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81 
On an integral related to Vinogradov's integral /Abramson, Daniel, January 1998 (has links)
Thesis (Ph. D.)University of Texas at Austin, 1998. / Vita. Includes bibliographical references (leaves 148149). Available also in a digital version from Dissertation Abstracts.

82 
Numerical evaluation and estimation of multiple integralsHirsch, Peter Max, January 1966 (has links)
Thesis (Ph. D.)University of WisconsinMadison, 1966. / Typescript. Vita. eContent providerneutral record in process. Description based on print version record. Includes bibliographical references.

83 
Characterisierungen von Saturationsklassen in L¹En)Trebels, Walter. January 1900 (has links)
Diss.Technische Hochscule, Aachen. / Vita. Bibliography: p. 8993.

84 
Numerical contour integrationBarnhill, Robert E. January 1964 (has links)
Thesis (Ph. D.)University of Wisconsin, 1964. / Typescript. Vita. eContent providerneutral record in process. Description based on print version record. Includes bibliographical references (p. 7881).

85 
Some boundary element methods for heat conduction problemsHamina, M. (Martti) 12 April 2000 (has links)
Abstract
This thesis summarizes certain boundary element methods
applied to some initial and boundary value problems.
Our model problem is the twodimensional homogeneous heat conduction
problem with vanishing initial data. We use the heat potential
representation of the solution. The given boundary conditions,
as well as the choice of the representation formula,
yield various boundary integral equations. For the sake of simplicity,
we use the direct boundary integral approach, where
the unknown boundary density appearing in the boundary integral
equation is a quantity of physical meaning.
We consider two different sets of boundary conditions, the Dirichlet problem,
where the boundary temperature is given and the Neumann problem,
where the heat flux across the boundary is given.
Even a nonlinear Neumann condition satisfying certain monotonicity
and growth conditions is possible. The approach yields
a nonlinear boundary integral equation of the second kind.
In the stationary case, the model problem reduces to a potential
problem with a nonlinear Neumann condition. We use the spaces of smoothest
splines as trial functions. The nonlinearity is approximated by using the
L2orthogonal projection. The resulting collocation scheme retains
the optimal L2convergence. Numerical experiments are in
agreement with this result.
This approach generalizes to the time dependent case.
The trial functions are tensor products of piecewise linear
and piecewise constant splines. The proposed projection method
uses interpolation with respect to the space variable and the orthogonal
projection with respect to the time variable. Compared to the
Galerkin method, this approach simplifies the realization of the
discrete matrix equations.
In addition, the rate of the convergence is of optimal order.
On the other hand,
the Dirichlet problem, where the boundary temperature is given,
leads to a single layer heat operator equation of the first kind.
In the first approach, we use tensor products of piecewise linear splines
as trial functions with collocation at the nodal points.
Stability and suboptimal L2convergence of the method were proved in the
case of a circular domain. Numerical experiments indicate the
expected quadratic L2convergence.
Later, a PetrovGalerkin approach was proposed, where the trial functions were
tensor products of piecewise linear and piecewise constant splines.
The resulting approximative scheme is stable and
convergent. The analysis has been carried out in the cases of
the single layer heat operator and the hypersingular heat operator.
The rate of the convergence with respect to the L2norm
is also here of suboptimal order.

86 
Vector field decomposition and first integrals with applications to nonlinear systemsScholes, Michael Timothy 20 August 2012 (has links)
M.Sc. / Roels [1] showed that on a two dimensional symplectic manifold, an arbitrary vector field can be locally decomposed into the sum of a gradient vector field and a Hamilton vector field. The Roels decomposition was extended to be applicable to compact even dimensional manifolds by Mendes and Duarte [2]. Some of the limitations of local decomposition are overcome by incorporating modern work on Hodge decomposition. This leads to a theorem which, in some cases, allows an arbitrary vector field on an even mdimensional noncompact manifold to be decomposed into one gradient vector field and up to m1 Hamiltonian vector fields. The method of decomposition is condensed into an algorithm which can be implemented using computer algebra. This decomposition is then applied to chaotic vector fields on noncompact manifolds [3]. This extended Roels decomposition is also compared to Helmholz decomposition in R 3 . The thesis shows how Legendre polynomials can be used to simplify the Helmholz decomposition in nontrivial cases. Finally, integral preserving iterators for both autonomous and nonautonomous first integrals are discussed [4]. The Hamilton vector fields which result from Roels' decomposition have their Hamiltonians as first integrals.

87 
Speech synthesis by Haar functions with comparison to a terminal analog device /Meltzer, David January 1972 (has links)
No description available.

88 
On the numerical evaluation of finitepart integrals involving an algebraic singularityKutt, H. R. (Helmut Richard) 08 1900 (has links)
Thesis (PhD)Stellenbosch University, 1975. / ENGLISH ABSTRACT: Some problems of applied mathematics, for instance in the fields of
aerodynamics or electron optics, involve certain singular integrals
which do not exist classically. The problems can, however, be solved
pLovided that such integrals are interpreted as finitepart integrals.
Although the concept of a finitepart integral has existed for
about fifty years, it was possible to define it rigorously only by means
of distribution theory, developed about twentyfive years ago. But, to
the best of our knowledge, no quadrature formula for the numerical eva=
luation of finitepart integrals ha~ been given in the literature.
The main concern of this thesis is the study and discussion of.two
kinds of quadrature formulae for evaluating finitepart integrals in=
volving an algebraic singularity.
Apart from a historical introduction, the first chapter contains
some physical examples of finitepart integrals and their definition
based on distribution theory. The second chapter treats the most im=
portant properties of finitepart integrals; in particular we study
their behaviour under the most common rules for ordinary integrals.
In chapters three and four we derive a quadrature formula for equispaced
stations and one which is optimal in the sense of the Gausstype quadra=
ture. In connection with the latter formula, we also study a new class
of orthogonal polynomials. In the fifth and.last chapter we give a
derivativefree error bound for the equispaced quadrature formula. The
error quantities which are independent of the integrand were computed
for the equispaced quadrature formula and are also given. In the case
of some examples, we compare the computed error bounds with the actual
errors.
~esides this theoretical investigation df finitepart integrals,
we also computed  for several orders of the algebraic singularity
the coefficients for both of the aforesaid quadrature formulae, in
which the number of stations ranges from three up to twenty. In the
case of the equispaced quadrature fortnu1a,we give the weights and 
for int~ger order of the singularity  the coefficients for a numerical
derivative of the integrand function. For the Gausstype quadrature,
we give the stations, the corresponding weights and the coefficients of
the orthogonal polynomials.
These data are being published in a separate report [18] which
also contains detailed instructions on the use of the tables.

89 
Computational techniques for evaluating extremely low frequency electromagnetic fields produced by a horizontal electric dipole in seawaterOrr, Andrew McLean White January 2000 (has links)
No description available.

90 
An exploration of stochastic modelsGross, Joshua January 1900 (has links)
Master of Science / Department of Mathematics / Nathan Albin / The term stochastic is defined as having a random probability distribution or pattern that may be analyzed statistically but may not be predicted precisely. A stochastic model attempts to estimate outcomes while allowing a random variation in one or more inputs over time. These models are used across a number of fields from gene expression in biology, to stock, asset, and insurance analysis in finance. In this thesis, we will build up the basic probability theory required to make an ``optimal estimate", as well as construct the stochastic integral. This information will then allow us to introduce stochastic differential equations, along with our overall model. We will conclude with the "optimal estimator", the Kalman Filter, along with an example of its application.

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