Thesis (doctoral)--Universität Marburg, 1911. / Vita. Includes bibliographical references.

Thesis (doctoral)--Agricultural University of Norway, 1997. / Summary in Norwegian and English. Includes bibliographical references.

Thesis (Ph. D.)--University of Missouri, 1929. / Vita. "Lithoprinted." Includes bibliographical references (p. 27).

Electromagnetic effects play an important role in many engineering problems. The fast and accurate numerical methods for electromagnetic analysis are highly desired in both the low-frequency analysis and the static analysis. In the first part of this thesis, a low-frequency stable domain decomposition method, the augmented equivalence principle algorithm (A-EPA) with augmented electric field integral equation (A-EFIE), is introduced for analyzing the electromagnetic problems at low frequencies. The A-EFIE is first employed as a inner current solver for the EPA algorithm so that it improves the low-frequency inaccuracy issue. This method, however, cannot completely remove the low-frequency breakdown. To overcome it, the A-EPA with A-EFIE is studied and developed so that it has the capability to solve low-frequency problems accurately. In the second part, novel Helmholtz decomposition based fast Poisson solvers for both 2-D and 3-D problems are introduced. These new methods are implemented through the quasi-Helmholtz decomposition technique, i.e. the loop-tree decomposition. In 2-D cases, the proposed method can achieve O(N) complexity in terms of both computational cost and memory consumption for moderate accuracy requirements. Although computational costs become higher when more accurate results are needed, a multilevel method by using the hierarchical loop basis functions can obtain the desired efficiency. The same idea can be extend to 3-D case for exploiting a new generation of fast method for electrostatic problems. / published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

Eigenvalue problems find important applications in engineering electromagnetics. The most studied examples are cavity resonance problems and wave guidance problems, in which the electromagnetic fields are bounded or semi-bounded. Efficient eigenvalue based analysis is developed to investigate both bounded and unbounded fields in a unified manner. Incorporating a locally-conformal finite difference technique, a modal expansion based model order reduction is proposed to elucidate complicated physics of wave-matter interaction, and the fast field approximation provides quick guidance to design and optimization problems of a variety of devices. As the key to modal expansion, modal analysis for interior spectrum needs to be carried out efficiently in large scale applications. A null-space shift algorithm and a fast cosine- and sine- transform based preconditioning scheme are proposed to greatly enhance the performance of a conventional eigensolver. To model multi-junction parallel plate waveguides, both explicit and implicit mode matching schemes are introduced, where eigenanalysis are incorporated. Both schemes intelligently conform to the geometrical characteristics, which are suitable for demonstrating interesting phenomena of zero index materials. Finally, a differential forms inspired discretization scheme is proposed for the edge element based finite element analysis of waveguide problems where the variational expressions involve transverse fields only. Differential forms provide useful insight on the discretization of complicated variational expressions. / published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

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Hindering important petroleum projects in Kuwait by the parliament under the pretext of preventing the violation of the oil ownership concepts included in the constitution is almost turning into a phenomenon. According to the Kuwaiti constitution, the natural resources are owned by the state, and consequently foreign oil ownership of national reserves is prohibited (Article 21 of the constitution). In addition, exploiting the national natural resources by other party than the state, though it is legally possibly, is restricted by several conditions (Article 152 of the constitution). The national petroleum project concerns the re-involvement of the international oil companies (IOCs) to develop production capacity from Kuwait’s northern oil fields, which is commonly known as the ‘Kuwait Project’, has met a considerable opposition by the parliament, and consequently has not been yet signed, in spite of the completion of its technical, financial and legal framework. The reason for opposing this project is that it, arguably, may include provisions contradicting with the constitutional framework for the exploitation of petroleum in Kuwait. Whether or not Kuwait’s oil ownership concepts stand as an obstacle to developing Kuwait’s oil production capacity requires examining the application of these concepts to the ‘Kuwait Project’. Such analysis will lead to accurately determine the effectiveness of these concepts when applied in practice and to identify aspects of possible incapability in addressing related issues.

Let K(q) be the finite field with q elements and characteristic p. Let f(x) be a monic polynomial of degree d with coefficients in K(q). Let C(f) denote the number of distinct values of f(x) as x ranges over K(q). It is easy to show that C(f) ≤ [|(q - 1)/d|] + 1. Now, there is a characterization of polynomials of degree d < √q for which C(f) = [|(q - 1)/d|] +1. The main object of this work is to give a characterization for polynomials of degree d < ⁴√q for which C(f) < 2q/d. Using two well known theorems: Hurwitz genus formula and Andre Weil's theorem, the Riemann Hypothesis for Algebraic Function Fields, it is shown that if d < ⁴√q and C(f) < 2q/d then f(x) - f(y) factors into at least d/2 absolutely irreducible factors and f(x) has one of the following forms: (UNFORMATTED TABLE FOLLOWS) f(x - λ) = D(d,a)(x) + c, d|(q² - 1), f(x - λ) = D(r,a)(∙ ∙ ∙ ((x²+b₁)²+b₂)²+ ∙ ∙ ∙ +b(m)), d|(q² - 1), d=2ᵐ∙r, and (2,r) = 1 f(x - λ) = (x² + a)ᵈ/² + b, d/2|(q - 1), f(x - λ) = (∙ ∙ ∙((x²+b₁)²+b₂)² + ∙ ∙ ∙ +b(m))ʳ+c, d|(q - 1), d=2ᵐ∙r, f(x - λ) = xᵈ + a, d|(q - 1), f(x - λ) = x(x³ + ax + b) + c, f(x - λ) = x(x³ + ax + b) (x² + a) + e, f(x - λ) = D₃,ₐ(x² + c), c² ≠ 4a, f(x - λ) = (x³ + a)ⁱ + b, i = 1, 2, 3, or 4, f(x - λ) = x³(x³ + a)³ +b, f(x - λ) = x⁴(x⁴ + a)² +b or f(x - λ) = (x⁴ + a) ⁱ + b, i = 1,2 or 3, where D(d,a)(x) denotes the Dickson’s polynomial of degree d. Finally to show other polynomials with small value set, the following equation is obtained C((fᵐ + b)ⁿ) = αq/d + O(√q) where α = (1 – (1 – 1/m)ⁿ)m and the constant implied in O(√q) is independent of q.

A number of effects of low to medium strength (< 2000 gauss photospheric) magnetic fields on otherwise normal stars are proposed and examined. We consider magnetic perturbations to the standard stellar structure and evolutionary calculations in the core, the deep envelope, and the extreme outer envelope in intermediate to high mass stars. In the stellar core the gas pressure probably far exceeds the (B²/8π) magnetic field pressure term so that the only effect of such a field may come from its inhibiting convection in the core. We present isochrones of both convective and radiative core models of 2-5 M(⊙). In the deep envelope, we may expect to see mixing of partially nuclear processed material driven by rising and falling magnetic flux tubes. The effects of this mixing will be brought to the surface during the deep convection phase of the star's tenure as a red giant. We use this model to predict a signature for magnetic mixing based on the CNO isotope and abundance ratios. In the outer envelope the gas pressure is low enough that we might expect to see a perturbation of the stellar structure due to the magnetic field pressure itself. We calculate this perturbation under several physical models for intermediate and high mass stars and determine that sufficient magnetic field energy may be available in the outer envelope to expand a star by about 20% over its unperturbed radius. Finally we consider the evidence for the existence of non-magnetic neutron stars, concluding that while no non-magnetic neutron stars have ever been positively identified, we have no evidence that prevents the existence of at least as many non-magnetic as magnetic neutron stars.

No description available.