Coincidences in numbers of graph vertices corresponding to regular planar hyperbolic mosaics

The aim of this paper is to determine the elements which are in two pairs of sequences linked to the regular mosaics $\{4,5\}$ and $\{p,q\}$ on the hyperbolic plane. The problem leads to the solution of diophantine equations of certain types.Comment: 10 pages, 2 figures, Annales Mathematicae et Informaticae 43 (2014

V473 Lyrae, a unique second-overtone Cepheid with two modulation cycles

V473 Lyrae is the only Galactic Cepheid with confirmed periodic amplitude and phase variations similar to the Blazhko effect observed in RR Lyrae stars. We collected all available photometric data and some radial velocity measurements to investigate the nature of the modulation. The comparison of the photometric and radial velocity amplitudes confirmed that the star pulsates in the second overtone. The extensive data set, spanning more than 40 years, allowed us to detect a secondary modulation cycle with a period of approximately 5300 days or 14.5 years. The secondary variations can be detected in the period of the primary modulation, as well. Phenomenologically, the light variations are analogous to the Blazhko effect. To find a physical link, we calculated linear hydrodynamic models to search for potential mode resonances that could drive the modulation and found two viable half-integer (n:2) and three n:4 resonances between the second overtone and other modes. If any of these resonances will be confirmed by non-linear models, it may confirm the mode resonance model, a common mechanism that can drive modulations both in RR Lyrae and Cepheid stars.Comment: 14 pages, 15 figures, accepted in MNRA

The structure of PX3 (X=Cl, Br, I) molecular liquids from X-ray diffraction, Molecular Dynamics simulations and Reverse Monte Carlo modeling

Synchrotron X-ray diffraction measurements have been conducted on liquid phosphorus trichloride, tribromide and triiodide. Molecular Dynamics simulations for these molecular liquids were performed with a dual purpose: (1) to establish whether existing intermolecular potential functions can provide a picture that is consistent with diffraction data; (2) to generate reliable starting configurations for subsequent Reverse Monte Carlo modelling. Structural models (i.e., sets of coordinates of thousands of atoms) that were fully consistent with experimental diffraction information, within errors, have been prepared by means of the Reverse Monte Carlo method. Comparison with reference systems, generated by hard sphere-like Monte Carlo simulations, was also carried out to demonstrate the extent to which simple space filling effects determine the structure of the liquids (and thus, also estimating the information content of measured data). Total scattering structure factors, partial radial distribution functions and orientational correlations as a function of distances between the molecular centres have been calculated from the models. In general, more or less antiparallel arrangements of the primary molecular axes that are found to be the most favourable orientation of two neighbouring molecules. In liquid PBr3 electrostatic interactions seem to play a more important role in determining intermolecular correlations than in the other two liquids; molecular arrangements in both PCl3 and PI3 are largely driven by steric effects.Comment: 25 pages, 6 figure

On the Diophantine equation ∑j=1kjFjp=Fnq\sum_{j=1}^kjF_j^p=F_n^q

Let $F_n$ denote the $n^{th}$ term of the Fibonacci sequence. In this paper, we investigate the Diophantine equation $F_1^p+2F_2^p+\cdots+kF_{k}^p=F_{n}^q$ in the positive integers $k$ and $n$, where $p$ and $q$ are given positive integers. A complete solution is given if the exponents are included in the set $\{1,2\}$. Based on the specific cases we could solve, and a computer search with $p,q,k\le100$ we conjecture that beside the trivial solutions only $F_8=F_1+2F_2+3F_3+4F_4$, $F_4^2=F_1+2F_2+3F_3$, and $F_4^3=F_1^3+2F_2^3+3F_3^3$ satisfy the title equation.Comment: 12 page

Agrobacterium-mediated barley transformation.

More than ten years have passed since the first successful Agrobacterium-mediated barley transformation experiment, however it is still quite challenging to establish a stably functioning agroinfiltration protocol. Efficiency of the method depends mainly on the transformation and co-cultivation conditions, and also the components of the tissue-culture media. With the use of an optimized media we have been able to set up a reliable, properly functioning transformation protocol. The first generation of transgenic barley plants, transformed with a transformation cassette carrying an aldo-keto-reductase gene from Arabidopsis thaliana and the hpt marker gene, were analyzed at nucleic acid (both DNA and RNA) and at protein levels. The key factors of success proved to be the use of Silwet L-77 (surfactant) in transformation inoculum, the Cu-content of regenerating media and the continuous visual monitoring of the transformed callus during the somatic embryogenesi