Asymptotic optimality of the bayes estimator in models differentiable in quadratic mean

We study the asymptotic properties of the Bayes estimator in models differentiable in quadratic mean (DQM) in the case of independent and identically distributed observations. The goal is to define weak assumptions on the model under which this estimator is asymptotically efficient, regular, and asymptotically of minimal risk. The results of the paper are applied to models based on a mixture distribution, the Cauchy distribution with location and scale parameter, and the Weibull distribution. Bibliography: 10 titles. Published in Zapiski Nauchnykh Seminarov POMI, Vol. 328, 2005, pp. 114–146.     

中医药抗衰老与微量元素的相关性

重点讨论了各类抗衰老中药和微量元素的相关性，探讨了中医中药衰老和现代微量元素的关系，为人类健康防病抗衰、益寿延年做出新的贡献。     

Hydrothermal synthesis,thermal decomposition and optical properties of Fe2F5(H2O)(Htaz)(taz)(Hdma)

Crystal structure of Fe₂F₅(H₂O)(Htaz)(taz)(Hdma) which crystallizes in the triclinic system space group $\text{P}\overline{1}$ with unit cell parameters a = 8.8392(5) Å, b = 9.1948(5) Å, c = 9.5877(5) Å, α = 82.070(3)°, β = 63.699(3)°, γ = 89.202(3)°, Z = 2, and V = 690.91(7) ų, was synthesized under hydrothermal conditions at 393 K for 72 h, by a mixture of FeF₂/FeF₃, 1,2,4-triazole molecule (Htaz), and hydrofluoric acid solution (HF 4%) in dimethylformamide solvent (DMF). The main feature of this material is the coexistence of two oxidation states for iron atoms (Fe²⁺, Fe³⁺) in the unit cell, which associate by opposite fluorine corners of FeF₅N and FeF₂N₄ octahedra, and/or triazole molecule which originates the 2D produces material. The structure determination, performed from single crystal X-ray diffraction data, lead to the R₁/_WR₂ reliability factors 0.031/0.087. Thermal stability studies (TG/DTG/DTA) show that the decomposition provides in the temperature range 473–773 K and no mass loss was detected before 473 K. Mass spectrometry (MS) has been used. The optical absorption of the solid was measured at the corresponding λ_max using UV–vis diffuse-reflectance spectrum.     

Maximum likelihood estimation for noncausal autoregressive processes

We discuss a maximum likelihood procedure for estimating parameters in possibly noncausal autoregressive processes driven by i.i.d. non-Gaussian noise. Under appropriate conditions, estimates of the parameters that are solutions to the likelihood equations exist and are asymptotically normal. The estimation procedure is illustrated with a simulation study for AR(2) processes.     

A model-based inverse method for positioning scatterers in a cladded component inspected by ultrasonic waves

Nondestructive methods aim at detecting, locating and identifying defects. Inversion of ultrasonic measurements obtained by inspecting a steel component of regular geometry with an immersed transducer leads to accurate location of defects. When the component is cladded, the irregular geometry of the surface and the anisotropic nature of the cladding material lead to aberrations of the radiated field (e.g., beam distortions, splitting and defocusing, these varying with the transducer scanning position). As a consequence, defect location may be inaccurate and defects (e.g., cracks) sizing impossible. In the present paper, a model-based inverse method is developed to solve this problem. It relies on the time-dependent simulation of ultrasonic propagation in this material of complex geometry and structure, in order to determine a set of probable positions for the defect at the origin of the measured ultrasonic echo-structure. The most probable position is determined by minimizing a cost-function of likeness between the simulated and measured ultrasonic images. The overall scheme shall generally apply to inverse measured ultrasonic echo-structures as soon as the simulation of the forward problem is tractable. To validate the method, examples of application are given dealing with actual measurements obtained in the real configuration of pressure vessel inspection.     

CONVERGENCE OF NUMERICAL SCHEMES FOR A CONSERVATION EQUATION WITH CONVECTION AND DEGENERATE DIFFUSION

The approximation of problems with linear convection and degenerate nonlinear difFusion,which arise in the framework of the transport of energy in porous media with thermodynamic transitions,is done usingθ-scheme based on the centred gradient discretisation method.The convergence of the numerical scheme is proved,although the test functions which can be chosen are restricted by the weak regularity hypotheses on the convection field,owing to the application of a discrete Gronwall lemma and a general result for the time translate in the gradient discretisation setting.Some numerical examples,using both the Control Volume Finite Element method and the Vertex Approximate Gradient scheme,show the role ofθfor stabilising the scheme.     

Study and validity of 13C stable carbon isotopic ratio analysis by mass spectrometry and 2H site-specific natural isotopic fractionation by nuclear magnetic resonance isotopic measurements to characterize and control the authenticity of honey

Honey samples were analyzed by stable carbon isotopic ratio analysis by mass spectrometry (SCIRA-MS) and site-specific natural isotopic fractionation measured by nuclear magnetic resonance (SNIF-NMR) to first determine their potentials for characterizing the substance and then to combat adulteration. Honey samples from several geographic and botanical origins were analyzed. The δ¹³C parameter was not significant for characterizing an origin, while the (D/H)_I ratio could be used to differentiate certain single-flower varieties. Application of the official control method of adding a C₄ syrup (AOAC official method 998.12) to our authentic samples revealed anomalies resulting from SCIRA indices that were more negative than −1‰ (permil). A filtration step was added to the experimental procedure and provided results that were compliant with the natural origin of our honey samples. In addition, spiking with a C₄ syrup could be detected starting at 9-10%. The use of SNIF-NMR is limited by the detection of a syrup spike starting only at 20%, which is far from satisfying.     

Modeling of ultrasonic fields radiated by contact transducer in a component of irregular surface

The wedge of a contact transducer is imperfectly coupled to a component of irregular surface. A volume between the wedge and the component (filled by water or oil used as a coupling) is created that fundamentally modifies transducer radiation behavior. As a result, phenomena like beam spreading, skewing and splitting, generation of unwanted contributions that possibly lead to false alarms may occur. At first, the paper describes a model to account for the main effects observable in such a situation. The model is based on a matrix method which describes the behavior of transient elementary contributions as the variation of a pencil propagating into homogeneous regions (namely, the wedge, the coupling and the component) and through interfaces between them (refraction and reflection). The elementary contributions accounting for the finite size of the transducer are summed to predict transducer diffraction effects. In a second part, predicted fields are compared to measured results. The comparison concerns particle velocity fields measurements at the surface opposite to that (irregular) on which the transducer acts. The very good agreement obtained proves the validity of our approach.     

The formulae and algorithms for Lagrange-power basis transformation and Lagrange-Newton transformation

The interpolation polynomials based on Lagrange, Newton and power basis play important roles in applied mathematics, computing method and many other emerging applications. In this paper, we present some coordinate transformation formulae and algorithms as demonstrated below. Firstly, we put forward the formulae of the Lagrange-power basis transformation and its inverse transformation, and as a byproduct, we provide a new method to arrive at the inversion of the Vandermonde matrix. Secondly, we give the formulae of Lagrange-Newton transformation and its inverse transformation. Moreover, we construct related algorithms of Lagrange-power basis transformation, Lagrange-Newton transformation and their inverse transformations.     

An approximate maximum likelihood estimation for non-Gaussian non-minimum phase moving average processes

An approximate maximum likelihood procedure is proposed for the estimation of parameters in possibly nonminimum phase (noninvertible) moving average processes driven by independent and identically distributed non-Gaussian noise. Under appropriate conditions, parameter estimates that are solutions of likelihood-like equations are consistent and are asymptotically normal. A simulation study for MA(2) processes illustrates the estimation procedure.