Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 64 for “"Complex Plane"”.
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A Polynomial Based Iterative Method for Linear Parabolic Equations
… (1 - exp(-z))/z,f(0) = 1,$ over ellipses in the complex plane using expansions of f in Chebychev polynomials. The calculation of the Fourier Coefficients requires numerical integration over only a single line segment in the complex plane whose length and orientation depend on the step size and …
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Analytic representations of quantum systems with Theta functions
… An analytic representation in a cell S in the complex plane using Theta functions, is defined. The analytic functions have exactly d zeros in a cell S. The reproducing kernel plays a central role in this formalism. Wigner and Weyl functions are also studied. Quantum systems with positions in a …
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"On the location of zeros of solutions to w"" + Aw = 0 for certain entire functions A"
… polynomials in $z$. We study the location in the complex plane of the zeros of solutions to $(\*)$. Under mild hypotheses on the $P\sb{j}$'s and $Q\sb{j}$'s, we show that there exist both ""zero-scarce"" regions and ""zero-rich"" regions. We call an unbounded region in the complex plane …
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A characterization of the circularity of certain balanced incomplete block designs.
… which are similar to their counterparts in the (complex) plane, the lines and circles which Euclid undoubtedly had in mind. In this manner, the geometer may employ his intuition from the complex plane to prove theorems about other systems. Most "finite geometries" have clearly defined notions of …
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Interpolation of Functions by Integer Points In Complex Analysis
… others provide a unique solution on the whole complex plane. In this thesis we shall concentrate on three such theorems.</p>
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Rodrigues Formula for Jacobi Polynomials on the Unit Circle
… polynomials on a Borel measurable subset of the complex plane. Then we focus on Jacobi polynomials and give a formula (analogous to the one discovered by R. D. Costin) for finding Jacobi polynomials on the unit circle. Finally, we consider some examples of Jacobi polynomials and demonstrate …
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Normal families of integer translations
Let f be a meromorphic function in the complex plane C. We consider the normality of the family of integer translations of f, $\{ f(z + n):n = 0,\pm 1,\pm2,\...\}$. If the family is normal on a set G in C, then the set G is open and periodic with period 1, i.e., $z\pm 1\in G$ for all $z\in G$.
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Asymptotics of Carleman Polynomials for Level Curves of the Inverse of a Shifted Joukowsky Transformation
… their degree increases) at every point of the complex plane.
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Model Theory of Fields With Multiplicative Groups
… subgroup of the unit circle group in the complex plane.
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An Interpolation-Based Approach to Optimal H<sub>∞</sub> Model Reduction
… the relationship between potential theory in the complex plane and the optimal H<sub>∞</sub>-norm interpolation points through several numerical experiments. The results of these experiments suggest that the optimal H<sub>∞</sub> approximation of order r yields an error system for which …
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Circle Packing in Euclidean and Hyperbolic Geometries
… used to find and output a circle packing on the complex plane and hyperbolic disc.
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On the Eigenvalues of the Manakov System
… then it must lie in a certain region in the complex plane. The second issue has to do with a chirped Manakov system. We show that if a system is chirped too much, the soliton effect disappears. While this has been known for some time experimentally, there has not yet been a theoretical result …
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Orthogonal Polynomials On An Arc Of The Unit Circle With Respect To A Generalized Jacobi Weight: A Riemann-Hilbert Method Approach
… polynomials are obtained at every point of the complex plane. Our method of proof is based on a characterization of the orthogonal polynomials as solutions of a 2X2 matrix Riemann-Hilbert problem, which extends to the unit circle the original Riemann-Hilbert characterization for orthogonal …
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The Lie Symmetries of a Few Classes of Harmonic Functions
… this theory to harmonic functions in the complex plane. We will consider harmonic functions in general, harmonic functions with constant Jacobian, harmonic functions with fixed convexity and a few other subclasses of harmonic functions.
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Electrochemical impedance spectroscopy of proton exchange membrane fuel cell stacks
… accurately the shape of the response in the complex plane at currents larger than 20 Amps and did not match the change in ohmic resistance with current.
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Optimal design problems for quasidisks and partially clamped drums: Existence, symmetrization, and numerical methods
It is shown that the class of quasidisks in the complex plane, with fixed quasicircle constant and area, is compact in both the Hausdorff metric and in the sense of Caratheodory convergence. Compactness for chord-arc domains with fixed chord-arc constant and area is shown as a result of the …
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Hardy Space Properties of the Cauchy Kernel Function for a Strictly Convex Planar Domain
… for any strictly convex bounded domain in the complex plane. Namely, we show that for any strictly convex bounded $D\subset\mathbb{C}$ of class $C^2$ if we fix $\zeta$ in the boundary of $D$ and consider the Cauchy Kernel Function</p> <p>\mathcal{K}(\zeta,z)=\frac{1}{2\pi …
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ΧΑΡΑΚΤΗΡΙΣΜΟΣ ΔΥΝΑΜΟΣΕΙΡΩΝ ΜΕ ΜΕΡΙΚΑ ΑΘΡΟΙΣΜΑΤΑ ΠΑΝΩ ΣΕ ΠΕΠΕΡΑΣΜΕΝΟ ΠΛΗΘΟΣ ΚΥΚΛΩΝ
… OF CIRCLES (A PRIORI DEPENDINGON X) IN THE COMPLEX PLANE. THE MAIN RESULT OF THIS PAPER IS THAT FOR EVERY MEMBER OF THE CLASS K, THERE EXIST A COMPLEX NUMBER Ω, /Ω/=1, AND TWO POSITIVE INTEGERS Ν,Κ, N<K, SUCH THAT FOR THE COEFFICIENTS CN WE HAVE: CΜ+Λ(Κ-Ν)=CΜΩΛ, Μ=Ν, Ν+1,...,Κ-1, Λ=1,2,3,... …
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An analytic representation of weak mutually unbiased bases
… The third is an analytic representation in the complex plane based on Theta functions, and their zeros. The analytic representation of the weak mutually unbiased bases is defined with the zeros examined. It is shown that there is a correspondence (triality) that links strongly these three …
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Inversion for subbottom sound velocity profiles in the deep and shallow ocean
… equation is evaluated. The input data is the complex plane-wave refection coefficient estimated from measurements of acoustic pressure in water. We apply the method to experimental data and estimate both the refection coefficient and the seabed svp. A rigorous inversion scheme is hence applied …
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