An Algorithm for Short-Circuit Current Interval in Distribution Networks with Inverter Type Distributed Generation Based on Affine Arithmetic

During faults in a distribution network,the output power of a distributed generation(DG)may be uncertain.Moreover,the output currents of distributed power sources are also affected by the output power,resulting in uncertainties in the calculation of the short-circuit current at the time of a fault.Additionally,the impacts of such uncertainties around short-circuit currents will increase with the increase of distributed power sources.Thus,it is very important to develop a method for calculating the short-circuit current while considering the uncertainties in a distribution network.In this study,an affine arithmetic algorithm for calculating short-circuit current intervals in distribution networks with distributed power sources while considering power fluctuations is presented.The proposed algorithm includes two stages.In the first stage,normal operations are considered to establish a conservative interval affine optimization model of injection currents in distributed power sources.Constrained by the fluctuation range of distributed generation power at the moment of fault occurrence,the model can then be used to solve for the fluctuation range of injected current amplitudes in distributed power sources.The second stage is implemented after a malfunction occurs.In this stage,an affine optimization model is first established.This model is developed to characterizes the short-circuit current interval of a transmission line,and is constrained by the fluctuation range of the injected current amplitude of DG during normal operations.Finally,the range of the short-circuit current amplitudes of distribution network lines after a short-circuit fault occurs is predicted.The algorithm proposed in this article obtains an interval range containing accurate results through interval operation.Compared with traditional point value calculation methods,interval calculation methods can provide more reliable analysis and calculation results.The range of short-circuit current amplitude obtained by this algorithm is slightly larger than those obtained using the Monte Carlo algorithm and the Latin hypercube sampling algorithm.Therefore,the proposed algorithm has good suitability and does not require iterative calculations,resulting in a significant improvement in computational speed compared to the Monte Carlo algorithm and the Latin hypercube sampling algorithm.Furthermore,the proposed algorithm can provide more reliable analysis and calculation results,improving the safety and stability of power systems.

A Remark on the Affine Coordinates for KdV Tau-Functions

We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy.

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.

Stability analysis for affine fuzzy system based on fuzzy Lyapunov functions

An analysis method based on the fuzzy Lyapunov functions is presented to analyze the stability of the continuous affine fuzzy systems. First, a method is introduced to deal with the consequent part of the fuzzy local model. Thus, the stability analysis method of the homogeneous fuzzy system can be used for reference. Stability conditions are derived in terms of linear matrix inequalities based on the fuzzy Lyapunov functions and the modified common Lyapunov functions, respectively. The results demonstrate that the stability result based on the fuzzy Lyapunov functions is less conservative than that based on the modified common Lyapunov functions via numerical examples. Compared with the method which does not expand the consequent part, the proposed method is simpler but its feasible region is reduced. Finally, in order to expand the application of the fuzzy Lyapunov functions, the piecewise fuzzy Lyapunov function is proposed, which can be used to analyze the stability for triangular or trapezoidal membership functions and obtain the stability conditions. A numerical example validates the effectiveness of the proposed approach.

REPRESENTATIONS OF AFFINE HECKEALGE BRAS OF TYPE G_2

Let k be a field and q a nonzero element in k such that the square roots of q are in k. We use Hq to denote an affne Hecke algebra over k of type G2 with parameter q. The purpose of this paper is to study representations of Hq by using based rings of two-sided cells of an affne Weyl group W of type G2. We shall give the classification of irreducible representations of Hq. We also remark that a calculation in [11] actually shows that Theorem 2 in [1] needs a modification, a fact is known to Grojnowski and Tanisaki long time ago. In this paper we also show an interesting relation between Hq and an Hecke algebra corresponding to a certain Coxeter group. Apparently the idea in this paper works for all affne Weyl groups, but that is the theme of another paper.

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.

LMI-based robust control of uncertain discrete-time piecewise affine systems

The main contribution of this paper is to present stability synthesis results for discrete-time piecewise affine （PWA） systems with polytopic time-varying uncertainties and for discrete-time PWA systems with norm-bounded uncertainties respectively.The basic idea of the proposed approaches is to construct piecewise-quadratic （PWQ） Lyapunov functions to guarantee the stability of the closed-loop systems.The partition information of the PWA systems is taken into account and each polytopic operating region is outer approximated by an ellipsoid,then sufficient conditions for the robust stabilization are derived and expressed as a set of linear matrix inequalities （LMIs）.Two examples are given to illustrate the proposed theoretical results.

THE GRAPH INDUCED BY AFFINE M-FLATS OVER FINITE FIELDS II

Let AG(n,F q) be the n-dimensional affine space over F q,where F q is a finite field with q elements.Denote by Γ (m) the graph induced by m-flats of AG(n,F q).For any two adjacent vertices E and F of Γ (m),Γ (m)(E)∩Γ (m)(F) is studied.In particular,sizes of maximal cliques in Γ (m) are determined and it is shown that Γ (m) is not edge-regular when m<n-1.

Variable step-size affine projection algorithm based on global speech absence probability for adaptive feedback cancellation

A novel approach is proposed for improving adaptive feedback cancellation using a variable step-size affine projection algorithm(VSS-APA) based on global speech absence probability(GSAP).The variable step-size of the proposed VSS-APA is adjusted according to the GSAP of the current frame.The weight vector of the adaptive filter is updated by the probability of the speech absence.The performance measure of acoustic feedback cancellation is evaluated using normalized misalignment.Experimental results demonstrate that the proposed approach has better performance than the normalized least mean square(NLMS) and the constant step-size affine projection algorithms.

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.

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.

Extraction of affine invariant features for shape recognition based on ant colony optimization

A new approach to extraction of affine invariant features of contour image and matching strategy is proposed for shape recognition.Firstly,the centroid distance and azimuth angle of each boundary point are computed.Then,with a prior-defined angle interval,all the points in the neighbor region of the sample point are considered to calculate the average distance for eliminating noise.After that,the centroid distance ratios（CDRs） of any two opposite contour points to the barycenter are achieved as the representation of the shape,which will be invariant to affine transformation.Since the angles of contour points will change non-linearly among affine related images,the CDRs should be resampled and combined sequentially to build one-by-one matching pairs of the corresponding points.The core issue is how to determine the angle positions for sampling,which can be regarded as an optimization problem of path planning.An ant colony optimization（ACO）-based path planning model with some constraints is presented to address this problem.Finally,the Euclidean distance is adopted to evaluate the similarity of shape features in different images.The experimental results demonstrate the efficiency of the proposed method in shape recognition with translation,scaling,rotation and distortion.

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.