ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we study the theory of the harmonic and the hyperharmonic Fibonacci numbers. Also, we get some combinatoric identities like as harmonic and hyperharmonic numbers and we obtain some useful formulas for $\mathbb{F}_{n}$, which is finite sums of reciprocals of Fibonacci numbers. We obtain spectral and Euclidean norms of circulant matrices involving harmonic and hyperharmonic Fibonacci numbers.
This paper discusses the Cosmic Background (CB) dipoles observations in the framework of the Planck mission. Dipoles observations can be used in three ways: (i) It gives a measurement of the peculiar velocity of our Galaxy which is an important observation in large scale structures formation model. (ii) Measuring the dipole can give unprecedent information on the monopole (that can be in some cases hard to obtain due to large foreground contaminations). (iii) The dipole can be an ideal absolute calibrator, easily detectable in cosmological experiments. Following the last two objectives, the main goal of the work presented here is twofold. First, we study the accuracy of the Planck-HFI calibration using the Cosmic Microwave Background (CMB) dipole measured by COBE as well as the Earth orbital motion dipole. We show that we can reach for HFI, a relative calibration between rings of about 1% and an absolute calibration better than 0.4% for the CMB channels (in the end, the absolute calibration will be limited by the uncertainties on the CMB temperature). We also show that Planck will be able to measure the CMB dipole direction at better than 1.7 arcmin and improve on the amplitude. Second, we investigate the detection of the Cosmic Far-Infrared Background (FIRB) dipole. Measuring this dipole could give a new and independent determination of the FIRB for which a direct determination is quite difficult due to Galactic dust emission contamination. We show that such a detection would require a Galactic dust emission removal at better than 1%, which will be very hard to achieve.
Itenberg and Shustin's pseudoholomorphic curve patchworking is in principle more flexible than Viro's original algebraic one. It was natural to wonder if the former method allows one to construct non-algebraic objects. In this paper we construct the first examples of patchworked real pseudoholomorphic curves in $\Sigma_n$ whose position with respect to the pencil of lines cannot be realised by any homologous real algebraic curve.
Long-range forces between macroscopic objects are mediated by light particles that interact with the electrons or nucleons, and include spin-dependent static components as well as spin- and velocity-dependent components. We parametrize the long-range potential between two fermions assuming rotational invariance, and find 16 different components. Applying this result to electrically neutral objects, we show that the macroscopic potential depends on 72 measurable parameters. We then derive the potential induced by the exchange of a new gauge boson or spinless particle, and compare the limits set by measurements of macroscopic forces to the astrophysical limits on the couplings of these particles.
We explore inelastic cotunneling through a strongly Coulomb-blockaded quantum dot attached to two ferromagnetic leads in the weak coupling limit using a generic quantum Langevin equation approach. We first develop a Bloch-type equation microscopically to describe the cotunneling-induced spin relaxation dynamics, and then develop explicit analytical expressions for the local magnetization, current, and its fluctuations. On this basis, we predict a novel zero-bias anomaly of the differential conductance in the absence of a magnetic field for the anti-parallel configuration, and asymmetric peak splitting in a magnetic field. Also, for the same system with large polarization, we find a negative zero-frequency differential shot noise in the low positive bias-voltage region. All these effects are ascribed to rapid spin-reversal due to underlying spin-flip cotunneling.
We report the results of 67h of CCD photometry of the recently discovered dwarf nova SDSS J210014.12+004446.0. The data were obtained on 24 nights spanning a month. During this time we observed four ordinary outbursts lasting about 2-3 days and reaching an amplitude of ~1.7 mag. On all nights our light curve revealed persistent modulation with the stable period of 0.081088(3) days. These humps were already observed on one night by Tramposch et al. (2005), who additionally observed superhumps during a superoutburst. Remarkably, from scant evidence at their disposal they were able to discern them as negative and positive (common) superhumps, respectively. Our period in quiescence clearly different from their superhump period confirmed this. Our discovery of an additional modulation, attributed by us to the orbital wave, completes the overall picture. Lack of superhumps in our data indicates that all eruptions we observed were ordinary outbursts. The earlier observation of the superhumps combined with the presence of the ordinary outbursts in our data enables classification of SDSS J2100 as an active SU UMa dwarf nova. Additionally, we have promoted SDSS J2100 to the group of cataclysmic variables exhibiting three periodic modulations of light from their accretion discs. We updated available information on positive and negative superhumps and thus provided enhanced evidence that their properties are strongly correlated mutually as well as with the orbital period. By recourse to these relations we were able to remove an alias ambiguity and to identify the orbital period of SDSS J2100 of 0.083304(6) days. SDSS J21000 is only third SU UMa dwarf nova showing both positive and negative superhumps. Their respective period excess and deficit equal to 4.99(3)% and -2.660(8)%, yielding the mass ratio q=0.24.
The interaction of a single photon with an individual two-level system is the textbook example of quantum electrodynamics. Achieving strong coupling in this system so far required confinement of the light field inside resonators or waveguides. Here, we demonstrate strong coherent coupling between a single Rydberg superatom, consisting of thousands of atoms behaving as a single two-level system due to the Rydberg blockade, and a propagating light pulse containing only a few photons. The strong light-matter coupling in combination with the direct access to the outgoing field allows us to observe for the first time the effect of the interactions on the driving field at the single photon level. We find that all our results are in quantitative agreement with the predictions of the theory of a single two-level system strongly coupled to a single quantized propagating light mode. The demonstrated coupling strength opens the way towards interfacing photonic and atomic qubits and preparation of propagating non-classical states of light, two crucial building blocks in future quantum networks.
In this paper we prove a Thomae derivative formula for trigonal curves admitting a non-singular affine model. This formula relates the derivatives of theta functions with rational characteristics on the curve to explicit expressions in the branching values.
Given a real number $x>0$, we determine $q_s(x):=\inf\mathscr{U}(x)$, where $\mathscr{U}(x)$ is the set of all bases $q\in(1,2]$ for which $x$ has a unique expansion of $0$'s and $1$'s. We give an explicit description of $q_s(x)$ for several regions of $x$-values. For others, we present an efficient algorithm to determine $q_s(x)$ and the lexicographically smallest unique expansion of $x$. We show that the infimum is attained for almost all $x$, but there is also a set of points of positive Hausdorff dimension for which the infimum is proper. In addition, we show that the function $q_s$ is right-continuous with left-hand limits and no downward jumps, and characterize the points of discontinuity of $q_s$.   A large part of the paper is devoted to the level sets $L(q):=\{x>0:q_s(x)=q\}$. We show that $L(q)$ is finite for almost every $q$, but there are also infinitely many infinite level sets. In particular, for the Komornik-Loreti constant $q_{KL}=\min\mathscr{U}(1)\approx 1.787$ we prove that $L(q_{KL})$ has both infinitely many left- and infinitely many right accumulation points.
We demonstrate that the generalization of the Lifshitz theory proposed by L. P. Pitaevskii arXiv:0801.0656 [Phys. Rev. Lett. v.101, 163202 (2008)] violates the Nernst heat theorem for many dielectric materials and is experimentally inconsistent.
An alternative approach introducing a 3 dimensional Ricci scalar curvature quantum operator given in terms of volume and area as well as new edge length operators is proposed. An example of monochromatic 4-valent node intertwiner state (equilateral tetrahedra) is studied and the scalar curvature measure for a regular tetrahedron shape is constructed. It is shown that all regular tetrahedron states are in the negative scalar curvature regime and for the semi-classical limit the spectrum is very close to the Euclidean regime.
The relationship between galaxies and supermassive black holes (SMBH) found in their cores plays a key role in the formation and evolution of both of these major constituents of the universe, as well as the evolution of the intergalactic medium. Neither can be fully understood on their own, and studies of galaxy and SMBH co-formation and co-evolution are now among the central topics of research in cosmology. Yet the very origins, and the early growth phases of the SMBH are still not firmly established. We review our current understanding of the relevant processes and their astrophysical and cosmological context, with an emphasis on the observability of the SMBH growth mechanisms at high redshifts, and their leftover progeny at low redshifts.
This paper is concerned with the linear ODE in the form $y'(t)=\lambda\rho(t)y(t)+b(t)$, $\lambda <0$ which represents a simplified storage model of the carbon in the soil. In the first part, we show that, for a periodic function $\rho(t)$, a linear drift in the coefficient $b(t)$ involves a linear drift for the solution of this ODE. In the second part, we extend the previous results to a classical heat non-homogeneous equation. The connection with an analytic semi-group associated to the ODE equation is considered in the third part. Numerical examples are given.
We provide a sufficient condition for the existence of a positive solution to $-\Delta u+V(|x|) u=u^p$ in $B_1$, when p is large enough. Here $B_1$ is the unit ball of $R^n$, n greater or equal to 2, and we deal both with Neumann and Dirichlet homogeneous boundary conditions. The solution turns to be a constrained minimum of the associated energy functional. As an application we show that, in case $V(|x|)$ is smooth, nonnegative and not identically zero, and p is sufficiently large, the Neumann problem always admits a solution.
It has been well established that nitrogen coordinated transition metal, TM-N$_{4}$-C (TM$=$Fe and Co) moieties, are responsible for the higher catalytic activity for the electrochemical oxygen reduction reaction. However, the results obtained using density functional theory calculations vary from one to another, which can lead to controversy. Herein, we assess the accuracy of the theoretical approach using different class of exchange-correlation functionals, i.e., Perdew-Burke-Ernzerhof (PBE) and revised PBE (RPBE), those with the Grimme's semiempirical dispersion correction (PBE+D3 and RPBE+D3), and the Bayesian error estimate functional with the nonlocal correlation (BEEF-vdW) on the reaction energies of oxygen reduction reaction on TM-N$_{4}$ moieties in graphene and those with OH-termination. We found that the predicted overpotentials using RPBE+D3 are comparable and consistent with those using BEEF-vdW. Our finding indicates that a proper choice of the exchange-correlation functional is crucial to a precise description of the catalytic activity of this system.
We consider the problem of placing $n$ nonattacking queens on a symmetric $n \times n$ Toeplitz matrix. As in the $N$-queens Problem on a chessboard, two queens may attack each other if they share a row or a column in the matrix. However, the usual diagonal restriction is replaced by specifying that queens may attack other queens that occupy squares with the same number value in the matrix. We will show that $n$ nonattacking queens can be placed on such a matrix if and only if $n\equiv 0,1 \mod 4$.
We present an analysis of new and archival VLA HI observations of a sample of eleven early-type galaxies rich in CO, with detailed comparisons of CO and HI distributions and kinematics. The early-type sample consists of both lenticular and elliptical galaxies in a variety of environments. A range of morphologies and environments were selected in order to give a broader understanding of the origins, distribution, and fate of the cold gas in early-type galaxies. Six of the eleven galaxies in the sample are detected in both HI and CO. The H$_{2}$ to HI mass ratios for this sample range from 0.2-120. The HI morphologies of the sample are consistent with that of recent HI surveys of early-type galaxies which also find a mix of HI morphologies and masses, low HI peak surface densities, and a lack of HI in early-type galaxies which reside in high density environments. The HI-detected galaxies have a wide range of HI masses (1.4$\times10^{6}$ to 1.1$\times10^{10}$ M$_{\odot}$). There does not appear to be any correlation between the HI mass and morphology (E versus S0). When HI is detected, it is centrally peaked - there are no central kpc-scale central HI depressions like those observed for early-type spiral galaxies at similar spatial resolutions and scales. A kinematic comparison between the HI and CO indicates that both cold gas components share the same origin. The primary goal of this and a series of future papers is to better understand the relationship between the atomic and molecular gas in early-type galaxies, and to compare the observed relationships with those of spiral galaxies where this relationship has been studied in depth.
We have studied the Kardar-Parisi-Zhang equation in the strong coupling regime in the mode-coupling approximation. We solved numerically in dimension d=1 for the correlation function at wavevector k. At large times t we found the predicted stretched exponential decay consistent with our previous saddle point analysis in [Phys. Rev. E {\bf 63}, 057103 (2001)], but we also observed that the decay to zero occurred in an unexpected oscillatory way. We have compared the results from mode-coupling for the scaling functions with the recent exact results from Praehofer and Spohn [cond-mat/0101200] for d=1 who also find an oscillatory decay to zero.
We describe two conjectures, one strictly stronger than the other, that give descriptions of the integral Bernstein center for GL_n(F) (that is, the center of the category of smooth W(k)[GL_n(F)]-modules, for F a p-adic field and k an algebraically closed field of characteristic l different from p) in terms of Galois theory. Moreover, we show that the weak version of the conjecture (for m at most n) implies the strong version of the conjecture. In a companion paper [HM] we show that the strong conjecture for n-1 implies the weak conjecture for n; thus the two papers together give an inductive proof of both conjectures. The upshot is a description of the integral Bernstein center for GL_n in purely Galois-theoretic terms; previous work of the author shows that such a description implies the conjectural "local Langlands correspondence in families" of Emerton and the author.
Using the Purple Mountain Observatory Delingha 13.7 m telescope, we conducted a large-scale $^{12}$CO $\left(J=1 \rightarrow 0\right)$ outflow survey (over $\sim$ 110 deg$^2$) toward the W3/4/5 complex and its surroundings. In total, 459 outflow candidates were identified. Approximately 62\% (284) were located in the Perseus arm, including W3/4/5 complex and its surroundings, while $\sim$ 35\% (162) were located in the Local arm, $\sim$ 1\% (5) in the Outer arm, and $\sim$ 2\% (8) in two interarm regions. This result indicated that star formation was concentrated in the Galactic spiral arms. The detailed spatial distribution of the outflow candidates showed that the Perseus arm presented the most active star formation among the study regions. The W3/4/5 complex is a great region to research massive star formation in a triggered environment. A key region, which has been well-studied by other researches, is in the eastern high-density W3 complex that neighbors the W4 complex. Two shell-like structures in the Local arm contain candidates that can be used to study the impact on star formation imposed by massive or intermediate-mass stars in relatively isolated systems. The majority of outflow candidates in the two interarm regions and the Outer arm are located in filamentary structures.
An efficiency-loophole-free quantum key distribution (QKD) scheme is proposed, which involves no hardware change but a modification in the data post-processing step. The scheme applies to a generic class of detection systems which allow correlations between the detection efficiency and the outcomes. We study the system transmittance and the detection error rate that allow implementing this scheme. We also consider the case that a quantum memory is used to boost the performance and investigate the criteria of the readout probability. The simulation result shows that the lowest tolerable system transmittance (readout probability) is 50%, while the necessary efficiency for an efficiency-loophole-free Bell's inequality test is 82.8%.
Solar active regions (ARs) that produce strong flares and coronal mass ejections (CMEs) are known to have a relatively high non-potentiality and are characterized by delta-sunspots and sheared magnetic structures. In this study, we conduct a series of flux emergence simulations from the convection zone to the corona and model four types of active regions that have been observationally suggested to cause strong flares, namely the Spot-Spot, Spot-Satellite, Quadrupole, and Inter-AR cases. As a result, we confirm that delta-spot formation is due to the complex geometry and interaction of emerging magnetic fields, with finding that the strong-field, high-gradient, highly-sheared polarity inversion line (PIL) is created by the combined effect of the advection, stretching, and compression of magnetic fields. We show that free magnetic energy builds up in the form of a current sheet above the PIL. It is also revealed that photospheric magnetic parameters that predict flare eruptions reflect the stored free energy with high accuracy, while CME-predicting parameters indicate the magnetic relationship between flaring zones and entire ARs.
Using elliptic regularity results in weighted spaces, stochastic calculus and the theory of non-symmetric Dirichlet forms, we first show weak existence of non-symmetric distorted Brownian motion for any starting point in some domain $E$ of $\mathbb{R}^d$, where $E$ is explicitly given as the points of strict positivity of the unique continuous version of the density to its invariant measure. Non-symmetric distorted Brownian motion is a singular diffusion, i.e. a diffusion that typically has an unbounded and discontinuous drift. Once having shown weak existence, we obtain from a result of \cite{KR} that the constructed weak solution is indeed strong and weakly as well as pathwise unique up to its explosion time. As a consequence of our approach, we can use the theory of Dirichlet forms to prove further properties of the solutions. More precisely, we obtain new non-explosion criteria for them. We finally present concrete existence and non-explosion results for non-symmetric distorted Brownian motion related to a class of Muckenhoupt weights and corresponding divergence free perturbations.
We have investigated a cosmological model of a phantom energy with a variable cosmological constant ($\Lambda$) depending on the energy density ($\rho$) as $\Lambda\propto \rho^{-\alpha}$, $\alpha=\rm const.$ and a variable gravitational constant ($G$). The model requires $\alpha<0$ and a negative gravitational constant. A negative gravitational constant may forbid \emph{black holes} to form a particle horizon in a background of phantom energy. This implies that black holes are naked, and consequently the \emph{Cosmic Censorship} theorem is violated. The cosmological constant evolves with time as, $\Lambda\propto t^{-2}$. For $\omega>-1$ and $\alpha<-1$ the cosmological constant, $\Lambda<0$, $G>0$ and $\rho$ decrease with cosmic expansion. For ordinary matter (or dark matter), i.e., $\omega>-1$ we have $-1<\alpha<0$ and $\beta>0$ so that $G>0$ increases with time and $\rho$ decreases with time. Cosmic acceleration with dust particles is granted provided $-{2/3}<\alpha <0$ and $\Lambda>0$.
The first parts of the thesis recalls the main features of the large MACRO experiment at the underground Gran Sasso Laboratory. It then describes the atmospheric muons measured by the experiment and the selection criteria to obtain and analyze a large sample of cosmic muons. The time series of MACRO muons was analyzed with two complementary approaches: search for the occurrence of bursts of muon events and search for periodicities in the muon time distribution. The Scan Statistics method was used in the first case and the Lomb-Scargle spectral analysis in the second case. The two techniques complete early analyses performed with "folding" methods. It is confirmed that the seasonal variation is the dominant periodic variation, and one also confirms the solar diurnal and sidereal modulations. A separate study concerns the analysis of the energy losses of the hypothetical Nuclearites in different materials and detectors; their importance for the searches performed by the MACRO and the SLIM experiments is discussed.
The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer entropy of the backward time series called the backward transfer entropy, and show that the backward transfer entropy quantifies how far it is from dynamics to a hidden Markov model. Furthermore, we discuss physical interpretations of the backward transfer entropy in completely different settings of thermodynamics for information processing and the gambling with side information. In both settings of thermodynamics and the gambling, the backward transfer entropy characterizes a possible loss of some benefit, where the conventional transfer entropy characterizes a possible benefit. Our result implies the deep connection between thermodynamics and the gambling in the presence of information flow, and that the backward transfer entropy would be useful as a novel measure of information flow in nonequilibrium thermodynamics, biochemical sciences, economics and statistics.