Banach空间中渐近非扩张映象具误差的强收敛定理

设E是一实的Banach空间,其范数是一致Gteaux可微的;D是E的一非空闭凸子集,设T:D→D是具有序列{k_n}[1,∞),lim_(n→∞) k_n=1的渐近非扩张映象.本文证明了,在一定条件下,由(1.3)和(1.5)式定义的具误差的迭代序列{x_n}强收敛于T的不动点.本文结果也推广和改进了最近一些人的最新结果.     

Orbit determination and time synchronization for a GEO/IGSO satellite navigation constellation with regional tracking network

Aiming at regional services,the space segment of COMPASS (Phase I) satellite navigation system is a constellation of Geostationary Earth Orbit (GEO),Inclined Geostationary Earth Orbit (IGSO) and Medium Earth Orbit (MEO) satellites.Precise orbit determination (POD) for the satellites is limited by the geographic distribution of regional tracking stations.Independent time synchronization (TS) system is developed to supplement the regional tracking network,and satellite clock errors and orbit data may be obtai...     

Error estimation in measuring strain fields with DIC on planar sheet metal specimens with a non-perpendicular camera alignment

The determination of strain fields based on displacement components obtained via 2D-DIC is subject to several errors that originate from various sources. In this contribution, we study the impact of a non-perpendicular camera alignment to a planar sheet metal specimen's surface. The errors are estimated in a numerical experiment. To this purpose, deformed images - that were obtained by imposing finite element (FE) displacement fields on an undeformed image - are numerically rotated for various Euler angles. It is shown that a 3D-DIC stereo configuration induces a substantial compensation for the introduced image-plane displacement gradients. However, higher strain accuracy and precision are obtained - up to the level of a perfect perpendicular alignment - in a proposed “rectified” 2D-DIC setup. This compensating technique gains benefit from both 2D-DIC (single camera view, basic amount of correlation runs, no cross-camera matching nor triangulation) and 3D-DIC (oblique angle compensation). Our conclusions are validated in a real experiment on SS304.     

60 Years of portfolio optimization: Practical challenges and current trends

The concepts of portfolio optimization and diversification have been instrumental in the development and understanding of financial markets and financial decision making. In light of the 60 year anniversary of Harry Markowitz’s paper “Portfolio Selection,” we review some of the approaches developed to address the challenges encountered when using portfolio optimization in practice, including the inclusion of transaction costs, portfolio management constraints, and the sensitivity to the estimates of expected returns and covariances. In addition, we selectively highlight some of the new trends and developments in the area such as diversification methods, risk-parity portfolios, the mixing of different sources of alpha, and practical multi-period portfolio optimization.     

A new high accuracy non-polynomial tension spline method for the solution of one dimensional wave equation in polar co-ordinates

In this paper, we propose a new three-level implicit nine point compact finite difference formulation of O(k² + h⁴) based on non-polynomial tension spline approximation in r-direction and finite difference approximation in t-direction for the numerical solution of one dimensional wave equation in polar co-ordinates. We describe the mathematical formulation procedure in details and also discuss the stability of the method. Numerical results are provided to justify the usefulness of the proposed method.     

Intramolecular basis set superposition errors

The effects of intramolecular basis set superposition errors are less well documented than the corresponding intermolecular effects. The intramolecular basis set superposition errors are examined, using the approach of Jensen, for several basis sets developed by Pople and his co‐workers, which are widely used in studies of larger molecules. Prototype calculations are reported for the ground state of the water molecule using both the matrix Hartree–Fock method and the many‐body perturbation expansion for the correlation energy taken through second order. A similar investigation is carried out for some of the correlation consistent basis sets published by Dunning and his collaborators. Specifically, the following aspects are investigated: (i) the magnitude of the intramolecular basis set superposition error, (ii) the nonadditivity of intramolecular counterpoise corrections when applied in a pairwise fashion, and (iii) the use of multiple “ghost” centers. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 282–292, 2001     

带反馈非对称信道的最优纠错编码

带反馈非对称信道的最优纠错编码等同于Ulam-Renyi问题的半谎搜索模型的最少提问次数qw(m).本文证明了qw(m)的取值分布具有非交叉性.借助于这一良好的分布特性,原始的确定最少提问次数精确值问题可以被简化为确定一个临界数问题并且这个临界数的存在性和唯一性得到了证明.同时本文也改进了Cicalese等人的结果,在更大的范围内明确地给出了最少提问次数qw(m)的精确值.     

Principal component analysis of urine metabolites detected by NMR and DESI–MS in patients with inborn errors of metabolism

Urine metabolic profiles of patients with inborn errors of metabolism were examined with nuclear magnetic resonance (NMR) and desorption electrospray ionization mass spectrometry (DESI-MS) methods. Spectra obtained from the study of urine samples from individual patients with argininosuccinic aciduria (ASA), classic homocystinuria (HCY), classic methylmalonic acidemia (MMA), maple syrup urine disease (MSUD), phenylketonuria (PKU) and type II tyrosinemia (TYRO) were compared with six control patient urine samples using principal component analysis (PCA). Target molecule spectra were identified from the loading plots of PCA output and compared with known metabolic profiles from the literature and metabolite databases. Results obtained from the two techniques were then correlated to obtain a common list of molecules associated with the different diseases and metabolic pathways. The combined approach discussed here may prove useful in the rapid screening of biological fluids from sick patients and may help to improve the understanding of these rare diseases.     

Analysis method of the effect of fabrication errors on a planar waveguide demultiplexer

The impact of fabrication errors on a planar waveguide demultiplexer is analyzed based on an analytical method. The explicit expression of the transfer function taking into account phase and amplitude errors is presented in order to analyze the loss and crosstalk of the demultiplexer caused by fabrication errors. A basic requirement for the demultiplexer with a certain crosstalk criterion can be easily obtained. Using an etched diffraction grating demultiplexer as an example, it is shown that the analytical results have a good agreement with results from a numerical method.     

Honest Importance Sampling With Multiple Markov Chains

Importance sampling is a classical Monte Carlo technique in which a random sample from one probability density, π₁, is used to estimate an expectation with respect to another, π. The importance sampling estimator is strongly consistent and, as long as two simple moment conditions are satisfied, it obeys a central limit theorem (CLT). Moreover, there is a simple consistent estimator for the asymptotic variance in the CLT, which makes for routine computation of standard errors. Importance sampling can also be used in the Markov chain Monte Carlo (MCMC) context. Indeed, if the random sample from π₁ is replaced by a Harris ergodic Markov chain with invariant density π₁, then the resulting estimator remains strongly consistent. There is a price to be paid, however, as the computation of standard errors becomes more complicated. First, the two simple moment conditions that guarantee a CLT in the iid case are not enough in the MCMC context. Second, even when a CLT does hold, the asymptotic variance has a complex form and is difficult to estimate consistently. In this article, we explain how to use regenerative simulation to overcome these problems. Actually, we consider a more general setup, where we assume that Markov chain samples from several probability densities, π₁, …, π_k, are available. We construct multiple-chain importance sampling estimators for which we obtain a CLT based on regeneration. We show that if the Markov chains converge to their respective target distributions at a geometric rate, then under moment conditions similar to those required in the iid case, the MCMC-based importance sampling estimator obeys a CLT. Furthermore, because the CLT is based on a regenerative process, there is a simple consistent estimator of the asymptotic variance. We illustrate the method with two applications in Bayesian sensitivity analysis. The first concerns one-way random effect models under different priors. The second involves Bayesian variable selection in linear regression, and for this application, importance sampling based on multiple chains enables an empirical Bayes approach to variable selection.