• Confidence intervals for ratio of variances of several statistical populations
• Mechanochemical syntheses of oxide nanomaterials
• Method for detection of a delta wave in the ECG signal based on continuous wavelet transform
• Methods of active infrared thermography

Result 1: Confidence intervals for ratio of variances of several statistical populations

Projects: VEGA 1/0077/09 (FMFI UK and Ústav merania SAV)

Author: F. Rublík

A new method for construction of confidence intervals for ratios of variances in the case of several populations was constructed. The reason for seeking the new method is the fact, that standard procedures based on the assumption that the observations have Gaussian distribution, are unreliable if this normality condition is not fulfilled. Therefore nonparametric statistical methods, not requiring known type of density of the distribution, are also used. For verification of equality of two variances the test based on the jackknife is used (Hollander-Wolfe: Nonparametric Statistical Methods, 1999). A test of the equality of variances for more than two populations was constructed in the work of Layard (JASA 1973). However, this does not solve this statistical problem completely, because after rejection of the hypothesis of the equality of variances of several populations one often wants to know which of the variances are different and to compute confidence intervals for ratios of variances of all the populations. In the paper of F. Rublík  simultaneous confidence intervals for ratios of variances in the case of several populations are derived  (this makes possible to find also those with  different variances), the probability of coverage of the true ratios has chosen nominal value simultaneously for each two variances without the normality assumption. Even though this nominal value is attained only asymptotically,  simulations suggest that the proposed method yields good results also for small sample sizes.

Publication:

RUBLÍK, F.: A note on simultaneous confidence intervals for ratio of variances. Communications in Statistics - Theory and Methods, 39( 2010), 1038 - 1045. 

Result 2: Mechanochemical syntheses of oxide nanomaterials

Project: VEGA 2/0160/10

Authors: P. Billik, A. Cigáň, A. Koňakovský, K. Jurča

The intensive ball milling process has a unique influence on the chemical reactions leading to the creation of new materials and nanostructures, Fig. 1. With decreasing particle size by milling, the as-prepared materials exhibit some unusual properties. For example, initially non-magnetic oxide particles change to paramagnetic one in the nanoregion. The results of our work are focused on the mechanochemical synthesis of TiO₂, YBa₂Cu₃O₇, Na₂Ti₆O₁₃, SnO₂, with their well-known application in the self-cleaning processes, high temperature superconductivity, or in the Li-ion batteries with large storage capacity and long life operation. Besides, mechanochemical syntheses of nanoparticles represent one of the low-cost industrial-scale method.

These results have been achieved in cooperation with these organizations: Department of Geology of Mineral Deposits and Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University in Bratislava; Institute of Inorganic Chemistry, Slovak Academy of Scienses; Institute of Physical Chemistry and Chemical Physics, Faculty of Chemical and Food Technology, Slovak University of Technology in Bratislava; Institute of Materials Science, Faculty of Materials Science and Technology in Trnava, Slovak University of Technology.

Fig. 1. SEM (a), TEM (b), microstructure of 1-D Na2Ti6O13 nanopartielces prepared by mechanochemical synhesis. (Photo: M. Čaplovičová.

Publications:

1.  BILLIK, Peter - ČAPLOVIČOVÁ, M. - ČAPLOVIČ, Ľ. Mechanochemical-molten salt synthesis of Na2Ti6O13 nanobelts . In Materials Research Bulletin, 2010, vol. 45, p. 621-627. ISSN 0025-5408. (1.879 - IF2009).
2. BREZOVÁ, V. - BILLIK, Peter - VRECKOVÁ, Z. - PLESCH, G. Photoinduced formation of reactive oxygen species in suspensions of titania mechanochemically synthesized from TiCl4. In Journal of Molecular Catalysis A : Chemical, 2010, vol. 327, p. 101-109. ISSN 1381-1169. (3.135 - IF2009).
3. HRACHOVÁ, J. - BILLIK, Peter - FAJNOR, V.Š. Influence of organic surfactants on structural stability of mechanochemically treated bentonite. In Journal of Thermal Analysis and Calorimetry, 2010, vol. 101, p. 161-168. ISSN 1388-6150. (1.587 - IF2009).

Result 3: Method for detection of a delta wave in the ECG signal based on continuous wavelet transform

Projects: VEGA 2/0210/10

Authors: S. Karas, M. Tyšler, M. Turzová

The method for detection of a delta wave in the ECG signal based on calculation and evaluation of modulus maxima lines (MML) of the wavelet transform was proposed. The delta wave, i.e. the decreased slope of the R-wave is one of the symptoms of disturbed excitation propagation in the Wolf-Parkinson-White syndrome. Theoretical analysis of the problem showed that with the use of the continuous wavelet transform it is possible to distinguish the changed slope of the ECG curve and simultaneously to determine its location in time. The method is baased on a) computation of the continuous wavelet transform of the analyzed signal, b) computation of points of maximal moduli and drawing MML in time-frequency-amplitude space, c) MML analysis in the frequency-amplitude projection, d) computation of energies bounded by MML that correspond with the ascending and descending signal in the R-wave and e) computation of their ratio - of the delta wave index. The method was verified on both, simulated a measured ecg signals (3 healthy persons, 7 patients) and it was shown that the method is able to correctly detect presence of the delta wave in ecg signals, except signals with antisymetric or negative biphasic shape.

Fig.1.: Left: Simulated ecg signal and depiction of the matrix of transform coefficients of its continuous wavelet transformin the time-frequency-amplitude space with MML marked by color. Right: Energy of the ascending part of the R-wave (line 4 in Figure left) in projection frequency-amplitude that is proportional to surface S below the line corresponding to the squared module of corresponding MML. 

Publications:

1. KARAS S.,Teplan M., Tyšler M.: Detection of Variations in Biomedical Signals Based on Continuous Wavelet Transform Modulus Maxima. MEASUREMENT 2009, Proceedings of the 7th International Conference on Measurement, Institute of Measurement Science SAS, 2009, 153-156, ISBN 978-80-969672-1-6.
2. KARAS S.: Metódy a meracie systémy na analýzu EKG signálov s využitím vlnkovej transformácie. Dissertation thesis. Institute of Measurement Science, Slovak Academy of Sciences. Bratislava. 2010.
   

Result 4: Methods of active infrared thermography 

Project: VEGA 2/0201/10

Authors: M. Hain, J. Bartl, V. Jacko

As part of the project VEGA "Progressive methods of measurement and non-destructive testing - active infrared thermography and X-ray microtomography" a theoretical method of optimization of active infrared thermography based on the modeling of heat transfer in inhomogeneous media by finite element method was proposed and applied. It was proposed to use thermal contrast as the most suitable optimization criterion of this method. Achieved theoretical results were experimentally verified qualitatively and quantitatively using the results of the laboratory and in situ measurements.
The results of the basic research are used to optimization of the method of active infrared thermography, which finds use as a nondestructive testing method for detecting hidden defects in materials, as well as in cultural heritage objects.

 

Publication: