Diophantine approximation by special primes

We show that whenever $\delta>0$, $\eta$ is real and constants $\lambda_i$ satisfy some necessary conditions, there are infinitely many prime triples $p_1,\, p_2,\, p_3$ satisfying the inequality $|\lambda_1p_1 + \lambda_2p_2 + \lambda_3p_3+\eta|<(\max p_j)^{-1/12+\delta}$ and such that, for each $i\in\{1,2,3\}$, $p_i+2$ has at most $28$ prime factors

Light curve solutions of six eclipsing binaries at the lower limit of periods of the W UMa stars

Photometric observations in V and I bands of six eclipsing binaries at the lower limit of the orbital periods of W UMa stars are presented. Three of them are newly discovered eclipsing systems. The light curve solutions revealed that all short-period targets were contact or overcontact binaries and added new six binaries to the family of short-period systems with estimated parameters. Four binaries have equal in size components and mass ratio near 1. The phase variability of the V-I colors of all targets may be explained by lower temperatures of their back surfaces than those of their side surfaces. Five systems revealed O'Connell effect that was reproduced by cool spots on the side surfaces of their primary components. The light curves of V1067 Her in 2011 and 2012 were fitted by diametrically opposite spots. The applying of the criteria for subdivision of the W UMa stars to our targets led to ambiguous results.Comment: 13 pages, 9 figures, accepted for publication in Research in Astronomy and Astrophysics (RAA

Exact Maps in Density Functional Theory for Lattice Models

In the present work, we employ exact diagonalization for model systems on a real-space lattice to explicitly construct the exact density-to-potential and for the first time the exact density-to-wavefunction map that underly the Hohenberg-Kohn theorem in density functional theory. Having the explicit wavefunction-to- density map at hand, we are able to construct arbitrary observables as functionals of the ground-state density. We analyze the density-to-potential map as the distance between the fragments of a system increases and the correlation in the system grows. We observe a feature that gradually develops in the density-to-potential map as well as in the density-to-wavefunction map. This feature is inherited by arbitrary expectation values as functional of the ground-state density. We explicitly show the excited-state energies, the excited-state densities, and the correlation entropy as functionals of the ground-state density. All of them show this exact feature that sharpens as the coupling of the fragments decreases and the correlation grows. We denominate this feature as intra-system steepening. We show that for fully decoupled subsystems the intra-system steepening transforms into the well-known inter-system derivative discontinuity. An important conclusion is that for e.g. charge transfer processes between localized fragments within the same system it is not the usual inter-system derivative discontinuity that is missing in common ground-state functionals, but rather the differentiable intra-system steepening that we illustrate in the present work

Observations and light curve solutions of ultrashort-period eclipsing binaries

Photometric observations in V and I bands and low-dispersion spectra of ten ultrashort-period binaries (NSVS 2175434, NSVS 2607629, NSVS 5038135, NSVS 8040227, NSVS 9747584, NSVS 4876238, ASAS 071829-0336.7, SWASP 074658.62+224448.5, NSVS 2729229, NSVS 10632802) are presented. One of them, NSVS 2729229, is newly discovered target. The results from modeling and analysis of our observations revealed that: (i) Eight targets have overcontact configurations with considerable fillout factor (up to 0.5) while NSVS 4876238 and ASAS 0718-03 have almost contact configurations; (ii) NSVS 4876238 is rare ultrashort-period binary of detached type; (iii) all stellar components are late dwarfs; (iv) the temperature difference of the components of each target does not exceed 400 K; (v) NSVS 2175434 and SWASP 074658.62+224448.5 exhibit total eclipses and their parameters could be assumed as well-determined; (v) NSVS 2729229 shows emission in the H_{alpha} line. Masses, radii and luminosities of the stellar components were estimated by the empirical relation "period, orbital axis" for short- and ultrashort-period binaries. We found linear relations mass-luminosity and mass-radius for the stellar components of our targets.Comment: Accepted for publication in PAS