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  • Author or Editor: T. Székely x
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Abstract  

Sufficient conditions of covariance type are presented for weighted averages of random variables with arbitrary dependence structure to converge to 0, both for logarithmic and general weighting. As an application, an a.s. local limit theorem of Csáki, Földes and Révész is revisited and slightly improved.

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Some possible elementary reactions are not included in the classical mathematical models of thermal decomposition. For example, we can assume that in the thermal decompositions of simple carbonates a proportion of the O2− ions produced on the reaction interface can migrate into the interior of the reactant phase, since at this temperature there is some probability of CO2 exchange between an O2− and a neighbouring CO3 2− ion. A similar diffusion-type process can be assumed in a wide class of decomposition reactions. The present state of computer science makes it possible to show by mathematical modelling how this migration influences the TG curves of the simplest contracting-sphere-type reactions. The resulting extended contracting-sphere model can provide the induction and the acceleration period of the TG curves.

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The aim of this paper is to represent any continuous local martingale as an almost sure limit of a nested sequence of simple, symmetric random walk, time changed by a discrete quadratic variation process. One basis of this is a similar construction of Brownian motion. The other major tool is a representation of continuous local martingales given by Dambis, Dubins and Schwarz (DDS) in terms of Brownian motion time-changed by the quadratic variation. Rates of convergence (which are conjectured to be nearly optimal in the given setting) are also supplied. A necessary and sufficient condition for the independence of the random walks and the discrete time changes or equivalently, for the independence of the DDS Brownian motion and the quadratic variation is proved to be the symmetry of increments of the martingale given the past, which is a reformulation of an earlier result by Ocone [8].

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Automated behavioural observations are routinely used in many fields of biology, including ethology, behavioural ecology and physiology. When preferences for certain resources are investigated, the focus is often on simple response variables, such as duration and frequency of visits to choice chambers. Here we present an automated motion detector system that use passive infrared sensors to eliminate many drawbacks of currently existing methods. Signals from the sensors are processed by a custom-built interface, and after unnecessary data is filtered by a computer software, the total time and frequency of the subject’s visits to each of the choice chambers are calculated. We validate the detector system by monitoring (using the system) and in the same time video recording mating preferences of zebra finches in a four-way choice apparatus. Manual scoring of the video recordings showed very high consistency with data from the detector system both for time and for frequency of visits. Furthermore, the validation revealed that if we used micro-switches or light barriers, the most commonly applied automatic detection techniques, this would have resulted in approximately 22% less information compared to our lossless system. The system provides a low-cost alternative for monitoring animal movements, and we discuss its further applicability.

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Periodica Mathematica Hungarica
Authors: S. Horváth, J. Kollár, G. Székely and T. Matolcsi
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This paper uses a multi-region DSGE model with collateral constrained households and residential investment to examine the effectiveness of fiscal policy stimulus measures in a credit crisis. The paper explores alternative scenarios which differ by the type of budgetary measure, their length, the degree of monetary accommodation and the level of international coordination. In particular we provide estimates for New EU Member States where we take into account two aspects. First, debt denomination in foreign currency and second, higher nominal interest rates, which makes it less likely that the Central Bank is restricted by the zero bound and will consequently not accommodate a fiscal stimulus. We also compare our results to other recent results obtained in the literature on fiscal policy which generally do not consider credit constrained households.

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It has been known from the very beginning of the thermal analysis that the transport processes can significantly influence the thermoanalytical results. In this paper, three characteristic examples are given to show that this problem is more complex and arises more frequently than it is generally believed. The studied reactions are the carbon monoxide evolution from calcium oxalate, the thermal degradation of polytetrafluoroethylene, and the thermal decomposition of azodicarbonamide. TG and DSC experiments were carried out with sample masses varying between 0.05 and 8 mg. The necessity of the development of new kinetic models is concluded.

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Alumina samples were produced by the thermal decomposition of hydrates of aluminium sulphate, nitrate and chloride. The kinetics of the chlorination were studied by means of isothermal TG measurements, using COCl2 as chlorinating agent. Apparent activation energies were determined in the temperature ranges where the reaction was controlled by chemical processes. The reaction rates related to unit surface area were similar for all the samples, and the isothermal TG curves could be described by the models of contracting cylinders and spheres.

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The reduction kinetics of a pure and a Ca-added hematite, as well as of two iron oxide-containing metallurgical wastes, were studied by means of isothermal TG measurements, using H2 or CO as reducing agents.

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