Search results for " Geometry."

Formation, Structural Characterization, and Calculated NMR Chemical Shifts of Selenium-Nitrogen Compounds from SeCl4 and ArNHLi (Ar = supermesityl, m…

2004

Supermesityl selenium diimide [Se{N(C6H2tBu3-2, 4, 6)}2; Se{N(mes*)}2] can be prepared in a good yield from the reaction of SeCl4 and (mes*)NHLi. The molecule adopts an unprecedented anti, anti-conformation, as deduced by DFT calculations at PBE0/TZVP level of theory and supported by 77Se NMR spectroscopy and a crystal structure determination. An analogous reaction involving (C6H2Me3-2, 4, 6)NHLi [(mes)NHLi] unexpectedly lead to the reduction of selenium and afforded the selenium diamide Se{NH(mes)}2 that was characterized by X-ray crystallography and 77Se NMR spectroscopy. The Se-N bonds of 1.847(3) and 1.852(3) A show normal single bond lengths. The <NSeN bond angle of 109.9(1)° also indi…

I poligoni stellati: origini storiche ed implicazioni didattiche

2019

The genesis of mathematical concepts in the evolutionary line of human thought in the long story and the genesis in individual optics possess evident analogies. Starting from this assumption, we describe an activity presented to 15-year-old students; the aim was to consolidate fundamental concepts of Euclidean geometry related to regular polygons. The experimentation has used a didactic approach based on the historical evolution of the formal definition of regular star polygon through the centuries. The activity and the results obtained in terms of internalization of the concepts in the students are showed.

On arithmetic sums of Ahlfors-regular sets

2021

Let $A,B \subset \mathbb{R}$ be closed Ahlfors-regular sets with dimensions $\dim_{\mathrm{H}} A =: \alpha$ and $\dim_{\mathrm{H}} B =: \beta$. I prove that $$\dim_{\mathrm{H}} [A + \theta B] \geq \alpha + \beta \cdot \tfrac{1 - \alpha}{2 - \alpha}$$ for all $\theta \in \mathbb{R} \, \setminus \, E$, where $\dim_{\mathrm{H}} E = 0$.

A multifractal approach of central place theory for sustainable planning

2013

International audience

The Poisson Point Process

2020

Poisson point processes can be used as a cornerstone in the construction of very different stochastic objects such as, for example, infinitely divisible distributions, Markov processes with complex dynamics, objects of stochastic geometry and so forth.

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.

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.

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.