On the convergence of Newton's method when estimating higher dimensional parameters

In this paper, we consider the estimation of a parameter of interest where the estimator is one of the possibly several solutions of a set of nonlinear empirical equations. Since Newton's method is often used in such a setting to obtain a solution, it is important to know whether the so obtained iteration converges to the locally unique consistent root to the aforementioned parameter of interest. Under some conditions, we show that this is eventually the case when starting the iteration from within a ball about the true parameter whose size does not depend on n. Any preliminary almost surely consistent estimate will eventually lie in such a ball and therefore provides a suitable starting point for large enough n. As examples, we will apply our results in the context of M-estimates, kernel density estimates, as well as minimum distance estimates.     

Asymptotic stability of semigroups associated with linear weak dissipative systems with memory

We study the asymptotic behavior of the solutions of a class of linear dissipative integral differential equations. We show in the abstract setting a necessary and sufficient condition to get an exponential decay of the solution. In the case of the lack of exponential decay, we find the polynomial rate of decay of the solution. Some examples are given.     

Algebraically Special Gravitational Fields with the Cosmological Constant and Energy-Momentum Tensor of Electromagnetic Radiation

A class of rigorous solutions of the Einstein–Maxwell equations is obtained within the Newman–Penrose formalism for algebraically special gravitational fields with the cosmological constant and energy-momentum tensor of electromagnetic radiation given that the photon flux specifying electromagnetic radiation determines isotropic-geodesic congruence. Designations within the Newman–Penrose formalism and numbers of formulas in references are the same as in [1].     

Study of archaeological ceramics by total-reflection X-ray fluorescence spectrometry: Semi-quantitative approach

Total-reflection X-ray fluorescence spectrometry has been compared with Instrumental Neutron Activation Analysis in order to test its potential application to the study of archaeological ceramics in the archaeometric field. Two direct solid non-chemical sample preparation procedures have been checked: solid sedimentation and solid chemical homogenization. For sedimentation procedure, total-reflection X-ray fluorescence allows the analysis of the elemental composition with respect to the size fraction but not the average evaluation of the composition. For solid chemical homogenization procedure, total-reflection X-ray fluorescence provides precise (from 0.8% to 27% of coefficient of variation) and accurate results (from 91% to 110% of recovery) for 15 elements (Cr, Hf, Ni, Rb, Al, Ba, Ca, K, Mn, Ti, V, Cu, Ga, Y and Fe) with an easy sample preparation process of the solid clay and without previous chemical treatment. The influence of the particle sizes has been checked by total-reflection X-ray fluorescence sample angle scans and anomalous behaviors have been found for three additional detected elements: As, Sr and Zn, which can be attributed to interference effects of the mineral grain sizes of their associated chemical phases in the total-reflection X-ray fluorescence interference region. The solid chemical homogenization procedure produces data useful for archaeological interpretation, which is briefly illustrated by a case-study. Finally, the decantation procedure data can be also useful for size chemical speciation and, consequently, for alternative environmental total-reflection X-ray fluorescence applications.     

Photothermal techniques applied to the determination of the water vapor diffusion coefficient and thermal diffusivity of edible films.

Water vapor diffusion coefficient (WVDC) and thermal diffusivity (alpha) were determined in gelatin-starch films through photothermal techniques. The effect of different variables in the elaboration of these films, such as starch and glycerol concentrations and pH, were evaluated through the response surface methodology. The results indicated that an increase in the glycerol concentration and pH favored the WVDC of the films. On the other hand, alpha was influenced principally by the starch content and pH of the film-forming solution. The minimum alpha value was 4.5 x 10(-4) cm2/s, which is compared with alpha values reported for commercial synthetic polymers.     

Monstrous Branes

 We study D-branes in the bosonic closed string theory whose automorphism group is the Bimonster group (the wreath product of the Monster simple group with ℤ₂). We give a complete classification of D-branes preserving the chiral subalgebra of Monster invariants and show that they transform in a representation of the Bimonster. Our results apply more generally to self-dual conformal field theories which admit the action of a compact Lie group on both the left- and right-moving sectors. Received: 20 February 2002 / Accepted: 17 August 2002 Published online: 19 December 2002 Communicated by R.H. Dijkgraaf     

不等式约束优化问题的一个势函数

基于Carroll(1961)建立的罚函数，本文给出了不等式约束优化问题的一个势函数，并且讨论了该函数的性质．最后证明了在此基础上建立的对偶算法具有Q-线性收敛性．