On modified Picard and Gauss—Weierstrass singular integrals

We introduce a certain modification of the Picard and Gauss—Weierstrass singular integrals and prove approximation theorems for them.Введено деяку модифікацію сингулярних інтегралів Пікара та Гаусса - Вейєрштрасса, a також доведено апроксимаційні теореми для цих інтегралів

Destruction of states in quantum mechanics

A description of destruction of states on the grounds of quantum mechanics rather than quantum field theory is proposed. Several kinds of maps called supertraces are defined and used to describe the destruction procedure. The introduced algorithm can be treated as a supplement to the von Neumann-Lueders measurement. The discussed formalism may be helpful in a description of EPR type experiments and in quantum information theory.Comment: 14 pp, 1 eps figure, LaTeX2e using iopart class. Final version, will be published in J. Phys. A: Math. Ge

Measurement of nitric oxide in exhaled air in primary school children in Ružomberok.

Nowadays, there are a number of respiratory illnesses that directly affect children. Exhaled nitric oxide measurement (FeNO) is one of the modern methods of investigation used for diagnosing and controlling allergic eosinophilic airway inflammation. It is a simple, painless and time-saving method for the patient. Because of its non-invasiveness and simplicity, it is a valuable diagnostic method, especially in younger children. Measurement of FeNO is a recognized biomarker and an accurate quantitative indicator in the detection, assessment and monitoring of airway inflammation, including asthma. However, only a few studies assess the relationship between FeNO and level of air pollution. The aim of our study is to determine the relationship between FeNO in third-grade students of primary schools and the level of air pollution in Ruzomberok. 146 children aged 8-10 years were included in the research. This is the first stage of a wider research project involving FeNO measurements in children at different times of the year. The goal of the research is to determine the concentration of FeNO in the studied group of children in the autumn when air pollution is lower than in second stage which is observed in winter. The study showed elevated values of FeNO>20 ppb in 11% of the tested children and correct values <20 ppb in 89% of them. Level of average air pollution in survey days for PM10 ranged from 23 to 40 μg/m3 and for NO2 – from 28 to 44 μg/m3. The study shows that the significant majority of children have normal levels of nitric oxide in the exhaled air when air pollution is low. Analysis of the second phase of FeNO measurements in winter, when air pollution was higher, will allow to compare the results and assess the correlation between the FeNO value and air pollution

A non-autonomous stochastic discrete time system with uniform disturbances

The main objective of this article is to present Bayesian optimal control over a class of non-autonomous linear stochastic discrete time systems with disturbances belonging to a family of the one parameter uniform distributions. It is proved that the Bayes control for the Pareto priors is the solution of a linear system of algebraic equations. For the case that this linear system is singular, we apply optimization techniques to gain the Bayesian optimal control. These results are extended to generalized linear stochastic systems of difference equations and provide the Bayesian optimal control for the case where the coefficients of these type of systems are non-square matrices. The paper extends the results of the authors developed for system with disturbances belonging to the exponential family

Entanglement and Tensor Product Decomposition for Two Fermions

The problem of the choice of tensor product decomposition in a system of two fermions with the help of Bogoliubov transformations of creation and annihilation operators is discussed. The set of physical states of the composite system is restricted by the superselection rule forbidding the superposition of fermions and bosons. It is shown that the Wootters concurrence is not proper entanglement measure in this case. The explicit formula for the entanglement of formation is found and its dependence on tensor product decompositions of the Hilbert space is discussed. It is shown that the set of separable states is narrower than in two-qubit case. Moreover, there exist states which are separable with respect to all tensor product decompositions of the Hilbert space.Comment: 8pp, published versio