Anisotropic inharmonic Higgs oscillator and related (MICZ-)Kepler-like systems

We propose the integrable (pseudo)spherical generalization of the four-dimensional anisotropic oscillator with additional nonlinear potential. Performing its Kustaanheimo-Stiefel transformation we then obtain the pseudospherical generalization of the MICZ-Kepler system with linear and $\cos\theta$ potential terms. We also present the generalization of the parabolic coordinates, in which this system admits the separation of variables. Finally, we get the spherical analog of the presented MICZ-Kepler-like system.Comment: 7 page

Purity-bounded uncertainty relations in multidimensional space -- generalized purity

Uncertainty relations for mixed quantum states (precisely, purity-bounded position-momentum relations, developed by Bastiaans and then by Man'ko and Dodonov) are studied in general multi-dimensional case. An expression for family of mixed states at the lower bound of uncertainty relation is obtained. It is shown, that in case of entropy-bounded uncertainty relations, lower-bound state is thermal, and a transition from one-dimensional problem to multi-dimensional one is trivial. Results of numerical calculation of the relation lower bound for different types of generalized purity are presented. Analytical expressions for general purity-bounded relations for highly mixed states are obtained.Comment: 12 pages, 2 figures. draft version, to appear in J. Phys. A Partially based on a poster "Multidimensional uncertainty relations for states with given generalized purity" presented on X Intl. Conf. on Quantum Optics'2004 (Minsk, Belarus, May 30 -- June 3, 2004) More actual report is to be presented on ICSSUR-2005, Besan\c{c}on, France and on EQEC'05, Munich. V. 5: amended article after referees' remark

3D Oscillator and Coulomb Systems reduced from Kahler spaces

We define the oscillator and Coulomb systems on four-dimensional spaces with U(2)-invariant Kahler metric and perform their Hamiltonian reduction to the three-dimensional oscillator and Coulomb systems specified by the presence of Dirac monopoles. We find the Kahler spaces with conic singularity, where the oscillator and Coulomb systems on three-dimensional sphere and two-sheet hyperboloid are originated. Then we construct the superintegrable oscillator system on three-dimensional sphere and hyperboloid, coupled to monopole, and find their four-dimensional origins. In the latter case the metric of configuration space is non-Kahler one. Finally, we extend these results to the family of Kahler spaces with conic singularities.Comment: To the memory of Professor Valery Ter-Antonyan, 11 page

Vitamin D status in children with myopia

Introduction. A dramatic increase of myopia worldwide has been observed in recent years. New risk factors for the development of myopia have been the target of numerous investigations. The basis of our research is the correlation between serum levels of vitamin D [25(OH)D] and myopia itself.Purpose: To find out the relationship between serum levels of 25(OH) D and myopia. Patients and methods: The study included 222 children with different refraction status. Full ophthalmologic examination, cycloplegic refraction, echobiometry were performed. The serum levels of 25(OH)D were measured by liquid chromatographic mass spectrometry (level of insufficiency < 80 nmol/L).Results: The average patients’ age (51% boys and 48,2% girls) was 11,7 y (SD ± 3,03). They were subdivided into two groups – children with myopia (84,7%) and those without myopia (15,3%). The mean serum 25(OH)D level of all tested was 61,48 nmol/L (16-140 nmol/L; SD ± 20,15); of myopia – 59,67 nmol/L (16-140 nmol/L; SD ± 19,30) and of the non-myopia group – 71,91 nmol/L (33-111 nmol/L; SD ± 21,79). There was a statistically significant difference in serum levels between the two groups (Р = 0,001). The risk of myopia was higher with the decrease of 25(OH)D values (OR = 1,028 ; 95% CI 1,008-1,048). Conclusion. In our investigation group we established low serum levels of 25(OH)D which indicated the need for conducting a population study of its status among Bulgarian children. The correlation between the higher risk of myopia and the vitamin D scarcity has to be further studied, also considering the factor of outdoor/sun-exposure time.

Quantum oscillator as 1D anyon

It is shown that in one spatial dimension the quantum oscillator is dual to the charged particle situated in the field described by the superposition of Coulomb and Calogero-Sutherland potentials.Comment: 9 pages, LaTe

A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow

Modelling incompressible ideal fluids as a finite collection of vortex filaments is important in physics (super-fluidity, models for the onset of turbulence) as well as for numerical algorithms used in computer graphics for the real time simulation of smoke. Here we introduce a time-discrete evolution equation for arbitrary closed polygons in 3-space that is a discretisation of the localised induction approximation of filament motion. This discretisation shares with its continuum limit the property that it is a completely integrable system. We apply this polygon evolution to a significant improvement of the numerical algorithms used in Computer Graphics.Comment: 15 pages, 3 figure

Why honey is effective as a medicine. 1. Its use in modern medicine

Honey has been used as a medicine for thousands of years and its curative properties are well documented. However, modern medicine turned its back on honey and it is only now, with the advent of multi-resistant bacteria, that the antibiotic properties of honey are being rediscovered