11 
Some properties of quartic functions of one variableVarnhorn, Mary Catherine. January 1939 (has links)
ThesisCatholic University of America. / Includes bibliographical references.

12 
Autour des équations d’Einstein dans le vide avec un champ de Killing spatial de translation. / Around vacuum Einstein equations with a translation spacelike Killing vector fieldHuneau, Cécile 09 December 2014 (has links)
Dans cette thèse, nous étudions les équations d’Einstein dans le vide avec un champ de Killing de translation. En présence de cette symétrie, les équations d’Einstein dans le vide en dimension 3+1 peuvent s’écrire, dans le cas polarisé, comme un système d’équations d’Einstein couplées à un champ scalaire en dimension 2+1. Dans la première partie de cette thèse, nous étudions les équations de contraintes dans le cas asymptotiquement plat. Les équations de contraintes sont des équations de compatibilité qui doivent être satisfaites par les données initiales. Nous montrons l’existence de solutions pour des données assez petites, et introduisons un développement asymptotique faisant intervenir des quantités correspondant aux charges globales. Dans une deuxième partie nous montrons la stabilité de l’espacetemps de Minkowski avec un champ de Killing de translation, en temps exponentiellement grand par rapport à la petitesse de la donnée initiale. Nous travaillons dans les coordonnées d’onde généralisées. Nous introduisons une famille de métriques Ricci plates, et imposons le comportement asymptotique de nos solutions à l’extérieur du cône de lumière en choisissant un élément de cette famille de manière adéquate. Ce choix permet la convergence de nos solutions à l’intérieur du cône de lumière vers la solution de Minkowski. Dans la dernière partie de cette thèse nous étudions les équations de contraintes dans le cas compact hyperbolique. Nous montrons l’existence d’une équation limite associée aux équations de contraintes. / This thesis aim sat studying vacuum Einstein equations with a spacelike Killing vector field. With this symmetry, 3+1 vacuum Einstein equations reduce, in the polarized case, to Einstein equations coupled to a scalar field in 2+ 1 dimensions. In the first part of this thesis, we study the constraint equations in the asymptotically flat case. The constraint equations correspond to computability conditions that the initial data must satisfy. We show the existence of solutions for small data, and we introduce an asymptotic expansion involving quantities which are the 2 dimensional equivalents for the global charges. In the second part, we show the stability of Minkowski spacetime with a translation spacelike Killing vector field in exponential time with respect to the smallness of initial data. We introduce a family of Ricci flat metrics, and we impose the asymptotic behaviour of our solutions in the exterior of the light cone by picking the right element in the family. This choice allows for the convergence to Minkowski solution in the interior of the light cone. In the last part of this thesis, we study the constraint equations in the compact hyperbolic case. We show the existence of a limit equation associated to the constraint equations.

13 
The solution of differential equations through integral equationsSwanson, Charles Andrew January 1953 (has links)
A method of writing the solution of a second order differential equation through a Volterra Integral Equation is developed. The method is applied to initial value problems, to special functions, and to bounded Quantum Mechanical problems.
Some of the results obtained are original, and other results agree essentially with the work done previously by others. / Science, Faculty of / Mathematics, Department of / Graduate

14 
Thermodynamic properties from cubic equations of stateMak, Patrick ChungNin January 1988 (has links)
The LielmezsMerriman equation of state has been modified in such a way that it can be applied over the entire PVT surface except along the critical isotherm. The dimensionless T* coordinate has been defined according to the two regions on the PVT surface as:
[Formula Omitted]
The two substancedependent constants p and q are generated from the vapor pressure data.
The applicability of the proposed modification has been tested by comparing its predictions of various pure compound physical and thermodynamic properties with known experimental data and with predictions from the SoaveRedlichKwong and PengRobinson equations of state. The proposed equation is the most accurate equation of state for calculating vapor pressure, and saturated vapor and liquid volumes. The PengRobinson equation is the best for enthalpy and entropy of vaporization estimations. The SoaveRedlichKwong equation is the least accurate equation for pressure and volume predictions in the single phase regions. For temperature prediction, all three equations of state give similar results in the subcritical and supercritical regions. None of the three equations is capable of representing all departure functions accurately. The PengRobinson equation and the proposed equation are very similar in accuracy except in the region where the temperature is near the critical. That is, between 0.95 ≤ Tr ≤ 1.05, the proposed equation gives rather poor results. For isobaric heat capacity calculation, both SoaveRedlichKwong and PengRobinson equations are adequate. The SoaveRedlichKwong equation gives the lowest overall average RMS % error for JouleThomson coefficient estimation. The SoaveRedlichKwong equation also provides the most reliable prediction for the JouleThomson inversion curve right up to the maximum inversion pressure.
None of the cubic equations of state studied in this work is recommended
for second virial coefficient calculation below Tr = 0.8. An αfunction specifically
designed for the calculation of second virial coefficient has been included in this
work. The estimation from the proposed function gives equal, if not better, accuracy than the Tsonopoulos correlation. / Applied Science, Faculty of / Chemical and Biological Engineering, Department of / Graduate

15 
Equations and equational theoriesSrour, Gabriel, 1958 January 1984 (has links)
No description available.

16 
Application of lie group methods to certain partial differential equations / Isaiah Elvis MhlangaMhlanga, Isaiah Elvis January 2012 (has links)
In the first part of this work, two nonlinear partial differential equations, namely, a
modified CamassaHolmDegasperisProcesi equation and the generalized Kortewegde Vries equation with two power law nonlinearities are studied. The Lie symmetry method along with the simplest equation method is used to construct exact Solutions for these two equations. The second part looks at two systems of partial
differential equations, namely, the generalized BoussinesqBurgers equations and the
(2+1)dimensional DaveyStewartson equations. The Lie symmetry method and the
travelling wave hypothesis approach are utilized to obtain exact solutions of the generalized BoussinesqBurgers equations. The travelling wave hypothesis approach is
used to find exact solutions of the (2+ 1 )dimensional DaveyStewartson equations. / Thesis (Msc. in Applied Mathematics) NorthWest University, Mafikeng Campus, 2012

17 
Lagrangian methods of cosmic web classificationFisher, Justin David January 2016 (has links)
A Research Report submitted to the Department of Physics, Faculty of Science, University
of the Witwatersrand, Johannesburg, in partial ful lment of the requirements for the degree
of Master of Science.
Signed on the 24th March 2016 in Johannesburg. / This research report uses cosmological Nbody simulations to examine the the large
scale mass distribution of the Universe, known as the cosmic web. The cosmic web can be
classi ed into nodes, laments, sheets and voids  each with its own characteristic density
and velocity elds. In this work, the author proposes a new Lagrangian cosmic web classi
cation algorithm, based on smoothed particle hydrodynamics. This scheme o ers adaptive
resolution, resolves smaller substructure and obeys similar statistical properties with existing
Eulerian methods. Using the new classi cation scheme, halo clustering dependence on cosmic
web type is examined. The author nds halo clustering is signi cantly correlated with
web type. Consequently, the mass dependence of halo clustering may be explained by the
fractions of web types found for a particular halo mass. Finally, an analysis of dark matter
halo spin, shape and fractional anisotropy is presented per web type to suggest avenues for
future work.

18 
Equivalent lagrangians and transformation maps for differential equationsWilson, Nicole 09 January 2013 (has links)
A dissertation submitted to the Faculty of Science, University of the
Witwatersrand, in fulflment of the requirements for the degree of
Master of Science. / The Method of Equivalent Lagrangians is used to find the solutions of a given
differential equation by exploiting the possible existence of an isomorphic Lie
point symmetry algebra and, more particularly, an isomorphic Noether point
symmetry algebra. Applications include ordinary differential equations such
as the Kummer Equation and the Combined GravityInertialRossby Wave
Equation and certain classes of partial differential equations related to the
(1 + 1) linear wave equation. We also make generalisations to the (2 + 1) and
(3 + 1) linear wave equations.

19 
Integral equations involving special functions /Johnson, Ben Clarence. January 1964 (has links)
Thesis (Ph. D.)Oregon State University, 1964. / Typescript. Includes bibliographical references (leaves 6768). Also available on the World Wide Web.

20 
Functions of positive type and related topics in general analysis ...Dines, Charles Ross, January 1900 (has links)
Thesis (Ph. D.)University of Chicago, 1915. / Vita. "A Private Edition Distributed by the University of Chicago Libraries." "Extracted from the Proceedings of the London mathematical society, series 2, vol. 15, part 4." Includes bibliographical references. Also available on the Internet.

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