On a discrimination problem for a class of stochastic processes with ordered first‐passage times

Consider the Bayes problem in which one has to discriminate if the random unknown initial state of a stochastic process is distributed according to either of two preassigned distributions, on the base of the observation of the first‐passage time of the process through 0. For processes whose first‐passage times to state 0 are increasing in the initial state according to the likelihood ratio order, such problem is solved by determining the Bayes decision function and the corresponding Bayes error. The special case of fixed initial values including a family of first‐passage times with proportional reversed hazard functions is then studied. Finally, various applications to birth‐and‐death and to diffusion processes are discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

Mixed Partitions of Projective Geometries

Starting from a linear collineation of PG(2n–1,q) suitably constructed from a Singer cycle of GL(n,q), we prove the existence of a partition of PG(2n–1,q) consisting of two (n–1)-subspaces and caps, all having size (qⁿ–1)/(q–1) or (qⁿ–1)/(q+1) according as n is odd or even respectively. Similar partitions of quadrics or hermitian varieties into two maximal totally isotropic subspaces and caps of equal size are also obtained. We finally consider the possibility of partitioning the Segre variety of PG(8,q) into caps of size q²+q+1 which are Veronese surfaces.     

Resonance and non-resonance in a problem of boundedness

This paper studies the existence of bounded solutions of a forced non-linear differential equation of arbitrary order. Necessary and sufficient conditions for the existence of such solutions are obtained. These results are inspired by classical results on the periodic problem, both in the resonant and non-resonant cases.

     

Experimental Study of Natural Convection from Electrically Heated Vertical Cylinders Immersed in Air

Abstract

An experimental study of laminar steady-state natural convection heat transfer from electrically heated vertical cylinders immersed in air has been undertaken. Three stainless steel (316 SS) test sections of different slenderness ratios were employed. Surface temperature profiles along the vertical cylinders were obtained using miniature thermocouples when the cylinders were heated with different power levels resulting in different total wall heat fluxes. After the mandatory corrections for the radiation heat fluxes were made, three correlation equations relating the local Nusselt number Nu_y with the local modified Rayleigh number Ra^* _y and the position-to-cylinder diameter y/d were developed. The correlation equations are valid for Ra^* _y ≤ 2 × 10¹².     

Some results on the proportional reversed hazards model

The proportional reversed hazards model consists in describing random failure times by a family {[F(x)]^θ, θ>0} of distribution functions, where F(x) is a baseline distribution function. We show various results on this model related to some topics in reliability theory, including ageing notions of random lifetimes, comparisons based on stochastic orders, and relative ageing of distributions.     

Examination of time-reversal acoustics in shallow water and applications to noncoherent underwater communications

The shallow water acoustic communication channel is characterized by strong signal degradation caused by multipath propagation and high spatial and temporal variability of the channel conditions. At the receiver, multipath propagation causes intersymbol interference and is considered the most important of the channel distortions. This paper examines the application of time-reversal acoustic (TRA) arrays, i.e., phase-conjugated arrays (PCAs), that generate a spatio-temporal focus of acoustic energy at the receiver location, eliminating distortions introduced by channel propagation. This technique is self-adaptive and automatically compensates for environmental effects and array imperfections without the need to explicitly characterize the environment. An attempt is made to characterize the influences of a PCA design on its focusing properties with particular attention given to applications in noncoherent underwater acoustic communication systems. Due to the PCA spatial diversity focusing properties, PC arrays may have an important role in an acoustic local area network. Each array is able to simultaneously transmit different messages that will focus only at the destination receiver node.     

Optimal Shape Design for Metal Forming Problems by the Finite Element Method

In this work, a method for calculation of the optimal shapes of axisymmetrical converging dies by the finite element method is presented. The shape optimization problem considered in this paper is to find the best shape of the die such that the flow rate will be uniform at the die exit.The optimization problem is to minimize an objective function by varying a part of boundary (ie: the shape of die) subject to constraints imposed by the metal forming problem. In this method, the B-spline functions allow us to determine the shape of the die, using its control points as design variables. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Tensor Approximation of Generalized Correlated Diffusions and Functional Copula Operators

In this paper we develop a class of applied probabilistic continuous time but discretized state space decompositions of the characterization of a multivariate generalized diffusion process. This decomposition is novel and, in particular, it allows one to construct families of mimicking classes of processes for such continuous state and continuous time diffusions in the form of a discrete state space but continuous time Markov chain representation. Furthermore, we present this novel decomposition and study its discretization properties from several perspectives. This class of decomposition both brings insight into understanding locally in the state space the induced dependence structures from the generalized diffusion process as well as admitting computationally efficient representations in order to evaluate functionals of generalized multivariate diffusion processes, which is based on a simple rank one tensor approximation of the exact representation. In particular, we investigate aspects of semimartingale decompositions, approximation and the martingale representation for multidimensional correlated Markov processes. A new interpretation of the dependence among processes is given using the martingale approach. We show that it is possible to represent, in both continuous and discrete space, that a multidimensional correlated generalized diffusion is a linear combination of processes originated from the decomposition of the starting multidimensional semimartingale. This result not only reconciles with the existing theory of diffusion approximations and decompositions, but defines the general representation of infinitesimal generators for both multidimensional generalized diffusions and, as we will demonstrate, also for the specification of copula density dependence structures. This new result provides immediate representation of the approximate weak solution for correlated stochastic differential equations. Finally, we demonstrate desirable convergence results for the proposed multidimensional semimartingales decomposition approximations.     

Influence of loudspeaker directivity and measurement geometry on direct acoustic levels over façades for acoustic insulation tests with the International Standard ISO 140-5

The International Standard ISO 140-5 on field measurements of airborne sound insulation of façades establishes that the directivity of the measurement loudspeaker should be such that the variation in the local direct sound pressure level (ΔSPL) on the sample is ΔSPL < 5 dB (or ΔSPL < 10 dB for large façades). This condition is usually not very easy to accomplish nor is it easy to verify whether the loudspeaker produces such a uniform level. Direct sound pressure levels on the ISO standard façade essentially depend on the distance and directivity of the loudspeaker used. This paper presents a comprehensive analysis of the test geometry for measuring sound insulation and explains how the loudspeaker directivity, combined with distance, affects the acoustic level distribution on the façade.The first sections of the paper are focused on analysing the measurement geometry and its influence on the direct acoustic level variations on the façade. The most favourable and least favourable positions to minimise these direct acoustic level differences are found, and the angles covered by the façade in the reference system of the loudspeaker are also determined. Then, the maximum dimensions of the façade that meet the conditions of the ISO 140-5 standard are obtained for the ideal omnidirectional sound source and the piston radiating in an infinite baffle, which is chosen as the typical radiation pattern for loudspeakers.Finally, a complete study of the behaviour of different loudspeaker radiation models (such as those usually utilised in the ISO 140-5 measurements) is performed, comparing their radiation maps on the façade for searching their maximum dimensions and the most appropriate radiation configurations.     

Procedure for verification of sound source coverage over façades according to the International Standard ISO 140–5

This paper presents a new verification procedure for sound source coverage according to ISO 140–5 requirements. The ISO 140–5 standard applies to the measurement of façade insulation and requires a sound source able to achieve a sufficiently uniform sound field in free field conditions on the façade under study. The proposed method involves the electroacoustic characterisation of the sound source in laboratory free field conditions (anechoic room) and the subsequent prediction by computer simulation of the sound free field radiated on a rectangular surface equal in size to the façade being measured. The loudspeaker is characterised in an anechoic room under laboratory controlled conditions, carefully measuring directivity, and then a computer model is designed to calculate the acoustic free field coverage for different loudspeaker positions and façade sizes. For each sound source position, the method provides the maximum direct acoustic level differences on a façade specimen and therefore determines whether the loudspeaker verifies the maximum allowed level difference of 5 dB (or 10 dB for façade dimensions greater than 5 m) required by the ISO standard. Additionally, the maximum horizontal dimension of the façade meeting the standard is calculated and provided for each sound source position, both with the 5 dB and 10 dB criteria. In the last section of the paper, the proposed procedure is compared with another method used by the authors in the past to achieve the same purpose: in situ outdoor measurements attempting to recreate free field conditions. From this comparison, it is concluded that the proposed method is able to reproduce the actual measurements with high accuracy, for example, the ground reflection effect, at least at low frequencies, which is difficult to avoid in the outdoor measurement method, and it is fully eliminated with the proposed method to achieve the free field requisite.