Topological and differentiable rigidity of submanifolds in space forms

Let $F^{n+p}(c)$ be an $(n+p)$-dimensional simply connected space form with nonnegative constant curvature $c$. We prove that if $M^n(n\geq4)$ is a compact submanifold in $F^{n+p}(c)$, and if $Ric_M>(n-2)(c+H^2),$ where $H$ is the mean curvature of $M$, then $M$ is homeomorphic to a sphere. We also show that the pinching condition above is sharp. Moreover, we obtain a new differentiable sphere theorem for submanifolds with positive Ricci curvature.Comment: 12 page

The Extended Wronskian Determinant Approach and the Iterative Solutions of One-Dimensional Dirac Equation

An approximation method, namely, the Extended Wronskian Determinant Approach, is suggested to study the one-dimensional Dirac equation. An integral equation which can be solved by iterative procedure to find the wave functions is established. We employ this approach to study the one-dimensional Dirac equation with one-well potential, and give the energy levels and wave functions up to the first order iterative approximation. For double-well potential, the energy levels up to the first order approximation are given.Comment: 3 figures, 21 page

Characterization and properties of weakly optimal entanglement witnesses

We present an analysis of the properties and characteristics of weakly optimal entanglement witnesses, that is witnesses whose expectation value vanishes on at least one product vector. Any weakly optimal entanglement witness can be written as the form of $W^{wopt}=\sigma-c_{\sigma}^{max} I$, where $c_{\sigma}^{max}$ is a non-negative number and $I$ is the identity matrix. We show the relation between the weakly optimal witness $W^{wopt}$ and the eigenvalues of the separable states $\sigma$. Further we give an application of weakly optimal witnesses for constructing entanglement witnesses in a larger Hilbert space by extending the result of [P. Badzi\c{a}g {\it et al}, Phys. Rev. A {\bf 88}, 010301(R) (2013)], and we examine their geometric properties.Comment: 13 pages, 2 figures, has been extensively redrafted and restructure

An Approach for Chinese-Japanese Named Entity Equivalents Extraction Using Inductive Learning and Hanzi-Kanji Mapping Table

Named Entity Translation Equivalents extraction plays a critical role in machine translation (MT) and cross language information retrieval (CLIR). Traditional methods are often based on large-scale parallel or comparable corpora. However, the applicability of these studies is constrained, mainly because of the scarcity of parallel corpora of the required scale, especially for language pairs of Chinese and Japanese. In this paper, we propose a method considering the characteristics of Chinese and Japanese to automatically extract the Chinese-Japanese Named Entity (NE) translation equivalents based on inductive learning (IL) from monolingual corpora. The method adopts the Chinese Hanzi and Japanese Kanji Mapping Table (HKMT) to calculate the similarity of the NE instances between Japanese and Chinese. Then, we use IL to obtain partial translation rules for NEs by extracting the different parts from high similarity NE instances in Chinese and Japanese. In the end, the feedback processing updates the Chinese and Japanese NE entity similarity and rule sets. Experimental results show that our simple, efficient method, which overcomes the insufficiency of the traditional methods, which are severely dependent on bilingual resource. Compared with other methods, our method combines the language features of Chinese and Japanese with IL for automatically extracting NE pairs. Our use of a weak correlation bilingual text sets and minimal additional knowledge to extract NE pairs effectively reduces the cost of building the corpus and the need for additional knowledge. Our method may help to build a large-scale Chinese-Japanese NE translation dictionary using mono-lingual corpora