Full-field speckle pattern image correlation with B-Spline deformation function

A full-field speckle pattern image correlation method is presented that will determine directly the complete, two-dimensional deformation field during the image correlation process on digital images obtained using computer vision systems. In this work, a B-Spline function is used to represent the object deformation field throughout the entire image area. This is an improvement over subset-based image correlation methods by implicitly maintaining position and derivative continuity constraints among subsets up to a specified order. The control point variables within the B-Spline deformation function are optimized iteratively with the Levenberg-Marquardt method to achieve minimum disparity between the predicted and actual deformed images. Results have shown that the proposed method is computationally efficient, accurate and robust. The general framework of this method can be applied ton-dimensional image correlation systems that solve for multi-dimension vector fields.     

啁啾微波场中里德伯锂原子的相干激发与控制

运用含时多态展开方法和B-样条函数研究了微波场中里德伯锂原子高激发态的性质,得到锂原子量子态n=70-75,l=0-5的能量,并分析了里德伯锂原子高激发态n=70-75,l=0-5在微波场中的跃迁几率.结果表明:通过优化微波场参数可以实现量子系统从初始态到目标态的完全跃迁,且在跃迁过程中,每个l态都起至关重要的作用.     

Products of B-patches

Products and tensor products of multivariate polynomials in B-patch form are viewed as linear combinations of higher degree B-patches. Univariate B-spline segments and certain regions of simplex splines are examples of B-patches. A recursive scheme for transforming tensor product B-patch representations into B-patch representations of more variables is presented. The scheme can also be applied for transforming ann-fold product of B-patch expansions into a B-patch expansion of higher degree. Degree raising formulas are obtained as special cases. The scheme calculates the blossom of the (tensor) product surface and generalizes the pyramidal recursive scheme for B-patches.     

Galerkin-FEM for obtaining the numerical solution of the linear fractional Klein-Gordon equation

In this paper, an efficient numerical method for solving the linear fractional Klein-Gordon equation (LFKGE) is introduced. The proposed method depends on the Galerkin finite element method (GFEM) using quadratic B-spline base functions and replaces the Caputo fractional derivative using $L2$ discretization formula. The introduced technique reduces LFKGE to a system of algebraic equations, which solved using conjugate gradient method. The study the stability analysis to the approximation obtained by the proposed scheme is given. To test the accuracy of the proposed method we evaluated the error norm $L_{2}$. It is shown that the presented scheme is unconditionally stable. Numerical example is given to show the validity and the accuracy of the introduced algorithm.     

An Affirmative Result of the Open Question on Determining Function Jumps by Spline Wavelets

We study the open question on determination of jumps for functions raised by Shi and Hu in 2009. An affirmative answer is given for the case that spline-wavelet series are used to approximate the functions.     

A numerical method for solving KdV equation with multilevel B-spline quasi-interpolation

In this article, we use a multilevel quartic spline quasi-interpolation scheme to solve the one-dimensional nonlinear Korteweg–de Vries (KdV) equation which exhibits a large number of physical phenomena. The presented scheme is obtained by using the second-order central divided difference of the spatial derivative to approximate the third-order spatial derivative, and the forward divided difference to approximate the temporal derivative, where the spatial derivative is approximated by the proposed quasi-interpolation operator. Compared to other numerical methods, the main advantages of our scheme are the higher accuracy and lower computational complexity. Meanwhile, the algorithm is very simple and easy to implement. Numerical experiments in this article also show that our scheme is feasible and valid.     

A baire approach to quantitative resonance principles

The main purpose of this paper is to give a proof of quantitative resonance and condensation principles via Baire category arguments in contrast to the gliding hump method used previously. Thereby a new nonquantitative resonance principle is established which is concerned with dominated convergence in Frechet spaces, by the way yielding more detailed information on the structure of the underlying spaces. On the other hand, Baire's approach is an easy tool to develop condensation principles by considering residual sets. Finally, some typical applications concerning trigonometric Fourier partial sums may illustrate the result received.     

Computational scheme for solving nonlinear fractional stochastic differential equations with delay

Abstract

This paper studies the numerical solution of fractional stochastic delay differential equations driven by Brownian motion. The proposed algorithm is based on linear B-spline interpolation. The convergence and the numerical performance of the method are analyzed. The technique is adopted for determining the statistical indicators of stochastic responses of fractional Langevin and Mackey-Glass models with stochastic excitations.