On arithmetic and asymptotic properties of up-down numbers

Let $\sigma=(\sigma_1,..., \sigma_N)$, where $\sigma_i =\pm 1$, and let $C(\sigma)$ denote the number of permutations $\pi$ of $1,2,..., N+1,$ whose up-down signature $\mathrm{sign}(\pi(i+1)-\pi(i))=\sigma_i$, for $i=1,...,N$. We prove that the set of all up-down numbers $C(\sigma)$ can be expressed by a single universal polynomial $\Phi$, whose coefficients are products of numbers from the Taylor series of the hyperbolic tangent function. We prove that $\Phi$ is a modified exponential, and deduce some remarkable congruence properties for the set of all numbers $C(\sigma)$, for fixed $N$. We prove a concise upper-bound for $C(\sigma)$, which describes the asymptotic behaviour of the up-down function $C(\sigma)$ in the limit $C(\sigma) \ll (N+1)!$.Comment: Recommended for publication in Discrete Mathematics subject to revision

Type Ia Supernovae and Accretion Induced Collapse

Using the population synthesis binary evolution code StarTrack, we present theoretical rates and delay times of Type Ia supernovae arising from various formation channels. These channels include binaries in which the exploding white dwarf reaches the Chandrasekhar mass limit (DDS, SDS, and helium-rich donor scenario) as well as the sub-Chandrasekhar mass scenario, in which a white dwarf accretes from a helium-rich companion and explodes as a SN Ia before reaching the Chandrasekhar mass limit. We find that using a common envelope parameterization employing energy balance with alpha=1 and lambda=1, the supernova rates per unit mass (born in stars) of sub-Chandrasekhar mass SNe Ia exceed those of all other progenitor channels at epochs t=0.7 - 4 Gyr for a burst of star formation at t=0. Additionally, the delay time distribution of the sub-Chandrasekhar model can be divided in to two distinct evolutionary channels: the `prompt' helium-star channel with delay times < 500 Myr, and the `delayed' double white dwarf channel with delay times > 800 Myr spanning up to a Hubble time. These findings are in agreement with recent observationally-derived delay time distributions which predict that a large number of SNe Ia have delay times < 1 Gyr, with a significant fraction having delay times < 500 Myr. We find that the DDS channel is also able to account for the observed rates of SNe Ia. However, detailed simulations of white dwarf mergers have shown that most of these mergers will not lead to SNe Ia but rather to the formation of a neutron star via accretion-induced collapse. If this is true, our standard population synthesis model predicts that the only progenitor channel which can account for the rates of SNe Ia is the sub-Chandrasekhar mass scenario, and none of the other progenitors considered can fully account for the observed rates.Comment: 6 pages, 1 figure, 1 table, to appear in proceedings for "Binary Star Evolution: Mass Loss, Accretion and Mergers

Reduction and analysis of photometric data on Comet Halley

The discovery that periodic variations in the brightness of Comet Halley were characterized by two unrelated frequencies implies that the nucleus is in a complex state of rotation. It either nutates as a result of the random addition of small torque perturbations accumulated over many perihelion passages, or the jet activity torques are so strong that it precesses wildly at each perihelion passage. To diagnose the state of nuclear rotation, researchers began a program to acquire photometric time series of the comet as it recedes from the sun. The intention is to observe the decay of the comet's atmosphere and then, when it is unemcumbered by the light of the coma, follow the light variation of the nucleus itself. The latter will be compared with preperihelion time series and the orientation of the nucleus at the time of Vega and Giotto flybys and an accurate rotational ephemeris constructed. Halley was observed on 38 nights during 1987 and approximately 21 nights in 1988. The comet moved from 5 AU to 8.5 AU during this time. The brightness of the coma was found to rapidly decrease in 1988 as the coma and cometary activity collapses. The magnitude in April 1988 was 19 mag (visual) and it is predicted that the nucleus itself will be the major contributor to the brightness in the 1988 and 1989 season

Subjective burden of government-imposed Covid-19 restrictions in Switzerland: evidence from the 2022 LINK Covid-19 survey

BACKGROUND: While a large literature has quantified the health and economic impact of COVID-19, estimates on the subjective losses in quality of life due to government imposed restrictions remain scarce. METHODS: We conducted a nationally representative online survey in Switzerland in February 2022 to measure average self-reported quality of life with government restrictions. We used a discrete choice experiment to compute average willingness to pay for avoiding specific restrictions and time-trade-off questions to quantify the relative quality of life under restrictions. RESULTS: A total of 1299 Swiss residents completed the online survey between February 9th and 15th, 2022. On average, respondents valued life under severe restrictions at 39% of their usual life (estimated relative utility 0.39 [0.37, 0.42]). Willingness to pay for avoiding restrictions was lowest for masks (CHF 663 [319, 1007]), and highest for schools and daycares (CHF 4123 [3443, 4803]) as well as private parties (CHF 4520 [3811, 5229]). We estimate that between March 2020 and February 2022 a total of 5.7 Million QALYs were lost due to light, moderate and severe restrictions imposed by the governments. CONCLUSIONS: The quality of life losses due to government restrictions are substantial, particularly when it comes to the closure of schools and daycares, as well as the prohibition of private gatherings. Future policies should weigh these costs against the health benefits achievable with specific measures

Manifestation of spin-charge separation in the dynamic dielectric response of one--dimensional Sr2CuO3

We have determined the dynamical dielectric response of a one-dimensional, correlated insulator by carrying out electron energy-loss spectroscopy on Sr2CuO3 single crystals. The observed momentum and energy dependence of the low-energy features, which correspond to collective transitions across the gap, are well described by an extended one-band Hubbard model with moderate nearest neighbor Coulomb interaction strength. An exciton-like peak appears with increasing momentum transfer. These observations provide experimental evidence for spin-charge separation in the relevant excitations of this compound, as theoretically expected for the one-dimensional Hubbard model.Comment: RevTex, 4 pages+2 figures, to appear in PRL (July 13

Origin of the peak-dip-hump structure in the photoemission spectra of Bi2212

The famous peak-dip-hump lineshape of the (\pi,0) photoemission spectrum of the bilayer Bi HTSC in the superconducting state is shown to be a superposition of spectral features originating from different electronic states which reside at different binding energies, but are each describable by essentially identical single-particle spectral functions. The 'superconducting' peak is due to the antibonding Cu-O-related band, while the hump is mainly formed by its bonding counterpart, with a c-axis bilayer coupling induced splitting of about 140 meV.Comment: 5 pages: text + 4 figures, revtex (Fig.2 is replaced by more suitable one

Quantitative spectral analysis of the sdB star HD 188112: a helium-core white dwarf progenitor

HD 188112 is a bright (V = 10.2 mag) hot subdwarf B (sdB) star with a mass too low to ignite core helium burning and is therefore considered as a pre-extremely low mass (ELM) white dwarf (WD). ELM WDs (M $\le$ 0.3 Msun) are He-core objects produced by the evolution of compact binary systems. We present in this paper a detailed abundance analysis of HD 188112 based on high-resolution Hubble Space Telescope (HST) near and far-ultraviolet spectroscopy. We also constrain the mass of the star's companion. We use hybrid non-LTE model atmospheres to fit the observed spectral lines and derive the abundances of more than a dozen elements as well as the rotational broadening of metallic lines. We confirm the previous binary system parameters by combining radial velocities measured in our UV spectra with the already published ones. The system has a period of 0.60658584 days and a WD companion with M $\geq$ 0.70 Msun. By assuming a tidally locked rotation, combined with the projected rotational velocity (v sin i = 7.9 $\pm$ 0.3 km s$^{-1}$) we constrain the companion mass to be between 0.9 and 1.3 Msun. We further discuss the future evolution of the system as a potential progenitor of a (underluminous) type Ia supernova. We measure abundances for Mg, Al, Si, P, S, Ca, Ti, Cr, Mn, Fe, Ni, and Zn, as well as for the trans-iron elements Ga, Sn, and Pb. In addition, we derive upper limits for the C, N, O elements and find HD 188112 to be strongly depleted in carbon. We find evidence of non-LTE effects on the line strength of some ionic species such as Si II and Ni II. The metallic abundances indicate that the star is metal-poor, with an abundance pattern most likely produced by diffusion effects.Comment: Accepted for publication in A&

Autowaves in a dc complex plasma confined behind a de Laval nozzle

Experiments to explore stability conditions and topology of a dense microparticle cloud supported against gravity by a gas flow were carried out. By using a nozzle shaped glass insert within the glass tube of a dc discharge plasma chamber a weakly ionized gas flow through a de Laval nozzle was produced. The experiments were performed using neon gas at a pressure of 100 Pa and melamine-formaldehyde particles with a diameter of 3.43 {\mu}m. The capturing and stable global confining of the particles behind the nozzle in the plasma were demonstrated. The particles inside the cloud behaved as a single convection cell inhomogeneously structured along the nozzle axis in a tube-like manner. The pulsed acceleration localized in the very head of the cloud mediated by collective plasma-particle interactions and the resulting wave pattern were studied in detail.Comment: 6 pages, 4 figure

Gamma-ray diagnostics of Type Ia supernovae: Predictions of observables from three-dimensional modeling

Besides the fact that the gamma-ray emission due to radioactive decays is responsible for powering the light curves of Type Ia supernovae (SNe Ia), gamma rays themselves are of particular interest as a diagnostic tool because they provide a direct way to obtain deeper insights into the nucleosynthesis and the kinematics of these explosion events. Focusing on two of the most broadly discussed SN Ia progenitor scenarios - a delayed detonation in a Chandrasekhar-mass white dwarf (WD) and a violent merger of two WDs - we use three-dimensional explosion models and perform radiative transfer simulations to obtain synthetic gamma-ray spectra. Both chosen models produce the same mass of 56Ni and have similar optical properties that are in reasonable agreement with the recently observed supernova SN 2011fe. In contrast to the optical regime, the gamma-ray emission of our two chosen models proves to be rather different. The almost direct connection of the emission of gamma rays to fundamental physical processes occuring in SNe Ia permits additional constraints concerning several explosion model properties that are not easily accessible within other wavelength ranges. Proposed future MeV missions such as GRIPS will resolve all spectral details only for nearby SNe Ia, but hardness ratio and light curve measurements still allow for a distinction of the two different models at 10 and 16 Mpc for an exposure time of 10^6 s, respectively. The possibility to detect the strongest line features up to the Virgo distance will offer the opportunity to build up a first sample of SN Ia detections in the gamma-ray energy range and underlines the importance of future space observatories for MeV gamma rays.Comment: 10 pages, 8 figures, accepted for publication by A&