A two-to-one map and abelian affine difference sets

Let D be an affine difference set of order n in an abelian group G relative to a subgroup N. Set = H \ {1, ω}, where H = G/N and . Using D we define a two-to-one map g from to N. The map g satisfies g(σ ^m ) = g(σ) ^m and g(σ) = g(σ ⁻¹) for any multiplier m of D and any element σ ∈ . As applications, we present some results which give a restriction on the possible order n and the group theoretic structure of G/N.      

Semilocal convergence for Halley’s method under weak Lipschitz condition

The semilocal convergence properties of Halley’s method for nonlinear operator equations are studied under the hypothesis that the second derivative satisfies some weak Lipschitz condition. The method employed in the present paper is based on a family of recurrence relations which will be satisfied by the involved operator. An application to a nonlinear Hammerstein integral equation of the second kind is provided.     

Geodesically equivalent metrics in general relativity

We discuss whether it is possible to reconstruct a metric from its nonparameterized geodesics, and how to do it effectively. We explain why this problem is interesting for general relativity. We show how to understand whether all curves from a sufficiently big family are nonparameterized geodesics of a certain affine connection, and how to reconstruct algorithmically a generic 4-dimensional metric from its nonparameterized geodesics. The algorithm works most effectively if the metric is Ricci-flat. We also prove that almost every metric does not allow nontrivial geodesic equivalence, and construct all pairs of 4-dimensional geodesically equivalent metrics of Lorentz signature.     

Laplacian affine sparse coding with tilt and orientation consistency for image classification

Recently, sparse coding has become popular for image classification. However, images are often captured under different conditions such as varied poses, scales and different camera parameters. This means local features may not be discriminative enough to cope with these variations. To solve this problem, affine transformation along with sparse coding is proposed. Although proven effective, the affine sparse coding has no constraints on the tilt and orientations as well as the encoding parameter consistency of the transformed local features. To solve these problems, we propose a Laplacian affine sparse coding algorithm which combines the tilt and orientations of affine local features as well as the dependency among local features. We add tilt and orientation smooth constraints into the objective function of sparse coding. Besides, a Laplacian regularization term is also used to characterize the encoding parameter similarity. Experimental results on several public datasets demonstrate the effectiveness of the proposed method.     

An improved radial basis function based method for image warping

A new image warping method is proposed in this letter, which can warp a given image by some manual defined features. Based on the radial basis interpolation function algorithm, the proposed method can transform the original optimized problem into nonsingular linear problem by adding one-order term and affine differentiable condition. This linear system can get the steady unique solution by choosing suitable kernel function. Furthermore, the proposed method demonstrates how to set up the radial basis function in the target image so as to achieve supports to adopt the backward re-sampling technology accordingly which could gain the very slippery warping image. The experimental result shows that the proposed method can implement smooth and gradual image warping with multi-anchor points‘ accurate interpolation.     

AnO(\sqrt n L) iteration bound primal-dual cone affine scaling algorithm for linear programmingiteration bound primal-dual cone affine scaling algorithm for linear programming

In this paper we introduce a primal-dual affine scaling method. The method uses a search-direction obtained by minimizing the duality gap over a linearly transformed conic section. This direction neither coincides with known primal-dual affine scaling directions (Jansen et al., 1993; Monteiro et al., 1990), nor does it fit in the generic primal-dual method (Kojima et al., 1989). The new method requires main iterations. It is shown that the iterates follow the primal-dual central path in a neighbourhood larger than the conventional neighbourhood. The proximity to the primal-dual central path is measured by trigonometric functions.     

Statistical feature extraction based technique for fast fractal image compression

Fractal image compression is an innovative way of image representation by using relationships among the sub-section of image itself. It utilizes the existence of self-symmetry and uses affine contractive transforms. This technique has manifold advantages like, very high compression ratio, high decompression speed, high bit-rate and resolution independence, but high computation time expenses of suitable domain search in coding phase is the major bottleneck of the technique. This paper presents a fast fractal compression scheme based on feature extraction and innovative way of image comparison. In proposed development the complexity of suitable domain search is reduced by transforming the problem from image domain to vector domain. Simulation results confirms that suggested variant leads to a faster system as compared to existing state-of art Fractal Image Compression techniques.     

素特征域上无扭仿型李代数的实现

在有单位元的可换环上研究仿型李代数有两种定义，一种是应用生成元和定义关系的方法［１］；另一种是应用Ｃｈｅｖａｌｌｅｙ生成元的张量扩张的方法［２］．本文做了以下两方面的工作：（ｉ）＃第一种方法应用到罗朗多项式环上，由素特征ｐ≠２，３的域上典型单李代数出发进行一维中心扩张得到无扭仿型李代数的实现，定理２．６．（ｉｉ）证明了以上两种方法定义的李代数在素特征ｐ≠２，３的域上是同构的．