Bayer et Stillman ont montré que si R est un anneau de polynômes sur un corps k et I un idéal homogène de R, alors la régularité de I est égal au maximum des degrés des générateurs de son idéal initial générique pour l'ordre lexicographique inverse. Ce résultat a motivé la recherche de bornes pour la régularité de Castelnuovo-Mumford en termes des degrés des générateurs d'un idéal ou d'un module gradué. Les travaux de Gruson-Peskine, Bertram-Ein-Lazarsfeld, Chardin-Ulrich, Caviglia-Sbarra, entre autres, ont prouvé qu'il existe des bornes assez fines pour certaines classes d'idéaux ou de modules, bien inférieures aux bornes générales. Dans un premier temps nous améliorons les bornes dans le cas des idéaux en petites dimensions et, en s'inspirant des exemples de Chardin-d'Cruz, nous construisons des exemples d'idéaux dont la régularité est proche de nos estimations. Dans un deuxième temps nous avons étendu aux modules et raffiné les méthodes et les bornes connues pour les idéaux. En utilisant la méthode des sections hyperplanes et un théorème de Bertini, nous établissons une borne pour la régularité d'un idéal homogène en fonction du degré de ses générateurs minimaux et de la dimension du lieu singulier du schéma qu'il défini.

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Techn. University, Diss., 2004--Kaiserslautern.

Made available in DSpace on 2014-06-11T19:26:46Z (GMT). No. of bitstreams: 0 Previous issue date: 2008-07-10Bitstream added on 2014-06-13T18:48:37Z : No. of bitstreams: 1 campos_jhr_me_ia.pdf: 4516439 bytes, checksum: 4452446809a6f50c1450b53a2015200e (MD5) / Este trabalho discorre sobre a obra musical Variazioni attraverso i secoli, op 71 de Mário Castelnuovo-Tedesco, sua primeira composição para o violão, atendendo um pedido do violonista espanhol Andrés Segóvia. As propostas foram as de analisar o contexto histórico do violão no início do século XX, uma época de grande efervescência em vários setores do conhecimento humano, em que o violão se encontrava em processo de afirmação no cenário da música erudita européia, bem como perceber a relação de Castelnuovo-Tedesco neste movimento. O trabalho demonstra a aplicabilidade da forma tema e variações na obra Variazioni attraverso i secoli, op 71, esforço necessário para a compreensão do processo composicional de Castelnuovo-Tedesco. / This work issues on the musical work Variazioni Attraverso I secoli, op 71 of Mário Castelnuovo-Tedesco, his first composition for guitar, attending a request from the spanish guitarist Andrés Segovia. The proposition is to analyse the historical context of the guitar in the beginning of the XX century, an epoch of great importance in a wide range of human knowledge. The guitar was in an affirmation process in the scenery of the European music, where Castelnuovo-Tedesco is placed. This work demonstrates the use of the form of Theme and Variations in Variazioni Attraverso i Secoli, op71, which is a necessary effort for the comprehension of the compositional process of Castelnuovo-Tedesco.

<p>Let S be a polynomial ring K[x1,...,xn] over a field K and let F be a non-negatively graded free module over S generated by m basis elements. In this thesis, we study four kinds of upper bounds: degree bounds for Gröbner bases of submodules of F, bounds for arithmetic degrees of S-ideals, regularity bounds for radicals of S-ideals, and Stillman bounds. </p> <p><br></p> <p>Let M be a submodule of F generated by elements with degrees bounded above by D and dim(F/M)=r. We prove that if M is graded, the degree of the reduced Gröbner basis of M for any term order is bounded above by 2[1/2((Dm)^{n-r}m+D)]^{2^{r-1}}. If M is not graded, the bound is 2[1/2((Dm)^{(n-r)^2}m+D)]^{2^{r}}. This is a generalization of bounds for ideals in a polynomial ring due to Dubé (1990) and Mayr-Ritscher (2013).</p> <p><br></p> <p>Our next results are concerned with a homogeneous ideal I in S generated by forms of degree at most d with dim(S/I)=r. In Chapter 4, we show how to derive from a result of Hoa (2008) an upper bound for the regularity of sqrt{I}, which denotes the radical of I. More specifically we show that reg(sqrt{I})<= d^{(n-1)2^{r-1}}. In Chapter 5, we show that the i-th arithmetic degree of I is bounded above by 2*d^{2^{n-i-1}}. This is done by proving upper bounds for arithmetic degrees of strongly stable ideals and ideals of Borel type.</p> <p><br></p> <p>In the last chapter, we explain our progress in attempting to make Stillman bounds explicit. Ananyan and Hochster (2020) were the first to show the existence of Stillman bounds. Together with G. Caviglia, we observe that a possible way of making their results explicit is to find an effective bound for an invariant called D(k,d) and supplement it into their proof. Although we are able to obtain this bound D(k,d) and realize Stillman bounds via an algorithm, it turns out that the computational complexity of Ananyan and Hochster's inductive proof would make the bounds too large to be meaningful. We explain the bad behavior of these Stillman bounds by giving estimates up to degree 3.</p>

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Au XXᵉ siècle, des compositeurs non-guitaristes commencent à composer des œuvres pour la guitare mais avec des lacunes dans leur compréhension des spécificités techniques de l'instrument. Certains consultaient un guitariste pour obtenir des conseils techniques, mais d'autres publiaient des œuvres souvent techniquement maladroites, voire impossibles. Un exemple notable en est Mario Castelnuovo-Tedesco (1895-1968). Au départ, il composa de la musique pour guitare en collaboration avec Andrés Segovia (1893-1987), puis en collaboration avec d'autres guitaristes. Ses dernières œuvres pour guitare furent publiées à titre posthume sans avoir été révisées par un guitariste, par exemple Platero y yo, op.190 pour guitare et narrateur, l'une de ses œuvres pour guitare les plus importantes. Cette recherche documente mon processus d'adaptation de Platero y yo dans lequel je me suis efforcé de trouver un équilibre entre la fidélité à la partition originale, le contexte narratif et l'efficacité technique et sonore des différentes solutions que j'ai expérimentées. / In the 20ᵗʰ century, non-guitarist composers began composing solo works for the guitar but lacked a sufficient understanding of the instrument's technical specificities. Some would consult with a guitarist for technical guidance, but others would publish works that are often technically awkward or even impossible. A notable example of this is Mario Castelnuovo-Tedesco (1895-1968). Initially, he wrote music for the guitar in collaboration with Andrés Segovia (1893-1987), then in collaboration with other guitarists. His late works for the guitar were posthumously published without having been revised by a guitarist. A notorious example of this is Platero y yo, op.190 for guitar and narrator, one of Castelnuovo-Tedesco's major guitar compositions. This research documents my adaptation process of Platero y yo in which I strived to find a balance between faithfulness to the composer's score and to the narrative context, and the technical and sonic effectiveness of the different solutions I experimented with.

Made available in DSpace on 2015-12-10T14:22:12Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-06-29. Added 1 bitstream(s) on 2015-12-10T14:28:15Z : No. of bitstreams: 1 000853688.pdf: 6118742 bytes, checksum: 0899a7dccc5c539045351d6c407feb52 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / No presente trabalho buscamos refletir a respeito de alguns dos diversos procedimentos extramusicais e interdisciplinares envolvidos na confecção da obra musical Romancero Gitano, de Autoria de Mario Castelnuovo-Tedesco com textos de Federico Garcia Lorca. Para o cumprimento desta tarefa foram considerados procedimentos como retórica e word-painting, bem como levantamento de dados biográficos de compositor e poeta, análises técnico -musicais de cada um dos movimentos da obra e leituras poéticas dos textos / In the present work our aim was to reflect on some of the various extra musical and interdisciplinary procedures involved in the confection of the musical work Romancero Gitano, Mario Castelnuovo-Tedesco's authorship, with texts by Federico Garcia Lorca. To achieve this aim we have considered procedures such as rhetoric and word-painting, as well as research on biographical data about composer and poet, technical -musical analysis of each one of the movements of the work and poetical readings of the texts

This thesis presents extended program notes for a recorded graduate classical guitar recital consisting of the following works for solo guitar with string quartet and chamber orchestra: Mario Castelnuovo-Tedesco: Quintet for Guitar and Strings, Op. 143; Leo Brouwer: Concerto No. 3 (“Elegiaco”). Both works are pioneering and invaluable contributions to guitar literature. Tedesco’s Quintet for Guitar and Strings, Op. 143 is the first quintet ever composed to properly showcase the virtuosity of the guitar within a chamber setting. Concerto “Elegiaco” demonstrates the refinement of Leo Brouwer’s use of post-modern tonality and minimalism within classical form, and showcases his unique compositional style.

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