Search results for " Geometry"

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.

Crystal structure and Hirshfeld surface analysis of (Z)-4-chloro-N′-(4-oxothiazolidin-2-ylidene)benzenesulfonohydrazide monohydrate

2018

The asymmetric unit of the title thiazole derivative containing a sulfonylhydrazinic moiety, C9H8ClN3O3S2·H2O, consists of two independent molecules and two water molecules. The central parts of the molecules are twisted as both the molecules are bent at both the S and N atoms. In the crystal, N—H...N, N—H...O, C—H...O and O—H...O hydrogen-bonding interactions connect the molecules, forming layers parallel to the ab plane. Two-dimensional fingerprint plots associated with the Hirshfeld surface show that the largest contributions to the crystal packing come from O...H/H...O (32.9%) and H...H (22.6%) interactions.

A survey on algebraic dilatations

2023

In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and theoretical aspects and the other applications to existing theories.

Crystal structure of trans-di­chlorido­(4-nitro­aniline-κN 1)(piperidine-κN)platinum(II)

2015

The packing of the title compound features N—H⋯Cl hydrogen bonds and π–π stacking inter­actions, which form one-dimensional chains of mol­ecules parallel to [001] further linked via N—H⋯O inter­actions.

The Equiangular Compass

2012

Læringspotensial i en digital interaktiv matematikkundervisning : en analyse av læringspotensialet i geometriundervisningen på 8. trinn med utstrakt …

2016

Masteroppgave matematikkdidaktikk – Universitetet i Agder 2016 The theme of this master thesis is learning potential in mathematical tasks designed for geometry teaching in GeoGebra in 8th grade. This thesis is written in connection to the project Digital interactive mathematics teaching (DIM), where the goal is to create innovative mathematics teaching by using digital tools in a pedagogic context. Previous research has documented that students learning outcome of the teaching is largely influenced and limited by the tasks that are given. In this context analysis of the tasks learning potential is particular interesting. Therefore, my research question is: What learning potential is it in …

Teaching and Learning of Geometry as a process of Objectification: conditions and obstacles to argumentation and proof. The role of natural language,…

2021

This paper examines some examples (taken from research conducted over the years) that show students’ linguistic attitudes in geometry tasks. The examples are framed within the Theory of Objectification with reference to the notion of sensuous cognition, semiotic means of objectification and levels of generality. We show the struggle students live, at higher levels of generality, in intertwining natural language, specific language and the spontaneous use of geometrical figures, bound to perception and kinaesthetic activity. Within the networking paradigm, we coordinate the Theory of Objectification and Duval’s semio-cognitive approach to frame the interplay between the ideal and the material…