正态分布的共轭分布及贝叶斯估计

本文介绍含有一个或两个未知参数的正态分布Ｎ（μ，）的共轭分布，以及对正态总体的未知参数进行估计的贝叶斯方法。     

The virtual NMR spectrometer: a computer program for efficient simulation of NMR experiments involving pulsed field gradients

This paper presents a software program, the Virtual NMR Spectrometer, for computer simulation of multichannel, multidimensional NMR experiments on user-defined spin systems. The program is capable of reproducing most features of the modern NMR experiment, including homo- and heteronuclear pulse sequences, phase cycling, pulsed field gradients, and shaped pulses. Two different approaches are implemented to simulate the effect of pulsed field gradients on coherence selection, an explicit calculation of all coherence transfer pathways, and an effective approximate method using integration over multiple positions in the sample. The applications of the Virtual NMR Spectrometer are illustrated using homonuclear COSY and DQF COSY experiments with gradient selection, heteronuclear HSQC, and TROSY. The program uses an intuitive graphical user interface, which resembles the appearance and operation of a real spectrometer. A translator is used to allow the user to design pulse sequences with the same programming language used in the actual experiment on a real spectrometer. The Virtual NMR Spectrometer is designed as a useful tool for developing new NMR experiments and for tuning and adjusting the experimental setup for existing ones prior to running costly NMR experiments, in order to reduce the setup time on a real spectrometer. It will also be a useful aid for learning the general principles of magnetic resonance and contemporary innovations in NMR pulse sequence design.     

Sharp Geometric Poincare Inequalities for Vector Fields and Non-Doubling Measures

We derive Sobolev–Poincaré inequalities that estimatethe L^q(d µ) norm of a function on a metric ball when µis an arbitrary Borel measure. The estimate is in terms of theL¹(d ) norm on the ball of a vector field gradient of the function,where d dx is a power of a fractional maximal function of µ.We show that the estimates are sharp in several senses, andwe derive isoperimetric inequalities as corollaries. 1991 MathematicsSubject Classification: 46E35, 42B25.     

结合图像讨论酸碱滴定曲线与酸碱平衡曲线的关系

The two distribution fraction curves of a weak acid and its conjugated base are integrated to the pH-δ_A, δ_HA coordinate system. The two curves coincide with each other to form a conjugate distribution fraction curve, which is also an acid-base equilibrium curve. The titration process is discussed with images to understand how a specific equilibrium curve to a titration.     

Joint neighbors approximation of macromolecular solvent accessible surface area

A new method for approximate analytical calculations of solvent accessible surface area (SASA) for arbitrary molecules and their gradients with respect to their atomic coordinates was developed. This method is based on the recursive procedure of pairwise joining of neighboring atoms. Unlike other available methods of approximate SASA calculations, the method has no empirical parameters, and therefore can be used with comparable accuracy in calculations of SASA in folded and unfolded conformations of macromolecules of any chemical nature. As shown by tests with globular proteins in folded conformations, average errors in absolute atomic surface area is around 1 A2, while for unfolded protein conformations it varies from 1.65 to 1.87 A2. Computational times of the method are comparable with those by GETAREA, one of the fastest exact analytical methods available today.     

Gold‐Nanoparticle‐Assisted Self‐Assembly of Chemical Gradients with Tunable Sub‐50 nm Molecular Domains

A simple and efficient principle for nanopatterning with wide applicability in the sub‐50 nanometer regime is chemisorption of nanoparticles; at homogeneous substrates, particles carrying surface charge may spontaneously self‐organize due to the electrostatic repulsion between adjacent particles. Guided by this principle, a method is presented to design, self‐assemble, and chemically functionalize gradient nanopatterns where the size of molecular domains can be tuned to match the level corresponding to single protein binding events. To modulate the binding of negatively charged gold nanoparticles both locally (<100 nm) and globally (>100 μm) onto a single modified gold substrate, ion diffusion is used to achieve spatial control of the particles’ mutual electrostatic interactions. By subsequent tailoring of different molecules to surface‐immobilized particles and the void areas surrounding them, nanopatterns are obtained with variable chemical domains along the gradient surface. Fimbriated Escherichia coli bacteria are bound to gradient nanopatterns with similar molecular composition and macroscopic contact angle, but different sizes of nanoscopic presentation of adhesive (hydrophobic) and repellent poly(ethylene) glycol (PEG) domains. It is shown that small hydrophobic domains, similar in size to the diameter of the bacterial fimbriae, supported firmly attached bacteria resembling catch‐bond binding, whereas a high number of loosely adhered bacteria are observed on larger hydrophobic domains.     

无约束优化问题的修正PRP共轭梯度法

本文通过结合牛顿法与PRP共轭梯度法提出一修正PRP方法,新方法中包含了二阶导数信息,在适当的假设下算法全局收敛,数值算例表明了算法的有效性.     

一个求解非线性不等式约束优化问题的带有共轭梯度参数的广义梯度投影算法

本文提出一个求解非线性不等式约束优化问题的带有共轭梯度参数的广义梯度投影算法.算法中的共轭梯度参数是很容易得到的,且算法的初始点可以任意选取.而且,由于算法仅使用前一步搜索方向的信息,因而减少了计算量.在较弱条件下得到了算法的全局收敛性.数值结果表明算法是有效的.     

A robust von Neumann minimax theorem for zero-sum games under bounded payoff uncertainty

The celebrated von Neumann minimax theorem is a fundamental theorem in two-person zero-sum games. In this paper, we present a generalization of the von Neumann minimax theorem, called robust von Neumann minimax theorem, in the face of data uncertainty in the payoff matrix via robust optimization approach. We establish that the robust von Neumann minimax theorem is guaranteed for various classes of bounded uncertainties, including the matrix 1-norm uncertainty, the rank-1 uncertainty and the columnwise affine parameter uncertainty.     

Well-balanced central finite volume methods for the Ripa system

We propose a new well-balanced central finite volume scheme for the Ripa system both in one and two space dimensions. The Ripa system is a nonhomogeneous hyperbolic system with a non-zero source term that is obtained from the shallow water equations system by incorporating horizontal temperature gradients. The proposed numerical scheme is a second-order accurate finite volume method that evolves a non-oscillatory numerical solution on a single grid, avoids the process of solving Riemann problems arising at the cell interfaces, and follows a well-balanced discretization that ensures the steady state requirement by discretizing the geometrical source term according to the discretization of the flux terms. Furthermore the proposed scheme mimics the surface gradient method and discretizes the water height according to the discretization of the water level. The proposed scheme is then applied and classical one and two-dimensional Ripa problems with flat or variable bottom topographies are successfully solved. The obtained numerical results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potential and efficiency of the proposed method.