Localization of Vector Field on Pure Geometrical Thick Brane

We investigate the localization of a five-dimensional vector field on a pure geometrical thick brahe. By introducing two types of interactions between the vector field and the background scalar field, we obtain a typical volcano potential for the first type of coupling and a Posehl-Teller potential for the second one. These two types of couplings guarantee that the vector zero mode can be localized on the pure geometrical thick brahe under certain conditions.

Local Geometric Proof of Riemann Conjecture

Riemann hypothesis (RH) is a difficult problem. So far one doesn’t know how to go about it. Studying ζ and using analysis method likely are two incor-rect guides. Actually, a unique hope may study Riemann function , , by geometric analysis, which has the symmetry: v=0 if β=0, and basic expression . We show that |u| is single peak in each root-interval of u for fixed β ∈(0,1/2]. Using the slope ut, we prove that v has opposite signs at two end-points of Ij. There surely exists an inner point such that , so {|u|,|v|/β} form a local peak-valley structure, and have positive lower bound in Ij. Because each t must lie in some Ij, then ||ξ|| > 0 is valid for any t (i.e. RH is true). Using the positivity of Lagarias (1999), we show the strict monotone for β > β0 ≥ 0 , and the peak-valley structure is equiva-lent to RH, which may be the geometric model expected by Bombieri (2000). This research follows Liuhui’s methodology: “Computing can detect the un-known and method”.

Discrete Plane Segmentation and Estimation from a Point Cloud Using Local Geometric Patterns

This paper presents a method for segmenting a 3D point cloud into planar surfaces using recently obtained discretegeometry results. In discrete geometry, a discrete plane is defined as a set of grid points lying between two parallel planes with a small distance, called thickness. In contrast to the continuous case, there exist a finite number of local geometric patterns （LGPs） appearing on discrete planes. Moreover, such an LGP does not possess the unique normal vector but a set of normal vectors. By using those LGP properties, we first reject non-linear points from a point cloud, and then classify non-rejected points whose LGPs have common normal vectors into a planar-surface-point set. From each segmented point set, we also estimate the values of parameters of a discrete plane by minimizing its thickness.

Unsupervised Feature Selection Using Structured Self-Representation

Unsupervised feature selection has become an important and challenging problem faced with vast amounts of unlabeled and high-dimension data in machine learning. We propose a novel unsupervised feature selection method using Structured Self-Representation( SSR) by simultaneously taking into account the selfrepresentation property and local geometrical structure of features. Concretely,according to the inherent selfrepresentation property of features,the most representative features can be selected. Mean while,to obtain more accurate results,we explore local geometrical structure to constrain the representation coefficients to be close to each other if the features are close to each other. Furthermore,an efficient algorithm is presented for optimizing the objective function. Finally,experiments on the synthetic dataset and six benchmark real-world datasets,including biomedical data,letter recognition digit data and face image data,demonstrate the encouraging performance of the proposed algorithm compared with state-of-the-art algorithms.

Modeling sintering behavior of metal fibers with different fiber angles

The formation of sintering necks between two metal fibers was investigated using the oval-oval model with respect to the fiber angle range of 0°-90°. Surface diffusion was assumed to be the predominant mechanism in every section of the junction of two metal fibers in this model, which was addressed numerically using the level- set method. The growth rates of the sintering necks in the direction of the bisector of obtuse angle, the bisector of acute angle and the fiber axis were discussed in detail. It is found that the growth rate of the sintering necks decreases with fiber angle increasing in the direction of the fiber axis and the bisector of acute angle. However, an opposite variation in growth rate of sintering necks can be found in the direction of the bisector of obtuse angle. The numerical simulation results show that the growth rate of the sintering necks is significantly affected by the initial local geomet- rical structure which is determined by the fiber angle.