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 $\ddot{z}(t) + D \dot{z} (t) + A_0 z(t) = 0$ 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 $A_0$. By means of the quadratic numerical range, we establish tight spectral estimates in terms of the unbounded operator coefficients $A_0$ and $D$ which improve earlier results for sectorial and selfadjoint $D$; 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

Dirac-Krein systems on star graphs

We study the spectrum of a self-adjoint Dirac-Krein operator with potential on a compact star graph $\mathcal G$ with a finite number $n$ of edges. This operator is defined by a Dirac-Krein differential expression with summable matrix potentials on each edge, by self-adjoint boundary conditions at the outer vertices, and by a self-adjoint matching condition at the common central vertex of $\mathcal G$. Special attention is paid to Robin matching conditions with parameter $\tau \in\mathbb R\cup\{\infty\}$. Choosing the decoupled operator with Dirichlet condition at the central vertex as a reference operator, we derive Krein's resolvent formula, introduce corresponding Weyl-Titchmarsh functions, study the multiplicities, dependence on $\tau$, and interlacing properties of the eigenvalues, and prove a trace formula. Moreover, we show that, asymptotically for $R\to \infty$, the difference of the number of eigenvalues in the intervals $[0,R)$ and $[-R,0)$ deviates from some integer $\kappa_0$, which we call dislocation index, at most by $n+2$.Comment: Accepted for publication in IEO

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.

Rate statistics for radio noise from lightning

Radio frequency noise from lightning was measured at several frequencies in the HF - VHF range at the Kennedy Space Center, Florida. The data were examined to determine flashing rate statistics during periods of strong activity from nearby storms. It was found that the time between flashes is modeled reasonably well by a random variable with a lognormal distribution

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

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