Abstract:
In this paper we construct the new coefficient which allows to measure quantitatively the independence of the two discrete random variables. The new inequalities for the matrices with non-negative elements are found

Abstract:
Purpose: Examining the differences in motivation between learners in schools with a choice-based physical education (PE) curriculum and those with a non-choice-based curriculum, and identifying which sport activities these students prefer, using SDT as a conceptual framework. Method: Participants were 536 pupils from grades 10 - 12 from eight schools. Four schools offered a choice- based curriculum in PE and the other operated according to a teacher-based curriculum. A questionnaire examined their PA habits in leisure time, their motives for activity in PE lessons, and their preferred activities in these lessons. Results showed that pupils in classes with no choice-based curricula reported higher levels of motives then pupils in classes with choice-based curricula. Girls reported higher level of motives than boys. Preferred areas of activity illustrated the traditional-social difference between boys and girls. Conclusion: Schools that offer choice-based curricula should sharpen the answer to the question-what constitutes a worthwhile or true choice.

Abstract:
In recent years, technological improvements have allowed for the creation of V.R. environments for different uses, especially in the training of pilots, astronauts, medical staff, soldiers, and athletes. In regards to physical activity, V.R. is currently being used in two main fields: Exergaming and Rehabilitation. The purpose of this article is to investigate the use of this technology as a means of demonstrating and learning motor abilities in many types of populations and situations. Three studies were done using V.R. In all three of them healthy participants were assigned to a control or test group. These studies were done using two main V.R. systems designed for motor learning: Timocco and IREX. Study 1 tested bi-lateral transfer in the upper limbs; Study 2 tested the differences in improvement using V.R. between internal and extrinsic focus of attention; Study 3 tested differences in different learning strategies in motor tasks—massed practice vs. distributed practice. Study 1 found significant differences between control and test groups; Study 2 did not find that external focus of attention was superior as expected but found a stronger correlation between tests at different days; Study 3 found no significant improvements (p > 0.05) for each group. In conclusion, V.R. can be an effective means of teaching and training basic motor skills, sometimes even superior to “real-life” because of the highly modifiable environment and difficulty in the comfort of one’s clinic or home.

Abstract:
In this paper we consider eigenvalues asymptotics of the energy operator in the one of the most interesting models of quantum physics, describing an interaction between two-level system and harmonic oscillator. The energy operator of this model can be reduced to some class of infinite Jacobi matrices. Discrete spectrum of this class of operators represents the perturbed spectrum of harmonic oscillator. The perturbation is an unbounded operator compact with respect to unperturbed one. We use slightly modified Janas-Naboko successive diagonalization approach and some new compactness criteria for infinite matrices. Two first terms of eigenvalues asymptotics and the estimation of remainder are found.

The approximation evaluations
by polynomial splines are well-known. They are obtained by the similarity
principle; in the
case of non-polynomial splines the implementation of this principle is
difficult. Another method for obtaining of the evaluations was discussed
earlier (see [1]) in the case of nonpolynomial splines of Lagrange type. The
aim of this paper is to obtain the evaluations of approximation by
non-polynomial splines of Hermite type. Considering a linearly independent
system of column-vectors, . Let be square matrix. Supposing that and are columns with components from the linear
space such that . Let be vector with components belonging to conjugate space . For an element we consider a linear combination of elements By definition, put . The discussions
are based on the next assertion. The following relation holds: where the second factor on the right-hand side
is the determinant of a block-matrix of order m + 2. Using this assertion, we get the representation of residual
of approximation by minimal splines of Hermite type. Taking into account the
representation,

Abstract:
Schroedinger bound-state problem in D dimensions is considered for a set of central polynomial potentials (containing 2q coupling constants). Its polynomial (harmonic-oscillator-like, quasi-exact, terminating) bound-state solutions of degree N are sought at a (q+1)-plet of exceptional couplings/energies, the values of which comply with (the same number of) termination conditions. We revealed certain hidden regularity in these coupled polynomial equations and in their roots. A particularly impressive simplification of the pattern occurred at the very large spatial dimensions D where all the "multi-spectra" of exceptional couplings/energies proved equidistant. In this way, one generalizes one of the key features of the elementary harmonic oscillators to (presumably, all) non-vanishing integers q.

Abstract:
A novel formulation to dope organic liquid scintillators (OLS) with indium at concentrations up to 10% is presented: it is based on specific indium carboxylate compounds adequately synthesized. The produced In-OLS has been characterized: it has light yield 8500 ph/MeV at indium concentration 5.5% and light attenuation length of 2,5 m at wavelength of 430 nm. The scintillator properties were stable during all time of investigation (~ 1 years). The produced In-OLS is compared to other In-OLS formulations and shows superior performances. The developed methodic to metal dope OLS can be easily extended to other metals as Gd, Nd, Cd.

Abstract:
Several liters of an organic liquid scintillator (LS) loaded with Nd have been made. We report on performances of this scintillator in terms of optical properties, radiopurity and light yield for a Nd concentration of 6.5 g/l. A possible application to search for the 150Nd neutrinoless double beta decay with a 10-ton scale LS detector is discussed together with further improvements.

Abstract:
A new type of exact solvability is reported. We study the general central polynomial potentials (with 2q anharmonic terms) which satisfy the Magyari's partial exact solvability conditions (this means that they possess a harmonic-oscillator-like wave function proportional to a polynomial of any integer degree N). Working in the space of a very large dimension D for simplicity, we reveal that in contrast to the usual version of the model in finite dimensions (requiring a purely numerical treatment of the Magyari's constraints), our large D problem acquires an explicit, closed form solution at all N and up to q = 5 at least. This means that our effective secular polynomials (generated via the standard technique of Groebner bases) happen to be all fully factorizable in an utterly mysterious manner (mostly, over integers).

Abstract:
General Schr\"{o}dinger equation is considered with a central polynomial potential depending on $2q$ arbitrary coupling constants. Its exceptional solutions of the so called Magyari type (i.e., exact bound states proportional to a polynomial of degree $N$) are sought. In any spatial dimension $D \geq 1$, this problem leads to the Magyari's system of coupled polynomial constraints, and only purely numerical solutions seem available at a generic choice of $q$ and $N$. Routinely, we solved the system by the construction of the Janet bases in a degree-reverse-lexicographical ordering, followed by their conversion into the pure lexicographical Gr\"obner bases. For very large $D$ we discovered that (a) the determination of the "acceptable" (which means, real) energies becomes extremely facilitated in this language; (b) the resulting univariate "secular" polynomial proved to factorize, utterly unexpectedly, in a fully non-numerical manner. This means that due to the use of the Janet bases we found a new exactly solvable class of models in quantum mechanics.