Coordinate-Independent Computations on Differential Equations

This project investigates the computational representation of differentiable manifolds, with the primary goal of solving partial differential equations using multiple coordinate systems on general n- dimensional spaces. In the process, this abstraction is used to perform accurate integrations of ordinary differential equations using multiple coordinate systems. In the case of linear partial differential equations, however, unexpected difficulties arise even with the simplest equations.

A Modern Differential Geometric Approach to Shape from Shading

How the visual system extracts shape information from a single grey-level image can be approached by examining how the information about shape is contained in the image. This technical report considers the characteristic equations derived by Horn as a dynamical system. Certain image critical points generate dynamical system critical points. The stable and unstable manifolds of these critical points correspond to convex and concave solution surfaces, giving more general existence and uniqueness results. A new kind of highly parallel, robust shape from shading algorithm is suggested on neighborhoods of these critical points. The information at bounding contours in the image is also analyzed.

Motion Planning with Six Degrees of Freedom

The motion planning problem is of central importance to the fields of robotics, spatial planning, and automated design. In robotics we are interested in the automatic synthesis of robot motions, given high-level specifications of tasks and geometric models of the robot and obstacles. The Mover's problem is to find a continuous, collision-free path for a moving object through an environment containing obstacles. We present an implemented algorithm for the classical formulation of the three-dimensional Mover's problem: given an arbitrary rigid polyhedral moving object P with three translational and three rotational degrees of freedom, find a continuous, collision-free path taking P from some initial configuration to a desired goal configuration. This thesis describes the first known implementation of a complete algorithm (at a given resolution) for the full six degree of freedom Movers' problem. The algorithm transforms the six degree of freedom planning problem into a point navigation problem in a six-dimensional configuration space (called C-Space). The C-Space obstacles, which characterize the physically unachievable configurations, are directly represented by six-dimensional manifolds whose boundaries are five dimensional C-surfaces. By characterizing these surfaces and their intersections, collision-free paths may be found by the closure of three operators which (i) slide along 5-dimensional intersections of level C-Space obstacles; (ii) slide along 1- to 4-dimensional intersections of level C-surfaces; and (iii) jump between 6 dimensional obstacles. Implementing the point navigation operators requires solving fundamental representational and algorithmic questions: we will derive new structural properties of the C-Space constraints and shoe how to construct and represent C-Surfaces and their intersection manifolds. A definition and new theoretical results are presented for a six-dimensional C-Space extension of the generalized Voronoi diagram, called the C-Voronoi diagram, whose structure we relate to the C-surface intersection manifolds. The representations and algorithms we develop impact many geometric planning problems, and extend to Cartesian manipulators with six degrees of freedom.

Exact Geosedics and Shortest Paths on Polyhedral Surface

We present two algorithms for computing distances along a non-convex polyhedral surface. The first algorithm computes exact minimal-geodesic distances and the second algorithm combines these distances to compute exact shortest-path distances along the surface. Both algorithms have been extended to compute the exact minimalgeodesic paths and shortest paths. These algorithms have been implemented and validated on surfaces for which the correct solutions are known, in order to verify the accuracy and to measure the run-time performance, which is cubic or less for each algorithm. The exact-distance computations carried out by these algorithms are feasible for large-scale surfaces containing tens of thousands of vertices, and are a necessary component of near-isometric surface flattening methods that accurately transform curved manifolds into flat representations.

The Construction of Arbitrary Stable Dynamics in Non-Linear Neural Networks

In this paper, two methods for constructing systems of ordinary differential equations realizing any fixed finite set of equilibria in any fixed finite dimension are introduced; no spurious equilibria are possible for either method. By using the first method, one can construct a system with the fewest number of equilibria, given a fixed set of attractors. Using a strict Lyapunov function for each of these differential equations, a large class of systems with the same set of equilibria is constructed. A method of fitting these nonlinear systems to trajectories is proposed. In addition, a general method which will produce an arbitrary number of periodic orbits of shapes of arbitrary complexity is also discussed. A more general second method is given to construct a differential equation which converges to a fixed given finite set of equilibria. This technique is much more general in that it allows this set of equilibria to have any of a large class of indices which are consistent with the Morse Inequalities. It is clear that this class is not universal, because there is a large class of additional vector fields with convergent dynamics which cannot be constructed by the above method. The easiest way to see this is to enumerate the set of Morse indices which can be obtained by the above method and compare this class with the class of Morse indices of arbitrary differential equations with convergent dynamics. The former set of indices are a proper subclass of the latter, therefore, the above construction cannot be universal. In general, it is a difficult open problem to construct a specific example of a differential equation with a given fixed set of equilibria, permissible Morse indices, and permissible connections between stable and unstable manifolds. A strict Lyapunov function is given for this second case as well. This strict Lyapunov function as above enables construction of a large class of examples consistent with these more complicated dynamics and indices. The determination of all the basins of attraction in the general case for these systems is also difficult and open.

The Synthesis of Arbitrary Stable Dynamics in Non-linear Neural Networks II: Feedback and Universality

We wish to construct a realization theory of stable neural networks and use this theory to model the variety of stable dynamics apparent in natural data. Such a theory should have numerous applications to constructing specific artificial neural networks with desired dynamical behavior. The networks used in this theory should have well understood dynamics yet be as diverse as possible to capture natural diversity. In this article, I describe a parameterized family of higher order, gradient-like neural networks which have known arbitrary equilibria with unstable manifolds of known specified dimension. Moreover, any system with hyperbolic dynamics is conjugate to one of these systems in a neighborhood of the equilibrium points. Prior work on how to synthesize attractors using dynamical systems theory, optimization, or direct parametric. fits to known stable systems, is either non-constructive, lacks generality, or has unspecified attracting equilibria. More specifically, We construct a parameterized family of gradient-like neural networks with a simple feedback rule which will generate equilibrium points with a set of unstable manifolds of specified dimension. Strict Lyapunov functions and nested periodic orbits are obtained for these systems and used as a method of synthesis to generate a large family of systems with the same local dynamics. This work is applied to show how one can interpolate finite sets of data, on nested periodic orbits.

Excitation of highly conjugated (porphinato)palladium(II) and (porphinato)platinum(II) oligomers produces long-lived, triplet states at unit quantum yield that absorb strongly over broad spectral domains of the NIR.

Transient dynamical studies of bis[(5,5'-10,20-bis(2,6-bis(3,3-dimethylbutoxy)phenyl)porphinato)palladium(II)]ethyne (PPd(2)), 5,15-bis{[(5'-10,20-bis(2,6-bis(3,3-dimethylbutoxy)phenyl)porphinato)palladium(II)]ethynyl}(10,20-bis(2,6-bis(3,3-dimethylbutoxy)phenyl)porphinato)palladium(II) (PPd(3)), bis[(5,5'-10,20-bis(2,6-bis(3,3-dimethylbutoxy)phenyl)porphinato)platinum(II)]ethyne (PPt(2)), and 5,15-bis{[(5'-10,20-bis(2,6-bis(3,3-dimethylbutoxy)phenyl)porphinato)platinum(II)]ethynyl}(10,20-bis(2,6-bis(3,3-dimethylbutoxy)phenyl)porphinato)platinum(II) (PPt(3)) show that the electronically excited triplet states of these highly conjugated supermolecular chromophores can be produced at unit quantum yield via fast S(1) → T(1) intersystem crossing dynamics (τ(isc): 5.2-49.4 ps). These species manifest high oscillator strength T(1) → T(n) transitions over broad NIR spectral windows. The facts that (i) the electronically excited triplet lifetimes of these PPd(n) and PPt(n) chromophores are long, ranging from 5 to 50 μs, and (ii) the ground and electronically excited absorptive manifolds of these multipigment ensembles can be extensively modulated over broad spectral domains indicate that these structures define a new precedent for conjugated materials featuring low-lying π-π* electronically excited states for NIR optical limiting and related long-wavelength nonlinear optical (NLO) applications.

Predicting the frequency dispersion of electronic hyperpolarizabilities on the basis of absorption data and thomas-kuhn sum rules

Successfully predicting the frequency dispersion of electronic hyperpolarizabilities is an unresolved challenge in materials science and electronic structure theory. We show that the generalized Thomas-Kuhn sum rules, combined with linear absorption data and measured hyperpolarizability at one or two frequencies, may be used to predict the entire frequency-dependent electronic hyperpolarizability spectrum. This treatment includes two- and three-level contributions that arise from the lowest two or three excited electronic state manifolds, enabling us to describe the unusual observed frequency dispersion of the dynamic hyperpolarizability in high oscillator strength M-PZn chromophores, where (porphinato)zinc(II) (PZn) and metal(II)polypyridyl (M) units are connected via an ethyne unit that aligns the high oscillator strength transition dipoles of these components in a head-to-tail arrangement. We show that some of these structures can possess very similar linear absorption spectra yet manifest dramatically different frequency dependent hyperpolarizabilities, because of three-level contributions that result from excited state-to excited state transition dipoles among charge polarized states. Importantly, this approach provides a quantitative scheme to use linear optical absorption spectra and very limited individual hyperpolarizability measurements to predict the entire frequency-dependent nonlinear optical response. Copyright © 2010 American Chemical Society.

Electron collisions with Fe-peak elements: Forbidden transitions between the low lying valence states 3d6, 3d54s, and 3d54p of Fe III:

Effective collision strengths are presented for the Fe-peak element Fe III at electron temperatures (Te in degrees Kelvin) in the range 2 × 103 to 1 × 106. Forbidden transitions results are given between the 3d6, 3d54s, and the 3d54p manifolds applicable to the modeling of laboratory and astrophysical plasmas.

Alkaline-earth aluminosilicate-based glass and glass-ceramic sealants for functional applications

The planar design of solid oxide fuel cell (SOFC) is the most promising one due to its easier fabrication, improved performance and relatively high power density. In planar SOFCs and other solid-electrolyte devices, gas-tight seals must be formed along the edges of each cell and between the stack and gas manifolds. Glass and glass-ceramic (GC), in particular alkaline-earth alumino silicate based glasses and GCs, are becoming the most promising materials for gas-tight sealing applications in SOFCs. Besides the development of new glass-based materials, new additional concepts are required to overcome the challenges being faced by the currently existing sealant technology. The present work deals with the development of glasses- and GCs-based materials to be used as a sealants for SOFCs and other electrochemical functional applications. In this pursuit, various glasses and GCs in the field of diopside crystalline materials have been synthesized and characterized by a wide array of techniques. All the glasses were prepared by melt-quenching technique while GCs were produced by sintering of glass powder compacts at the temperature ranges from 800−900 ºC for 1−1000 h. Furthermore, the influence of various ionic substitutions, especially SrO for CaO, and Ln2O3 (Ln=La, Nd, Gd, and Yb), for MgO + SiO2 in Al-containing diopside on the structure, sintering and crystallization behaviour of glasses and properties of resultant GCs has been investigated, in relevance with final application as sealants in SOFC. From the results obtained in the study of diopside-based glasses, a bilayered concept of GC sealant is proposed to overcome the challenges being faced by (SOFCs). The systems designated as Gd−0.3 (in mol%: 20.62MgO−18.05CaO−7.74SrO−46.40SiO2−1.29Al2O3 − 2.04 B2O3−3.87Gd2O3) and Sr−0.3 (in mol%: 24.54 MgO−14.73 CaO−7.36 SrO−0.55 BaO−47.73 SiO2−1.23 Al2O3−1.23 La2O3−1.79 B2O3−0.84 NiO) have been utilized to realize the bi-layer concept. Both GCs exhibit similar thermal properties, while differing in their amorphous fractions, revealed excellent thermal stability along a period of 1,000 h. They also bonded well to the metallic interconnect (Crofer22APU) and 8 mol% yttrium stabilized zirconium (8YSZ) ceramic electrolyte without forming undesirable interfacial layers at the joints of SOFC components and GC. Two separated layers composed of glasses (Gd−0.3 and Sr−0.3) were prepared and deposited onto interconnect materials using a tape casting approach. The bi-layered GC showed good wetting and bonding ability to Crofer22APU plate, suitable thermal expansion coefficient (9.7–11.1 × 10–6 K−1), mechanical reliability, high electrical resistivity, and strong adhesion to the SOFC componets. All these features confirm the good suitability of the investigated bi-layered sealant system for SOFC applications.

Coletores de distribuição e sua otimização hidráulica, aplicados a uma instalação de produção de água arrefecida em sistemas de AVAC ( Fórum Picoas)

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Mecânica

Recueil de lettres originales et de copies de pièces indiquées comme telles dans le dépouillement qui suit.

Contient : 1 « Discours sur la mort du roy Henry [II] et succession du roy François » II. 22 juin à 19 juillet 1559. En italien. Minute ; 2 Sur la mort de François II et le commencement du règne de Charles IX. En italien. Minute ; 3 Première séance du conseil où fut résolue la convocation des États généraux d'Orléans. « Fontanablio, il 21 d'agosto 1560 ». En italien. Minute ; 4 « Interrogatoires de [Jean de Merei, dit] Poltrot, 21 fevrier 1562 ». Copie ; 5 Lettres d'«OTTAVIO FARNESE,... al cavalier Tiburtio Burty,... Da Parma, alli XII di febraro 1562 » ; 6 « Articoli mandati dal re CARLO IX al papa » Pie IV sur les réformes à introduire dans l'Église touchant les images, l'administration des sacrements, la messe. Janvier 1561 ; 7 Lettre de « CHARLES IX,... à mon cousin, le prince de Portian,... Escript au Mont de Marsan, le XXIe jour de may 1565 » ; 8 « Instruction à monseigneur le general d'Auvergne de l'ordre qu'il aura à tenir et observer et faire tenir et observer par ceulx qu'il commectera à la levée des douze cens mullets à batz que le roy a ordonné estre levez pour le service de son armée en païs d'Auvergne, et chargés de Lyon, Thoulouze, Montpelier et Provence... Faict à Fontainebleau, le XIIe jour de mars, l'an mil cinq cens cinquante sept ». Copie ; 9 « Roolle de la monstre et veue faicte en la ville de Riom en Auvergne, le treizeiesme may V.C. cinquante huict, du nombre et quantité de cinquante mulletz à batz, levez pour le service du roy aud. païs... presentez par devant Michel Veyny, seigneur d'Arbouze, general des finances en la generalité de Languedoc ». Copie ; 10 Ordonnance de payement desdits mulets. Copie ; 11 Reçu des vendeurs desdits mulets. Copie ; 12 « Reglement que le roi CHARLES [IX] voulut estre observé » pour « pourveoir à la garde et seureté de sa bonne ville de Paris... 18 nov. 1568 ». Minute ; 13 Lettre de « LOYS DE BOURBON, prince DE CONDE,... à monsieur le duc de Montpensier,... De ce camp, à La Fontayne, ce VIIIe decembre 1568 ». Copie ; 14 « Escrit difamatoire envoié de la part des huguenots ou de Mr le mareschal de Villevieille,... Melun, 1568, decembre », factum du prince DE CONDE contre « le cardinal de Lorraine et aultres pensionnaires du roy d'Espaigne, ses adherans » ; 15 « Copie d'un advis escrit de la main du Sr DE CARNAVALLET », sur les mesures à prendre pour empêcher les troupes du prince de Condé et de l'amiral de Coligni « de pouvoir joindre avec les Allemans » envoyés par le duc des Deux Ponts. « S. Mor, 5 janvier 1569 » ; 16 « Sur la Negotiation de la paix », préliminaires de la paix conclue à Saint Germain en Laye, le 8 août 1570, entre Charles IX et les protestants ; 17 « Copia d'una lettera di mons. CAPI LUPI, vescovo di Fano, al Sr duca d'Urbino. Di Roma, il 23 settembre 1571 ». En italien ; 18 « Discours de [LOUIS DE GONZAGUE, duc DE NEVERS], sur la maniere de bien governer les affaires du roy [Charles IX], qu'il a mis es mains de monseigneur le duc d'Anjou,... et de l'entreprise de la Floride pour luy... Chenonceau, ce 20 may 1572 ». Minute ; 19 Lettre de LOUIS DE GONZAGUE, duc DE NEVERS, gouverneur de Piémont, au roi Charles IX. « Estampes, dernier may 1572 » ; 20 « Trois Discours faits par [LOUIS DE GONZAGUE, duc DE NEVERS] et baillés à monsieur [le duc d'Anjou], sur les propositions que monseigneur l'admiral volloit faire pour induire le roy à faire la guere en Flandre... Paris, 19 juing 1572 ». Copie ; 21 Discours du duc DE NEVERS sur le même sujet. « 26 de juin 1572 ». Minute ; 22 Lettre de « LODOVICO GONZAGA », duc DE NEVERS, au roi Charles IX. « Ce 26 juign 1572 ». Minute ; 23 Avis motivé du duc DE NEVERS au roi Charles IX, pour le détourner d'entreprendre la guerre de Flandre. « 26 juin 1572 ». Minute ; 24 « Advis du mareschal DE TAVANES, par commandement du roy » Charles IX, avec même conclusion. « Paris, 26 juign 1572 ». Copie ; 25 « Discours comancé sur l'infidelité des Rochellois de la couronne de France, et come l'on s'y doit bien peu fier », commencement d'un mémoire rédigé par le duc DE NEVERS contre les protestants. « Paris, juillet 1572 ». Minute ; 26 « Copie d'un memoire de LODOVICO GONZAGA [duc DE NEVERS], doné à Monsieur [le duc d'Anjou] pour bailler au roy, par lequel est discouru bien amplement l'estat auquel se trovent les villes de [son] governement de Piemont... Paris, 8 aoust 1572 » ; 27 « Discours » du duc DE NEVERS « sur ce quy se pouroit faire à l'endroit dès huguenaulx reduis al la religion catolique et des autres opiniastres... Paris, 20 settembre 1572 ». Copie ; 28 « Discours et advis » du duc DE NEVERS, « comancé sur le reglement de la France et baillé au roy [Charles IX]... Paris, septembre 1572 ». Minute ; 29 « Instruction dressée » par le duc DE NEVERS, « pour supplier [le roi Charles IX] de faire haster les Suysses, et « l'argent » dont le duc d'Anjou avait « grandement affaire » pour le siége de La Rochelle. « La Guiche, 18 fevrier 1573 ». Copie ; 30 « Advis » du duc DE NEVERS, « doné à Monsieur [le duc d'Anjou], sur la depesche du capitaine Bourg », qui étant en contradiction avec celle donnée au « Sr de Crillon » pour le même objet, pouvait donner à l'amiral Honorat de Savoie lieu de penser qu'il y avait « peu de stabillité et de consideration aux depesches » dudit duc. « Chatelleraut, 23 febvrier 1573 ». Minute ; 31 Avis du duc DE NEVERS sur la conduite à tenir pour permettre au duc d'Anjou d'éviter et le blâmé des étrangers en accordant aux Rochellois une capitulation trop avantageuse et la colère du roi en refusant ladite capitulation. « 1 de fevrier 1573 ». Minute ; 32 Journal du siége de La Rochelle, du 11 février au 21 mars 1573 ; 33 « Responce du seigneur DE BIRON au memoire que monseigneur [le duc d'Aujou] luy a envoyé par le Sr de Beaulieu », relativement aux mesures prises pour faciliter les approches de La Rochelle. « Rochelle, 19 may 1573 » ; 34 « Coppie d'un memoire faict par monseigneur [le duc DE NEVERS] à Monsieur [le duc d'Anjou], frere du roy » Charles IX, relativement aux mesures à prendre pour préparer l'assaut d'un bastion de La Rochelle. « Au camp, 25 mars 1573 » ; 35 « Memoire pour interojer » relativement au même sujet. « Au camp, 26 mars 1573 ». Copie ; 36 Mémoire sur le même sujet. « Camp, 12 avril 1573 » ; 37 Mémoire du duc D'ANJOU, pour justifier les demandes de forces qu'il avait adressées au roi Charles IX et la lenteur des opérations du siége de La Rochelle. Fin de février 1573. Minute ; 38 Lettre de « HENRI [duc D'ANJOU]... à monsieur de Nevers,... May 1573 » ; 39 Lettre du duc DE NEVERS au duc d'Anjou. « De Lagor, 2 may 1573 ». Copie ; 40 Lettre du duc DE NEVERS « à monseigneur de Villeclerc,... De Lagor, 2 may 1573 ». Copie ; 41 Mesures à prendre pour le siége de La Rochelle. « May 1573 ». Copie ; 42 « Discours du duc DE NEVERS sur le traitté que Monsieur [le duc d'Anjou] veult faire aux Rochellois pour pacifier les chauses, lequel contient qu'il ne fault leur accorder la pais, ains les recevoir à mercy et à discretion... Du camp, ce XIe may 1573 ». Minute ; 43 Lettre de CATHERINE DE MEDICIS au duc de Nevers. « De Boullongne, ce sixme juillet 1573 ». Copie ; 44 Lettre de « HENRY [duc D'ANJOU]... à monsieur le duc de Nevers,... Juin 1573 » ; 45 « Discours » du duc DE NEVERS « sur l'entrée aux affaires du roy, baillé au roy de Poullogne [Henri, duc d'Anjou]... Tours, 21 julliet 1573 ». Minute ; 46 « Discours doné par monseigneur le conte DE RETZ au roy de Poullogne [Henri, duc d'Anjou], sur le voiage de La Rochelle et reglement du roiaulme de France, pour bailler au roy [Charles IX]... 30 de juillet 1573 ». Copie ; 47 « Aultre Discours ensuivant l'aultre de monseigneur le conte de Retz,... Fin juillet 1573 ». Copie ; 48 Procès-verbal de la lecture en conseil d'un mémoire de HENRI, duc D'ANJOU et roi de Pologne, sur le fait de La Rochelle et le rétablissement des affaires du royaume de France. Du 2 au 14 août 1573. Minute ; 49 « Article de la justice, fait par M. DE CHIVERNY sur [les] memoires » du duc de Nevers. Sujet traité par Henri, duc d'Anjou, roi de Pologne, dans son discours sur le rétablissement des affaires du royaume de France. « Madril, 6 aoust 1573 ». Copie ; 50 « Discours presenté au roy [Charles IX] par le roy de Pollongne, son frere, touchant sommairement son voiage faict à La Rochelle et aultres choses concernant le bien et repos de son royaulme ». Rédigé par le duc DE NEVERS. « Paris, 14 aoust 1573 ». Copie ; 51 « Discours en voyé à la royne mere du roy [Charles IX par monseigneur [le duc DE NEVERS]... Au bois de Vincennes, 20 aoust 1573 ». Pour rassurer Catherine de Médicis contre la crainte d'une éme???ute dans Paris. Copie ; 52 « Advis » du duc DE NEVERS, « doné à monseigneur [le duc d'Anjou], sur la descente des Anglois [envoyés au secours des Rochellois]... Niort, 3 febvrier 1573 ». Minute ; 53 « Coppie d'une lectre escripte par monseigneur [le duc DE NEVERS] à monsieur de Chiverny,... De Vuormes, ce XIIIIe decembre 1573 »

An analysis of the methyl rotation dynamics in the So (x' A) and T (a A) states of thioacetaldehyde from Pyrolysis jet spectra /

Jet-cooled, laser-induced phosphorescence excitation spectra (LIP) of thioacetaldehyde CH3CHS, CH3CDS, CD3CHS and CD3CDS have been observed over the region 15800 - 17300 cm"^ in a continuous pyrolysis jet. The vibronic band structure of the singlet-triplet n -* n* transition were attributed to the strong coupling of the methyl torsion and aldehydic hydrogen wagging modes . The vibronic peaks have been assigned in terms of two upper electronic state (T^) vibrations; the methyl torsion mode v^g, and the aldehydic hydrogen wagging mode v^^. The electronic origin O^a^ is unequivocally assigned as follows: CH3CHS (16294.9 cm"'' ), CH3CDS (16360.9 cm"'' ), CD3CHS (16299.7 cm"^ ), and CD3CDS (16367.2 cm"'' ). To obtain structural and dynamical information about the two electronic states, potential surfaces V(e,a) for the 6 (methyl torsion) and a (hydrogen wagging) motions were generated by ab initio quantum mechanical calculations with a 6-3 IG* basis in which the structural parameters were fully relaxed. The kinetic energy coefficients BQ(a,e) , B^(a,G) , and the cross coupling term B^(a,e) , were accurately represented as functions of the two active coordinates, a and 9. The calculations reveal that the molecule adopts an eclipsed conformation for the lower Sq electronic state (a=0°,e=0"') with a barrier height to internal rotation of 541.5 cm"^ which is to be compared to 549.8 cm"^ obtained from the microwave experiment. The conformation of the upper T^ electronic state was found to be staggered (a=24 . 68° ,e=-45. 66° ) . The saddle point in the path traced out by the aldehyde wagging motion was calculated to be 175 cm"^ above the equilibrium configuration. The corresponding maxima in the path taken by methyl torsion was found to be 322 cm'\ The small amplitude normal vibrational modes were also calculated to aid in the assignment of the spectra. Torsional-wagging energy manifolds for the two states were derived from the Hamiltonian H(a,e) which was solved variationally using an extended two dimensional Fourier expansion as a basis set. A torsionalinversion band spectrum was derived from the calculated energy levels and Franck-Condon factors, and was compared with the experimental supersonic-jet spectra. Most of the anomalies which were associated with the interpretation of the observed spectrum could be accounted for by the band profiles derived from ab initio SCF calculations. A model describing the jet spectra was derived by scaling the ab initio potential functions. The global least squares fitting generates a triplet state potential which has a minimum at (a=22.38° ,e=-41.08°) . The flatter potential in the scaled model yielded excellent agreement between the observed and calculated frequency intervals.

Traité elementaire de chirurgie

UANL

Les conditions d'une musicalité du sonore : étude comparative sur le statut musical du bruit en musique et au cinéma

La création cinématographique de l’étudiante qui accompagne ce mémoire sous la forme d’un DVD est disponible à la Médiathèque de la Bibliothèque des lettres et sciences humaines sous le titre : Qui va droit son chemin.(http://atrium.umontreal.ca/notice/UM-ALEPH002343834)