A new method is presented for the numerical computation of the generalized eigen- values of real Hamiltonian or symplectic pencils and matrices. The method is strongly backward stable, i.e., it is numerically backward stable and preserves the structure (i.e., Hamiltonian or symplectic). In the case of a Hamiltonian matrix the method is closely related to the square reduced method of Van Loan, but in contrast to that method which may suffer from a loss of accuracy of order sqrt(epsilon), where epsilon is the machine precision, the new method computes the eigenvalues to full possible accuracy.

The diploma thesis deals with the creation of a detail FEM model all-composite wing of glider. Reduction created FEM model of the beam model. The models are calculated natural frequencies, vibration shapes wings and then subsequently compared the results of analyzes of both models.

The aim of this dissertation is to characterize the MIMO channel in two very distinct indoor scenarios: an office building and an industrial environment. The study investigates the use of single- and dual-polarized antenna MIMO systems, and attempts to model the channel using well-known analytical models. The suitability of MIMO architectures employing either single or dual-polarization antennas is presented, with the purpose of identifying not only which architecture provides better average capacity performance, but also which is more robust for avoiding low channel rank. A measurement campaign employing dual-polarized 8×8 patch arrays at 2.4 GHz and 5.2 GHz is analyzed. For both environments the performance of three 4×4 subsystems (dual-polarized, vertical-polarized and horizontal-polarized) are compared in terms of the average capacities attained by these systems and their eigenvalue distributions. Average capacities are found to be only marginally different, indicating little advantage of dual-polarized elements for average performance. However, an eigenvalue analysis indicates that the dual-polarized system is most robust for full-rank MIMO communications, by providing orthogonal channels with more equal gain. The analysis of the analytical models shows that the Kronecker and Weichselberger models underestimate the measured data. Kronecker models are known to perform poorly for large antenna sizes and the performance of the Weichselberger model can be attributed to certain parts of the channel not fading enough. / Dissertation (MEng)--University of Pretoria, 2009. / Electrical, Electronic and Computer Engineering / unrestricted

We characterize trees that have greatest maximum p-Laplacian eigenvalue among all trees with a given degree sequence. We show that such extremal trees can be obtained by breadth-first search where the vertex degrees are non-increasing. These trees are uniquely determined up to isomorphism. Moreover, their structure does not depend on p. / Series: Research Report Series / Department of Statistics and Mathematics

The inverse eigenvalue problem for a given operator is to determine the coefficients by using knowledge of its eigenfunctions and eigenvalues. These are determined by the behavior of the solutions on the domain boundaries. In our problem, the Schrödinger operator acting on functions defined on the unit ball of $\mathbb{R}^3$ has a radial potential taken from $L^2_{\mathbb{R}}[0,1].$ Hence the set of the eigenvalues of this problem is the union of the eigenvalues of infinitely many Sturm-Liouville operators on $[0,1]$ with the Dirichlet boundary conditions. Each Sturm-Liouville operator corresponds to an angular momentum $l =0,1,2....$. In this research we focus on the uniqueness property. This is, if two potentials $p,q \in L^2_{\mathbb{R}}[0,1]$ have the same set of eigenvalues then $p=q.$ An early result of P\"oschel and Trubowitz is that the uniqueness of the potential holds when the potentials are restricted to the subspace of the even functions of $L_{\mathbb{R}}^2[0,1]$ in the $l=0$ case. Similarly when $l=0$, by using their method we proved that two potentials $p,q \in L^2_{\mathbb{R}}[0,1]$ are equal if their even extension on $[-1,1]$ have the same eigenvalues. Also we expect to prove the uniqueness if $p$ and $q$ have the same eigenvalues for finitely many $l.$ For this idea we handle the problem by focusing on some geometric properties of the isospectral sets and trying to use these properties to prove the uniqueness of the radial potential by using finitely many of the angular momentum.

The diploma thesis deals with the creation of a detail FEM model all-composite wing of glider. Reduction created FEM model of the beam model. The models are calculated natural frequencies, vibration shapes wings and then subsequently compared the results of analyzes of both models.

When the eigenvalues of a given eigenvalue problem are symmetric with respect to the real and the imaginary axes, we speak about a Hamiltonian eigenvalue symmetry or a Hamiltonian structure of the spectrum. This property can be exploited for an efficient computation of the eigenvalues. For some elliptic boundary value problems it is known that the derived eigenvalue problems have this Hamiltonian symmetry. Without having a specific application in mind, we trace the question, under which assumptions the spectrum of a given quadratic eigenvalue problem possesses the Hamiltonian structure.

This cumulative habilitation thesis is concerned with eigenvalues of compactly perturbed operators in Banach and Hilbert spaces. A general theory for studying such eigenvalues is developed and applied to the study of some concrete operators of mathematical physics.

In this thesis, we generalize a recent result of A. Eremenko and A. Gabrielov on irreducibility of the spectral discriminant for the Schroedinger equation with quartic potentials. In the first paper, we consider the eigenvalue problem with a complex-valued polynomial potential of arbitrary degree d and show that the spectral determinant of this problem is connected and irreducible. In other words, every eigenvalue can be reached from any other by analytic continuation. We also prove connectedness of the parameter spaces of the potentials that admit eigenfunctions satisfying k > 2 boundary conditions, except for the case d is even and k = d/2. In the latter case, connected components of the parameter space are distinguished by the number of zeros of the eigenfunctions. In the second paper, we only consider even polynomial potentials, and show that the spectral determinant for the eigenvalue problem consists of two irreducible components. A similar result to that of paper I is proved for k boundary conditions.

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第18400号 / 情博第515号 / 新制||情||91(附属図書館) / 31258 / 京都大学大学院情報学研究科数理工学専攻 / (主査)准教授 辻本 諭, 教授 中村 佳正, 教授 梅野 健 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM