ShantanuT01/DACTYL-Pretraining huggingface dataset:
We propose a new generalisation of jump-telegraph process with variable velocities and jumps. Amplitude of the jumps and velocity values are random, and they depend on the time spent by the process in the previous state of the underlying Markov process.   This construction is applied to markets modelling. The distribution densities and the moments satisfy some integral equations of the Volterra type. We use them for characterisation of the equivalent risk-neutral measure and for the expression of historical volatility in various settings. The fundamental equation is derived by similar arguments.   Historical volatilities are computed numerically.
We have used the images from the ACS on HST in Halpha, and in the neighboring continuum, to produce flux calibrated images of the large spiral galaxy M51, and the dwarf irregular NGC 4449. From these images we have derived the absolute luminosities in Halpha, the areas, and the positions with respect to the galactic centers as reference points, of over 2600 HII regions in M51 and over 270 HII regions in NGC 4449. Using this database we have derived luminosity (L)--volume (V) relations for the regions in the two galaxies, showing that within the error limits these obey the equation L ~ V^(2/3), which differs from the linear relation expected for regions of constant uniform electron density. We discuss briefly possible models which would give rise to this behavior, notably models with strong density inhomogeneities within the regions. Plotting the luminosity functions for the two galaxies we find a break in the slope for M51 at log(L) = 38.5 dex (units in erg s^(-1)) for M51 in good agreement with the previous ground-based study by Rand, and above this luminosity NGC 4449 also shows a sharp decline in its luminosity function, although the number of regions is too small to plot the function well at higher luminosities. The cumulative diameter distribution for the HII regions of M51 shows dual behaviour, with a break at a radius close to 100 pc, the radius of regions with the break luminosity. Here too we indicate the possible physical implications.
An abelian cover is a finite morphism $X\to Y$ of varieties which is the quotient map for a generically faithful action of a finite abelian group $G$. Abelian covers with $Y$ smooth and $X$ normal were studied in \cite{Pardini_AbelianCovers}.   Here we study the non-normal case, assuming that $X$ and $Y$ are $S_2$ varieties that have at worst normal crossings outside a subset of codimension $\ge 2$. Special attention is paid to the case of $\Z_2^r$-covers of surfaces, which is used in arxiv:0901.4431 to construct explicitly compactifications of some components of the moduli space of surfaces of general type.
We consider the existence and uniqueness of solutions of an initial-boundary value problem for a coupled system of PDE's arising in a model for Alzheimer's disease. Apart from reaction diffusion equations, the system contains a transport equation in a bounded interval for a probability measure which is related to the malfunctioning of neurons. The main ingredients to prove existence are: the method of characteristics for the transport equation, a priori estimates for solutions of the reaction diffusion equations, a variant of the classical contraction theorem, and the Wasserstein metric for the part concerning the probability measure. We stress that all hypotheses on the data are not suggested by mathematical artefacts, but are naturally imposed by modelling considerations. In particular the use of a probability measure is natural from a modelling point of view. The nontrivial part of the analysis is the suitable combination of the various mathematical tools, which is not quite routine and requires various technical adjustments.
Casimir forces in a critical media are produced by spatial suppression of order parameter fluctuations. In this paper we address the question how fluctuations of a critical media relates the magnitude of critical Casimir interactions. Namely, for the Ising model we express the potential of critical Casimir interactions in terms of Fortuin-Kasteleyn site-bond correlated percolation clusters. These clusters are quantitative representation of fluctuations in the media. New Monte Carlo method for the computation of the Casimir force potential which is based on this relation is proposed. We verify this method by computation of Casimir interactions between two disks for 2D Ising model. The new method is also applied to the investigation of non-additivity of the critical Casimir potential. The non-additive contribution to three-particles interaction is computed as a function of the temperature.
In this paper, we prove that the Leray weak solution $u : \mathbb{R}^3\times (0, T)\rightarrow\mathbb{R}^3 $ of the Navier-Stokes equations is regular in $\mathbb{R}^3\times (0,T)$ under the scaling invariant Serrin condition imposed on one component of the velocity $u_3\in L^{q,1}(0, T;L^p(\mathbb{R}^3))$ with \[ \frac{2}{q}+\frac{3}{p}\leq 1,\quad 3<p<+\infty. \] This result is an immediate consequence of a new local regularity criterion in terms of one velocity component for suitable weak solutions.
We develop a formalism for the scattering of a particle on the $q$-deformed Euclidean space. We write down $q$-versions of the Lippmann-Schwinger equation. Their iterative solutions for a weak scattering potential lead us to $q$-versions of the Born series. With the expressions for the wave functions of the scattered particle, we can write down S-matrix elements. We show that these S-matrix elements satisfy unitarity conditions. Considerations about the interaction picture for a quantum system in the $q$-deformed Euclidean space and a discussion of a $q$-version of time-dependent perturbation theory conclude our studies.
A recently introduced separable pairing force for relativistic Hartree-Bogoliubov (RHB) calculations, adjusted in nuclear matter to the pairing gap of the Gogny force, is employed in the 3D RHB model for triaxial shapes. The pairing force is separable in momentum space but, when transformed to coordinate space in calculations of finite nuclei, it is no longer separable because of translational invariance. The corresponding pairing matrix elements are represented as a sum of a finite number of separable terms in the basis of a 3D harmonic oscillator. The 3D RHB model is applied to the calculation of binding energy surfaces and pairing energy maps for a sequence of even-A Sm isotopes.
We investigate the luminous star ELHC 10 located in the bar of the Large Magellanic Cloud, concluding that it is a SB1 long-period eclipsing binary where the main eclipse is produced by an opaque structure hiding the secondary star. For the more luminous component we determine an effective temperature of 6500 $\pm$ 250 $K$, log\,g = 1.0 $\pm$ 0.5 and luminosity 5970 L$_{\sun}$. From the radial velocities of their photospheric lines we calculate a mass function of 7.37 $\pm$ 0.55 M$_{\sun}$. Besides Balmer and forbidden N II emission, we find splitting of metallic lines, characterized by strong discrete absorption components (DACs), alternatively seen at the blue and red side of the photospheric spectrum. These observations hardly can be interpreted in terms of an structured atmosphere but might reflect mass streams in an interacting binary. The primary shows signatures of s-process nucleosynthesis and might be a low-mass post-AGB star with a rare evolutionary past if the binary is semi-detached. The peak separation and constancy of radial velocity in H$\alpha$ suggest that most of the Balmer emission comes from a circumbinary disc.
We propose a new mechanism for the delivery of gas to the heart of galactic nuclei. We show that warm halo clouds must periodically impact galactic centers and potentially deliver a large (~10^{4-6} M_{solar}) mass of gas to the galactic nucleus in a singular event. The impact of an accreting warm halo cloud originating far in the galactic halo can, depending on mixing, produce a nuclear starburst of low metallicity stars as well as low luminosity accretion onto the central black hole. Based on multiphase cooling around a LambdaCDM distribution of halos we calculate the nuclear impact rate, the mass captured by the central black hole and the fraction of active nuclei for impacting cloud masses in the range ~10^{4}-10^{6}M_{solar}. If there is moderate braking during cloud infall, our model predicts an average fraction of low luminosity active nuclei consistent with observations.
We study acoustic oscillations (eigenfrequencies, velocity distributions, damping times) of normal crusts of strange stars. These oscillations are very specific because of huge density jump at the interface between the normal crust and the strange matter core. The oscillation problem is shown to be self-similar. For a low (but non-zero) multipolarity l the fundamental mode (without radial nodes) has a frequency ~300 Hz and mostly horizontal oscillation velocity; other pressure modes have frequencies >=20 kHz and almost radial oscillation velocities. The latter modes are similar to radial oscillations (have approximately the same frequencies and radial velocity profiles). The oscillation spectrum of strange stars with crust differs from the spectrum of neutron stars. If detected, acoustic oscillations would allow one to discriminate between strange stars with crust and neutron stars and constrain the mass and radius of the star.
In this paper, we prove the lower bound for the number of balancing non-Wieferich primes in arithmetic progressions. More precisely, for any given integer $r\geq2$ there are $\gg\log x$ balancing non-Wieferich primes $p\leq x$ such that $p\equiv\pm1 \pmod{r}$, under the assumption of the $abc$ conjecture for the number field $\mathbb{Q}(\sqrt{2})$. Further, we discuss some applications of balancing sequences in cryptography.
The Green-Lazarsfeld secant conjecture predicts that the syzygies of a curve of sufficiently high degree are controlled by its special secants. We prove this conjecture for all curves of Clifford index at least two and not bielliptic and for all line bundles of a certain degree. Our proof is based on a classic result of Martens and Mumford on Brill-Noether varieties and on a simple vanishing criterion that comes from the interpretation of syzygies through symmetric products of curves.
We describe near-field imaging of sample sheet resistance via frequency shifts in a resonant coaxial scanning microwave microscope. The frequency shifts are related to local sample properties, such as surface resistance and dielectric constant. We use a feedback circuit to track a given resonant frequency, allowing measurements with a sensitivity to frequency shifts as small as one parts in 50000 for a 30 ms sampling time. The frequency shifts can be converted to sheet resistance based on a simple model of the system.
We have studied the transport process in the two dimensional electron gas (2DEG) in presence of a magnetic field and a dissipative environment at temperature T. By means of imaginary time series functional integral method we calculate the decay rates at finite temperature and in the presence of dissipation. We have studied decay rates for wide range of temperatures -- from the thermally activated region to very low temperature region where the system decays by quantum tunneling. We have shown that dissipation and impurity helps the tunneling. We have also shown that tunneling is strongly affected by the magnetic field. We have demonstrated analytical results for all the cases mentioned above.
We report on the anomalous magnetization reversal under hydrostatic pressure in the lightly electron-doped manganite compound (Ca$_{1-x}$Sr$_{x}$)Mn$_{0.95}$Sb$_{0.05}$O$_{3}$ with its fixed carrier content. In a weakly magnetic field cooled measurement, diamagnetic magnetization is observed for $x\leq 15\%$, which changes to positive values for $x>15\%$. However, on an application of pressure on the samples with $x=16\%$ and 17$\%$, magnetization reverses sign and diamagnetism is restored. We present a magnetic phase diagram as a function of Sr concentration, under both ambient and hydrostatic pressures. To understand better the thermodynamical properties of this system, we have measured the specific heat as a function of temperature under a field cooling of 100 Oe. Our data show no anomalies associated with the temperature dependent magnetization reversal, indicating the absence of a long-rang magnetic ordering. The $ac$ magnetic susceptibility measurement points to the existence of magnetic frustration for the Sr substituted samples exhibiting diamagnetic behavior.
We have considered the model of the phase transition of the second order for the Coulomb frustrated 2D charged system. The coupling of the order parameter with the charge was considered as the local temperature. We have found that in such system, an appearance of the phase-separated state is possible. By numerical simulation, we have obtained different types ("stripes", "rings", "snakes") of phase-separated states and determined the parameter ranges for these states. Thus the system undergoes a series of phase transitions when the temperature decreases. First, the system moves from the homogeneous state with a zero order parameter to the phase-separated state with two phases in one of which the order parameter is zero and, in the other, it is nonzero ($\tau>0$). Then a first-order transition occurs to another phase-separated state, in which both phases have different and nonzero values of the order parameter (for $\tau<0$). And only a further decrease of temperature leads to a transition to a homogeneous ordered state.
We calculate the finite temperature compressibility for two-dimensional semiconductor systems, monolayer graphene, and bilayer graphene within the Hartree-Fock approximation. We find that the calculated temperature dependent compressibility including exchange energy is non-monotonic. In 2D systems at low temperatures the inverse compressibility decreases first with increasing temperature, but after reaching a minimum it increases as temperature is raised further. At high enough temperatures the negative compressibility of low density systems induced by the exchange energy becomes positive due to the dominance of the finite temperature kinetic energy. The inverse compressibility in monolayer graphene is always positive and its temperature dependence appears to be reverse of the 2D semiconductor systems, i.e., it increases first with temperature and then decreases at high temperatures. The inverse compressibility of bilayer graphene shows the same non-monotonic behavior as ordinary 2D systems, but at high temperatures it approaches a constant which is smaller than the value of the non-interacting bilayer graphene. We find the leading order temperature correction to the compressibility within Hartree-Fock approximation to be $T^2 \ln T$ at low temperatures for all three systems.
Combining Angle resolved photoelectron spectroscopy (ARPES) and a $\mu$-focused Laser, we have performed scanning ARPES microscopy measurements of the domain population within the nematic phase of FeSe single crystals. We are able to demonstrate a variation of the domain population density on a scale of a few 10 $\mu$m while constraining the upper limit of the single domain size to less than 5 $\mu m$. This experiment serves as a demonstration of how combining the advantages of high resolution Laser ARPES and an ultimate control over the spatial dimension can improve investigations of materials by reducing the cross contamination of spectral features of different domains.
Conformal Regge theory predicts the existence of analytically continued CFT data for complex spin. How could this work when there are so many more operators with large spin compared to small spin? Using planar N=4 SYM as a testground we find a simple physical picture. Operators do organize themselves into analytic families but the continuation of the higher families have zeroes in their structure OPE constants for lower integer spins. They thus decouple. Newton's interpolation series technique is perfectly suited to this physical problem and will allow us to explore the right complex spin half-plane.
When a photon is detected after passing through an interferometer one might wonder which path it took, and a meaningful answer can only be given if one has the means of monitoring the photon's whereabouts. We report the realization of a single-photon experiment for a two-path interferometer with path marking. In this experiment, the path of a photon ("signal") through a Mach--Zehnder interferometer becomes known by unambiguous discrimination between the two paths. We encode the signal path in the polarization state of a partner photon ("idler") whose polarization is examined by a three-outcome measurement: one outcome each for the two signal paths plus an inconclusive outcome. Our results agree fully with the theoretical predictions from a common-sense analysis of what can be said about the past of a quantum particle: The signals for which we get the inconclusive result have full interference strength, as their paths through the interferometer \emph{cannot be known}; and every photon that emerges from the dark output port of the balanced interferometer has a \emph{known path}.
Elastic effects due to lattice strain modify the local equilibrium condition at the solid-solid interface compared to the classical dendritic growth. Both, the thermal and the elastic fields are eliminated by the Green's function techniques and a closed nonlinear integro-differential equation for the evolution of the interface is derived. In the case of pure dilatation, the elastic effects lead only to a trivial shift of the transition temperature while in the case of shear transitions, dendritic patterns are found even for isotropic surface energy.
A population of distant dusty galaxies emitting in the submillimetre waveband has recently been detected using the Submillimetre Common-User Bolometer Array (SCUBA) camera on the James Clerk Maxwell Telescope (JCMT). This population can be used to trace the amount of high-redshift star-formation activity that is obscured from view in the optical waveband by dust, and so is missing from existing inventories of star formation in the distant Universe. By including this population we can construct a complete and consistent picture of the history of star formation. The evolution of obscured star formation at redshifts less than unity is constrained by mid- and far-infrared counts of dusty galaxies. Activity increases with redshift z as (1+z) to a power of about 4, consistent with the form of evolution found in the optical waveband by the Canada-France Redshift Survey (CFRS) to redshifts less than about 1. The form of evolution at higher redshifts is constrained by both our faint SCUBA counts and the intensity of background radiation in the millimetre/submillimetre waveband. We find that the total amount of energy emitted by dusty galaxies is about five times greater than that inferred from restframe ultraviolet observations, and that a larger fraction of this energy is emitted at high redshifts. The simplest explanation for these results is that a large population of luminous strongly-obscured sources at redshifts less than about 5 is missing from optical surveys. We discuss the possible contribution of obscured active galactic nuclei to the submillimetre-wave background and counts. More accurate constraints on the history of star formation will be provided by determinations of the counts in several submillimetre wavebands and crucially, by a reliable redshift distribution of the detected galaxies.
In the present paper we study the asymptotic behavior of trigonometric products of the form $\prod_{k=1}^N 2 \sin(\pi x_k)$ for $N \to \infty$, where the numbers $\omega=(x_k)_{k=1}^N$ are evenly distributed in the unit interval $[0,1]$. The main result are matching lower and upper bounds for such products in terms of the star-discrepancy of the underlying points $\omega$, thereby improving earlier results obtained by Hlawka in 1969. Furthermore, we consider the special cases when the points $\omega$ are the initial segment of a Kronecker or van der Corput sequence. The paper concludes with some probabilistic analogues.
An approximate formula connecting the true and the HBT homogeneity regions in multiparticle production processes is derived. It implies that when calculating the HBT radii one should use the ceter of mass systems of the pairs rather than the now popular LCMS system. A discussion of several examples clarifies the potential and limitations of the HBT method. The even cumulants of the X-distribution, inculding the HBT radii, can be determined for each homogeneity region, but the relative positions of the homogeneity regions are unconstrained. This makes the HBT radii of little use for calculating quantities dependent on the interparticle interactions in coordinate space.
Context. Asteroseismic determinations of structural parameters of hot B subdwarfs (sdB) have been carried out for more than a decade now. These analyses rely on stellar models whose reliability for the required task needs to be evaluated critically. Aims. We present new models of the so-called third generation (3G) dedicated to the asteroseismology of sdB stars. These parameterized models are complete static structures suitable for analyzing both p- and g-mode pulsators, contrary to the former second generation (2G) models that were limited to p-modes. While the reliability of the 2G models has been successfully verified in the past, this important test still has to be conducted on the 3G structures. Methods. The close eclipsing binary PG 1336-018 provides a unique opportunity to test the reliability of sdB models. We compared the structural parameters of the sdB component in PG 1336-018 obtained from asteroseismology based on the 3G models, with those derived independently from the modeling of the reflection/irradiation effect and the eclipses observed in the light curve. Results. The stellar parameters inferred from asteroseismology using the 3G models are found to be remarkably consistent with both the preferred orbital solution obtained from the binary light curve modeling and the updated spectroscopic estimates for the surface gravity of the star. We also show that the uncertainties on the input physics included in stellar models have no noticeable impact, at the current level of accuracy, on the structural parameters derived by asteroseismology. Conclusions. The stellar models presently used to carry out quantitative seismic analyses of sdB stars are reliable for the task. The stellar parameters inferred by this technique, at least for those that could be tested (M*, R*, and log g), appear to be both very precise and accurate, as no significant systematic effect has been found.
HBT correlations of $\pi^--\pi^-$ pairs at FAIR/AGS energies are investigated by using the UrQMD transport model and the CRAB analyzing program. Three different possible sources (treatment of resonance lifetimes, a soft equation of state and non-Gaussian effects) to understand the HBT $R_O/R_S$ puzzle are investigated. Firstly, we find that different treatments of the resonance decay time can not resolve the HBT time-related puzzle, however it can modify the HBT radii at low transverse momenta to some extent to explain the data slightly. Secondly, with a soft equation of state with momentum dependence, the measured transverse momentum dependent HBT radii and $R_O/R_S$ ratio can be described fairly well. Thirdly, non-Gaussian effects are visible in the calculated correlation function. Using the Edgeworth expansion, one finds that the non-Gaussian effect is strongest in the longitudinal direction and weakest in the sideward direction.
We prove quenched~$L^p$--type estimates for the gradient of a solution of a quasilinear elliptic equation with random coefficients.