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Showing 1 to 20 of 410 for “"eigenvalues"”.
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On the Eigenvalues of the Manakov System
… optic cables. The first issue is a bound on the eigenvalues of the Manakov system: if the parameter ξ is an eigenvalue, 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 …
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Matchings, Connectivity, and Eigenvalues in Regular Graphs
We study extremal and structural problems in regular graphs involving various parameters. In Chapter 2, we obtain the best lower bound for the matching number over $n$-vertex connected regular graphs in terms of edge-connectedness and determine when the matching number is minimized. We also …
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Eigenvalues and condition numbers of random matrices
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1989.
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Exponentially Accurate Error Estimates of Quasiclassical Eigenvalues
… Rayleigh-Schröodinger series for the low-lying eigenvalues of the time-independent Schröodinger equation, when the Planck's constant is considered in the semiclassical limit. Under certain hypotheses on the potential energy, we prove that, for any given small value of the Planck's constant, …
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Positive Solutions, Existence Of Smallest Eigenvalues, And Comparison Of Smallest Eigenvalues Of A Fourth Order Three Point Boundary Value Problem
<p>The existence of smallest positive eigenvalues is established for the linear differential equations $u^{(4)}+\lambda_{1} q(t)u=0$ and $u^{(4)}+\lambda_{2} r(t)u=0$, $0\leq t \leq 1$, with each satisfying the boundary conditions $u(0)=u'(p)=u''(1)=u'''(1)=0$ where $1-\frac{\sqrt{3}}{3}\le p < 1$. …
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Dynamic Analysis of Modified Structural Systems (Eigenvalues, Vibrations, Frequencies)
The subject of this study is the development of a set of methods for the calculation of the changes in the frequency of vibration and mode shape of a structure due to changes in the physical system. Such changes may consist of variations of the structural properties of a given system or even of the …
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Asymptotically optimal shapes for counting lattice points and eigenvalues
… case p = 2 corresponds to minimization of high eigenvalues of the Dirichlet Laplacian on rectangles, and so our work generalizes a result of Antunes and Freitas. Similarly, we generalize a Neumann eigenvalue maximization result of van den Berg, Bucur and Gittins. Further, Ariturk and Laugesen …
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Convergence of the Arnoldi Iteration for Estimating Extreme Eigenvalues
Krylov subspace methods, like the Arnoldi iteration, are a powerful tool for efficiently solving high-dimensional linear algebra problems. In this work, we analyze the convergence of Krylov methods for estimating the numerical range of a matrix. Prior bounds on approximation error often depend on …
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Eigenvalues and low energy eigenvectors of quantum many-body systems
… into two parts. The first part is devoted to eigenvalues of quantum many-body systems (QMBS). I introduce Isotropic Entanglement (IE) and show that the distribution of QMBS with generic interactions can be accurately obtained using IE. Next, I discuss the eigenvalue distribution of one …
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Moderate, large, and superlarge Deviations for extremal Eigenvalues of unitarily invariant Ensembles
… appears not only in the description of extremal eigenvalues for a large class of matrix ensembles but also provides the limit law for a variety of stochastic quantities in statistical mechanics. This phenomenon is called universality in Random Matrix Theory. It should be noted that the …
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Existence of Eigenvalues for Second Order Nonhomogeneous Multi-Parameter Boundary Value Problems.
In contrast to the growing literature on homogeneous multi-parameter boundary problems, there has been no study of nonhomogeneous boundary problems involving more than one parameter of which this author is aware.In this paper, the nonhomogeneous second order differential system is considered.
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The high energy asymptotic distribution of the eigenvalues of the scattering matrix
… the high energy asymptotic density of the eigenvalues of the scat- tering matrix associated with the operators H0 = −∆ and H = (i∇ + A)2 + V (x), where V : Rd → R is a smooth short-range real-valued electric potential and<br/>A = (A1, . . . , Ad) : Rd → Rd is a smooth short-range magnetic …
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Norms on cohomology, harmonic forms, eigenvalues and minimal surfaces in hyperbolic manifolds
… principles, we also obtain results on eigenvalues of infinite volume geometrically finite hyperbolic manifolds.
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Band topology beyond symmetry eigenvalues with applications to electronic and phononic systems
Topology and physics share a long and eminent history. In this dissertation, we apply the tools of topology to study the physics of electrons and phonons in periodic media. The ultimate goal is to understand what topological properties are hidden in the electronic and phononic band structures, and …
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Lower bounds to eigenvalues by the method of arbitrary choice without truncation
… variation theorem for upper bound calculation of eigenvalues, many standard procedures for determining lower bounds to eigenvalues are presented with chemical applications in mind. A new lower bound method, arbitrary choice without trunctation is presented and tested on the helium atom. This …
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Smallest Eigenvalues For A Fractional Boundary Value Problem With A Fractional Boundary Condition
… the existence of and then compare smallest eigenvalues for the fractional boundary value problems D_(0^+)^α u+λ_1 p(t)u=0 and $D_(0^+)^α u+λ_2 q(t)u=0,0< t< 1, satisfying the boundary conditions when n-1<α≤ n. First, we consider the case when 0<β<n-1, satisfying u^(i) (0)=0, …
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Iterative Solution of Matrix Equations for Symmetric Matrices Possessing Positive and Negative Eigenvalues
Made available in DSpace on 2014-12-13T18:02:12Z (GMT). No. of bitstreams: 1 8009149.pdf: 1281854 bytes, checksum: 9f64b6dbac35e0e479827eaf188ed0c7 (MD5) Previous issue date: 1979
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Upper bounds of second Laplacian eigenvalues on the sphere and the projective space
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2026-05-01
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