Некоторые необходимые условия для усиленной устойчивости последовательности случайных величин

[Obretenov A.; Obretenov Apostol; Обретенов Апостол]Bulgarian. Russian, English summar

Об усиленном законе больших чисел

[Obretenov A.; Obretenov Apostol; Обретенов Апостол]Bulgarian. Russian, French summar

On the dependence function of Sibuya in multivariate extreme value theory

The set of the functions H, which are limiting distributions of linearly normalized maxima of n independent and identically distributed random vectors, is treated. It is shown that there is a connection between Pickands' representation for H and the one given by D. G. Kendall for the p-function of Kingman. This is realized through the dependence function of Sibuya.independent and identically distributed random vectors multivariate extreme value distributions dependence function p-function of Kingman Pickands' representation Kendall's representation concave functions

Restricted domains of attraction of exp(-e-x)

For independent and identically distributed random variables the domain of attraction of exp(-e-x) for the maximum is investigated under the restriction that the population distribution has a density. Necessary and sufficient conditions are established in term of the expected residual life and hazard rate. Furthermore, it is shown that, for ultimately concave distributions with increasing hazard rate, the von Mises condition is both necessary and sufficient for a population distribution to be in the domain of attraction of exp(-e-x).independent and identically distributed random variables density maximum domain of attraction of exp(-e-x) expected residual life hazard rate monotonic hazard rate necessary and sufficient condition von Mises condition

Virtual bronchoscopy, importance of the method, application and prospects for tumors of the trachea and bronchi

Virtual bronchoscopy (VB) is 3-dimensional computer-generated technology, creating endobronchial images from spiral CT data. The study aims to present summarized results from researches of different foreign authors about the advantages of VB, the possibilities for its application and the effectiveness of its use in routine practice in the diagnosis of tumors of the trachea and bronchi. The three-dimensional model of the tracheobronchial tree allows assessment of the airways from inside. The majority of the examined studies relate to the diagnosis of new formations of the respiratory tract, preparation for surgery, assessment of the results of surgery, etc. VB is a noninvasive method allowing to examine the smallest bronchi. Relatively few studies in Bulgaria as well as the ensured during recent years new modern equipment for VB and MDCT, provide great opportunities for making VB examinations to study the effectiveness and its wide application in daily X-ray practice

Multidetector computed tomography approach to the diagnosis of a foreign body

Introduction: The introduction of a foreign body in the respiratory tract is a serious global problem requiring urgent medical assistance. Purpose: The aim of the study is to assess the applicability of the Virtual bronchoscopy with MDCT for patients (adults and children) with suspected foreign body. Methods: To all 9 patients Virtual bronchoscopy and Fiberoptic bronchoscopy were carried out. The studies were carried out with an optimized protocol. In order to compare the results of FB and VB the sensitivity and precision indicators were determined. Results: When comparing the results of the study of patients with suspected foreign body, both methods established 4 positive results each (44.45%). Conclusions: VB is particularly reliable and suitable for children and adults with poor general condition. The results of VB with MDCT could be used for early diagnosis of suspected foreign bodies

Diagnostic capabilities of the virtual bronchoscopy at advanced neoplastic process of esophagus with formation of tracheobronchial fistula: Description of a case

The relevance of the problem is related to the continued increase in the neoplastic processes, and at the same time also to the development and improvement of the endoscopic and CT equipment, and thus expanding the diagnostic capabilities. Purpose: The presented research examines the results of the study of a rare case of ruptured trachea as a result of cancer of the esophagus. Methods: Fiberoptic esophagoscopy (FOE) and CT of the chest followed by virtual bronchoscopy on a patient with a ruptured trachea, a 63 year-old man, were performed. Result: Performing MDCT with virtual bronchoscopy, according to this study, is crucial as the sole and complex methodology for the described case in connection with the finding of the trachea-oesophageal fistula and evaluation of the mediastinum and the pulmonary parenchyma. Conclusion: The VB is a successful method equally effective compared to the FB, to diagnose of advanced neoplastic processes