Abstract:
We propose a modification of the weak Galerkin methods and show its equivalence to a new version of virtual element methods. We also show the original weak Galerkin method is equivalent to the non-conforming virtual element method. As a consequence, ideas and techniques used for one method can be transferred to another. The key of the connection is the degree of freedoms.

Abstract:
In order to obtain a decent trade-off between the low-cost, low-accuracy Global Positioning System (GPS) receivers and the requirements of high-precision digital maps for modern railways, using the concept of constraint K-segment principal curves (CKPCS) and the expert knowledge on railways, we propose three practical CKPCS generation algorithms with reduced computational complexity, and thereafter more suitable for engineering applications. The three algorithms are named ALLopt, MPMopt, and DCopt, in which ALLopt exploits global optimization and MPMopt and DCopt apply local optimization with different initial solutions. We compare the three practical algorithms according to their performance on average projection error, stability, and the fitness for simple and complex simulated trajectories with noise data. It is found that ALLopt only works well for simple curves and small data sets. The other two algorithms can work better for complex curves and large data sets. Moreover, MPMopt runs faster than DCopt, but DCopt can work better for some curves with cross points. The three algorithms are also applied in generating GPS digital maps for two railway GPS data sets measured in Qinghai-Tibet Railway (QTR). Similar results like the ones in synthetic data are obtained. Because the trajectory of a railway is relatively simple and straight, we conclude that MPMopt works best according to the comprehensive considerations on the speed of computation and the quality of generated CKPCS. MPMopt can be used to obtain some key points to represent a large amount of GPS data. Hence, it can greatly reduce the data storage requirements and increase the positioning speed for real-time digital map applications. 1. Introduction 1.1. Principal Curves Spearman proposed principal component analysis (PCA) in 1904, and now PCA is one of the most important tools for statistical data analysis [1]. But PCA is one linear analysis method which cannot deal with some intrinsic nonlinear data sets. Then Hastie proposed the concept of principal curves and its generation algorithm in 1983 [2]. As the nonlinear extension of PCA, principal curve uses a smooth curve instead of a straight line to summarize the given data set of the symmetric variables. Recently, the principal curves have been widely used in different real engineering problems such as control of the electron beam trajectory in Linear Collider [3], sound data model reduction, and data visualization in speech processing [4–6] and chemical process monitoring [7, 8]. In 1992, Banfield and Raftery proposed BR principal curves,

Abstract:
This paper introduces a management information system for the publication of books and periodicals published in different languages. The system serves agencies and subscribers all over the world. Life cycle of the system, including system programming, design, realization and maintenance is described.

Abstract:
Background and objective The bromodomain-containing protein 7 (BRD7) gene belongs to the bromodomain family. The majority of the members of this family are closely related to epithelial tumors. The aim of this study is to explore BRD7 expression and its clinical significance in non-small cell lung cancer (NSCLC). Methods BRD7 protein expression was detected in tissues samples from 101 NSCLC cases and 33 normal lung tissue samples using streptavidin-peroxidase immunohistochemistry. Results BRD7 expression was significantly higher in cancer tissues than that in normal lung tissues. Positive BRD7 expression in the lymph node metastasis group was significantly higher than that in the non-lymph node metastasis group. The positive expression rate of BRD7 increased with the increasing Tumor-Nodes-Metastasis (TNM) stage. No significant differences in positive BRD7 expression were observed with age, smoking, gender, pathology type, and degree of differentiation among the NSCLC patients (P>0.05). Conclusion BRD7 is highly expressed in NSCLC. In addition to the degree of differentiation and extent of lymphatic metastasis, BRD7 expression is correlated with TNM stage, which indicates that BRD7 may be related to the occurrence, development, and metastasis of lung cancers.

Abstract:
We provide an algebraic way to calculate the quasi-normal modes of a black hole, which possesses a hidden conformal symmetry. We construct an infinite tower of quasi-normal modes from the highest-weight mode, in a simple and elegant way. For the scalar, the hidden conformal symmetry manifest itself in the fact that the scalar Laplacian could be rewritten in terms of the $SL(2,R)$ quadratic Casimir. For the vector and the tensor, the hidden conformal symmetry acts on them through Lie derivatives. We show that for three-dimensional black holes, with appropriate combination of the components the radial equations of the vector and the tensor could be written in terms of the Lie-induced quadratic Casimir. This allows the algebraic construction of the quasi-normal modes feasible. Our results are in good agreement with the previous study.

Abstract:
In this paper, we derive some local a priori estimates for Ricci flow. This gives rise to some strong uniqueness theorems. As a corollary, let $g(t)$ be a smooth complete solution to the Ricci flow on $\mathbb{R}^{3}$, with the canonical Euclidean metric $E$ as initial data, then $g(t)$ is trivial, i.e. $g(t)\equiv E$.

Abstract:
In this paper, we established the existence and uniqueness of the spherically symmetric monopole solutions in SO(5) gauge theory with Higgs scalar fields in the vector representation in six-dimensional Minkowski space-time and obtain sharp asymptotic estimates for the solutions. Our method is based on a dynamical shooting approach that depends on two shooting parameters which provides an effective framework for constructing the generalized monopoles in six-dimensional Minkowski space-time.

Abstract:
Let R be an associative ring with unity 1. The existence of the Moore-Penrose inverses of block matrices over R is investigated and the sufficient and necessary conditions for such existence are obtained. Furthermore, the representation of the Moore-Penrose inverse of M=［0 AC B］ is given under the condition of EBF=0, where E=I-CC？ and F=I-A？A. This result generalizes the representation of the Moore-Penrose inverse of the companion matrix M=［0 aInn b］ due to Pedro Patrício. As for applications, some examples are given to illustrate the obtained results.