Inclusion isotonicity of circular complex centered forms

This paper presents a proof for the fact that the circular complex centered form is inclusion isotone for arbitrary analytic functions.     

Variational principles and convergence of finite element approximations of a holonomic elastic-plastic problem

Summary It is shown that a boundary-value problem based on a holonomic elastic-plastic constitutive law may be formulated equivalently as a variational inequality of the second kind. A regularised form of the problem is analysed, and finite element approximations are considered. It is shown that solutions based on finite element approximation of the regularised problem converge.     

Arbitrage possibilities in Bessel processes and their relations to local martingales

Summary We show that, if we allow general admissible integrands as trading strategies, the three dimensional Bessel process, Bes³, admits arbitrage possibilities. This is in contrast with the fact that the inverse process is a local martingale and hence is arbitrage free. This leads to some economic interpretation for the analysis of the property of arbitrage in foreign exchange rates. This notion (relative to general admissible integrands) does depend on the fact, which of the two currencies under consideration is chosen as numéraire. The results rely on a general construction of strictly positive local martingales. The construction is related to the Föllmer measure of a positive super-martingale.Part of this research was supported by the European Community Stimulation Plan for Economic Science contract Number SPES-CT91-0089     

Efficient nonparametric estimation of distribution density in the basis of algebraic polynomials

A nonparametric estimatef ^* of an unknown distribution densityf W is called locally minimax iff it is minimax for all not too small neighborhoodsW _g ,g W, simultaneously, whereW is some dense subset ofW. Radaviius and Rudzkis proved the existence of such an estimate under some general conditions. However, the construction of the estimate is rather complicated. In this paper, a new estimate is proposed. This estimate is locally minimax under some additional assumptions which usually hold for orthobases of algebraic polynomial and is almost as simple as the linear projective estimate. Thus, it takes a form convenient for the construction of an adaptive estimator, which does not usea-priori information about the smoothness of the density. The adaptive estimation problem is briefly discussed and an unknown density fitting by Jacobi polynomials is investigated more explicitly.     

Arbitrariness of the general solution and symmetries

The computation of a number of arbitrary functions in the general solution is briefly reviewed. The results are used to study normal systems and their symmetry reduction. We discuss the treatment of gauge systems, especially the analysis of gauge fixing conditions. As examples, the Yang-Mills equations with the Lorentz gauge and Einstein's vacuum field equations with harmonic coordinates are considered.     

Numerical solution of delay differential equations by uniform corrections to an implicit Runge-Kutta method

Summary In this paper we develop a class of numerical methods to approximate the solutions of delay differential equations. They are essentially based on a modified version, in a predictor-corrector mode, of the one-step collocation method atn Gaussian points. These methods, applied to ODE's, provide a continuous approximate solution which is accurate of order 2n at the nodes and of ordern+1 uniformly in the whole interval. In order to extend the methods to delay differential equations, the uniform accuracy is raised to the order 2n by some a posteriori corrections. Numerical tests and comparisons with other methods are made on real-life problems.This work was supported by CNR within the Progetto Finalizzato Informatica-Sottopr. P1-SOFMAT     

Pointwise consistency of the hermite series density estimate

The Hermite series estimate of a density f?L_p, p > 1, convergessin the mean square to f (x) for almost all x? |R, ifN (n) → ∞ and N (n) / n² → ) as n → ∞, where N is the number of the Hermite functions in the estimate while n is the number of observations. Moreover, the mean square and weak consistency are equivalent. For m times differentiable densities, the mean squares convergence rate is O(n^?(2m?1)/2m). Results for complete convergence are also given.     

Betti numbers of 3-Sasakian manifolds

A vanishing theorem and constraints are given for the Betti numbers of compact 3-Sasakian manifolds.     

Laser-based photoacoustic ammonia sensors for industrial applications

An industrial trace-ammonia sensor based on photoacoustic spectroscopy and CO₂ lasers has been developed for measuring ammonia with a 1σ detection limit of 220 parts-per-trillion (ppt) in an integration time of 30 s. The instrument response time for measuring ammonia was 200 s, limited by adsorption effects due to the polar nature of ammonia. The minimum detectable fractional absorbance was 2.0×10^-7, and the minimum normalized detectable absorption coefficient for this system was 2.4×10^-7 W cm^-1/z. The 9R(30) transition of the CO₂ laser at 9.22 μm with 2 W of output power was used to probe the strong sR(5,K) multiplet of ammonia at the same wavelength. This sensor was demonstrated with an optically multiplexed configuration for simultaneous measurement in four cells. Received: 3 April 2002 / Revised version: 31 May 2002 / Published online: 21 August 2002 RID="*" ID="*"Corresponding author. Fax: +1-310/458-0171, E-mail: webber@pranalytica.com