The Two-Point Codes with the Designed Distance on a Hermitian Curve in Even Characteristic

In Homma M and Kim SJ [2], the authors considered two-point codes on a Hermitian curve defined over fields of odd characteristic. In this paper, we study the geometry of a Hermitian curve over fields of even characteristic and classify the two-point codes whose minimum distances agree with the designed ones.     

商标数据库存储模式及其检索算法研究

依据商标专家的先验知识和基于内容的图像检索技术，提出了一种新的商标库存储结构，并依据该存储结构设计了以三级检索算法为核心的实用商标登记注册管理系统，对于检索算法，一级检索采用人工确认，二级检索采用傅立叶描述子作为边缘特征向量，三级检索采用hu不变矩组作为矩特征向量，从而达到提高商标申请注册中的检索速度和查准率。     

全站仪线路纵、横断面测量

运用全站仪放样及对边测量功能，在已知控制点上设站，方便、快捷、精确的进行线路的纵、横断面测量。     

关于Gerber不等式的一个猜想

本文证明了陈计-单墫关于Ｇｅｒｂｅｒ不等式的一个猜想，作为其应用，导出了单形内一点到顶点的距离与到面的距离的两个不等式．     

Proof of the Mixing Theorem for Statistical Systems in Classical Physics

In a general measure-theoretic context, it is proved that the action of a stochastic map on a pair of probability distributions can be characterized by the criterion of decreasing mixing distance.     

Transition state geometry in radical abstraction reactions: comparison of interatomic distances in the intersecting parabolas and Morse curves models with quantum-chemical calculations

Interatomic distances in the transition state were estimated for the reactions of radical abstraction: H^· + H₂, H^· + HCl, H^· + CH₄, N^·H₂ + NH₃, HO^· + H₂O, HO₂ ^· + HOOH, and C^·H₃ + SiH₄. The calculation was performed by the quantum-chemical density functional method or coupled clusters method (QCH), as well as by the methods of intersecting parabolas (IPM) and Morse curves (IMM), using experimental data (activation energies and reaction enthalpies). The results of the latter two methods are close to the quantum-chemical calculation and differ only by the increment a: r(IPM or IMM) = a + r(QCH), where a = –4.5·10^–12 m for IPM and a = +1.9·10^–12 m for IMM.     

Molecular conformation search by distance matrix perturbations

Three-dimensional molecular structure is fundamental in chemical function identification and computer-aided drug design. The enumeration of a small number of feasible conformations provides a rigorous way to determine the optimal or a few acceptable conformations. Our contribution concerns a heuristic enhancement of a method based on distance geometry, typically in relation with experiments of the NMR type. Distance geometry has been approached by different viewpoints; ours is expected to help in several subtasks arising in the process that determines 3D structure from distance information. More precisely, the input to our algorithm consists of a set of approximate distances of varying precision; some are specified by the covalent structure and others by Nuclear Magnetic Resonance (NMR) experiments (or X-ray crystallography which, however, requires crystallization). The output is a valid tertiary structure in a specified neighborhood of the input. Our approach should help in detecting outliers of the NMR experiments, and handles inputs with partial information. Moreover, our technique is able to bound the number of degrees of freedom of the conformation manifold. We have used numerical linear algebra algorithms for reasons of speed, and because they are well-implemented, fully documented and widely available. Our main tools include, besides distance matrices, structure-preserving matrix perturbations for minimizing singular values. Our MATLAB (or SCILAB) implementation is described and illustrated.AMS subject Classification: 92E10 Molecular structure, 92C40 Biochemistry, molecular biology, 65F15 Eigenvalues, eigenvectors, 15A18 Eigenvalues, singular values, and eigenvectors     

Resistance distance and Laplacian spectrum

The resistance distance r _ij between two vertices v _i and v _j of a (connected, molecular) graph G is equal to the resistance between the respective two points of an electrical network, constructed so as to correspond to G, such that the resistance of any two adjacent points is unity. We show how the matrix elements r _ij can be expressed in terms of the Laplacian eigenvalues and eigenvectors of G. In addition, we determine certain properties of the resistance matrix R=||r _ij ||. AcknowledgementsThis research was supported by the Natural Science Foundation of China and Fujian Province, and by the Ministry of Sciences, Technologies and Development of Serbia, within Project no. 1389. The authors thank Douglas J. Klein (Galveston) for useful comments.     

Data loci in algebraic optimization

We consider parametric optimization problems from an algebraic viewpoint. The idea is to find all of the critical points of an objective function thereby determining a global optimum. For generic parameters (data) in the objective function the number of critical points remains constant. This number is known as the algebraic degree of an optimization problem. In this article, we go further by considering the inverse problem of finding parameters of the objective function so it gives rise to critical points exhibiting a special structure. For example if the critical point is in the singular locus, has some symmetry, or satisfies some other algebraic property. Our main result is a theorem describing such parameters.     

Extragradient and extrapolation methods with generalized Bregman distances for saddle point problems

In this paper, we introduce two Bregman-type algorithmic frameworks to generalize the extragradient and extrapolation methods. With the help of relative Lipschitzness and the Bregman distance tool, the iteration properties of the proposed frameworks are analyzed. As applied to smooth convex-concave saddle point problems, our theory rediscovers the main results in Mokhtari et al. (2020) [14] for wider frameworks under weaker assumptions via a conceptually different approach.