On conjectures and problems of Ruzsa concerning difference graphs of S-units

Given a finite nonempty set of primes S, we build a graph $\mathcal{G}$ with vertex set $\mathbb{Q}$ by connecting x and y if the prime divisors of both the numerator and denominator of x-y are from S. In this paper we resolve two conjectures posed by Ruzsa concerning the possible sizes of induced nondegenerate cycles of $\mathcal{G}$, and also a problem of Ruzsa concerning the existence of subgraphs of $\mathcal{G}$ which are not induced subgraphs.Comment: 15 page

Electron spin-orbit splitting in InGaAs/InP quantum well studied by means of the weak antilocalization and spin-zero effects in tilted magnetic fields

The coupling between Zeeman spin splitting and Rashba spin-orbit terms has been studied experimentally in a gated InGaAs/InP quantum well structure by means of simultaneous measurements of the weak antilocalization (WAL) effect and beating in the SdH oscillations. The strength of the Zeeman splitting was regulated by tilting the magnetic field with the spin-zeros in the SdH oscillations, which are not always present, being enhanced by the tilt. In tilted fields the spin-orbit and Zeeman splittings are not additive, and a simple expression is given for the energy levels. The Rashba parameter and the electron g-factor were extracted from the position of the spin zeros in tilted fields. A good agreement is obtained for the spin-orbit coupling strength from the spin-zeros and weak antilocalization measurements.Comment: Accepted for publication in Semiconductors Science and Technolog

Overtone and multi-mode RR Lyrae stars in the globular cluster M3

The overtone and multi-mode RR Lyrae stars in the globular cluster M3 are studied using a 200-d long, $B,V$ and $I_{\mathrm C}$ time-series photometry obtained in 2012. 70\% of the 52 overtone variables observed show some kind of multi-periodicity (additional frequency at ${f_{0.61}}={f_{\mathrm {1O}}}/0.61$ frequency ratio, Blazhko effect, double/multi-mode pulsation, period doubling). A signal at 0.587 frequency ratio to the fundamental-mode frequency is detected in the double-mode star, V13, which may be identified as the second radial overtone mode. If this mode-identification is correct, than V13 is the first RR Lyrae star showing triple-mode pulsation of the first three radial modes. Either the Blazhko effect or the ${f_{0.61}}$ frequency (or both of these phenomena) appear in 7 double-mode stars. The $P_{\mathrm{1O}}/P_{\mathrm{F}}$ period ratio of RRd stars showing the Blazhko effect are anomalous. A displacement of the main frequency component at the fundamental-mode with the value of modulation frequency (or its half) is detected in three Blazhko RRd stars parallel with the appearance of the overtone-mode pulsation. The ${f_{0.61}}$ frequency appears in RRc stars that lie at the blue side of the double-mode region and in RRd stars, raising the suspicion that its occurrence may be connected to double-mode pulsation. The changes of the Blazhko and double-mode properties of the stars are also reviewed using the recent and archive photometric data.Comment: accepted for publication in ApJ Suppl. 26 pages, 25 figure

Effects of Magnetic Field on Josephson Current in SNS System

The effect of a magnetic field on Josephson current has been studied for a superconductor/normal-metal/superconductor (SNS) system, where N is a two-dimensional electron gas in a confining potential. It is found that the dependence of Josephson currents on the magnetic field are sensitive to the width of the normal metal. If the normal metal is wide and contains many channels (subbands), the current on a weak magnetic field shows a dependence similar to a Fraunhofer-pattern in SIS system and, as the field gets strong, it shows another type of oscillatory dependence on the field resulting from the Aharonov-Bohm interference between the edge states. As the number of channels decreases (i.e. normal metal gets narrower), however, the dependence in the region of the weak field deviates from a clear Fraunhofer pattern and the amplitude of the oscillatory dependence in the region of the strong field is reduced.Comment: 14 pages, 9 figure

An extensive photometric study of the Blazhko RR Lyrae star RZ Lyr

The analysis of recent, extended multicolour CCD and archive photoelectric, photographic and visual observations has revealed several important properties of RZ Lyr, an RRab-type variable exhibiting large-amplitude Blazhko modulation. On the time-base of \sim110 yr, a strict anticorrelation between the pulsation and modulation period changes is established. The light curve of RZ Lyr shows a remarkable bump on the descending branch in the small-amplitude phase of the modulation, similarly to the light curves of bump Cepheids. We speculate that the stellar structure temporally suits a 4:1 resonance between the periods of the fundamental and one of the higher-order radial modes in this modulation phase. The light-curve variation of RZ Lyr can be correctly fitted with a two-modulation-component solution; the 121 d period of the main modulation is nearly but not exactly four times longer than the period of the secondary modulation component. Using the inverse photometric method, the variations in the pulsation-averaged values of the physical parameters in different phases of both modulation components are determined.Comment: 15 pages, 14 figures, 8 tables. Published in MNRAS, 2012. [v3]: Only change: title correcte

Orbital Magnetism and Current Distribution of Two-Dimensional Electrons under Confining Potential

The spatial distribution of electric current under magnetic field and the resultant orbital magnetism have been studied for two-dimensional electrons under a harmonic confining potential V(\vecvar{r})=m \omega_0^2 r^2/2 in various regimes of temperature and magnetic field, and the microscopic conditions for the validity of Landau diamagnetism are clarified. Under a weak magnetic field (\omega_c\lsim\omega_0, \omega_c being a cyclotron frequency) and at low temperature (T\lsim\hbar\omega_0), where the orbital magnetic moment fluctuates as a function of the field, the currents are irregularly distributed paramagnetically or diamagnetically inside the bulk region. As the temperature is raised under such a weak field, however, the currents in the bulk region are immediately reduced and finally there only remains the diamagnetic current flowing along the edge. At the same time, the usual Landau diamagnetism results for the total magnetic moment. The origin of this dramatic temperature dependence is seen to be in the multiple reflection of electron waves by the boundary confining potential, which becomes important once the coherence length of electrons gets longer than the system length. Under a stronger field (\omega_c\gsim\omega_0), on the other hand, the currents in the bulk region cause de Haas-van Alphen effect at low temperature as T\lsim\hbar\omega_c. As the temperature gets higher (T\gsim\hbar\omega_c) under such a strong field, the bulk currents are reduced and the Landau diamagnetism by the edge current is recovered.Comment: 15 pages, 11 figure

The compact multiple system HIP 41431

The nearby (50 pc) K7V dwarf HIP 41431 (EPIC 212096658) is a compact three-tier hierarchy. Three K7V stars with similar masses, from 0.61 to 0.63 solar, make a triple-lined spectroscopic system where the inner binary with a period of 2.9 d is eclipsing, and the outer companion on a 59-d orbit exerts strong dynamical influence revealed by the eclipse time variation in the Kepler photometry. Moreover, the centre of mass of the triple system moves on a 3.9-yr orbit, modulating the proper motion. The mass of the fourth star is 0.35 solar. The Kepler and ground-based photometry and radial velocities from four different spectrographs are used to adjust the spectro-photodynamical model that accounts for dynamical interaction. The mutual inclination between the two inner orbits is 2{^{circ}.}16 ± 0{^{circ}.}11, while the outer orbit is inclined to their common plane by 21°±16°. The inner orbit precesses under the influence of both outer orbits, causing observable variation of the eclipse depth. Moreover, the phase of the inner binary is strongly modulated with a 59-d period and its line of apsides precesses. The middle orbit with eccentricity e = 0.28 also precesses, causing the observed variation of its radial velocity curve. Masses and other parameters of stars in this unique hierarchy are determined. This system is dynamically stable and likely old

Cryptotomography: reconstructing 3D Fourier intensities from randomly oriented single-shot diffraction patterns

We reconstructed the 3D Fourier intensity distribution of mono-disperse prolate nano-particles using single-shot 2D coherent diffraction patterns collected at DESY's FLASH facility when a bright, coherent, ultrafast X-ray pulse intercepted individual particles of random, unmeasured orientations. This first experimental demonstration of cryptotomography extended the Expansion-Maximization-Compression (EMC) framework to accommodate unmeasured fluctuations in photon fluence and loss of data due to saturation or background scatter. This work is an important step towards realizing single-shot diffraction imaging of single biomolecules.Comment: 4 pages, 4 figure