Asymmetrical spiral spectra and orbital angular momentum density of non-uniformly polarized vortex beams in uniaxial crystals

To explore the effect of non-uniform polarization on orbital angular momentum(OAM) in anisotropic medium, in this work investigated are the evolution of the spiral spectra and OAM densities of non-uniformly polarized vortex(NUPV)beams in uniaxial crystals propagating orthogonal to the optical axis, and also the case of uniformly polarized vortex(UPV)beams with left-handed elliptical polarization. In the input plane, the NUPV beams present their spiral spectra of m-mode concentrated at m = l ± 1 modes rather than m = l mode, and reveal the relation among topological charge l, mode of spiral spectra m and the power weight value Rmexpressed by l=∑^(∞)_(m)=-∞Rm. is still satisfied for UPV beams in uniaxially anisotropic crystals, whereas for NUPV beams their relations are no longer valid owing to non-uniform polarization. Furthermore, the analysis indicates that the asymmetrical distribution of power weight of spiral spectra and the non-zero value in the sum of longitudinal OAM densities originate from the initial non-uniform polarization and anisotropy in uniaxial crystals rather than topological charges. In addition, the relation between spiral spectrum and longitudinal OAM density is numerically discussed. This work may provide an avenue for OAM-based communications,optical metrology, and imaging by varying the initial non-uniform polarization.

A Remark on Pl Type Interpolation on Non-Uniformly Distributed Nodes on the Unit Circle

In this paper we study the problem of explicit representation and convergence of Pal type （0;1） interpolation and its converse, with some additional conditions, on the non-uniformly distributed nodes on the unit circle obtaIned by projecting the interlaced zeros of Pn （x） and Pn′ （x） on the unit circle. The motivation to this problem can be traced to the recent studies on the regularity of Birkhoff interpolation and Pal type interpolations on non-uniformly distributed zeros on the unit circle.

Modeling of Non-uniformly Sampled Systems by Support Vector Regression with Applications

This paper presents a modeling method for a non-uniformly sampled system bused on support vector regression （ SVR ）. First, a lifted discrete-time state-space model for a non-uniformly sampled system is derived by using the lifting technique to reduce the modeling difficulty caused by multirate sampling. Then, the system is divided into several parallel subsystems and their input-output model is presented to satisfy the SVR model. Finally, an on-line SVR technique is utilized to establish the models of all subsystems to deal with uncertainty. Furthermore, the presented method is applied in a multichannel electrohydraulic force servo synchronous loading system to predict the system outputs over the control sample interval and the prediction mean absolute percentage error reaches 0. 092%. The results demonstrate that the presented method has a high modeling precision and the subsystems have the same level of prediction error.

Finite element prediction on the response of non-uniformly arranged pile groups considering progressive failure of pile-soil system

A uniform arrangement of individual piles is commonly adopted in the conventional pile group foundation,and basin-shaped settlement is often observed in practice.Large differential settlement of pile groups will decrease the use-safety requirements of building,even cause the whole-building tilt or collapse.To reduce differential settlement among individual piles,non-uniformly arranged pile groups can be adopted.This paper presents a finite element analysis on the response of pile groups with different layouts of individual piles in pile groups.Using the userdefined subroutine FRIC as the secondary development platform,a softening model of skin friction and a hyperbolic model of end resistance are introduced into the contact pair calculation of ABAQUS software.As to the response analysis of a single pile,the reliability of the proposed secondary development method of ABAQUS software is verified using an iterative computer program.The reinforcing effects of individual piles is then analyzed using the present finite element analysis.Furthermore,the response of non-uniformly arranged pile groups,e.g.,individual piles with variable length and individual piles with variable diameter,is analyzed using the proposed numerical analysis method.Some suggestions on the layout of individual piles are proposed to reduce differential settlement and make full use of the bearing capacity of individual piles in pile groups for practical purposes.

Fuzzy Modeling of Non-Uniformly Sampling Nonlinear Systems Based on Clustering Method and Convergence Analysis

The studying motivation of this paper is that there exist many modeling issues of nonuniformly sampling nonlinear systems in industrial systems.Based on multi-model modeling principle,the corresponding model of non-uniformly sampling nonlinear systems is described by the nonlinear weighted combination of some linear models at local working points.Fuzzy modeling based on multimodel scheme is a common method to describe the dynamic process of non-linear systems.In this paper,the fuzzy modeling method of non-uniformly sampling nonlinear systems is studied.The premise structure of the fuzzy model is confirmed by GK fuzzy clustering,and the conclusion parameters of the fuzzy model are estimated by the recursive least squared algorithm.The convergence perfromance of the proposed identification algorithm is given by using lemmas and martingale theorem.Finally,the simulation example is given to demonstrate the effectiveness of the proposed method.

基于奇异值分解递推辨识非均匀采样系统的状态空间模型（英文）

In this paper a recursive state-space model identification method is proposed for non-uniformly sampled systems in industrial applications. Two cases for measuring all states and only output(s) of such a system are considered for identification. In the case of state measurement, an identification algorithm based on the singular value decomposition(SVD) is developed to estimate the model parameter matrices by using the least-squares fitting. In the case of output measurement only, another identification algorithm is given by combining the SVD approach with a hierarchical identification strategy. An example is used to demonstrate the effectiveness of the proposed identification method.

A NOTE ON REGULARITY AND EXISTENCE OF SOLUTIONS FOR A CLASS OF NON－UNIFORMLY DEGENERATE ELLIPTIC EQUATIONS

In this paper we consider the Dirichlet problems of a non-uniformly digenerate elliptic equations of the formwhose prototype iswhere n C 1 N is a bounded domain,0<b(x)<1,0<o<P.We establish that if Aand B are under some structure conditions and 0<or S P<max{aam +k,o+1}tthen there exists a CI+o-solution of(0.1)associated with the Dirichlet boundary dsta.

Quasi-shadowing for Z^(d)-actions

A diffeomorphism is non-uniformly partially hyperbolic if it preserves an ergodic measure with at least one zero Lyapunov exponent.We prove that a C^(1)-smooth Z^(d)-action has the quasishadowing property if one of the generators is C^(1+α)(α>0)non-uniformly partially hyperbolic.

Lyapunov exponent,Liao perturbation and persistence

Consider a C1 vector eld together with an ergodic invariant probability that hasℓnonzero Lya-punov exponents.Using orthonormal moving frames along a generic orbit we construct a linear system ofℓdi erential equations which is a linearized Liao standard system.We show that Lyapunov exponents of this linear system coincide with all the nonzero exponents of the given vector eld with respect to the given ergodic probability.Moreover,we prove that these Lyapunov exponents have a persistence property meaning that a small perturbation to the linear system(Liao perturbation)preserves both the sign and the value of the nonzero Lyapunov exponents.

Generalized Jacobi-Gauss-Lobatto interpolation

We introduce the generalized Jacobi-Gauss-Lobatto interpolation involving the values of functions and their derivatives at the endpoints, which play important roles in the Jacobi pseudospectral methods for high order problems. We establish some results on these interpolations in non-uniformly weighted Sobolev spaces, which serve as the basic tools in analysis of numerical quadratures and various numerical methods of differential and integral equations.