CCD摄像机的误差及其检校

在利用面阵CCD摄像机进行摄影测量和检测的系统中,CCD摄像机所产生的误差是系统的主要误差,这种误差是在图像输入的过程中产生的。CCD摄像机的误差一般分光学误差、机械误差和电学误差。在摄像机光学镜头与CCD器件质量比较好的情况下,其主要表现是电学误差,重点讨论电学误差及其检测。     

A B3LYP study on counterpoise-corrected geometry optimizations for hydrated complexes of [K(H2O)n] and [Na(H2O)n]

We report the basis set dependencies and the basis set superposition errors for the hydrated complexes of K⁺ and Na⁺ ions in relation to the recent studies of the KcsA potassium channel. The basis set superposition errors are estimated by the geometry optimizations at the counterpoise-corrected B3LYP level. The counterpoise optimizations alter the hydration distances by about 0.02–0.03 Å. The enthalpies and free energies for K⁺ + n(H₂O) → [K(H₂O)_n]⁺ and Na⁺ + n(H₂O) → [Na(H₂O)_n]⁺ (n = 1–6) are compared between the theoretical and experimental values. The results show that the addition of diffuse functions to K, Na, and O species are effective. However, it is also found that the counterpoise corrections using diffuse functions work so as to underestimate the free energies for the complexes with increasing the hydration number. The stabilization energies in aqueous solution are larger for a Na⁺ ion than for a K⁺ ion, suggesting the contributions of their dehydration processes to the ion selectivity of the KcsA potassium channel. The changes in coordination distance between the isolated [K(H₂O)₈]⁺ and the [K(H₂O)₈]⁺ in the KcsA potassium channel indicate the importance of hydrogen bondings between the first hydration shell and the outer hydration shells.     

DFT study on the intermolecular interactions between Aun (n = 2–4) and thymine

Density functional B3LYP method with 6-31++G** basis set is applied to optimize the geometries of the luteolin, water and luteolin–(H₂O)_n complexes. The vibrational frequencies are also studied at the same level to analyze these complexes. We obtained four steady luteolin–H₂O, nine steady luteolin–(H₂O)₂ and ten steady luteolin–(H₂O)₃, respectively. Theories of atoms in molecules (AIM) and natural bond orbital (NBO) are used to investigate the hydrogen bonds involved in all the systems. The interaction energies of all the complexes corrected by basis set superposition error, are within −13.7 to −82.5 kJ/mol. The strong hydrogen bonding mainly contribute to the interaction energies, Natural bond orbital analysis is performed to reveal the origin of the interaction. All calculations also indicate that there are strong hydrogen bonding interactions in luteolin–(H₂O)_n complexes. The OH stretching modes of complexes are red-shifted relative to those of the monomer.     

On the p-version approximation in the boundary element method for a variational inequality of the second kind modelling unilateral contact and given friction

In this paper we complement recent work of Maischak and Stephan on adaptive hp-versions of the BEM for unilateral Signorini problems, respectively on FEM-BEM coupling in its h-version for a nonlinear transmission problem modelling Coulomb friction contact. Here we focus on the boundary element method in its p-version to treat a scalar variational inequality of the second kind that models unilateral contact and Coulomb friction in elasticity together. This leads to a nonconforming discretization scheme. In contrast to the work cited above and to a related paper of Guediri on a boundary variational inequality of the second kind modelling friction we take the quadrature error of the friction functional into account of the error analysis. At first without any regularity assumptions, we prove convergence of the BEM Galerkin approximation in the energy norm. Then under mild regularity assumptions, we establish an a priori error estimate that is based on a novel Céa–Falk lemma for abstract variational inequalities of the second kind.     

Local linear regression for data with AR errors

In many statistical applications, data are collected over time, and they are likely correlated. In this paper, we investigate how to incorporate the correlation information into the local linear regression. Under the assumption that the error process is an auto-regressive process, a new estimation procedure is proposed for the nonparametric regression by using local linear regression method and the profile least squares techniques. We further propose the SCAD penalized profile least squares method to determine the order of auto-regressive process. Extensive Monte Carlo simulation studies are conducted to examine the finite sample performance of the proposed procedure, and to compare the performance of the proposed procedures with the existing one. From our empirical studies, the newly proposed procedures can dramatically improve the accuracy of naive local linear regression with working-independent error structure. We illustrate the proposed methodology by an analysis of real data set.     

Tracking error: a multistage portfolio model

We study multistage tracking error problems. Different tracking error measures, commonly used in static models, are discussed as well as some problems which arise when we move from static to dynamic models. We are interested in dynamically replicating a benchmark using only a small subset of assets, considering transaction costs due to rebalancing and introducing a liquidity component in the portfolio. We formulate and solve a multistage tracking error model in a stochastic programming framework. We numerically test our model by dynamically replicating the MSCI Euro index. We consider an increasing number of scenarios and assets and show the superior performance of the dynamically optimized tracking portfolio over static strategies.     

Interpolation and rates of convergence for a class of neural networks

This paper presents a type of feedforward neural networks (FNNs), which can be used to approximately interpolate, with arbitrary precision, any set of distinct data in multidimensional Euclidean spaces. They can also uniformly approximate any continuous functions of one variable or two variables. By using the modulus of continuity of function as metric, the rates of convergence of approximate interpolation networks are estimated, and two Jackson-type inequalities are established.     

On dependence of dynamical structure of numerical solutions of fluid simulations on forcibly added randomness

In the present paper, the dependencies of the numerical results of fluid simulations on forcibly added randomness are discussed. The incompressible Navier-Stokes equations and the continuity equation are solved numerically by using the MAC (Maker-And-Cell) method and implicit temporal scheme. The model adopted in the present study is a flow around a two-dimensional circular cylinder and the Reynolds number is 1500. The randomness which is given by using the pseudo-random number is forcibly added in the time marching step of the discretized Navier-Stokes equations. Dependencies of the averaged structure of asymptotic numerical solutions on the randomness are discussed. Furthermore, the dependence of the qualitative structure of the asymptotic solution of each sample calculation on the amplitude of randomness is also studied. It is clarified that forcibly added random errors may cover the nonlinear errors which make the system unstable.     

Superconvergence of the - version of the finite element method in one dimension

In this paper, we investigate the superconvergence properties of the h-p version of the finite element method (FEM) for two-point boundary value problems. A postprocessing technique for the h-p finite element approximation is analyzed. The analysis shows that the postprocess improves the order of convergence. Furthermore, we obtain asymptotically exact a posteriori error estimators based on the postprocessing results. Numerical examples are included to illustrate the theoretical analysis.