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 39 for “"unit circle"”.
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Rodrigues Formula for Jacobi Polynomials on the Unit Circle
… D. Costin) for finding Jacobi polynomials on the unit circle. Finally, we consider some examples of Jacobi polynomials and demonstrate different methods of discovering them.
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Root distribution of polynomials and distance sums on the unit circle
… polynomials to have all zeros on the unit circle. We examine how such polynomials are used to generate further such polynomials. We also analyze the distribution of zeros of certain families of self-inversive polynomials and evaluate their discriminants. Our second topic is the sum of …
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On the Convergence and Divergence of Q-Continued Fractions on and Off the Unit Circle
… sense at an uncountable set of points on the unit circle. We also show that the Rogers-Ramanujan continued fraction converges generally at all roots of unity (in contrast to classical convergence) and that it does not converge generally at any point outside the unit circle."
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Poncelet polygons through the lenses of orthogonal polynomials on the unit circle, finite Blaschke products, and numerical ranges.
… of families of polygons inscribed in the unit circle with interlacing vertices. In projective geometry, we consider Poncelet curves which admit a family of circum-scribed polygons. From the perspective of linear algebra, we consider the eigenvalues of a one parameter family of matrices …
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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
… orthogonal over a symmetric arc of the unit circle with respect to a generalized Jacobi-type weight. Full asymptotic expansions for the orthogonal polynomials are obtained at every point of the complex plane. Our method of proof is based on a characterization of the orthogonal …
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Zeros of partial sums of power series
… radius of convergence one, every point on the unit circle is a limit point of zeros of partial sums of the power series. In this thesis, the relationship between the properties of the function and the behavior of the zeros of its partial sums is investigated. We prove that the set of limit …
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Classifying expansions of the real field by complex subgroups
… by a subgroup generated by an element of the unit circle and a positive real number. We then consider expansions by a subgroup generated by a complex number and a positive real number. In both of these cases, we investigate the sets definable in these structures and their open cores.
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Model Theory of Fields With Multiplicative Groups
… real field with a distinguished subgroup of the unit circle group in the complex plane.
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The density of complex zeros of random sums
… complex polynomial largely tend towards the unit circle as the degree approaches infinity. For complex zeros, the expected density was dealt with by Shepp and Vanderbei for real independent and identically distributed normal coefficients. Their technique exploits the argument principle and …
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Using Dynamic Graphing Software to Develop Conceptual Understanding of Transformations of Trigonometric Functions
… exploration of right triangle trigonometry, the unit circle, and their relationship to parent trigonometric functions. This project also applies Desmos to explore unique mathematical representations that can support student understanding of relationships between right triangle trigonometry and …
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On the discrete nonlinear Schrödinger equation with PT-Symmetry
… operator has no spectrum outside nor inside the unit circle, there is no blow up; 2) when it does, mirror symmetric initial conditions are sufficient, but not necessary, for bounded solutions; 3) to obtain bounded solutions, each spectrum outside the unit circle needs (but is not sufficient) to …
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Integrals of harmonic functions over curves and surfaces
… functions given by the Cantors measures on the unit circle in terms of the porosity of the Cantor set. The exact lower bound of it for all normalized positive harmonic functions in the unit ball of $R\sp{n}$ is established. Also, its value for the functions given by the Dirac measure on the unit …
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Hybrid Control For Aerospace Systems
… angular measurements that evolve on the unit circle. To this end, we make use of a recent formalism tailored to hybrid dynamical systems for both modeling and proving desirable properties of the proposed algorithms, which are as well confirmed by simulative and experimental validations.
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A topological generalization of Schwarz' lemma
… = zg(z) where g(z) is holomorphic inside the unit circle, and if |f(z)| < 1 when |s| < 1, then |f(z)| < |z| when |z| < 2. The proof for this is based on the fast that if f(s) is holomorphic in a region, its absolute value has no relative maxima in the interior of the region. Max Zorn has …
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VLSI implementation of an efficient method for the computation of line spectral frequencies
… polynomials to map the upper portion of the unit circle onto the real interval [-1,1] by converting the polynomials into a Chebyshev polynomial series representation. Because Chebyshev polynomials may be evaluated efficiently using the Clenshaw recurrence formula, far fewer computations are …
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Bayesian dynamic borrowing strategies with power priors and quantifying prior information for circular priors.
… prior. Circular data are measurements on a unit circle, with the von Mises model being the most widely used model for such data. We gauge the information contained in priors for the von Mises data model using prior equivalent sample size.
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Sensitivity analysis of digital filter structures
… imply system poles which are almost on the unit circle in the z-plane; therefore, it is proposed to scale the radii of the pole and zero magnitudes. Thus, the scaled system has the same frequency information as the original system, but performs better numerically. The direct II form …
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Robust self-tuning predictive control for industrial applications
… are penalized rather than their integral on the unit circle. Both one degree and two degree of freedom MPC algorithms are developed. The two degree of freedom design leads to mixed $H\sb2/H\sb{\infty}$ (minimax) predictive control law design. Extensions of the method to the multivariable case are …
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Self-shrinkers of mean curvature flow and harmonic map heat flow with rough boundary data
… for the harmonic map heat flow from the unit circle into a closed manifold, and use it to construct sweepouts with the following good property: each curve in the tightened sweepout, whose energy is close to the maximal energy of curves in the sweepout, is itself close to a closed …
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Boundary perturbation of the Laplace eigenvalues and applications to electron bubbles and polygons
… The polygon is treated as a perturbation of the unit circle and its eigenvalues are approximated by a Taylor series. The accuracy of our approach is measured by comparison with finite element estimates. For the lowest eigenvalue, the first Taylor term provides an estimate within 10-5 of the true …
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