ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $E(z,s)$ be the non-holomorphic Eisenstein series for the modular group $SL(2,{\mathbb Z})$. The classical Kronecker limit formula shows that the second term in the Laurent expansion at $s=1$ of $E(z,s)$ is essentially the logarithm of the Dedekind eta function. This eta function is a weight $1/2$ modular form and Dedekind expressed its multiplier system in terms of Dedekind sums. Building on work of Goldstein, we extend these results from the modular group to more general Fuchsian groups $\Gamma$. The analogue of the eta function has a multiplier system that may be expressed in terms of a map $S:\Gamma \to {\mathbb R}$ which we call a modular Dedekind symbol. We obtain detailed properties of these symbols by means of the limit formula.   Twisting the usual Eisenstein series with powers of additive homomorphisms from $\Gamma$ to ${\mathbb C}$ produces higher-order Eisenstein series. These series share many of the properties of $E(z,s)$ though they have a more complicated automorphy condition. They satisfy a Kronecker limit formula and produce higher-order Dedekind symbols $S^*:\Gamma \to {\mathbb R}$. As an application of our general results, we prove that higher-order Dedekind symbols associated to genus one congruence groups $\Gamma_0(N)$ are rational.
In recent years cosmic shear, the weak gravitational lensing effect by the large-scale structure of the Universe, has proven to be one of the observational pillars on which the cosmological concordance model is founded. Several cosmic shear statistics have been developed in order to analyze data from surveys. For the covariances of the prevalent second-order measures we present simple and handy formulae, valid under the assumptions of Gaussian density fluctuations and a simple survey geometry. We also formulate these results in the context of shear tomography, i.e. the inclusion of redshift information, and generalize them to arbitrary data field geometries. We define estimators for the E- and B-mode projected power spectra and show them to be unbiased in the case of Gaussianity and a simple survey geometry. From the covariance of these estimators we demonstrate how to derive covariances of arbitrary combinations of second-order cosmic shear measures. We then recalculate the power spectrum covariance for general survey geometries and examine the bias thereby introduced on the estimators for exemplary configurations. Our results for the covariances are considerably simpler than and analytically shown to be equivalent to the real-space approach presented in the first paper of this series. We find good agreement with other numerical evaluations and confirm the general properties of the covariance matrices. The studies of the specific survey configurations suggest that our simplified covariances may be employed for realistic survey geometries to good approximation.
Capacitance measurements from cyclic voltammetry, galvanostatic chronopotentiometry and calculation of capacitance from imaginary part of impedance are widely used in investigations of supercapacitors. The methods assume the supercapacitor is a capacitor, while real objects correspond to different equivalent electric circuits and show various contributions of non-capacitive currents to the current which is used for calculation of capacitance. Specific capacitances which are presented in F g-1 units in publications not always refer to electric capacitance. The inadequateness of the capacitance characterization has already resulted in groundless attribution to supercapacitors of various systems with electrochemical responses of poorly reversible electrochemical reactions. The number of publications that present false capacitances is terrible and still increases. A widespread neglect of energy dissipation in calculations of specific capacitance leads to further confusion in the characterization of supercapacitors.
The quality of HFB wave functions are tested by comparing the theoretically calculated results with the available experimental data for a number of spectroscopic properties like yrast spectra, reduced B(E2) transition probabilities, quadrupole moments and g-factors for the nuclei involved in 2$\nu $ $\beta \beta $ decay. It is observed that the np interactions vis-\`{a}-vis the deformations of the intrinsic ground states of medium mass nuclei play a crucial role in the fine tuning of the nuclear matrix elements, M$_{2\nu}.$
Given a domain $\Omega$ of a complete Riemannian manifold $\mathcal{M}$ and define $\mathcal{A}$ to be the Laplacian with Neumann boundary condition on $\Omega$. We prove that, under appropriate conditions, the corresponding heat kernel satisfies the Gaussian upper bound $$ h(t,x,y)\leq \frac{C}{\left[V\_\Omega(x,\sqrt{t})V\_\Omega (y,\sqrt{t})\right]^{1/2}}\left( 1+\frac{d^2(x,y)}{4t}\right)^{\delta}e^{-\frac{d^2(x,y)}{4t}},\;\; t\textgreater{}0,\; x,y\in \Omega . $$ Here $d$ is the geodesic distance on $\mathcal{M}$, $V\_\Omega (x,r)$ is the Riemannian volume of $B(x,r)\cap \Omega$, where $B(x,r)$ is the geodesic ball of center $x$ and radius $r$, and $\delta$ is a constant related to the doubling property of $\Omega$.   As a consequence we obtain analyticity of the semigroup $e^{-t {\mathcal A}}$ on $L^p(\Omega)$ for all $p \in [1, \infty)$ as well as a spectral multiplier result.
We present the results of a search for short-period variable stars in Leo A. We have found 92 candidate variables, including eight candidate RR Lyrae stars.   From the RR Lyraes, we measure a distance modulus of (m-M)_0 = 24.51 +/- 0.12, or 0.80 +/- 0.04 Mpc. This discovery of RR Lyraes confirms, for the first time, the presence of an ancient (> ~11 Gyr) population in Leo A accounting for at least 0.1% of the galaxy's V luminosity. We have also discovered a halo of old (> ~2 Gyr) stars surrounding Leo A, with a scale length roughly 50% larger than that of the dominant young population.   We also report the discovery of a large population of Cepheids in Leo A. The median absolute magnitude of our Cepheid sample is M_V = -1.1, fainter than 96% of SMC and 99% of LMC Cepheids. Their periods are also unusual, with three Cepheids that are deduced to be pulsating in the fundamental mode having periods of under 1 day. Upon examination, these characteristics of the Leo A Cepheid population appear to be a natural extension of the classical Cepheid period-luminosity relations to low metallicity, rather than being indicative of a large population of ``anomalous'' Cepheids. We demonstrate that the periods and luminosities are consistent with the expected values of low-metallicity blue helium-burning stars (BHeBs), which populate the instability strip at lower luminosities than do higher-metallicity BHeBs.
In this paper we propose a highly accurate approximate performance analysis of a heterogeneous server system with a processor sharing service discipline and a general job-size distribution under a generalized join the shortest queue (GJSQ) routing protocol. The GJSQ routing protocol is a natural extension of the well-known join the shortest queue routing policy that takes into account the non-identical service rates in addition to the number of jobs at each server. The performance metrics that are of interest here are the equilibrium distribution and the mean and standard deviation of the number of jobs at each server. We show that the latter metrics are near-insensitive to the job-size distribution using simulation experiments. By applying a single queue approximation we model each server as a single server queue with a state-dependent arrival process, independent of other servers in the system, and derive the distribution of the number of jobs at the server. These state-dependent arrival rates are intended to capture the inherent correlation between servers in the original system and behave in a rather atypical way.
We demonstrate that the output statistics of a quantum annealing protocol run on D-Wave 2000Q can be explained by static disorder garnishing an otherwise ideal device hardware. A Boltzmann-like distribution over distinct output states emerges with increasing problem size, and significantly reduces the chances for a correct identification of the sought-after optimal solutions.
We evaluated the individual atom contributions to the second harmonic generation (SHG) coefficients of LiCs2PO4 (LCPO) by introducing the partial response functionals on the basis of first principles calculations. The SHG response of LCPO is dominated by the metal-cation-centered groups CsO6 and LiO4, not by the nonmetal-cation-centered groups PO4 one expects from the existing models and theories. The SHG coefficients of LCPO are determined mainly by the occupied orbitals O-2p and Cs-5p as well as by the unoccupied orbitals Cs-5d and Li-2p. For the SHG response of a material, the polarizable atomic orbitals of the occupied and the unoccupied states are both important.
We pursue various restricted variable generalizations of the Chevalley-Warning theorem for low degree polynomial systems over a finite field. Our first such result involves variables restricted to Cartesian products of the Vandermonde subsets of $\F_q$ defined by G\'acs-Weiner and Sziklai-Tak\'ats. We then define an invariant $\uomega(X)$ of a nonempty subset of $\F_q^n$. Our second result involves $X$-restricted variables when the degrees of the polynomials are small compared to $\uomega(X)$. We end by exploring various classes of subsets for which $\uomega(X)$ can be bounded from below.
We apply Cauchy's interlacing theorem to derive some eigenvalue bounds to the chromatic number using the normalized Laplacian matrix, including a combinatorial characterization of when equality occurs. Further, we introduce some new expansion type of parameters which generalize the Cheeger constant of a graph, and relate them to the colourings which meet our eigenvalue bound with equality. Finally, we exhibit a family of examples, which include the graphs that appear in the statement of the Erd\H{o}s-Faber-Lov\'asz conjecture.
In this work, we explore the charmed pentaquarks, where the relativistic five-quark equations are obtained by the dispersion relation technique. By solving these equations with the method based on the extraction of the leading singularities of the amplitudes, we predict the mass spectrum of charmed pentaquarks with $J^P=1/2^{\pm}$ and $3/2^{\pm}$, which is valuable to further experimental study of charmed pentaquark.
We present evolutionary synthesis models applied to near--infrared spectral features observed in the spectra of young Magellanic Cloud clusters and starburst galaxies. The temporal evolution of the first and second overtones of CO at 2.29 micron (2-0 bandhead) and 1.62 micron (6-3 bandhead) and of the (U-B), (B-V) and (J-K) colors are investigated. We find that the current evolutionary tracks of massive stars with sub-solar chemical composition in the red supergiant phase are not reliable for any synthesis of the temporal evolution of infrared stellar features. The high sensitivity of the selected infrared features to the atmospheric parameters of cool stars allows us to place constraints on the temperature and the fraction of time spent in the red part of the Hertzsprung-Russell diagram by massive stars during their core-helium burning phase. We derive a set of empirically calibrated spectrophotometric models by adjusting the red supergiant parameters such that the properties of the observed templates are reproduced.
The presence and evolution of apparent horizons in a two-parameter family of spherically symmetric, time-dependent solutions of Brans-Dicke gravity are analyzed. These solutions were introduced to model space- and time-varying gravitational couplings and are supposed to represent central objects embedded in a spatially flat universe. We find that the solutions possess multiple evolving apparent horizons, both black hole horizons covering a central singularity and cosmological ones. It is not uncommon for two of these horizons to merge, leaving behind a naked singularity covered only by a cosmological horizon. Two characteristic limits are also explicitly worked out: the limit where the theory reduces to general relativity and the limit where the solutions become static. The physical relevance of this family of solutions is discussed.
A very simple physical model of galaxies, in which the formation of stars is instantaneously regulated by the mass of gas in a reservoir, links together three different aspects of the evolving galaxy population:(a) the cosmic time evolution of the specific star-formation rate sSFR relative to the growth of haloes, (b) the gas-phase metallicities across the galaxy population and over cosmic time, and (c) the ratio of the stellar to dark matter mass of haloes. If the SFR efficiency and wind mass loading are constant, the sSFR is set to the specific accretion rate of the galaxy: more realistic situations lead to an sSFR which is perturbed from this identity. The metallicity is set by the instantaneous operation of the regulator system rather than by the past history of the system. The regulator system naturally produces a Z(mstar, SFR) relation, with SFR as a second parameter in the mass-metallicity relation. This will be the same at all epochs unless the efficiency and mass-loading change with time, naturally producing a so-called "fundamental metallicity relation". The observed Z(mstar) relation of SDSS galaxies implies a strong dependence of stellar mass on halo mass that reconciles the different faint end slopes of the stellar and halo mass-functions in standard {\Lambda}CDM. It also boosts the sSFR relative to the specific accretion rate and produces a different dependence on mass, both of which are observed. The derived Z(mstar, SFR) relation for the regulator system is fit to published Z(mstar, SFR) data. The fitted efficiency is consistent with observed molecular gas-depletion timescales in galaxies while the fitted mass-loading is also plausible. The model also successfully reproduces the mass-metallicity relation of star-forming galaxies at z ~ 2.
We present a method to determine the shot noise in quantum systems from knowledge of their time evolution - the latter being obtained using numerical simulation techniques. While our ultimate goal is the study of interacting systems, the main issues for the numerical determination of the noise do not depend on the interactions. To discuss them, we concentrate on the single resonant level model, which consists in a single impurity attached to non-interacting leads, with spinless fermions. We use exact diagonalisations (ED) to obtain time evolution, and are able to use known analytic results as benchmarks. We obtain a complete characterization of finite size effects at zero frequency, where we find that the finite size corrections scale $\propto G^2$, $G$ the differential conductance. We also discuss finite frequency noise, as well as the effects of damping in the leads.
We present the results of a mini-survey for associated HI 21-cm absorption at z < 0.42 with the Giant Metrewave Radio Telescope. Our targets are radio galaxies, selected on the basis that the 1216 Angstrom luminosities are below 10^23 W/Hz, above which there has never been a detection of 21-cm absorption. Of the three sources for which we obtained good data, two are unclassified active galactic nuclei (AGN) and one is type-2. Being a non-detection, the type-2 object is consistent with our previous result that 21-cm absorption in radio sources is not dictated by unified schemes of AGN. In the case of the detection, the absorption only occurs towards one of the two resolved radio lobes in PKS 1649-062. If the absorption is due to an another intervening galaxy, or cool HI gas in the intergalactic medium, covering only the south-west lobe, then, being at the same redshift, this is likely to be gravitationally bound to the optical object identified as PKS 1649-062. If the absorption is due to an inclined disk centred between the lobes, intervening the SW lobe while being located behind the NE lobe, by assuming that it covers the emission peak at 150 kpc from the nucleus, we estimate a dynamical mass of ~3 x 10^12 solar masses for the disk.
Line intensity mapping (LIM) is an emerging technique with a unique potential to probe a wide range of scales and redshifts. Realizing the full potential of LIM, however, relies on accurate modeling of the signal. We introduce an extended halo model for the power spectrum of intensity fluctuations of CO rotational lines and [CII] fine transition line in real space, modeling nonlinearities in matter fluctuations and biasing relation between the line intensity fluctuations and the underlying dark matter distribution. We also compute the stochastic contributions beyond the Poisson approximation using the halo model framework. To establish the accuracy of the model, we create the first cosmological-scale simulations of CO and [CII] intensity maps, \textsf{MithraLIMSims}, at redshifts $0.5 \leq z\leq6$, using halo catalogs from Hidden-Valley simulations, and painting halos according to mass-redshift-luminosity relations for each line. We show that at $z=1$ on scales $k_{\rm max} \lesssim 0.8 \ {\rm Mpc}^{-1}h$, the model predictions of clustering power (with only two free parameters) are in agreement with the measured power spectrum at better than 5\%. At higher redshift of $z=4.5$, this remarkable agreement extends to smaller scale of $ k_{\rm max} \lesssim 2 \ {\rm Mpc}^{-1}h$. Furthermore, we show that on large scales, the stochastic contributions to CO and CII power spectra are non-Poissonian, with amplitudes reproduced reasonably well by the halo model prescription. Lastly, we assess the performance of the theoretical model of the baryon acoustic oscillations (BAO) and show that hypothetical LIM surveys probing CO lines at $z=1$, that can be deployed within this decade, will be able to make a high significance measurement of the BAO. On a longer time scale, a space-based mission probing [CII] line can uniquely measure the BAO on a wide range of redshifts at an unprecedented precision.
The zeroes of Goss polynomials $G_{k, \Lambda}(X)$ for $\Lambda = A \defeq \mathbb{F}_{q}[T]$ and similar lattices $\Lambda$ are studied. Generically, the zero distribution follows a simple pattern governed by the $q$-adic expansion of $k-1$. However, if $q=p^{f}$ with $f \geq 2$ is a proper power of the prime $p$, irregularities of the $q$-adic sum-of-digits function may lead to deviations from this pattern, to irregular zeroes, and an abundance of trivial zeroes of $G_{k, \Lambda}$ compared to the generic formula. These phenomena are related to properties of the Sheats compositions of natural numbers $n$ divisible by $q-1$. Among other things, we give a necessary and sufficient condition for the existence of irregular zeroes of $G_{k,A}$ and a formula for the vanishing order of $G_{k,A}$ at $x=0$.
The electron-electron interactions affect the low-energy excitations of an electronic system and induce deformations of the Fermi surface. These effects are especially important in anisotropic materials with strong correlations, such as copper oxides superconductors or ruthenates. Here we analyze the deformations produced by electronic correlations in the Fermi surface of anisotropic two-dimensional systems, treating the regular and singular regions of the Fermi surface on the same footing. Simple analytical expressions are obtained for the corrections, based on local features of the Fermi surface. It is shown that, even for weak local interactions, the behavior of the self-energy is non trivial, showing a momentum dependence and a self-consistent interplay with the Fermi surface topology. Results are compared to experimental observations and to other theoretical results.
Voevodsky has conjectured that numerical and smash equivalence coincide on a smooth projective variety. We prove the conjecture for one dimensional cycles on an arbitrary product of curves. As a consequence we get that numerically trivial 1-cycles on an abelian variety are smash nilpotent.
We report the first two-dimensional mapping of the stellar population and non-stellar continua within the inner 180 pc (radius) of NGC 1068 at a spatial resolution of 8 pc, using integral field spectroscopy in the near-infrared. We have applied the technique of spectral synthesis to data obtained with the instrument NIFS and the adaptive optics module ALTAIR at the Gemini North Telescope. Two episodes of recent star formation are found to dominate the stellar population contribution: the first occurred 300 Myr ago, extending over most of the nuclear region; the second occurred just 30 Myr ago, in a ring-like structure at ~100 pc from the nucleus, where it is coincident with an expanding ring of H2 emission. Inside the ring, where a decrease in the stellar velocity dispersion is observed, the stellar population is dominated by the 300 Myr age component. In the inner 35 pc, the oldest age component (age > 2Gyr) dominates the mass, while the flux is dominated by black-body components with temperatures in the range 700 < T < 800 K which we attribute to the dusty torus. We also find some contribution from black-body and power-law components beyond the nucleus which we attribute to dust emission and scattered light.
Taking advantage of the high sensitivity of the Chandra Advanced CCD Imaging Spectrometer, we have conducted a snap-shot survey of pulsars previously undetected in X-rays. We detected 12 pulsars and established deep flux limits for 11 pulsars. Using these new results, we revisit the relationship between the X-ray luminosity, L_psr_x, and spin-down power, Edot. We find that the obtained limits further increase the extremely large spread in the non-thermal X-ray efficiencies, eta_psr_x=L_psr_x/Edot, with some of them being now below 1e-5. Such a spread cannot be explained by poorly known distances or by beaming of pulsar radiation. We also find evidence of a break in the dependence of L_psr_x on Edot, such that pulsars become more X-ray efficient at Edot<~ 1e34-1e35 erg/s. We examine the relationship between the gamma-ray luminosity, L_psr_g, and Edot, which exhibits a smaller scatter compared to that in X-rays. This confirms that the very large spread in the X-ray efficiencies cannot be explained just by beaming because the gamma-ray emission is generally expected to be beamed stronger than the X-ray emission. Intriguingly, there is also an indication of a break in the L_psr_g(Edot) dependence at Edot~1e35 erg/s, with lower-Edot pulsars becoming less gamma-ray efficient. We also examine the distance-independent L_psr_f/L_psr_x ratio as a function of Edot for a sample of gamma-ray pulsars observed by Chandra and find that it peaks at Edot~1e35 erg/s, showing that the breaks cannot originate from poorly measured distances. We discuss the implications of our findings for existing models of magnetospheric emission and venues for further exploration.
In this paper, we study the problem of finding the solution of a multi-dimensional time fractional reactiondiffusion equation with nonlinear source from the final value data. We prove that the present problem is not well-posed. Then regularized problems are constructed using the truncated expansion method (in the case of two-dimensional) and the quasi-boundary value method (in the case of multi-dimensional). Finally, convergence rates of the regularized solutions are given and investigated numerically.