ShantanuT01/DACTYL-Pretraining huggingface dataset:
We have investigated a non-static and rotating model of the universe with an imperfect fluid distribution. It is found that the model is free from singularity and represents an ever expanding universe with shear and rotation vanishing for large value of time.
The minimal SUSY SO(10) GUT models with {\bf 10}, {\bf 126} and {\bf 210} Higgs and only renormalizable couplings has been shown to provide a simple way to understand the neutrino mixings as well as the ratio $\Delta m^2_\odot/\Delta m^2_A$ in terms of quark mixing parameter $\theta_{Cabibbo}$, provided neutrino masses are described by type II seesaw formula. However, in this minimal picture, it is impossible to realize type II dominance with renormalizable couplings in 4-dimensions. We show that this problem can be cured by embedding this model into a warped 5-dimensional space time with warping between the Planck and the GUT scale, where both type II as well as mixed seesaw formulae can be realized in a natural manner without expanding the Higgs sector. These models also avoid the possible problem of threshold effects associated with large Higgs representations since the theory above the GUT scale is now strongly coupled.
Past studies based on optical spectroscopy suggest that the five $\omega$ Cen pulsators form a rather homogeneous group of hydrogen-rich subdwarf O stars with effective temperatures of around 50 000 K. This places the stars below the red edge of the theoretical instability strip in the log $g$ $-$ Teff diagram, where no pulsation modes are predicted to be excited. Our goal is to determine whether this temperature discrepancy is real, or whether the stars' effective temperatures were simply underestimated. We present a spectral analysis of two rapidly pulsating extreme horizontal branch (EHB) stars found in $\omega$ Cen. We obtained Hubble Space Telescope/COS UV spectra of two $\omega$ Cen pulsators, V1 and V5, and used the ionisation equilibrium of UV metallic lines to better constrain their effective temperatures. As a by-product we also obtained FUV lightcurves of the two pulsators. Using the relative strength of the N IV and N V lines as a temperature indicator yields Teff values close to 60 000 K, significantly hotter than the temperatures previously derived. From the FUV light curves we were able to confirm the main pulsation periods known from optical data. With the UV spectra indicating higher effective temperatures than previously assumed, the sdO stars would now be found within the predicted instability strip. Such higher temperatures also provide consistent spectroscopic masses for both the cool and hot EHB stars of our previously studied sample.
Self-testing protocols are methods to determine the presence of shared entangled states in a device independent scenario, where no assumptions on the measurements involved in the protocol are made. A particular type of self-testing protocol, called parallel self-testing, can certify the presence of copies of a state, however such protocols typically suffer from the problem of requiring a number of measurements that increases with respect to the number of copies one aims to certify. Here we propose a procedure to transform single-copy self-testing protocols into a procedure that certifies the tensor product of an arbitrary number of (not necessarily equal) quantum states, without increasing the number of parties or measurement choices. Moreover, we prove that self-testing protocols that certify a state and rank-one measurements can always be parallelized to certify many copies of the state. Our results suggest a method to achieve device-independent unbounded randomness expansion with high-dimensional quantum states.
It is shown that there exist infinitely many triangular numbers (congruent to 3 mod 12) which cannot be the distance between two perfect numbers.
We present a simple but effective technique for measuring angular variation in $R_V$ across the sky. We divide stars from the Pan-STARRS1 catalog into Healpix pixels and determine the posterior distribution of reddening and $R_V$ for each pixel using two independent Monte Carlo methods. We find the two methods to be self-consistent in the limits where they are expected to perform similarly. We also find some agreement with high-precision photometric studies of $R_V$ in Perseus and Ophiuchus, as well as with a map of reddening near the Galactic plane based on stellar spectra from APOGEE. While current studies of $R_V$ are mostly limited to isolated clouds, we have developed a systematic method for comparing $R_V$ values for the majority of observable dust. This is a proof of concept for a more rigorous Galactic reddening map.x
We prove subsequential tightness of centered maxima of two-dimensional Ginzburg-Landau fields with bounded elliptic contrast.
Inversion asymmetry in two-dimensional materials grants them fascinating properties such as spin-coupled valley degrees of freedom and piezoelectricity, but at the cost of inversion domain boundaries if the epitaxy of the grown 2D layer -- on a polar substrate -- cannot adequately distinguish what are often near-degenerate 0{\deg} and 180{\deg} orientations. We employ first-principles calculations to identify a method to lift this near-degeneracy: the energetic distinction between eclipsed and staggered configurations during nucleation at a point defect in the substrate. For monolayer MoS2 grown on hexagonal boron nitride, the predicted defect complex can be more stable than common MoS2 point defects because it is both a donor-acceptor pair and a Frenkel pair shared between adjacent layers of a 2D heterostack. Orientation control is verified in experiments that achieve ~90% consistency in the orientation of as-grown triangular MoS2 flakes on hBN, as confirmed by aberration-corrected scanning/transmission electron microscopy. This defect-enhanced orientational epitaxy could provide a general mechanism to break the near-degeneracy of 0/180{\deg} orientations of polar 2D materials on polar substrates, overcoming a long-standing impediment to scalable synthesis of single-crystal 2D semiconductors.
In order to study the solar corona during eclipses, a new telescope was constructed. Three coronal images were obtained simultaneously from one objective of the telescope as the coronal radiation passed through three polarisers (whose transmission directions were turned through 0^{\circ}, 60^{\circ}, and 120^{\circ} to the chosen direction); one image without polariser was also obtained. The telescope was used to observe the solar corona during the eclipse of 1 August 2008. We obtained distributions of the polarisation brightness, K-corona brightness, degree of the K-corona polarisation and total polarisation degree; polarisation direction depending on the latitude and radius in the plane of the sky was also obtained. We calculated radial distributions of electron density, depending on the latitude. Properties of all these distributions in different coronal structures were compared. We determined temperature of coronal plasma in different coronal structures on the assumption that there is a hydrostatic equilibrium.
We studied in a microscopic multiphonon approach the proton-neutron symmetry and phonon structure of some low-lying states recently discovered in 92Zr. We confirm the breaking of F-spin symmetry, but argue that the breaking mechanism is more complex than the one suggested in the original shell model analysis of the data. We found other new intriguing features of the spectrum, like a pronounced multiphonon fragmentation of the states and a tentative evidence of a three-phonon mixed symmetry state.
We investigate the hypercube networks that their nodes are considered as quantum harmonic oscillators. The entanglement of the ground state can be used to quantify the amount of information each part of a network shares with the rest of the system via quantum fluctuations. Therefore, the Schmidt numbers and entanglement entropy between two special parts of Hypercube network, can be calculated. To this aim, first we use the stratification method to rewrite the adjacency matrix of the network in the stratification basis which is the matrix representation of the angular momentum. Then the entanglement entropy and Schmidt number for special partitions are calculated an- alytically by using the generalized Schur complement method. Also, we calculate the entanglement entropy between two arbitrary equal subsets (two equal subsets have the same number of vertices) in H(3, 2) and H(4, 2) numerically, and we give the minimum and maximum values of entanglement entropy in these two Hypercube network. Then we can conjecture the minimum and maximum values of entanglement entropy for equal subsets in H(d, 2).
In the class of vacuum Petrov type D spacetimes with cosmological constant, which includes the Kerr-(A)dS black hole as a particular case, we find a set of four-dimensional operators that, when composed {\em off shell} with the Dirac, Maxwell and linearized gravity equations, give a system of equations for spin weighted scalars associated to the linear fields, that decouple on shell. Using these operator relations we give compact reconstruction formulae for solutions of the original spinor and tensor field equations in terms of solutions of the decoupled scalar equations. We also analyze the role of Killing spinors and Killing-Yano tensors in the spin weight zero equations and, in the case of spherical symmetry, we compare our four-dimensional formulation with the standard $2+2$ decomposition and particularize to the Schwarzschild-(A)dS black hole. Our results uncover a pattern that generalizes a number of previous results on Teukolsky-like equations and Debye potentials for higher spin fields.
We present theoretical and experimental data on the threshold behaviour of nanodot creation with swift heavy ions. A model calculation based on a two-temperature model taking the spatially resolved electron density into account gives a threshold of 12 keV/nm below which the energy density at the end of the track is no longer high enough to melt the material. In the corresponding experiments we irradiated SrTiO$_3$ surfaces under grazing incidence with swift heavy ions. The resulting chains of nanodots were analyzed by atomic force microscopy. In addition, samples irradiated under normal incidence were analyzed by transmission electron microscopy. Both experiments show two thresholds, connected to the appearance of tracks and to the creation of fully developed tracks, respectively. The threshold values are similar for surface and bulk tracks, suggesting that the same processes occur at glancing and normal incidence. The experimental threshold for the formation of fully developed tracks compares well to the value obtained by the theoretical description.
The paper summarizes the parallel session B3 {\em Analytic approximations, perturbation methods, and their applications} of the GR18 conference. The talks in the session reported notably recent advances in black hole perturbations and post-Newtonian approximations as applied to sources of gravitational waves.
The spontaneous violation of Lorentz and diffeomorphism invariance in a phase near the big bang lowers the entropy, allowing for an arrow of time and the second law of thermodynamics. The spontaneous symmetry breaking leads to $O(3,1)\rightarrow O(3)\times R$, where $O(3)$ is the rotational symmetry of the Friedmann-Lema\^{i}tre-Robertson-Walker spacetime. The Weyl curvature tensor $C_{\mu\nu\rho\sigma}$ vanishes in the FLRW spacetime satisfying the Penrose zero Weyl curvature conjecture. The requirement of a measure of gravitational entropy is discussed. The vacuum expectation value $\langle 0\vert\psi_\mu\vert 0\rangle\neq 0$ for a vector field $\psi_\mu$ acts as an order parameter and at the critical temperature $T_c$ a phase transition occurs breaking the Lorentz symmetry spontaneously. During the ordered $O(3)$ symmetry phase the entropy is vanishingly small and for $T < T_c$ as the universe expands the anti-restored $O(3,1)$ Lorentz symmetry leads to a disordered phase and a large increase in entropy creating the arrow of time.
Necessary and sufficient conditions for rigidity of the perimeter inequality under spherical symmetrisation are given. That is, a characterisation for the uniqueness (up to orthogonal transformations) of the extremals is provided. This is obtained through a careful analysis of the equality cases, and studying fine properties of the circular symmetrisation, which was firstly introduced by P\'olya in 1950.
Using the X-ray-selected active galactic nuclei (AGN) from the XMM-XXL north survey and the SDSS Baryon Oscillation Spectroscopic Survey (BOSS) spectroscopic follow-up of them, we compare the properties of X-ray unobscured and obscured broad-line AGN (BLAGN1 and BLAGN2; $N_\textrm{H}$below and above $10^{21.5}$ cm$^{-2}$), including their X-ray luminosity $L_X$, black hole mass, Eddington ratio $\lambda_{\textrm{Edd}}$, optical continuum and line features. We find that BLAGN2 have systematically larger broad line widths and hence apparently higher (lower) $M_{\textrm{BH}}$ ($\lambda_{\textrm{Edd}}$) than BLAGN1. We also find that the X-ray obscuration in BLAGN tends to coincide with optical dust extinction, which is optically thinner than that in narrow-line AGN (NLAGN) and likely partial-covering to the broad line region. All the results can be explained in the framework of a multi-component, clumpy torus model by interpreting BLAGN2 as an intermediate type between BLAGN1 and NLAGN in terms of an intermediate inclination angle.
Cranked Relativistic Hartree-Bogoliubov theory without and with approximate particle number projection by means of the Lipkin-Nogami method is presented in detail as an extension of Relativistic Mean Field theory with pairing correlations to the rotating frame. Pairing correlations are taken into account by a finite range two-body force of Gogny type. The applicability of this theory to the description of rotating nuclei is studied in detail on the example of superdeformed bands in even-even nuclei of the $A\sim 190$ mass region. Different aspects such as the importance of pairing and particle number projection, the dependence of the results on the parametrization of the RMF Lagrangian and Gogny force etc. are investigated in detail. It is shown that without any adjustment of new parameters the best description of experimental data is obtained by using the well established parameter sets NL1 for the Lagrangian and D1S for the pairing force. Contrary to previous studies at spin zero it is found that the increase of the strength of the Gogny force is not necessary in the framework of Relativistic Hartree-Bogoliubov theory provided that particle number projection is performed.
Retrieving 3D models from 2D human sketches has received considerable attention in the areas of graphics, image retrieval, and computer vision. Almost always in state of the art approaches a large amount of "best views" are computed for 3D models, with the hope that the query sketch matches one of these 2D projections of 3D models using predefined features.   We argue that this two stage approach (view selection -- matching) is pragmatic but also problematic because the "best views" are subjective and ambiguous, which makes the matching inputs obscure. This imprecise nature of matching further makes it challenging to choose features manually. Instead of relying on the elusive concept of "best views" and the hand-crafted features, we propose to define our views using a minimalism approach and learn features for both sketches and views. Specifically, we drastically reduce the number of views to only two predefined directions for the whole dataset. Then, we learn two Siamese Convolutional Neural Networks (CNNs), one for the views and one for the sketches. The loss function is defined on the within-domain as well as the cross-domain similarities. Our experiments on three benchmark datasets demonstrate that our method is significantly better than state of the art approaches, and outperforms them in all conventional metrics.
We introduce two dual, purely quantum protocols: for entanglement distillation assisted by quantum communication (``mother'' protocol) and for entanglement assisted quantum communication (``father'' protocol). We show how a large class of ``children'' protocols (including many previously known ones) can be derived from the two by direct application of teleportation or super-dense coding. Furthermore, the parent may be recovered from most of the children protocols by making them ``coherent''. We also summarize the various resource trade-offs these protocols give rise to.
We introduce a novel mechanism for itinerant ferromagnetism, which is based on a simple two-band model, and using numerical and analytical methods, we show that the Periodic Anderson Model (PAM) contains this mechanism. We propose that the mechanism, which does not assume an intra-atomic Hund's coupling, is present in both the iron group and some $f$ electron compounds.
In this work, following the paper by Romain Ruzziconi and C\'eline Zwikel \cite{Ruzziconi:2020wrb} we extend the questions of conservation, integrability and renormalization in Bondi gauge and in GR to the theory of Topological Massive Gravity (TMG). We construct the phase space and renormalize the divergences arising within the symplectic structure through a holographic renormalization procedure. We show that the charge expressions are generically finite, conserved and can be made integrable by a field$-$dependent redefinition of the asymptotic symmetry parameters.
In this paper we will show the existence of a face $2$-colourable biembedding of the complete graph onto an orientable surface where each face is a cycle of a fixed length $k$, for infinitely many values of $k$. In particular, under certain conditions, we show that there exists at least $(n-2)[(p-2)!]^2/(e^2 kn)$ non-isomorphic face $2$-colourable biembeddings of $K_{2nk+1}$ in which all faces are cycles of length $k=4p+3$. These conditions are: $n\equiv 1\mod 4$, $k\equiv 3\mod 4$ and either $n$ is prime or $n\gg k$ and $n\equiv 0\mod 3$ implies $p\equiv 1\mod 3$. To achieve this result we begin by verifying the existence of $(n-2)[(p-2)!/e]^2$ non-equivalent Heffter arrays, $H(n;k)$, which satisfy the conditions: (1) for each row and each column the sequential partial sums determined by the natural ordering must be distinct modulo $2nk+1$; (2) the composition of the natural orderings of the rows and columns is equivalent to a single cycle permutation on the entries in the array. The existence of Heffter arrays $H(n;k)$ that satisfy condition (1) was established earlier in \cite{BCDY} and in this current paper we vary this construction and show that there are at least $(n-2)[(p-2)!/e]^2$ such non-equivalent $H(n;k)$ that satisfy condition (1) and then show that each of these Heffter arrays also satisfy condition (2) under certain conditions.
We investigate the relation between various statistical ensembles of finite systems. If ensembles differ at the level of fluctuations of the order parameter, we show that the equations of states can present major differences. A sufficient condition for this inequivalence to survive at the thermodynamical limit is worked out. If energy consists in a kinetic and a potential part, the microcanonical ensemble does not converge towards the canonical ensemble when the partial heat capacities per particle fulfill the relation $c_{k}^{-1}+c_{p}^{-1}<0$.
Magnetic, transport, and x-ray diffraction measurements of ferromagnetic shape memory alloy Ni$_{2.16}$Mn$_{0.84}$Ga revealed that this alloy undergoes an intermartensitic transition upon cooling, whereas no such a transition is observed upon subsequent heating. The difference in the modulation of the martensite forming upon cooling from the high-temperature austenitic state [5-layered (5M) martensite], and the martensite forming upon the intermartensitic transition [7-layered (7M) martensite] strongly affects the magnetic and transport properties of the alloy and results in a large thermal hysteresis of the resistivity $\rho$ and magnetization $M$. The intermartensitic transition has an especially marked influence on the transport properties, as is evident from a large difference in the resistivity of the 5M and 7M martensite, $(\rho_{\mathrm{5M}} - \rho_{\mathrm{7M}})/\rho _{\mathrm{5M}} \approx 15%$, which is larger than the jump of resistivity at the martensitic transition from the cubic austenitic phase to the monoclinic 5M martensitic phase. We assume that this significant difference in $\rho$ between the martensitic phases is accounted for by nesting features of the Fermi surface. It is also suggested that the nesting hypothesis can explain the uncommon behavior of the resistivity at the martensitic transition, observed in stoichiometric and near-stoichiometric Ni-Mn-Ga alloys.
Let $P$ be a polynomial that depends on two variables $X$ and $Y$ and has algebraic coefficients. If $x$ and $y$ are algebraic numbers with $P(x,y)=0$, then by work of N\'eron $h(x)/q$ is asymptotically equal to $h(y)/p$ where $p$ and $q$ are the partial degrees of $P$ in $X$ and $Y$, respectively. In this paper we compute a completely explicit bound for $|h(x)/q-h(y)/p|$ in terms of $P$ which grows asymptotically as $\max\{h(x),h(y)\}^{1/2}$. We apply this bound to obtain a simple version of Runge's Theorem on the integral solutions of certain polynomial equations.
This article deals with IDT processes, i.e. processes which are infinitely divisible with respect to time. Given an IDT process $(X_{t},\,t\geq0)$, there exists a unique (in law) L\'evy process $(L_{t}; t\geq0)$ which has the same one-dimensional marginals distributions, i.e for any $t\geq0$ fixed, we have $$X_{t}\stackrel{(law)}{=}L_{t}.$$ Such processes are said to be associated. The main objective of this work is to exhibit numerous examples of IDT processes and their associated L\'evy processes. To this end, we take up ideas of the monograph \textit{Peacocks and associated martingales} from F. Hirsch, C. Profeta, B. Roynette and M. Yor (L\'evy, Sato and Gaussian sheet methods) and apply them in the framework of IDT processes. This gives a new interesting outlook to the study of processes whose only one-dimensional marginals are known. Also, we give an integrated weak It\^o type formula for IDT processes (in the same spirit as the one for Gaussian processes) and some links between IDT processes and selfdecomposability. The last sections are devoted to the study of some extensions of the notion of IDT processes in the weak sense as well as in the multiparameter sense. In particular, a new approach for multiparameter IDT processes is introduced and studied. Main examples of this kind of processes are the $\mathbb{R}_{+}^{N}$-parameter L\'{e}vy process and the L\'{e}vy's $\mathbb{R}^{M}$-parameter Brownian motion. These results give some better understanding of IDT processes, and may be seen as some continuation of the works of K. Es-Sebaiy and Y. Ouknine [\textit{How rich is the class of processes which are infinitely divisible with respect to time ?}] and R. Mansuy [\textit{On processes which are infinitely divisible with respect to time}].
It has been shown that the mass of the scalar field in the charged stringy black hole is never able to generate a potential well outside the event horizon to trap the superradiant modes. This is to say that the charged stringy black hole is stable against the massive charged scalar perturbation. In this paper we will study the superradiant instability of the massless scalar field in the background of charged stringy black hole due to a mirror-like boundary condition. The analytical expression of the unstable superradiant modes is derived by using the asymptotic matching method. It is also pointed out that the black hole mirror system becomes extremely unstable for a large charge $q$ of scalar field and the small mirror radius $r_m$.