2,203 research outputs found
The damped wave equation with unbounded damping
We analyze new phenomena arising in linear damped wave equations on unbounded
domains when the damping is allowed to become unbounded at infinity. We prove
the generation of a contraction semigroup, study the relation between the
spectra of the semigroup generator and the associated quadratic operator
function, the convergence of non-real eigenvalues in the asymptotic regime of
diverging damping on a subdomain, and we investigate the appearance of
essential spectrum on the negative real axis. We further show that the presence
of the latter prevents exponential estimates for the semigroup and turns out to
be a robust effect that cannot be easily canceled by adding a positive
potential. These analytic results are illustrated by examples.Comment: 26 pages, 2 figure
Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings
We solve two inverse spectral problems for star graphs of Stieltjes strings
with Dirichlet and Neumann boundary conditions, respectively, at a selected
vertex called root. The root is either the central vertex or, in the more
challenging problem, a pendant vertex of the star graph. At all other pendant
vertices Dirichlet conditions are imposed; at the central vertex, at which a
mass may be placed, continuity and Kirchhoff conditions are assumed. We derive
conditions on two sets of real numbers to be the spectra of the above Dirichlet
and Neumann problems. Our solution for the inverse problems is constructive: we
establish algorithms to recover the mass distribution on the star graph (i.e.
the point masses and lengths of subintervals between them) from these two
spectra and from the lengths of the separate strings. If the root is a pendant
vertex, the two spectra uniquely determine the parameters on the main string
(i.e. the string incident to the root) if the length of the main string is
known. The mass distribution on the other edges need not be unique; the reason
for this is the non-uniqueness caused by the non-strict interlacing of the
given data in the case when the root is the central vertex. Finally, we relate
of our results to tree-patterned matrix inverse problems.Comment: 32 pages, 3 figure
Bounds on the spectrum and reducing subspaces of a J-self-adjoint operator
Given a self-adjoint involution J on a Hilbert space H, we consider a
J-self-adjoint operator L=A+V on H where A is a possibly unbounded self-adjoint
operator commuting with J and V a bounded J-self-adjoint operator
anti-commuting with J. We establish optimal estimates on the position of the
spectrum of L with respect to the spectrum of A and we obtain norm bounds on
the operator angles between maximal uniformly definite reducing subspaces of
the unperturbed operator A and the perturbed operator L. All the bounds are
given in terms of the norm of V and the distances between pairs of disjoint
spectral sets associated with the operator L and/or the operator A. As an
example, the quantum harmonic oscillator under a PT-symmetric perturbation is
discussed. The sharp norm bounds obtained for the operator angles generalize
the celebrated Davis-Kahan trigonometric theorems to the case of J-self-adjoint
perturbations.Comment: (http://www.iumj.indiana.edu/IUMJ/FULLTEXT/2010/59/4225
Efficient detection, analysis and classification of lightning radiation fields
Modeling the large scale lightning flash structure is considered. Large scale flash data has been measured from strip charts of storms of August 5, August 26, and September 12, 1975. The data is being processed by a computer program called SASEV to estimate the large scale flash statistics. The program, experimental results, and conclusions for the large scale flash structure are described. The progress made in examining the internal flash structure consists mainly of developing the software required to process the NASA digital tape data. A FORTRAN program has been written for the statistical analysis of series of events. The statistics computed and tests performed are found to be particularly useful in the analysis of lightning data
Numerical Range and Quadratic Numerical Range for Damped Systems
We prove new enclosures for the spectrum of non-selfadjoint operator matrices
associated with second order linear differential equations in a Hilbert space. Our main tool is the quadratic
numerical range for which we establish the spectral inclusion property under
weak assumptions on the operators involved; in particular, the damping operator
only needs to be accretive and may have the same strength as . By means of
the quadratic numerical range, we establish tight spectral estimates in terms
of the unbounded operator coefficients and which improve earlier
results for sectorial and selfadjoint ; in contrast to numerical range
bounds, our enclosures may even provide bounded imaginary part of the spectrum
or a spectral free vertical strip. An application to small transverse
oscillations of a horizontal pipe carrying a steady-state flow of an ideal
incompressible fluid illustrates that our new bounds are explicit.Comment: 27 page
Optimal estimation for discrete time jump processes
Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are obtained. The approach is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. A general representation for optimum estimates and recursive equations for minimum mean squared error (MMSE) estimates are obtained. MMSE estimates are nonlinear functions of the observations. The problem of estimating the rate of a DTJP when the rate is a random variable with a probability density function of the form cx super K (l-x) super m and show that the MMSE estimates are linear in this case. This class of density functions explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems
Biometric Image Data Classifier
Cílem této práce je navrhnout a implementovat klasifikátor otisků prstů, který klasifikuje otisky prstů na základě typu snímače, ze kterého byly nasnímány. Čtenáři jsou v práci popsány existující typy snímačů otisků prstů a jednotlivé fáze klasifikace. Navržený klasifikátor využívá kaskády klasifikátorů vytrénovaných učícím algoritmem AdaBoost. Aplikace byla implementovaná v jazyce C++, s využitím knihovny OpenCV, pro operační systémy GNU/Linux a MS Windows.The aim of this thesis is to design and implement fingerprint classifier, which classifies the fingerprints based on the scanner used. Reader is presented with existing types of fingerprint scanners and phases of classification. Designed classifier is using a cascade of classifiers, trained using the AdaBoost learning algorithm. The application was implemented in the C++ language using OpenCV library for operational systems GNU/Linux and MS Windows.
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