997 resultados para Rational Solutions
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Die q-Analysis ist eine spezielle Diskretisierung der Analysis auf einem Gitter, welches eine geometrische Folge darstellt, und findet insbesondere in der Quantenphysik eine breite Anwendung, ist aber auch in der Theorie der q-orthogonalen Polynome und speziellen Funktionen von großer Bedeutung. Die betrachteten mathematischen Objekte aus der q-Welt weisen meist eine recht komplizierte Struktur auf und es liegt daher nahe, sie mit Computeralgebrasystemen zu behandeln. In der vorliegenden Dissertation werden Algorithmen für q-holonome Funktionen und q-hypergeometrische Reihen vorgestellt. Alle Algorithmen sind in dem Maple-Package qFPS, welches integraler Bestandteil der Arbeit ist, implementiert. Nachdem in den ersten beiden Kapiteln Grundlagen geschaffen werden, werden im dritten Kapitel Algorithmen präsentiert, mit denen man zu einer q-holonomen Funktion q-holonome Rekursionsgleichungen durch Kenntnis derer q-Shifts aufstellen kann. Operationen mit q-holonomen Rekursionen werden ebenfalls behandelt. Im vierten Kapitel werden effiziente Methoden zur Bestimmung polynomialer, rationaler und q-hypergeometrischer Lösungen von q-holonomen Rekursionen beschrieben. Das fünfte Kapitel beschäftigt sich mit q-hypergeometrischen Potenzreihen bzgl. spezieller Polynombasen. Wir formulieren einen neuen Algorithmus, der zu einer q-holonomen Rekursionsgleichung einer q-hypergeometrischen Reihe mit nichttrivialem Entwicklungspunkt die entsprechende q-holonome Rekursionsgleichung für die Koeffizienten ermittelt. Ferner können wir einen neuen Algorithmus angeben, der umgekehrt zu einer q-holonomen Rekursionsgleichung für die Koeffizienten eine q-holonome Rekursionsgleichung der Reihe bestimmt und der nützlich ist, um q-holonome Rekursionen für bestimmte verallgemeinerte q-hypergeometrische Funktionen aufzustellen. Mit Formulierung des q-Taylorsatzes haben wir schließlich alle Zutaten zusammen, um das Hauptergebnis dieser Arbeit, das q-Analogon des FPS-Algorithmus zu erhalten. Wolfram Koepfs FPS-Algorithmus aus dem Jahre 1992 bestimmt zu einer gegebenen holonomen Funktion die entsprechende hypergeometrische Reihe. Wir erweitern den Algorithmus dahingehend, dass sogar Linearkombinationen q-hypergeometrischer Potenzreihen bestimmt werden können. ________________________________________________________________________________________________________________
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The main aim of this paper is the development of suitable bases (replacing the power basis x^n (n\in\IN_\le 0) which enable the direct series representation of orthogonal polynomial systems on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable). We present two bases of this type, the first of which allows to write solutions of arbitrary divided-difference equations in terms of series representations extending results given in [16] for the q-case. Furthermore it enables the representation of the Stieltjes function which can be used to prove the equivalence between the Pearson equation for a given linear functional and the Riccati equation for the formal Stieltjes function. If the Askey-Wilson polynomials are written in terms of this basis, however, the coefficients turn out to be not q-hypergeometric. Therefore, we present a second basis, which shares several relevant properties with the first one. This basis enables to generate the defining representation of the Askey-Wilson polynomials directly from their divided-difference equation. For this purpose the divided-difference equation must be rewritten in terms of suitable divided-difference operators developed in [5], see also [6].
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The accurate transport of an ion over macroscopic distances represents a challenging control problem due to the different length and time scales that enter and the experimental limitations on the controls that need to be accounted for. Here, we investigate the performance of different control techniques for ion transport in state-of-the-art segmented miniaturized ion traps. We employ numerical optimization of classical trajectories and quantum wavepacket propagation as well as analytical solutions derived from invariant based inverse engineering and geometric optimal control. The applicability of each of the control methods depends on the length and time scales of the transport. Our comprehensive set of tools allows us make a number of observations. We find that accurate shuttling can be performed with operation times below the trap oscillation period. The maximum speed is limited by the maximum acceleration that can be exerted on the ion. When using controls obtained from classical dynamics for wavepacket propagation, wavepacket squeezing is the only quantum effect that comes into play for a large range of trapping parameters. We show that this can be corrected by a compensating force derived from invariant based inverse engineering, without a significant increase in the operation time.
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Presentation in CODAWORK'03, session 4: Applications to archeometry
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Exam questions and solutions in PDF
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Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files
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Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files
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Exam questions and solutions in PDF
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Exam questions and solutions in PDF
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Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files
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This presentation explains how we move from a problem definition to an algorithmic solution using simple tools like noun verb analysis. It also looks at how we might judge the quality of a solution through coupling, cohesion and generalisation.
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This work aims to test the equilibrium relations of two international macroeconomics models for Colombia, Chile, Mexico and Brazil. The first model is the rational expectation hypothesis (REH) where three key relations will be tested: Purchasing Power Parity (PPP), Uncovered Interest Rate Parity (UIP) and the Fisher Parity condition. The second model follows the line of though of Imperfect Knowledge Economics (IKE) where two equilibrium relations will be tested. According to IKE, even under the assumption that agents are rational, the presence of speculative behavior in financial markets helps explain the long swings often observed in the behavior of exchange rates. The results support the view that the predictions of the IKE model hold for Colombia, while those of the REH hold for both Brazil and Mexico. Mixed findings are obtained for Chile.
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La solución a las necesidades de vivienda de los colombianos, ha ocupado espacios importantes en las políticas públicas de diferentes gobiernos a lo largo del tiempo. Para ello, se han implementado diversas estrategias, que han ido desde la creación de entidades responsables de la administración de proyectos habitacionales, pasando por la incorporación de entidades oficiales y privadas que se vinculan a través de la otorgación de créditos, estimulo a la construcción de diferentes soluciones habitacionales y llegando al diseño de medidas financieras que buscan el estimulo al desembolso de créditos exequibles a través instituciones financieras. El FNA, desempeña un papel trascendental en la solución a las necesidades de los colombianos en su aspiración a tener vivienda propia, ahí se ha entendido que la vivienda usada también hace parte de la solución, para ello, se busca integrar dentro de los estudios de financiamiento del crédito, este proyecto, con el fin de que enlace vendedores y compradores, clasificados por rangos de precio de inmuebles y montos de crédito aprobado, con el fin de optimizar la labor del FNA y disminuir los casos de devolución del crédito por parte del beneficiario, a causa de ausencia de opciones de vivienda que se ajusten a su presupuesto. Así mismo dentro del marco de la Responsabilidad Social Empresarial y para dar respuesta a las expectativas de uno de los Grupos de Interés prioritario del FNA, en concordancia con una de las siete materias fundamentales que consagra la Norma ISO 26.000, denominada “Asunto de los Consumidores”, es un valor agregado a las funciones y servicios brindados por el FNA a sus afiliados para facilitarles la adquisición de su vivienda.
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Executives must walk in a fine line between two ends: by a part, the arbitrary decision making without a rigorous study of the problematic situation, being based on hunches or intuition; on the other hand, to lean too much in rational and quantitative analyses. The decisions generally are not taken by a single executive, requires of the participation of certain groups involved in the problematic one and in this social sense, it is doubtless that, sometimes, conflict of interests coexists frustating the participating and collaborative context on the solution and implantation have arisen from decisions; whereas on the other hand, contexts arise where the collaboration is converted in consensus solutions.