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  • Author or Editor: Zoltán Sebestyén x
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Abstract

We give an extension of a classical result due to Krein on biorthogonal expansions of compact operators which are symmetrizable with respect to a nondegenerate positive operator. Our approach makes essential use of the spectral expansion of an appropriate compact selfadjoint operator, the existence of which is due to Dieudonné.

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Abstract

T T is selfadjoint if T is a densely defined closed Hilbert space operator. This result of von Neumann can be generalized for not necessarily closed operators: T T always admits a positive selfadjoint extension. The Friedrichs extension also will be obtained whenever T T is assumed to be densely defined. Selfadjointness of T T will be investigated. Densely defined positive operators and their Friedrichs extension A and A F, respectively, will be described by showing the existence of a closable operator T such that A=T T and at the same time A F=T T ∗∗.

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Abstract

The notions of parallel sum and parallel difference of two nonnegative forms were introduced and studied by Hassi, Sebestyén, and de Snoo in [13] and [14]. In this paper we consider the parallel subtraction with much circumstances. Criteria are established for the solvability of the equation with an unknown when and are given. We identify as the minimal solution, and characterize all the solutions under the assumption where λ>1. The Galois correspondence induced by the map is also studied. We show that if the equation is solvable, then there is a unique -closed solution, namely . Finally, we consider some extremal problems such as the extreme points of the interval , and the characterization of the minimal forms in terms of the parallel sum.

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In this paper we will demonstrate the use and efficiency of the bootstrap on a geologic problem. The tools of classical statistics are often not applicable because they strongly depend on certain conditions that are not fulfilled. Explicit mathematical formulas for standard errors and confidence intervals with respect to a parameter either require some specific (generally normal) distribution, or they do not exist at all. Hypothesis tests may also only be carried out if some conditions are satisfied. Using the bootstrap method one can simulate the unknown distribution of an arbitrary statistic by its bootstrap replicates; hence any characteristics (standard error, confidence intervals, and test significance levels) can be obtained through direct empirical calculations. We applied the bootstrap to the chemical composition data of rock samples from the Boda Claystone Formation, Hungary. First we investigated the distribution of 8 chemical components in a rock sample group of few elements, computing standard errors and confidence intervals for the mean, the standard deviation and the skewness of these distributions. Then two groups of rock samples from different sampling regions were compared using hypothesis tests.  

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The uncertainty in the semivariogram has hardly been investigated in previous geostatistical studies. This paper presents an efficient methodology of uncertainty assessment based on the bootstrap. By applying this computer-intensive statistical method one can easily simulate the distribution of the empirical semivariogram estimate for each lag. The lag-wise standard errors and confidence intervals of a given level can then be easily calculated from the bootstrap replicates. These estimations are valid in any situation when classical statistics fail. The bootstrap also provides a mathematical-statistical tool to decide whether the semivariogram reaches its maximum at a given lag or not. It leads directly to a simple determination of the range of influence. Effects beyond the range, such as the hole effect, can be explored with the same approach. The empirical semivariogram, supplied by measures of uncertainty, adequately describes the true spatial behavior of the studied variable. This universal method renders the customary theoretical semivariogram models obsolete.

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The purpose of this paper is to revise von Neumann’s characterizations of selfadjoint operators among symmetric ones. In fact, we do not assume that the underlying Hilbert space is complex, nor that the corresponding operator is densely defined, moreover, that it is closed. Following Arens, we employ algebraic arguments instead of the geometric approach of von Neumann using the Cayley transform.

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A bounded, not necessarily everywhere defined, nonnegative operator A in a Hilbert space \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $\mathfrak{H}$ \end{document} is assumed to intertwine in a certain sense two bounded everywhere defined operators B and C. If the range of A is provided with a natural inner product then the operators B and C induce two new operators on the completion space. This construction is used to show the existence of selfadjoint and nonnegative extensions of B*A and C*A.

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Abstract

The goal of this study was to clarify the effect of alkaline pretreatments on the thermal decomposition and composition of industrial hemp (Cannabis sativa L.) samples. Thermogravimetric/mass spectrometric measurements (TG/MS) have been performed, on untreated, hot water washed, and alkali-treated hemp samples. The main differences between the thermal decomposition of the samples are interpreted in terms of the different alkali ion contents which have been determined using inductively coupled plasma-optical emission spectroscopy (ICP-OES) method. Principal component analysis (PCA) has been used to find statistical correlations between the data. Correlations have been obtained between the parameters of the thermal decomposition and the alkali ion content as well as the altered chemical structure of the samples. The differences in the thermal behavior of the samples are explained by the different K+ and Na+ contents and the changed structure of the hemicellulose component of the samples due to the pretreatments. The more alkali ions remain in the hemp samples after the alkali treatment, the more ash, char and lower molecular products are formed during thermal decomposition.

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Abstract

The thermal behaviours of a sewage sludge sample, woody (black locust, poplar and willow) and herbaceous (energy grass and wheat straw) biomass as well as mixed (sewage sludge and black locust in ratios 1:1 and 1:3) samples were compared under inert and oxidative atmosphere. The thermogravimetric experiments of each sample demonstrate that the beginning temperature of decomposition is similar in inert and oxidative atmospheres, i.e. the primary bond scissions are not affected by the atmosphere. Nevertheless, oxygen increases the decomposition rate and the volatile evolution of all samples at higher temperatures. Thermogravimetry/mass spectrometry (TG/MS) experiments have been performed to determine the mass loss of the samples and the formation of volatile products as a function of temperature in inert atmosphere. Wood and herbaceous biomass samples evolved various organic products (aldehydes, ketones, acids, furan derivatives, etc.) beside water and gaseous products. Sewage sludge released mainly water, carbon oxides, methane, hydrogen, hydrocarbons, ketones, acids as well as sulphur- and nitrogen-containing products. High heating value and low heating value of the samples have been determined by a bomb calorimeter. Principal component analysis (PCA) has been used to find statistical correlation between the data. The results unambiguously support the correlation between the thermogravimetric parameters (e.g. DTGmax) and the heating values of the samples.

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Orvosi Hetilap
Authors: Szabolcs Szappanos, Róbert Farkas, Zoltán Lőcsei, Zoltán László, Judit Kalincsák, Szabolcs Bellyei, Zsolt Sebestyén, László Csapó, Klára Sebestyén, Judit Halász, Zoltán Musch, Tamás Beöthe, László Farkas, and László Mangel

Bevezetés: A prosztatarák az idősebb életkor és a fejlett világ daganatos megbetegedése. Lokalizált prosztatarák esetében a műtéti ellátás mellett komoly szerepe van a definitív sugárkezelésnek. Célkitűzés: A szerzők intézetében telepített Novalis TX gyorsító segítségével úgynevezett intenzitásmodulált sugárterápia, annak dinamikus ívbesugárzással elvégzett formája, illetve verifikáció során háromdimenziós lágy szöveti képellenőrzést biztosító, integrált kilovoltos cone-beam komputertomográfiával végzett képvezérelt sugárterápia került bevezetésre, amely módszerekkel szerzett első tapasztalataikat ismertetik a szerzők. Módszer: 2011 decembere és 2013 februárja között, dóziseszkalációt követően, 102 dinamikus ívbesugárzással elvégzett kezelést végeztek, majd 10-10 szelektált, alacsony és magas kockázatú betegnél (átlagéletkor 72,5 év) elkészítették a háromdimenziós konformális besugárzási terveket is. Azonos célterület-lefedettség mellett összevetették a rizikószervek dózisterhelését. Eredmények: A dinamikus ívbesugárzással elvégzett kezelések mellett a rizikószervek szignifikánsan alacsonyabb dózisterhelését érték el, amelyet a kedvező korai mellékhatásprofil is alátámaszt. Következtetések: Az intenzitásmodulált sugárterápia dinamikus ívbesugárzással elvégzett formája biztonsággal alkalmazott standard kezelési módozattá vált a szerzők intézetében. Késői mellékhatások és lokális kontroll további vizsgálata szükséges. Orv. Hetil., 2014, 155(32), 1265–1272.

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