis of non-renormalizable scalar models as well as Einstein’s general relativity.

Zonotope parameter identification for piecewise affine systems

The problem of how to identify the piecewise affine system is studied in this paper, where this considered piecewise affine system is a special nonlinear system. The reason why it is not easy to identify this piecewise affine system is that each separated region and each unknown parameter vector are all needed to be determined simultaneously. Then, firstly, in order to achieve the identification goal, a multi-class classification process is proposed to determine each separated region. As the proposed multi-class classification process is the same with the classical data clustering strategy, the multi-class classification process can combine the first order algorithm of convex optimization, while achieving the goal of the classification process. Secondly, a zonotope parameter identification algorithm is used to construct a set, which contains the unknown parameter vector. In this zonotope parameter identification algorithm, the strict probabilistic description about the external noise is relaxed, and each unknown parameter vector is also identified. Furthermore, this constructed set is consistent with the measured output and the given bound corresponding to the noise. Thirdly, a sufficient condition about guaranteeing our derived zonotope not growing unbounded with iterations is formulated as an explicit linear matrix inequality. Finally, the effectiveness of this zonotope parameter identification algorithm is proven through a simulation example.

An Integrating Algorithm and Theoretical Analysis for Fully Rheonomous Affine Constraints: Completely Integrable Case

This paper develops an integrating algorithm for fully rheonomous affine constraints and gives theoretical analysis of the algorithm for the completely integrable case. First, some preliminaries on the fully rheonomous affine constraints are shown. Next, an integrating algorithm that calculates independent first integrals is derived. In addition, the existence of an inverse function utilized in the algorithm is investigated. Then, an example is shown in order to evaluate the effectiveness of the proposed method. By using the proposed integrating algorithm, we can easily calculate independent first integrals for given constraints, and hence it can be utilized for various research fields.

The Line Clipping Algorithm Basing on Affine Transformation

A new algorithm for clipping line segments by a rectangular window on rectangular coordinate system is presented in this paper. The algorithm is very different to the other line clipping algorithms. For the line segments that cannot be identified as completely inside or outside the window by simple testings, this algorithm applies affine transformations (the shearing transformations) to the line segments and the window, and changes the slopes of the line segments and the shape of the window. Thus, it is clear for the line segment to be outside or inside of the window. If the line segments intersect the window, the algorithm immediately (no solving equations) gets the intersection points. Having applied the inverse transformations to the intersection points, the algorithm has the final results. The algorithm is successful to avoid the complex classifications and computations. Besides, the algorithm is effective to simplify the processes of finding the intersection points. Comparing to some classical algorithms, the algorithm of this paper is faster for clipping line segments and more efficient for calculations.

AFFINE TRANSFORMATION IN RANDOM ITERATED FUNCTION SYSTEMS

Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach.

AFFINE SPINOR DECOMPOSITION IN THREE-DIMENSIONAL AFFINE GEOMETRY

Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and engineering.In threedimensional projective geometry,when acting on lines,each projective transformation can be decomposed into at most three harmonic projective reflections with respect to projective lines,or equivalently,each projective spinor can be decomposed into at most three orthogonal Minkowski bispinors,each inducing a harmonic projective line reflection.In this paper,we establish the corresponding result for three-dimensional affine geometry:with each affine transformation is found a minimal decomposition into general affine reflections,where the number of general affine reflections is at most three;equivalently,each affine spinor can be decomposed into at most three affine Minkowski bispinors,each inducing a general affine line reflection.

A Simple Factor in Canonical Quantization Yields Affine Quantization Even for Quantum Gravity

Canonical quantization (CQ) is built around [Q, P] = iħ1l , while affine quantization (AQ) is built around [Q,D] = iħQ, where D ≡ (PQ +QP) / 2 . The basic CQ operators must fit -∞ < P, Q < ∞ , while the basic AQ operators can fit -∞ < P < ∞ and 0 < Q < ∞ , -∞ < Q < 0 , or even -∞ < Q ≠ 0 < ∞ . AQ can also be the key to quantum gravity, as our simple outline demonstrates.

Heteroclinic cycles in a new class of four-dimensional discontinuous piecewise affine systems

It is a huge challenge to give an existence theorem for heteroclinic cycles in the high-dimensional discontinuous piecewise systems(DPSs). This paper first provides a new class of four-dimensional(4 D) two-zone discontinuous piecewise affine systems(DPASs), and then gives a useful criterion to ensure the existence of heteroclinic cycles in the systems by rigorous mathematical analysis. To illustrate the feasibility and efficiency of the theory, two numerical examples, exhibiting chaotic behaviors in a small neighborhood of heteroclinic cycles, are discussed.

Self-Affine Multifractal Spectrum and Levy Stability Index from NA27 Data

A self-affine analysis of multiparticle production in pp collisions at 400 GeV/c was performed by using the method of continuously varying scale and the method of the factorial moments of continuous order.The self-affine generalized fractal dimensions and multifractal spectrum have been obtained.The self-affine multifractal spectrum is concave downward with a maximum at q=0,f(α(0))=D(0)=1.D(q)decreases with increasing q showing that there is self-affine multifractal behaviour in multiparticle production at the 400GeV/c pp collisions.The Levy indexμ>1 indicates that a non-thermal phase transition may exist in the pp collisions at 400 GeV/c.