Théorème de Pleijel pour l'oscillateur harmonique quantique

L'objectif de ce mémoire est de démontrer certaines propriétés géométriques des fonctions propres de l'oscillateur harmonique quantique. Nous étudierons les domaines nodaux, c'est-à-dire les composantes connexes du complément de l'ensemble nodal. Supposons que les valeurs propres ont été ordonnées en ordre croissant. Selon un théorème fondamental dû à Courant, une fonction propre associée à la $n$-ième valeur propre ne peut avoir plus de $n$ domaines nodaux. Ce résultat a été prouvé initialement pour le laplacien de Dirichlet sur un domaine borné mais il est aussi vrai pour l'oscillateur harmonique quantique isotrope. Le théorème a été amélioré par Pleijel en 1956 pour le laplacien de Dirichlet. En effet, on peut donner un résultat asymptotique plus fort pour le nombre de domaines nodaux lorsque les valeurs propres tendent vers l'infini. Dans ce mémoire, nous prouvons un résultat du même type pour l'oscillateur harmonique quantique isotrope. Pour ce faire, nous utiliserons une combinaison d'outils classiques de la géométrie spectrale (dont certains ont été utilisés dans la preuve originale de Pleijel) et de plusieurs nouvelles idées, notamment l'application de certaines techniques tirées de la géométrie algébrique et l'étude des domaines nodaux non-bornés.

Le personnage-figurant : absence de monde et corps spectral dans l’œuvre de Béla Tarr

Ce mémoire examine le rapport du visible à l’invisible dans l’œuvre du cinéaste hongrois Béla Tarr afin de montrer comment cette œuvre fait sa plus grande place, quoique le plus souvent sous la forme d’une absence-présence, à la question du néant et de la mort. À travers une étude tripartite, tour à tour concernant le traitement cinématographique et thématique du monde, du temps et du personnage et de leurs fonctions, l’objectif de cette recherche est celui de montrer comment cette œuvre soustractive interroge le rapport de l’existant à un monde qui fait défaut. C’est la promesse, en partie telle que théorisée par Peter Sloterdijk, qui permettra ultimement d’éclairer la démarche tragique des personnages tarriens : lutte contre la mort au moyen d’un constant effort de soi et ce, jusqu’à l’épuisement radical. La notion de personnage-figurant développée dans ce mémoire se propose d’articuler ensemble les valeurs figuratives et thématiques communes aux différents personnages qui traversent l’œuvre afin d’en mieux comprendre, malgré les ruptures stylistiques et narratives, la continuité. Enfin, le dialogue engagé ici entre l’œuvre du cinéaste et certains concepts-clé de la tradition philosophique (le monde, le soi, le temps) entend montrer comment la première ouvre des pistes pertinentes pour une réflexion sur le sujet contemporain et son époque.

Structural, Spectral, Biological and Electrochemical Studies Of Some 3d Transition Metal Complexes of O-N-S and N-N-S Donor Ligands

The primary aim of these investigations was to probe the spectroscopic, electrochemical, biological and single crystal X-ray diffraction studies of some selected transition metal complexes of 4N-monosubstituted thiosemicarbazones. Transition metal complexes with thiosemicarbazones exhibit a wide range of stereochemistries and possess potential biological activity. Metal complexes of thiosemicarbazones are proved to have improved pharmacological and therapeutic effects. The studies are conducted to bring about a fair understanding of the structure activity relationship and to develop certain effective and economical metal-based antimicrobial agents. Study showed that the thiosemicarbazones have antibacterial, antiviral and antiproliferative properties and hence used against tuberculosis, leprosy, psoriasis, rheumatism, trypanosomiasis and coccidiosis. Certain thiosemicarbazones showed a selective inhibition of HSV and HIV infections. The insolubility of most thiosemicarbazones in water causes difficulty in the oral administration in clinical practice. Transition metal complexes are found to have more activity than uncombined thiosemicarbazones. They exhibit a variety of denticity and can be varied by proper substitution. The stereochemistry assumed by the thiosemicarbazones during the coordination with transition metal ions depends on the factors such as preparative conditions and availability of additional bonding site in the ligand moiety and charge of the ligand. The resulting complexes exhibited a wide range of stereochemistries and have biomimic activity and potential application as sensors.

Synthesis, Spectral Characterization, Structural Studies and Biological Investigations of Transition Metal Complexes of Some Acid Hydrazones

This study concentrates the chemical properties of hydrazones due to its chelating capability and their pharmacological applications. Studies cover the preparation of different acid hydrazones and their structural studies and studies on their antimicrobial activity, synthesis and spectral characterization of different complexes of copper oxovanadium, manganese, nickel etc. Effect of incorporation of heterocyclic bases to the coordination sphere, change in the biological activity of acid hydrazones upon coordination, development of X-ray quality single crystals and its X-ray diffraction studies, studies on the redox behavior of the coordinated metal ions and correlation between the stereochemistry and biological activities.

Spectral Characteristics of the Blood of Streptozotocin Diabetic Rats using Photoacoustic Technique

Optical absorption characteristics of rat blood affected by diabetes has been studied using photoacoustic (PA) technique. PA spectrum of blood depends on the molecular structure of haemoglobin. The peak value ratio ylQ increases with increase in the diabetic state. Externally added glucose to normal blood does not show any increase in y//3 ratio as seen in the diabetic condition . The increase in yl,8 ratio may be due to the decrease in DPG level and the resultant shift from R -> T conformation of majority of diabetic haemoglobin.

Structural and Spectral Investigations of Transition Metal Complexes Of Di-2-Pyridyl Ketone N (4), N (4)-Disubstituted Thiosemicarbazones

The study deals with structural and spectral investigations of transition metal complexes of di-2-pyridyl ketone N(4),N(4)-disubstituted thiosemicarbazones. The main objective and scope of the work deals with di-2-pyridyl ketone N(4),N(4)-disubstituted thiosemicarbazones are quardridentate NNNS donor ligands. To chosen this ligand for study because, the ligands are prepared and characterized for the first time, since there are two pyridyl nitorgens, dimmers and polymers of complexes may result leading to interesting structural aspects. The work includes the preparation of the thiosemicarbzones and their structural and spectral studies, synthesis and spectral characterization of complexes of copper(II),,nickel(II),manganese(II), dioxovanadium(V),cobalt(III),zinc(II),cadmium(II) of the ligand HL, synthesis and spectral characterization of complexes of copper(II),manganese(II), of the ligand HL and the development of X-ray quality crystals and its X-ray diffraction studies. The structural characterization techniques are elemental analysis, conductivity measurements, magnetic measurements, electronic spectroscopy, H NMR spectroscopy, Infrared spectroscopy and X-ray crystallography.

Structural, Spectral, Biological and Electrochemical Studies Of Some 3d Transition Metal Complexes of O-N-S and N-N-S Donor Ligands

The primary aim of these investigations was to probe the spectroscopic, electrochemical, biological and single crystal X-ray diffraction studies of some selected transition metal complexes of 4N-monosubstituted thiosemicarbazones. Transition metal complexes with thiosemicarbazones exhibit a wide range of stereochemistries and possess potential biological activity. Metal complexes of thiosemicarbazones are proved to have improved pharmacological and therapeutic effects. The studies are conducted to bring about a fair understanding of the structure activity relationship and to develop certain effective and economical metal-based antimicrobial agents. Study showed that the thiosemicarbazones have antibacterial, antiviral and antiproliferative properties and hence used against tuberculosis, leprosy, psoriasis, rheumatism, trypanosomiasis and coccidiosis. Certain thiosemicarbazones showed a selective inhibition of HSV and HIV infections. The insolubility of most thiosemicarbazones in water causes difficulty in the oral administration in clinical practice. Transition metal complexes are found to have more activity than uncombined thiosemicarbazones. They exhibit a variety of denticity and can be varied by proper substitution. The stereochemistry assumed by the thiosemicarbazones during the coordination with transition metal ions depends on the factors such as preparative conditions and availability of additional bonding site in the ligand moiety and charge of the ligand. The resulting complexes exhibited a wide range of stereochemistries and have biomimic activity and potential application as sensors

A Simple Free-Space Method for Measuring the Complex Permittivity of Single and Compound Dielectric Materials

A simple and efficient method for determining the complex permittivity of dielectric materials from both reflected and transmitted signals is presented. It is also novel because the technique is implemented using two pyramidal horns without any focusing mechanisms. The dielectric constant of a noninteractive and distributive (NID) mixture of dielectrics is also determined

Two new fluorescent heterocyclic perimidines: first syntheses, crystal structure and spectral characterization

An efficient one-pot synthesis of two new heterocyclic perimidines 4-(2,3-dihydro-1H-perimidin-2-yl)-2-methoxyphenol and 2-(quinoxalin-2-yl)-2,3-dihydro-1H-perimidine in good yields is presented. This methodology provides a simple, straightforward synthetic route to these interesting classes of heterocycles. Crystal structure, solvatochromism and antibacterial activity of these organic compounds are discussed.