ShantanuT01/DACTYL-Pretraining huggingface dataset:
We offer a new proof that a certain q-analogue of multinomial coeffi- cients furnishes a q-counting of the set of permutations of an associated multiset of positive integers, according to the number of inversions in such arrangements. Our proof uses the fact that such q-multinomial coefficients enumerate certain classes of chains of subspaces of a fnite dimensional vector space over a fnite field of cardinality q. Additionally, we investigate the function that counts the number of permutations of a multiset having a fixed number of inversions.
A 20-hour VLBI observation with the NRAO VLBA and GBT in the NOAO Bootes field reaches an rms noise of 9 microJy per beam at 1.4 GHz. Three sources were detected at 10-milliarcsecond resolution within the GBT primary beam of FWHM 8.6', including the 20-milliJy calibrator and two sub-milliJy sources. By tapering the visibility data, portions of the VLBA primary beam of FWHM 29' were imaged at poorer sensitivity and resolution to yield five further detections. New developments at JIVE will permit deeper and wider VLBI surveys at full sensitivity and resolution, enabling new types of survey science.
Recently we studied the effects of information carrying waves propagating through isotropic cosmologies. By information carrying we mean that the waves have an arbitrary dependence on a function. We found that the waves introduce shear and anisotropic stress into the universe. We then constructed explicit examples of pure gravity wave perturbations for which the presence of this anisotropic stress is essential and the null hypersurfaces playing the role of the histories of the wave-fronts in the background space-time are shear-free. Motivated by this result we now prove that these two properties are true for all information carrying waves in isotropic cosmologies.
In this paper we study the problem of prescribing fractional $Q$-curvature of order $2\sigma$ for a conformal metric on the standard sphere $\Sn$ with $\sigma\in (0,n/2)$ and $n\geq2$. Compactness and existence results are obtained in terms of the flatness order $\beta$ of the prescribed curvature function $K$. Making use of integral representations and perturbation result, we develop a unified approach to obtain these results when $\beta\in [n-2\sigma,n)$ for all $\sigma\in (0,n/2)$. This work generalizes the corresponding results of Jin-Li-Xiong [Math. Ann. 369: 109--151, 2017] for $\beta\in (n-2\sigma,n)$.
Interior structure of non-Abelian black holes is shown to exhibit in a general case either an oscillating mass-inflationary behavior, or power-law behavior with a divergent mass function. In both cases no Cauchy horizon forms.
We survey a collection of closely related methods for generalizing fans of toric varieties, include skeletons, Kato fans, Artin fans, and polyhedral cone complexes, all of which apply in the wider context of logarithmic geometry. Under appropriate assumptions these structures are equivalent, but their different realizations have provided for surprisingly disparate uses. We highlight several current applications and suggest some future possibilities.
Strong spin-orbit interaction (SOI) in graphene grown on tungsten disulfide (WS2) has been recently observed, leading to energy gap opening by SOI. Energy gap in graphene may also be induced by sublattice symmetry breaking (SSB) where energy level in A-sublattice is not equal to that in B-sublattice. SSB-gap may be produced by growing graphene on hexagonal boron nitride or silicon carbide. In this work, we investigate transport property in a SOI/SSB/SOI gapped graphene junction, focusing the effect of interplay of SOI and SSB. We find that, lattice-pseudospin polarization (L-PSP) can be controlled perfectly from +100% to -100% by gate voltage. This is due to the fact that in graphene grown on WS2, the carriers carry lattice-pseudo spin degree of freedom "up and down". The SSB-gapped graphene exhibits pseudo-ferromagnetism to play the role of lattice-pseudospin filtering barrier. It is also found that the SOI and SSB-gaps in graphene may be measured by characteristic of L-PSP in the junction. The proposed controllable-lattice-pseudospin currents may be applicable for graphene-based pseudospintronics.
The fluctuations and the distribution of the conductance peak spacings of a quantum dot in the Coulomb-blockade regime are studied and compared with the predictions of random matrix theory (RMT). The experimental data were obtained in transport measurements performed on a semiconductor quantum dot fabricated in a GaAs-AlGaAs heterostructure. It is found that the fluctuations in the peak spacings are considerably larger than the mean level spacing in the quantum dot. The distribution of the spacings appears Gaussian both for zero and for non-zero magnetic field and deviates strongly from the RMT-predictions.
Studying the threshold of black hole formation via numerical evolution has led to the discovery of fascinating nonlinear phenomena. Power-law mass scaling, aspects of universality, and self-similarity have now been found for a large variety of models. However, questions remain. Here I briefly review critical phenomena, discuss some recent results, and describe a model which demonstrates similar phenomena without gravity.
We demonstrate for the first time a linear-zigzag phase transition induced solely by temperature of the $^{40}$Ca$^{+}$ ion crystals in a surface-electrode trap. In contrast to the previously observed counterparts based on change of the mechanical equilibrium conditions of the ions, our presented structural phase transition occurs due to controllable influence of thermal fluctuation. The ions' temperature is well controlled by tuning the cooling laser and the experimental observation could be fully understood by classical Langevin equation in addition to the effects from thermal fluctuation. Our experimental investigation indicates the fantastic role of thermal fluctuation played in the thermodynamic process at atomic level, which might bridge the thermodynamics from the macroscopic domain to the quantum regime.
Loop quantum cosmology(LQC) is the symmetric model of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogenous cosmological model in n+1 dimensions is quantized by the loop quantization method. Interestingly, we find that the underlying quantum theories are divided into two qualitatively different sectors according to spacetime dimensions. The effective Hamiltonian and modified dynamical equations of n+1 dimensional LQC are obtained. Moreover, our results indicate that the classical big bang singularity is resolved in arbitrary spacetime dimensions by a quantum bounce. We also briefly discuss the similarities and differences between the n+1 dimensional model and the 3+1 dimensional one. Our model serves as a first example of higher dimensional loop quantum cosmology and offers possibility to investigate quantum gravity effects in higher dimensional cosmology.
We model and analyse the secular evolution of stellar bars in spinning dark matter (DM) haloes with the cosmological spin lambda ~ 0 -- 0.09. Using high-resolution stellar and DM numerical simulations, we focus on angular momentum exchange between stellar discs and DM haloes of various axisymmetric shapes --- spherical, oblate and prolate. We find that stellar bars experience a diverse evolution which is guided by the ability of parent haloes to absorb angular momentum lost by the disc through the action of gravitational torques, resonant and non-resonant. We confirm the previous claim that dynamical bar instability is accelerated via resonant angular momentum transfer to the halo. Our main findings relate to the long-term, secular evolution of disc-halo systems: with an increasing lambda, bars experience less growth and dissolve after they pass through the vertical buckling instability. Specifically, with an increasing halo spin, (1) The vertical buckling instability in stellar bars colludes with inability of the inner halo to absorb angular momentum --- this emerges as the main factor weakening or destroying bars in spinning haloes; (2) Bars lose progressively less angular momentum, and their pattern speeds level off; (3) Bars are smaller, and for lambda >= 0.06 cease their growth completely following buckling; (4) Bars in lambda > 0.03 haloes have ratio of corotation-to-bar radii, R_CR / R_b > 2, and represent so-called slow bars which do not show offset dust lanes. We provide a quantitative analysis of angular momentum transfer in disc-halo systems, and explain the reasons for absence of growth in fast spinning haloes and its observational corollaries. We conclude that stellar bar evolution is substantially more complex than anticipated, and bars are not as resilient as has been considered so far.
The \emph{Tur\'an function} $\ex(n,F)$ of a graph $F$ is the maximum number of edges in an $F$-free graph with $n$ vertices. The classical results of Tur\'an and Rademacher from 1941 led to the study of supersaturated graphs where the key question is to determine $h_F(n,q)$, the minimum number of copies of $F$ that a graph with $n$ vertices and $\ex(n,F)+q$ edges can have.   We determine $h_F(n,q)$ asymptotically when $F$ is \emph{color-critical} (that is, $F$ contains an edge whose deletion reduces its chromatic number) and $q=o(n^2)$.   Determining the exact value of $h_F(n,q)$ seems rather difficult. For example, let $c_1$ be the limit superior of $q/n$ for which the extremal structures are obtained by adding some $q$ edges to a maximum $F$-free graph. The problem of determining $c_1$ for cliques was a well-known question of Erd\H os that was solved only decades later by Lov\'asz and Simonovits. Here we prove that $c_1>0$ for every {color-critical}~$F$. Our approach also allows us to determine $c_1$ for a number of graphs, including odd cycles, cliques with one edge removed, and complete bipartite graphs plus an edge.
The magnetoresistance (MR) effect is widely employed in technologies that pervade our world from magnetic reading heads to sensors. Diverse contributions to MR, such as anisotropic, giant, tunnel, colossal, and spin-Hall, are revealed in materials depending on the specific system and measuring configuration. Half-metallic manganites hold promise for spintronic applications but the complexity of competing interactions has not permitted the understanding and control of their magnetotransport properties to enable the realization of their technological potential. Here we report on the ability to induce a dominant switchable magnetoresistance in La0.7Sr0.3MnO3 epitaxial films, at room temperature (RT). By engineering an extrinsic magnetic anisotropy, we show a large enhancement of anisotropic magnetoresistance (AMR) which leads to, at RT, signal changes much larger than the other contributions such as the colossal magnetoresistance (CMR). The dominant extrinsic AMR exhibits large variation in the resistance in low field region, showing high sensitivity to applied low magnetic fields. These findings have a strong impact on the real applications of manganite based devices for the high-resolution low field magnetic sensors or spintronics.
An ultra-stripped supernova (SN) is an explosion of a helium or C+O star whose outer envelope has been stripped away by a companion neutron star. A double neutron star (DNS) binary is believed to be left after the explosion, which will emit the gravitational wave later at the coalescence. Recent detections of a few candidates for the ultra-stripped SN have constrained the properties of the explosion and the progenitor, but little information is given as to whether the remnant DNS binary will merge within the cosmic age. A large fraction of the material stripped away from the helium star through the binary interaction is expected to escape from the system and form circumstellar material (CSM). The CSM should be traced by radio emission induced by the collision with the SN ejecta. Based on the stellar evolution models previously developed, we calculate the expected radio luminosities from ultra-stripped SNe. We find that high radio luminosity at its maximum can be an indicator of small separation of a DNS binary leading to its merger within the cosmic age. Our results can be used to optimize the strategy for the radio follow-up observations such as observational epochs and frequencies.
We calculate the local Fourier transforms for formal connections. In particular, we verify an analogous conjecture suggested in Laumon's paper: "Transformation de Fourier, constantes d'equations fonctionnelles et conjecture de Weil, 2.6.3".
We discuss and summarize some aspects concerning the study of the positronium system to probe new physics beyond the Standard Model.
On the road of searching for Majorana zero modes (MZMs) in topological insulator-based Josephson junctions, a highly-sought signature is the protected full transparency of electron transport through the junctions due to the existence of the MZMs, associated with complete gap closing between the electron-like and hole-like Andreev bound states (ABSs). Here, we present direct experimental evidence of gap closing and full transparency in single Josephson junctions constructed on the surface of three-dimensional topological insulator (3D TI) Bi$_2$Te$_3$. Our results demonstrate that the 2D surface of 3D TIs provides a promising platform for hosting and manipulating MZMs.
The $Z_2$ bosonic orbifold models with compactification radius $R^2=1/2k$ are examined in the presence of boundaries.   Demanding the extended algebra characters to have definite conformal dimension and to consist of an integer sum of Virasoro characters, we arrive at the right splitting of the partition function. This is used to derive a free field representation of a complete, consistent set of boundary states, without resorting to a basis of the extended algebra Ishibashi states. Finally the modules of the extended symmetry algebra that correspond to the finitely many characters are identified inside the direct sum of Fock modules that constitute the space of states of the theory.
Mathematical morphology (MM) helps to describe and analyze shapes using set theory. MM can be effectively applied to binary images which are treated as sets. Basic morphological operators defined can be used as an effective tool in image processing. Morphological operators are also developed based on graph and hypergraph. These operators have found better performance and applications in image processing. Bino et al. [8], [9] developed the theory of morphological operators on hypergraph. A hypergraph structure is considered and basic morphological operation erosion/dilation is defined. Several new operators opening/closing and filtering are also defined on the hypergraphs. Hypergraph based filtering have found comparatively better performance with morphological filters based on graph. In this paper we evaluate the effectiveness of hypergraph based ASF on binary images. Experimental results shows that hypergraph based ASF filters have outperformed graph based ASF.
We present an ab-initio study of electron mobility and electron-phonon coupling in chemically modified graphene, considering fluorinated and hydrogenated graphene at different percentage coverage. Hexagonal Boron Carbon Nitrogen (h-BCN) is also investigated due the increased interest shown by the research community towards this material. In particular, the Deformation Potentials are computed by means of Density Functional Theory (DFT), while the carrier mobility is obtained according to the Takagi model (S. Takagi, A. Toriumi, and H. Tango, IEEE Trans. Electr. Dev. 41, 2363 (1994)). We will show that graphene with a reduced degree of hydrogenation can compete, in terms of mobility, with silicon technology.
One of the most classical results in Ramsey theory is the theorem of Erd\H{o}s and Szekeres from 1935, which says that every sequence of more than $k^2$ numbers contains a monotone subsequence of length $k+1$. We address the following natural question motivated by this result: Given integers $k$ and $n$ with $n \geq k^2+1$, how many monotone subsequences of length $k+1$ must every sequence of $n$ numbers contain? We answer this question precisely for all sufficiently large $k$ and $n \leq k^2 + c k^{3/2} / \log k$, where $c$ is some absolute positive constant.
We construct a category of Breuil-Kisin $G_K$-modules to classify integral semi-stable Galois representations. Our theory uses Breuil-Kisin modules and Breuil-Kisin-Fargues modules with Galois actions, and can be regarded as the algebraic avatar of the integral $p$-adic cohomology theories of Bhatt-Morrow-Scholze and Bhatt-Scholze. As a key ingredient, we classify Galois representations that are of finite $E(u)$-height.
It is shown, that fitting parameters of a $\bar{K}N$ interaction model to different sets of experimental data can lead to physical conclusions which might provide a deeper insight into the physics of this multichannel system. The available experimental data are divided into three parts: the "classical" set consisting of the low-energy $K^-p$ cross sections and the threshold branching ratios, the SIDDHARTA $1s$ level shift in kaonic hydrogen and the CLAS photoproduction data. We have fitted the parameters of the potential to different combinations of these data. We found, that the two poles corresponding to the $I=0$ nuclear quasi-bound state ($\Lam$) and to the $K^-p$ $1s$ atomic level seem to resist to their simultaneous reproduction at the right place, though a more or less satisfactory compromise can be achieved. Potentials with the $\Lam$ pole pinned down close to the PDG value fail to reproduce the classical two-body data with an acceptable accuracy. We also added comments on two papers criticizing the potential used in the fits.
The thermodynamic characteristics of hot $\beta$-equilibrium three-flavor quark matter with neutrino confinement are studied in terms of the local SU(3) Nambu-Jona-Lasinio (NJL) model, which also accounts for the 't Hooft interaction which leads to mixing of quark flavors. For different temperatures $T \in [20 \div 100]$ MeV and baryon number densities $n_B \in [0 \div 1.8]$ fm$^{-3}$ the constituent quark masses, quark condensates, and relative contributions of individual types of particles to the pressure and chemical potentials of the constituent particles are determined. In order to determine the role of neutrinos in the hot quark matter, the pressures and energies in states with and without neutrinos are compared. Keywords: hot quark matter: neutrino confinement: NJL model: equation of state.
We present numerical simulations of the SU(2) Boltzmann-Vlasov equation including both hard elastic particle collisions and soft interactions mediated by classical Yang-Mills fields. We provide an estimate of the coupling of jets to a hot isotropic plasma, which is independent of infrared cutoffs. In addition, we investigate jet propagation in anisotropic plasmas, as created in heavy-ion collisions. The broadening of jets is found to be stronger along the beam line than in azimuth due to the creation of field configurations with B_t>E_t and E_z>B_z via plasma instabilities.
Stars form in spatially and temporarily correlated star formation events (CSFEs) and the dynamical processes within these "embedded clusters" leave imprints in the stellar populations in galactic fields. Such imprints are correlations in phase space (e.g. gravitationally bound star clusters, tidal streams), in the binary properties of stars and in the present-day stellar mass functions in the surviving clusters. The dynamical processes include expulsion of massive stars from cluster cores, disruption of CSFEs due to residual gas expulsion and energy-equipartition driven evaporation of stars from clusters leading to dark star clusters and cold kinematical streams with epicyclic overdensities. The properties of such phase-space structures in the Milky Way (MW) field depend on the effective gravitational potential of the MW. GAIA data will significantly constrain all of these aspects, and will in particular impact on gravitational dynamics via the properties of cold streams and on star-formation via the constraint on the gas expulsion process through the expanding unbound populations that must be associated with every CSFE.
We study the fractional laplacian problem (-\Delta)^s u &=& u^p -\epsilon u^q \quad\text{in }\quad \Omega, u &\in& H^s(\Omega)\cap L^{q+1}(\Omega),u &>&0 \quad\text{in }\quad \Omega, u&=&0 \quad\text{in}\quad \mathbb{R}^N\setminus\Omega, where $s\in(0,1)$, $q>p\geq \frac{N+2s}{N-2s}$ and $\epsilon>0$ is a parameter. Here $\Omega\subseteq\mathbb{R}^N$ is a bounded star-shaped domain with smooth boundary and $N> 2 s$. We establish existence of a variational positive solution $u_{\epsilon}$ and characterize the asymptotic behaviour of $u_{\epsilon}$ as $\epsilon\to 0$. When $p=\frac{N+2s}{N-2s}$, we describe how the solution $u_{\epsilon}$ concentrates and blows up at a interior point of the domain. Furthermore, we prove the local uniqueness of solution of the above problem when $\Omega$ is a convex symmetric domain of $\mathbb{R}^N$ with $N>4s$ and $p=\frac{N+2s}{N-2s}$.
In this paper we discuss the inflationary universe in the context of a Chaplygin gas equation of state within the framework of the effective theory of loop quantum cosmology. Under the slow-roll approximation, we calculate the primordial perturbations for this model. We give the general expressions of the scalar spectral index, its running, and the tensor-to-scalar ratio, etc. For the chaotic inflation with a quadratic potential, using the WMAP 5-year results, we determine the parameters of the Chaplygin inflation model in loop quantum cosmology. The results are consistent with the WMAP observations.
The uncertainty principle sets lower bound on the uncertainties of two incompatible observables measured on a particle. The uncertainty lower bound can be reduced by considering a particle as a quantum memory entangled with the measured particle. In this paper, we consider a tripartite scenario in which a quantum state has been shared between Alice, Bob, and Charlie. The aim of Bob and Charlie is to minimize Charlie's lower bound about Alice's measurement outcomes. To this aim, they concentrate their correlation with Alice in Charlie's side via a cooperative strategy based on local operations and classical communication. We obtain lower bound for Charlie's uncertainty about Alice's measurement outcomes after concentrating information and compare it with the lower bound without concentrating information in some examples. We also provide a physical interpretation of the entropic uncertainty lower bound based on the dense coding capacity.
A projective log variety (X, D) is called "a log Fano manifold" if X is smooth and if D is a reduced simple normal crossing divisor on X with -(K_X+D) ample. The n-dimensional log Fano manifolds (X, D) with nonzero D are classified in this article when the log Fano index r of (X, D) satisfies either r\geq n/2 with \rho(X)\geq 2 or r\geq n-2. This result is a partial generalization of the classification of logarithmic Fano threefolds by Maeda.
In a combined analysis of the experimental data on the coupled processes $\pi\pi\to\pi\pi,K\bar{K}$ in the channel with $I^GJ^{PC}=0^+0^{++}$, the various scenarios of these reactions (with different numbers of resonances) are considered. In a model-independent approach, based only on analyticity and unitarity, a resonance is represented by of a pole cluster (poles on the Riemann surface) of the definite type that is defined by the state nature. The best scenario contains the resonances $f_0(665)$ (with properties of the $\sigma$-meson), ${f_0}(980)$ (with a dominant $s{\bar s}$ component), $f_0(1500)$ (with a dominant flavour-singlet, {\it e.g.}, glueball component) and the ${f_0}(1710)$ (with a considerable $s{\bar s}$ component). If the ${f_0}(1370)$ exists, it has a dominant $s{\bar s}$ component. The coupling constants of observed states with the considered channels and the $\pi\pi$ and $K\bar{K}$ scattering lengths are obtained. The conclusion on the linear realization of chiral symmetry is drawn.