21,397 research outputs found
Sobre el soporte de soluciones de la ecuación de korteweg de vries
No full textEn este trabajo se considera la ecuación de Korteweg-de Vries (KdV): ∂∂_T u+u∂_x u=0 u = u(x; t), x ∈ R, t ∈ R y se demuestra que si u(; 0) y u(; 1) tienen soporte en un intervalo espacial [-∞;B], para cierto B 0, entonces u es idénticamente nula./ Abstract. In this paper we consider the equation of Korteweg-de Vries (KdV) ∂∂_T u+u∂_x u=0 u = u (x, t), x ∈ R, t ∈ R and show that if u (, 0) u (, 1) are supported on an interval space [- ∞, B], for some B 0, then u is identically zeroMaestrí
Vredeman de Vries: geometry and freedom
No full textAs a result of his highly imaginative perspectival illustrations, late sixteenth-century Dutch architect Hans Vredeman de Vries remained at the pivot point of transferring perspectival developments from Italy to a northern European setting. He brought about a revolution in the genre of the architectural city-view, stood as a giant of that artistic category, and initiated a widespread architectural following that could be felt in buildings from every province of his home country to as far away as regional towns in Peru.
This essay introduces the use of geometry in Vredeman’s illustrations from his 1604 treatise Perspective and gives an account of the meanings behind vantage points, picture planes, and the viewing subject in those representations. A commentary on the notion of repetition in perspectival vistas and an explanation of the significance surrounding the placement of the centric point in his engravings is also dealt with. The centric points of Vredeman’s plates are seldom placed on a blank architectural surface. Instead, we encounter deliberate openings that allow us to travel beyond the pictorial plane and that remind us of the artificial nature of the environment being shown. Someone might theoretically be looking back at us, configuring the world before us, and thereby reinforcing the arbitrariness of our point of view.
Overall, this paper aims to look anew at the symbolic significance of the perspective engravings of Vredeman de Vries. The writing ends with a summary on what it might mean to transcend a perspective.Publisher PD
Continuación única de soluciones de la ecuación de Korteweg-de Vries (KdV)
No full textEn el presente trabajo demostramos un principio de continuación única de soluciones para la ecuación de Korteweg-de Vries (KdV) ∂u/∂t + (∂^3)u/∂x^3 + u(∂u/∂x)=0; u=u(x,t), x ∈ R, t≥0, que afirma lo siguiente: Si u1, u2 ∈ C([0,1]; H^6(R)∩L^2((1 + x^2)^2α dx) ∩ C^1([0, 1];H^3(R)), para algún α 1, son soluciones de la ecuación KdV tales que existe b ∈ R para el cual u1(t)(x)=u2(t)(x), si (x, t)∈(b,∞)×{0, 1}, entonces u1(t)(x)=u2(t)(x) para (x, t) ∈ R×[0, 1]. / Abstract: In this paper we demonstrate a principle of unique continuation for solutions to the equation of Korteweg-de Vries (KdV) ∂u/∂t + (∂^3)u/∂x^3 + u(∂u/∂x)=0; u=u(x, t), x ∈ R, t≥0, which states: If u1, u2 ∈ C([0, 1];H^6(R)∩L^2((1 + x^2)^2α dx) ∩ C^1([0, 1];H^3(R)), for some α 1, are solutions of the KdV equation such that there exists b ∈ R for which u1(t)(x)=u2(t)(x), if (x, t)∈(b,∞)×{0, 1}, then u1(t)(x)=u2(t)(x) for (x, t) ∈ R×[0, 1].Maestrí
Umm El-Jimal, Bourgade de "Frontière" : à propos de Bert De Vries (ed.) Umm el-Jimal. I.
No full textVilleneuve François, Parker S. Thomas, De Vries Bert, Sauer J., Brown R., Betlyon J., Toplyn M. Umm El-Jimal, Bourgade de "Frontière" : à propos de Bert De Vries (ed.) Umm el-Jimal. I.. In: Syria. Tome 78, 2001. pp. 209-217
Global well-posedness of Korteweg–de Vries equation in H−3/4(R)
No full textAbstractWe prove that the Korteweg–de Vries initial-value problem is globally well-posed in H−3/4(R) and the modified Korteweg–de Vries initial-value problem is globally well-posed in H1/4(R). The new ingredient is that we use directly the contraction principle to prove local well-posedness for KdV equation in H−3/4 by constructing some special resolution spaces in order to avoid some ‘logarithmic divergence’ from the high–high interactions. Our local solution has almost the same properties as those for Hs (s>−3/4) solution which enable us to apply the I-method to extend it to a global solution
Estudo de invariantes em sistemas dinamicos continuos e não-lineares
No full textDissertação (mestrado) - Universidade Federal de Santa Catarina. Centro de Ciencias Fisicas e MatematicasNo presente trabalho investigamos vários aspectos relacionados com a existência de invariantes em sistemas dinâmicos contínuos e não-lineares. Apresentamos relações de recorrência para gerar os termos presentes nas densidades e fluxos da equação de Korteweg-de Vries e nas densidades da equação modificada de Korteweg-de Vries. Nossas relações são baseadas na observação empírica de que, para um dado rank r, o conjunto {P2r} de todas as partições do inteiro 2r contém todos os monômios de {Xr-1} e {Tr}. As relações são facilmente implementáveis em máquinas capazes de efetuar manipulações algébricas. Obtivemos, através de nossas relações de recorrência, quatro novos invariantes para a equação de Korteweg-de Vries e três para a equação modificada de Korteweg-de Vries. Testamos a validade de conjecturas estabelecidas recentemente por Torriani usando análise combinatorial. Além disso, analisamos três métodos encontrados na literatura recente para a obtenção de constante de movimento de equações de evolução não-lineares. São eles: uma relação entre constantes de movimento e equações variacionais; um procedimento para a obtenção de constantes de movimento associadas a cada simetria de Lie da equação diferencial que descreve o sistema; e a obtenção de novas constantes a partir de constantes conhecidas usando os operadores das transformações infinitesimais que deixam a equação de evolução invariante. São feitas aplicações destes métodos a equações conhecidas com ênfase em física atômica e óptica quântica
On the well-posedness of the Schrödinger–Korteweg–de Vries system
No full textAbstractWe prove that the Cauchy problem for the Schrödinger–Korteweg–de Vries system is locally well-posed for the initial data belonging to the Sobolev spaces L2(R)×H−3/4(R), and Hs(R)×H−3/4(R) (s>−1/16) for the resonant case. The new ingredient is that we use the F¯s-type space, introduced by the first author in Guo (2009) [10], to deal with the KdV part of the system and the coupling terms. In order to overcome the difficulty caused by the lack of scaling invariance, we prove uniform estimates for the multiplier. This result improves the previous one by Corcho and Linares (2007) [6]
Dr. G. J. De Vries, Spel bij Plato
No full textLeijs R. Dr. G. J. De Vries, Spel bij Plato. In: L'antiquité classique, Tome 19, fasc. 1, 1950. pp. 258-259
Teoria quase-linear de Kato e a KdV transicional
No full textDissertação (mestrado) - Universidade Federal de Santa Catarina. Centro de Ciências Físicas e Matemáticas.Neste trabalho desenvolvemos a teoria linear e quase-linear de T. Kato e fazemos uma aplicação à equação de Korteweg-de Vries transicional (t-KdV), mostramos que o problema de Cauchy associado a esta equação tem solução única local nos espaços de Sobolev usuais
On the Stochastic Korteweg–de Vries Equation
No full textAbstractWe consider a stochastic Korteweg–de Vries equation forced by a random term of white noise type. This can be a model of water waves on a fluid submitted to a random pressure. We prove existence and uniqueness of solutions inH1(R) in the case of additive noise and existence of martingales solutions inL2(R) in the case of multiplicative noise.Copyright 1998 Academic Press.Nous étudions une équation de Korteweg–de Vries stochastique comportant une force aléatoire de type bruit blanc. Cette équation peut décrire les ondes de surface sur un fluide soumis à un champ de pression aléatoire. Nous montrons l'existence et l'unicité de solutions dansH1(R) lorsque le bruit est additif. Puis, dans le cas du bruit multiplicatif, nous établissons l'existence de solutions martingales dansL2(R)
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