The double sum sum_(s >= 1) sum_p 1/(p^s log p^s) = 2.00666645... over the inverse of the product of prime powers p^s and their logarithms, is computed to 24 decimal digits. The sum covers all primes p and all integer exponents s>=1. The calculationa
l strategy is adopted from Cohens work which basically looks at the fraction as the underivative of the Prime Zeta Function, and then evaluates the integral by numerical methods.
We present the first observations of H$^{13}$CN$(1-0)$, H$^{13}$CO$^+(1-0)$ and SiO$(2-1)$ in NGC,6240, obtained with the IRAM PdBI. Combining a Markov Chain Monte Carlo (MCMC) code with Large Velocity Gradient (LVG) modelling, and with additional da
ta from the literature, we simultaneously fit three gas phases and six molecular species to constrain the physical condition of the molecular gas, including mass$-$luminosity conversion factors. We find $sim10^{10}M_odot$ of dense molecular gas in cold, dense clouds ($T_{rm k}sim10$,K, $n_{{rm H}_2}sim10^6$,cm$^{-3}$) with a volume filling factor $<0.002$, embedded in a shock heated molecular medium ($T_{rm k}sim2000$,K, $n_{{rm H}_2}sim10^{3.6}$,cm$^{-3}$), both surrounded by an extended diffuse phase ($T_{rm k}sim200$,K, $n_{{rm H}_2}sim10^{2.5}$,cm$^{-3}$). We derive a global $alpha_{rm CO}=1.5^{7.1}_{1.1}$ with gas masses $log_{10}left(M / [M_odot]right)=10.1_{10.0}^{10.8}$, dominated by the dense gas. We also find $alpha_{rm HCN} = 32^{89}_{13}$, which traces the cold, dense gas. The [$^{12}$C]/[$^{13}$C] ratio is only slightly elevated ($98^{230}_{65}$), contrary to the very high [CO]/[$^{13}$CO] ratio (300-500) reported in the literature. However, we find very high [HCN]/[H$^{13}$CN] and [HCO$^+$]/[H$^{13}$CO$^+$] abundance ratios $(300^{500}_{200})$ which we attribute to isotope fractionation in the cold, dense clouds.
We describe the difference imaging pipeline (DiffImg) used to detect transients in deep images from the Dark Energy Survey Supernova program (DES-SN) in its first observing season from Aug 2013 through Feb 2014. DES-SN is a search for transients in w
hich ten 3-deg^2 fields are repeatedly observed in the g,r,i,z passbands with a cadence of about 1 week. The observing strategy has been optimized to measure high-quality light curves and redshifts for thousands of Type Ia supernova (SN Ia) with the goal of measuring dark energy parameters. The essential DiffImg functions are to align each search image to a deep reference image, do a pixel-by-pixel subtraction, and then examine the subtracted image for significant positive detections of point-source objects. The vast majority of detections are subtraction artifacts, but after selection requirements and image filtering with an automated scanning program, there are 130 detections per deg^2 per observation in each band, of which only 25% are artifacts. Of the 7500 transients discovered by DES-SN in its first observing season, each requiring a detection on at least 2 separate nights, Monte Carlo simulations predict that 27% are expected to be supernova. Another 30% of the transients are artifacts, and most of the remaining transients are AGN and variable stars. Fake SNe Ia are overlaid onto the images to rigorously evaluate detection efficiencies, and to understand the DiffImg performance. The DiffImg efficiency measured with fake SNe agrees well with expectations from a Monte Carlo simulation that uses analytical calculations of the fluxes and their uncertainties. In our 8 shallow fields with single-epoch 50% completeness depth 23.5, the SN Ia efficiency falls to 1/2 at redshift z 0.7, in our 2 deep fields with mag-depth 24.5, the efficiency falls to 1/2 at z 1.1.
In this paper we present some basic uniqueness results for evolutive equations under density constraints. First, we develop a rigorous proof of a well-known result (among specialists) in the case where the spontaneous velocity field satisfies a monot
onicity assumption: we prove the uniqueness of a solution for first order systems modeling crowd motion with hard congestion effects, introduced recently by emph{Maury et al.} The monotonicity of the velocity field implies that the $2-$Wasserstein distance along two solutions is $lambda$-contractive, which in particular implies uniqueness. In the case of diffusive models, we prove the uniqueness of a solution passing through the dual equation, where we use some well-known parabolic estimates to conclude an $L^1-$contraction property. In this case, by the regularization effect of the non-degenerate diffusion, the result follows even if the given velocity field is only $L^infty$ as in the standard Fokker-Planck equation.
The velocity potential in the Kelvin ship-wave source can be partly expressed in terms of space derivatives of the single integral [F(x,rho,alpha)=int_{-infty}^infty exp,[-frac{1}{2}rho cosh (2u-ialpha)] cos (xcosh u),du,] where $(x, rho, alpha)$ are
cylindrical polar coordinates with origin based at the source and $-pi/2leqalphaleqpi/2$. An asymptotic expansion of $F(x,rho,alpha)$ when $x$ and $rho$ are small, but such that $Mequiv x^2/(4rho)$ is large, was given using a non-rigorous approach by Bessho in 1964 as a sum involving products of Bessel functions. This expansion, together with an additional integral term, was subsequently proved by Ursell in 1988. Our aim here is to present an alternative asymptotic procedure for the case of large $M$. The resulting expansion consists of three distinct parts: a convergent sum involving the Struve functions, an asymptotic series and an exponentially small saddle-point contribution. Numerical computations are carried out to verify the accuracy of our expansion.
Reliable low-latency gravitational wave parameter estimation is essential to target limited electromagnetic followup facilities toward astrophysically interesting and electromagnetically relevant sources of gravitational waves. In this study, we exam
ine the tradeoff between speed and accuracy. Specifically, we estimate the astrophysical relevance of systematic errors in the posterior parameter distributions derived using a fast-but-approximate waveform model, SpinTaylorF2 (STF2), in parameter estimation with lalinference_mcmc. Though efficient, the STF2 approximation to compact binary inspiral employs approximate kinematics (e.g., a single spin) and an approximate waveform (e.g., frequency domain versus time domain). More broadly, using a large astrophysically-motivated population of generic compact binary merger signals, we report on the effectualness and limitations of this single-spin approximation as a method to infer parameters of generic compact binary sources. For most low-mass compact binary sources, we find that the STF2 approximation estimates compact binary parameters with biases comparable to systematic uncertainties in the waveform. We illustrate by example the effect these systematic errors have on posterior probabilities most relevant to low-latency electromagnetic followup: whether the secondary is has a mass consistent with a neutron star; whether the masses, spins, and orbit are consistent with that neutron stars tidal disruption; and whether the binarys angular momentum axis is oriented along the line of sight.
We report a polarized Raman study of Weyl semimetal TaAs. We observe all the optical phonons, with energies and symmetries consistent with our first-principles calculations. We detect additional excitations assigned to multiple-phonon excitations. Th
ese excitations are accompanied by broad peaks separated by 140~cm$^{-1}$ that are also most likely associated with multiple-phonon excitations. We also noticed a sizable B$_1$ component for the spectral background, for which the origin remains unclear.
In this paper we analyze the behavior of the distance function under Ricci flows whose scalar curvature is uniformly bounded. We will show that on small time-intervals the distance function is $frac12$-Holder continuous in a uniform sense. This impli
es that the distance function can be extended continuously up to the singular time.
We examine a class of exact solutions for the eigenvalues and eigenfunctions of a doubly anharmonic oscillator defined by the potential $V(x)=omega^2/2 x^2+lambda x^4/4+eta x^6/6$, $eta>0$. These solutions hold provided certain constraints on the cou
pling parameters $omega^2$, $lambda$ and $eta$ are satisfied.
The modelling of the adherence energy during peeling of Pressure Sensitive Adhesives (PSA) has received much attention since the 1950s, uncovering several factors that aim at explaining their high adherence on most substrates, such as the softness an
d strong viscoelastic behaviour of the adhesive, the low thickness of the adhesive layer and its confinement by a rigid backing. The more recent investigation of adhesives by probe-tack methods also revealed the importance of cavitation and stringing mechanisms during debonding, underlining the influence of large deformations and of the related non-linear response of the material, which also intervenes during peeling. Although a global modelling of the complex coupling of all these ingredients remains a formidable issue, we report here some key experiments and modelling arguments that should constitute an important step forward. We first measure a non-trivial dependence of the adherence energy on the loading geometry, namely through the influence of the peeling angle, which is found to be separable from the peeling velocity dependence. This is the first time to our knowledge that such adherence energy dependence on the peeling angle is systematically investigated and unambiguously demonstrated. Secondly, we reveal an independent strong influence of the large strain rheology of the adhesives on the adherence energy. We complete both measurements with a microscopic investigation of the debonding region. We discuss existing modellings in light of these measurements and of recent soft material mechanics arguments, to show that the adherence energy during peeling of PSA should not be associated to the propagation of an interfacial stress singularity. The relevant deformation mechanisms are actually located over the whole adhesive thickness, and the adherence energy during peeling of PSA should rather be associated to the energy loss by viscous friction and by rate-dependent elastic hysteresis.
