Search results for "geometry."

Openness and Discreteness

2013

The aim of this chapter is to study conditions under which a mapping of finite distortion is open (maps open sets to open sets) and discrete (preimage of each point is a discrete set).

Complex objects classified by morphological shape analysis and elliptical Fourier descriptors

2005

This chapter deals with the classification of complex objects by morphological shape analysis and elliptical Fourier descriptors. An unsupervised method has been proposed to identify components with specific shapes by a simple edge detector and to classify them via the description of their contours. A particular application has been arranged in order to evaluate the goodness of this approach when discriminating between normal and pathological human megakaryocytes. Alterations in these cells can occur in many pathological processes and in such cases the pattern, size and shape of the cytoplasm and/or of the nucleus are extremely varied.

Gaussian plane and spherical means in separable Hilbert spaces

1982

Operator (Quasi-)Similarity, Quasi-Hermitian Operators and All that

2016

Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we consider the notions of similarity and quasi-similarity between operators and explore to what extent they preserve spectral properties. Then we study quasi-Hermitian operators, bounded or not, that is, operators that are quasi-similar to their adjoint and we discuss their application in pseudo-Hermitian quantum mechanics. Finally, we extend the analysis to operators in a partial inner product space (pip-space), in particular the scale of Hilbert space s generated by a single unbounded metric operator.

Predictive Model for Cut-Edge Corrosion of Galvanized Steels

2006

A numerical model for the electrochemical behavior of cut-edge of galvanized steels is proposed. Some experimental data of current densities above cut-edge immersed in a 0.03M NaCl solution have been measured, using a scanning vibrating electrode technique, and compared with some simulated ones. A good fit has been obtained. The model geometry has been modified by decreasing the electrolyte thickness in order to tend towards an atmospheric corrosion case; such situation that is not easily accessible by electrochemical studies. Three regions can be distinguished according to the efficiency of the galvanic coupling to protect steel.

High Resolution Coherent Raman Spectroscopy: Studies of Molecular Structures

1992

One of the main advantages of the non-linear coherent Raman techniques is the high resolution that can be achieved in rovibrational spectroscopy. Typically an instrumental function of the order of several thousandths of a wavenumber is routinely achieved in SRS or CARS experiments. Since the first recording of the stimulated Raman spectrum of 12CH4 in 1978 [1], numerous studies of molecules have been performed [2–8]. We have built a stimulated Raman experiment in Dijon in which particular attention has been paid to the frequency measurement of the Raman lines [9]. We will describe the application of our experiment to a wide variety of molecules over the last few years: linear molecules, sph…

Rectifiability and singular integrals

1995

Mappings of finite distortion: Reverse inequalities for the Jacobian

2007

Let f be a nonconstant mapping of finite distortion. We establish integrability results on 1/Jf by studying weights that satisfy a weak reverse Holder inequality where the associated constant can depend on the ball in question. Here Jf is the Jacobian determinant of f.

Computing Difficulties for Deriving Poverty Indices from Some Functional Forms of Lorenz Curves

2014

We examine three families of classical one-parameter functional forms for estimating a Lorenz curve: the power form (Pareto, elementary form), the exponential form (Gupta, elementary form) and fractional form (Rohde). For the first time, we systematically study these functions not for their ability to be estimated but on the point of view of the possibility of deriving poverty indices, which implies first determining the headcount ratio (i.e., the percentage of poor). We show that computing difficulties have been largely underestimated. Two forms, the most simple ones, pose no problem: the elementary power and exponential forms. However, the Pareto functional form poses problem with a restr…

Optimal control of the Schrödinger equation with two or three levels

2007

In this paper, we present how techniques of “control theory”, “sub-Riemannian geometry” and “singular Riemannian geometry” can be applied to some classical problems of quantum mechanics and yield improvements to some previous results.