Septoku is a Sudoku variant invented by Bruce Oberg, played on a hexagonal grid of 37 cells. We show that up to rotations, reflections, and symbol permutations, there are only six valid Septoku boards. In order to have a unique solution, we show that
the minimum number of given values is six. We generalize the puzzle to other board shapes, and devise a puzzle on a star-shaped board with 73 cells with six givens which has a unique solution. We show how this puzzle relates to the unsolved Hadwiger-Nelson problem in combinatorial geometry.
We present a list of ``local axioms and an explicit combinatorial construction for the regular $B_2$-crystals (crystal graphs of highest weight integrable modules over $U_q(sp_4)$). Also a new combinatorial model for these crystals is developed.
It has been shown recently [J. L. Lado et al., Phys. Rev. Lett. 113, 027203 (2014)] that edge magnetic moments in graphene-like nanoribbons are strongly influenced by the intrinsic spin-orbit interaction. Due to this interaction an anisotropy comes a
bout which makes the in-plane arrangement of magnetic moments energetically more favorable than that corresponding to the out-of-plane configuration. In this paper we raise both the edge magnetism problem as well as differential conductance and shot noise Fano factor issues, in the context of finite-size flakes within the Coulomb blockade (CB) transport regime. Our findings elucidate the following problems: (i) modification of the CB diamonds by the appearance of the in-plane magnetic moments, (ii) modification of the CB diamonds by intrinsic spin-orbit interaction.
The electron spin resonance spectrum of a quasi 1D S=1/2 antiferromagnet K2CuSO4Br2 was found to demonstrate an energy gap and a doublet of resonance lines in a wide temperature range between the Curie--Weiss and Ne`{e}l temperatures. This type of ma
gnetic resonance absorption corresponds well to the two-spinon continuum of excitations in S=1/2 antiferromagnetic spin chain with a uniform Dzyaloshinskii--Moriya interaction between the magnetic ions. A resonance mode of paramagnetic defects demonstrating strongly anisotropic behavior due to interaction with spinon excitations in the main matrix is also observed.
Heat produced during a reset operation is meant to show a fundamental bound known as Landauer limit, while simple switch operations have an expected minimum amount of produced heat equal to zero. However, in both cases, present-day technology realiza
tions dissipate far beyond these theoretical limits. In this paper we present a study based on molecular dynamics simulations, where reset and switch protocols are applied on a graphene buckled ribbon, employed here as a nano electromechanical switch working at the thermodynamic limit.
We present measurements of positions and relative proper motions in the 30 Doradus region of the Large Magellanic Cloud (LMC). We detail the construction of a single-epoch astrometric reference frame, based on specially-designed observations obtained
with the two main imaging instruments ACS/WFC and WFC3/UVIS onboard the Hubble Space Telescope (HST). Internal comparisons indicate a sub milli-arc-second (mas) precision in the positions and the presence of semi-periodic systematics with a mean amplitude of ~0.8 mas. We combined these observations with numerous archival images taken with WFPC2 and spanning 17 years. The precision of the resulting proper motions for well-measured stars around the massive cluster R 136 can be as good as ~20 microarcsec/yr, although the true accuracy of proper motions is generally lower due to the residual systematic errors. The observed proper-motion dispersion for our highest-quality measurements is ~0.1 mas/yr. Our catalog of positions and proper motions contains 86,590 stars down to V~25 and over a total area of ~70 square arcmin. We examined the proper motions of 105 relatively bright stars and identified a total of 6 candidate runaway stars. We are able to tentatively confirm the runaway status of star VFTS 285, consistent with the findings from line-of-sight velocities, and to show that this star has likely been ejected from R 136. This study demonstrates that with HST it is now possible to reliably measure proper motions of individual stars in the nearest dwarf galaxies such as the LMC.
We use one single, few-picosecond-long, variably polarized laser pulse to deterministically write any selected spin state of a quantum dot confined dark exciton whose life and coherence time are six and five orders of magnitude longer than the laser
pulse duration, respectively. The pulse is tuned to an absorption resonance of an excited dark exciton state, which acquires non-negligible oscillator strength due to residual mixing with bright exciton states. We obtain a high fidelity one-to-one mapping from any point on the Poincare sphere of the pulse polarization to a corresponding point on the Bloch sphere of the spin of the deterministically photogenerated dark exciton.
Cosmic rays (CRs) interact with the gas, the radiation field and the magnetic field in the Milky Way, producing diffuse emission from radio to gamma rays. Observations of this diffuse emission and comparison with detailed predictions are powerful too
ls to unveil the CR properties and to study CR propagation. We present various GALPROP CR propagation scenarios based on current CR measurements. The predicted synchrotron emission is compared to radio surveys, and synchrotron temperature maps from WMAP and Planck, while the predicted interstellar gamma-ray emission is compared to Fermi-LAT observations. We show how multi-wavelength observations of the Galactic diffuse emission can be used to help constrain the CR lepton spectrum and propagation. Finally we discuss how radio and microwave data could be used in understanding the diffuse Galactic gamma-ray emission observed with Fermi-LAT, especially at low energies.
We consistently analyse for the first time the impact of survey depth and spatial resolution on the most used morphological parameters for classifying galaxies through non-parametric methods: Abraham and Conselice-Bershady concentration indices, Gini
, M20 moment of light, asymmetry, and smoothness. Three different non-local datasets are used, ALHAMBRA and SXDS (examples of deep ground-based surveys), and COSMOS (deep space-based survey). We used a sample of 3000 local, visually classified galaxies, measuring their morphological parameters at their real redshifts (z ~ 0). Then we simulated them to match the redshift and magnitude distributions of galaxies in the non-local surveys. The comparisons of the two sets allow to put constraints on the use of each parameter for morphological classification and evaluate the effectiveness of the commonly used morphological diagnostic diagrams. All analysed parameters suffer from biases related to spatial resolution and depth, the impact of the former being much stronger. When including asymmetry and smoothness in classification diagrams, the noise effects must be taken into account carefully, especially for ground-based surveys. M20 is significantly affected, changing both the shape and range of its distribution at all brightness levels.We suggest that diagnostic diagrams based on 2 - 3 parameters should be avoided when classifying galaxies in ground-based surveys, independently of their brightness; for COSMOS they should be avoided for galaxies fainter than F814 = 23.0. These results can be applied directly to surveys similar to ALHAMBRA, SXDS and COSMOS, and also can serve as an upper/lower limit for shallower/deeper ones.
Nowadays the number of models aimed at explaining the Type Ia supernova phenomenon is high and discriminating between them is a must-do. In this work we explore the influence of rotation in the evolution of the nuclear flame which drives the explosio
n in the so called gravitational confined detonation models. Assuming that the flame starts in a point-like region slightly above the center of the white dwarf (WD) and adding a moderate amount of angular velocity to the star we follow the evolution of the deflagration using a smoothed particle hydrodynamics code. We find that the results are very dependent on the angle between the rotational axis and the line connecting the initial bubble of burned material with the center of the white dwarf at the moment of the ignition. The impact of rotation is larger for angles close to 90{deg} because the Coriolis force on a floating element of fluid is maximum, and its principal effect is to break the symmetry of the deflagration. Such symmetry breaking weakens the convergence of the nuclear flame at the antipodes of the initial ignition volume, changing the environmental conditions around the convergence region with respect to non-rotating models. These changes seem to disfavor the emergence of a detonation in the compressed volume at the antipodes, thus compromising the viability of the so called gravitational confined detonation mechanism.
