Analytic hierarchy process for multi-sensor data fusion based on belief function theory

Multi-sensor data fusion is an evolving technology whereby data from multiple sensor inputs are processed and combined. The data derived from multiple sensors can, however, be uncertain, imperfect, and conflicting. The present study is undertaken to help contribute to the continuous search for viable approaches to overcome the problems associated with data conflict and imperfection. Sensor readings, represented by belief functions, have to be fused according to their corresponding weights. Previous studies have often estimated the weights of sensor readings based on a single criterion. Mono-criteria approaches for the assessment of sensor reading weights are, however, often unreliable and inadequate for the reflection of reality. Accordingly, this work opts for the use of a multi-criteria decision aid. A modified Analytical Hierarchy Process (AHP) that incorporates several criteria is proposed to determine the weights of a sensor reading set. The approach relies on the automation of pairwise comparisons to eliminate subjectivity and reduce inconsistency. It assesses the weight of each sensor reading, and fuses the weighed readings obtained using a modified average combination rule. The efficiency of this approach is evaluated in a target recognition context. Several tests, sensitivity analysis, and comparisons with other approaches available in the literature are described.     

B-Fredholm Properties of Closed Invertible Operators

In this paper, we study B-Fredholm spectral properties of an invertible closed linear operator in relation with the B-Fredholm spectral properties of its bounded inverse. Precisely, for such operator, we characterize its B-Fredholm spectrum and other related spectra in terms of the corresponding spectra of its bounded inverse. As an application, we show that every normal operator with nonempty resolvent set, in particular self-adjoint Schrödinger operators, satisfies generalized Weyl’s theorem.

     

On a transport operator arising in growing cell populations II. Cauchy problem

This paper deals with Rotenberg's models of cell populations with general boundary conditions. It is shown, first, that the associated Cauchy problem is governed by a C₀‐semigroup. Second, we have proved that if the boundary operator is positive, the transport semigroup is irreducible. And finally, a spectral decomposition of the solution into an asymptotic term was derived. Copyright © 2004 John Wiley & Sons, Ltd.     

Fredholm Operators and Riesz Theory for Polynomially Compact Operators

In this article, we give a characterization of a class of bounded Fredholm operators on a Banach space which is developed to present some general existence results of the operators equation of the second kind. The obtained results are used to describe the Riesz–Schauder theory of compact operators in the more general setting of polynomially compact operators.     

Sur quelques Théorémes globaux en geometrie finslérienne

Résumè Le travail suivant établit des théorèmes globaux relatifs aux variétes finslériennes completes dont le tenseur de courbure vérifie certaines hypothèses. Le théorème de Hopf-Rinow est d’abord démontrè, puis au moyen du calcul variationnel, on établit une géneralisation des théoremes de Myers, de Cartan et de L. W. Green.     

Generalized qd algorithm and Markov–Bernstein inequalities for Jacobi weight

The Markov–Bernstein inequalities for the Jacobi measure remained to be studied in detail. Indeed the tools used for obtaining lower and upper bounds of the constant which appear in these inequalities, did not work, since it is linked with the smallest eigenvalue of a five diagonal positive definite symmetric matrix. The aim of this paper is to generalize the qd algorithm for positive definite symmetric band matrices and to give the mean to expand the determinant of a five diagonal symmetric matrix. After that these new tools are applied to the problem to produce effective lower and upper bounds of the Markov–Bernstein constant in the Jacobi case. In the last part we com pare, in the particular case of the Gegenbauer measure, the lower and upper bounds which can be deduced from this paper, with those given in Draux and Elhami (Comput J Appl Math 106:203–243, 1999) and Draux (Numer Algor 24:31–58, 2000).      

Essential spectra of some matrix operators and application to two-group transport operators with general boundary conditions

In this article we investigate the essential spectra of a 2×2 block operator matrix on a Banach space. Furthermore, we apply the obtained results to determine the essential spectra of two-group transport operators with general boundary conditions in the Banach space Lp([−a,a]×[−1,1])×Lp([−a,a]×[−1,1]), a>0.     

On the essential spectra of coupled operators matrix and application

We define an abstract setting to treat essential spectra of unbounded coupled operator matrix. We prove a well‐posedness result and develop a spectral theory which also allows us to prove an amelioration to many earlier works. We point out that a concrete example from integro‐differential equation fit into this abstract framework involving a general class of regular operator in L₁ spaces.     

Polysiloxane-Diamine Modified Gel as Precursor to Crystalline/Amorphous Si3N4

New hybrid organic-inorganic materials are prepared by reaction of polymethylhydrosiloxane (PMHS) with aniline (An) or 4,4-diamino,diphenyl methane (APM) through a condensation between NH₂-terminated amines and Si—H groups. The obtained modified-polysiloxane is a liquid polymer (PS-An) in the first case and a cross-linked gel (PS-APM) in the second one. The chemical structures of PS-An and PS-APM were investigated by ²⁹Si nuclear magnetic resonance and were proved to be formed of created (Si—O)₂(Me)Si—N(H)— and unreacted (Si—O)₂(Me)Si—H sites. The pyrolysis of the diamine-based gel has been carried out in N₂ atmosphere up to 1450°C. FTIR, ²⁹Si MAS NMR and X-ray diffraction have shown that Si—O and Si—C bonds are totally broken during pyrolysis and that the final product is formed of crystalline and amorphous silicon nitride in the presence of a free carbon phase.