ShantanuT01/DACTYL-Pretraining huggingface dataset:
In the Euclidean path integral approach, we calculate the actions and the entropies for the Reissner-Nordstr\"om-de Sitter solutions. When the temperatures of black hole and cosmological horizons are equal, the entropy is the sum of one-quarter areas of black hole and cosmological horizons; when the inner and outer black hole horizons coincide, the entropy is only one-quarter area of cosmological horizon; and the entropy vanishes when the two black hole horizons and cosmological horizon coincide. We also calculate the Euler numbers of the corresponding Euclidean manifolds, and discuss the relationship between the entropy of instanton and the Euler number.
We have fabricated nanometer sized magnetic tunnel junctions using a new nanoindentation technique in order to study the transport properties of a single metallic nanoparticle. Coulomb blockade effects show clear evidence for single electron tunneling through a single 2.5 nm Au cluster. The observed magnetoresistance is the signature of spin conservation during the transport process through a non magnetic cluster.
The Large Hadron Collider (LHC) has measured the Higgs boson couplings with the heavier particles of the Standard Model (SM), and they seem to lay on a single line as function of the particle mass, as predicted in the SM. However a complete test of this property must involve the lighter generations, and the coming measurements at LHC, or future colliders, may reveal hidden patterns associated with physics beyond the SM. In renormalizable multi-Higgs models, the Higgs-fermion couplings could still be linear, but they could lay on multiple lines. Then, the angle subtended by these lines, with respect to the SM line, can be used to characterize different models, as it is shown here for the Two-Higgs doublet Model (2HDM). Models where fermion masses arise from higher-dimensional operators, may also result in large deviations from the SM values for the Higgs couplings, which would show an irregular pattern as a function of the fermion masses. In the case of neutrino masses, when they arise from the see-saw mechanism, one finds that the Higgs Yukawa couplings will show a non-linear mass relation.
Given a non-singular variety with a K3 fibration f : X --> S we construct dual fibrations Y --> S by replacing each fibre X_s of f by a two-dimensional moduli space of stable sheaves on X_s. In certain cases we prove that the resulting scheme Y is a non-singular variety and construct an equivalence of derived categories of coherent sheaves \Phi : D(Y) --> D(X). Our methods also apply to elliptic and abelian surface fibrations. As an application we show how the equivalences \Phi identify certain moduli spaces of stable bundles on elliptic threefolds with Hilbert schemes of curves.
A series of spectra of the RV Tauri star R Scuti taken as it rose from a deep minimum to a bright maximum during 2013 October and November reveals major changes taking place in the photosphere and outer atmosphere of the star. This may be the first such series of spectra and demonstrates the capability of amateur spectroscopy for studying these complex stars.
Spin splitting of the energy spectrum of single-layer graphene on Au/Ni(111) substrate has been recently reported. I show that eigenstates of spin-orbit coupled graphene are polarized in-plane and perpendicular to electron momentum $\bf k$; the magnitude of spin polarization $\bf S$ vanishes when $k \to 0$. In a perpendicular magnetic field $\bf B$, $\bf S$ is parallel to $\bf B$, and two zero modes emerge in the Landau level spectrum. Singular $\bf B$-dependence of their magnetization suggests existence of a novel magnetic instability. They also manifest themselves in a new unconventional quantum Hall effect.
With standard Einstein gravity not being renormalizable at the quantum level there is much interest in studying higher-derivative quantum gravity theories. Thus just as a Ricci-scalar-based action produces a propagator that behaves as a non-renormalizable $1/k^2$ at large $k^2$, an action based on the square of the Ricci scalar behaves as a renormalizable $1/k^4$ at large $k^2$. An action based on both the Ricci scalar and its square leads to a renormalizable propagator of the generic Pauli-Villars form. However, given the form of the Hamiltonian and the propagator such theories are thought to be plagued by either energies that are unbounded from below or states of negative Dirac norm (the overlap of a ket with its Hermitian conjugate bra). But when one constructs the quantum Hilbert space one finds (Bender and Mannheim) that in fact neither of these problems is actually present. The Hamiltonian turns out to not be Hermitian but to instead have an antilinear $PT$ symmetry, and for this symmetry the needed inner product is the overlap of a ket with its $PT$ conjugate bra. And this inner product is positive definite. Moreover, for the pure $1/k^4$ propagator the Hamiltonian turns out to not be diagonalizable, and again there are no states of negative energy or of negative norm. Instead there are states of zero norm, non-standard but perfectly acceptable states that serve to maintain probability conservation. With the locally conformal invariant fourth-order derivative conformal gravity theory being in this category, it can be offered as a candidate theory of quantum gravity that is renormalizable and unitary in four spacetime dimensions.
We interpret instantons on a torus with twisted boundary conditions, in terms of bound states of branes. The interplay between the SU(N) and U(1) parts of the U(N) theory of N 4-branes allows the construction of a variety of bound states. The SU(N) and U(1) parts can contribute fractional amounts to the total instanton number which is integral. The geometry of non-self intersecting two-cycles in $T^4$ sheds some light on a number of properties of these solutions.
Radio jet and core data for a complete sample of 98 FRII sources with z < 1 are analysed with a Markov-Chain Monte Carlo (MCMC) model fitting method to obtain constraints on bulk-flow speeds in the beam. The Bayesian parameter-inference method is described and demonstrated to be capable of providing meaningful constraints on the Lorentz factor at both kiloparsec and parsec scales. For both jets and cores we show that models in which some intrinsic dispersion is present in the features' intrinsic prominence, bulk-flow speeds or both provide the best fit to the data. The constraints on the Lorentz factor on parsec scales are found to be consistent with the expected values given VLBI observations and other evidence, with mean gamma ~ 10-14. On kiloparsec scales, the Lorentz factor is found to be ~ 1.18 - 1.49, in agreement with the results of previous analyses of radio jet data. These values are clearly not consistent with the gamma ~ 10 speeds required by beamed inverse-Compton models of X-ray emission from quasar jets; our results therefore support models that require velocity structure in powerful jets.
We analyze high-resolution UV spectra of a small sample of Herbig Ae/Be stars (HAEBES) in order to explore the origin of the $T\sim10^5$ K gas in these stars. The C IV 1548,1550 \AA\ line luminosities are compared to non--simultaneous accretion rate estimates for the objects showing C IV emission. We show that the correlation between $L_{CIV}$ and $\dot{M}$ previously established for classical T Tauri stars (CTTSs) seems to extend into the HAEBE mass regime, although the large spread in literature $\dot{M}$ and $A_V$ values makes the actual relationship highly uncertain. With the exception of DX Cha, we find no evidence for hot, optically thick winds in our HAEBE sample. All other objects showing clear doublet emission in C IV can be well described by a two component (i.e., a single component for each doublet member) or four component (i.e., two components for each doublet member) Gaussian emission line fit. The morphologies and peak-flux velocities of these lines suggest they are formed in weak, optically thin stellar winds and not in an accretion flow, as is the case for the hot lines observed in CTTSs. The lack of strong outflow signatures and lack of evidence for line formation in accretion flows is consistent with the conclusion presented in our recent optical and He I 10830 \AA\ studies that the immediate circumstellar environments of HAEBES, in general, are not scaled-up analogs of the immediate environments around CTTSs. The conclusions presented here for hot gas lines around HAEBES should be verified with a larger sample of objects.
In part I (math.PR/0406392) we proved for an arbitrary one-dimensional random walk with independent increments that the probability of crossing a level at a given time n is of the maximal order square root of n. In higher dimensions we call a random walk 'polygonally recurrent' (resp. transient) if a.s. infinitely many (resp. finitely many) of the straight lines between two consecutive sites hit a given bounded set. The above estimate implies that three-dimensional random walks with independent components are polygonally transient. Similarly a directionally reinforced random walk on Z^3 in the sense of Mauldin, Monticino and v.Weizsaecker [1] is transient. On the other hand we construct an example of a transient but polygonally recurrent random walk with independent components on Z^2.
In quantum estimation theory, the Holevo bound is known as a lower bound of weighed traces of covariances of unbiased estimators. The Holevo bound is defined by a solution of a minimization problem, and in general, explicit solution is not known. When the dimension of Hilbert space is two and the number of parameters is two, a explicit form of the Holevo bound was given by Suzuki. In this paper, we focus on a logarithmic derivative lies between the symmetric logarithmic derivative (SLD) and the right logarithmic derivative (RLD) parameterized by $\beta\in[0,1]$ to obtain lower bounds of weighted trace of covariance of unbiased estimator. We introduce the maximum logarithmic derivative bound as the maximum of bounds with respect to $\beta$. We show that all monotone metrics induce lower bounds, and the maximum logarithmic derivative bound is the largest bound among them. We show that the maximum logarithmic derivative bound has explicit solution when the $d$ dimensional model has $d+1$ dimensional $\mathcal{D}$ invariant extension of the SLD tangent space. Furthermore, when $d=2$, we show that the maximization problem to define the maximum logarithmic derivative bound is the Lagrangian duality of the minimization problem to define Holevo bound, and is the same as the Holevo bound. This explicit solution is a generalization of the solution for a two dimensional Hilbert space given by Suzuki. We give also examples of families of quantum states to which our theory can be applied not only for two dimensional Hilbert spaces.
A result due to Gy\'arf\'as, Hubenko, and Solymosi (answering a question of Erd\"os) states that if a graph $G$ on $n$ vertices does not contain $K_{2,2}$ as an induced subgraph yet has at least $c\binom{n}{2}$ edges, then $G$ has a complete subgraph on at least $\frac{c^2}{10}n$ vertices. In this paper we suggest a "higher-dimensional" analogue of the notion of an induced $K_{2,2}$ which allows us to generalize their result to $k$-uniform hypergraphs. Our result also has an interesting consequence in discrete geometry. In particular, it implies that the fractional Helly theorem can be derived as a purely combinatorial consequence of the colorful Helly theorem.
Upward through-going muons in the Lake Baikal Neutrino Experiment arriving from the ecliptic plane have been analyzed using NT200 data samples of the years 1998-2002 (1007 live days). We derive upper limits on muon fluxes from annihilation processes of hypothetical WIMP dark matter particles in the center of the Sun.
This article examines the existence and uniqueness of weak solutions to the d-dimensional micropolar equations ($d=2$ or $d=3$) with general fractional dissipation $(-\Delta)^{\alpha}u$ and $(-\Delta)^{\beta}w$. The micropolar equations with standard Laplacian dissipation model fluids with microstructure. The generalization to include fractional dissipation allows simultaneous study of a family of equations and is relevant in some physical circumstances. We establish that, when $\alpha\ge \frac12$ and $\beta\ge \frac12$, any initial data $(u_0, w_0)$ in the critical Besov space $u_0\in B^{1+\frac{d}{2}-2\alpha}_{2,1}(\mathbb R^d)$ and $w_0\in B^{1+\frac{d}{2}-2\beta}_{2,1}(\mathbb R^d)$ yields a unique weak solution. For $\alpha\ge 1$ and $\beta=0$, any initial data $u_0\in B^{1+\frac{d}{2}-2\alpha}_{2,1}(\mathbb R^d)$ and $w_0\in B^{\frac{d}{2}}_{2,1}(\mathbb R^d)$ also leads to a unique weak solution as well. The regularity indices in these Besov spaces appear to be optimal and can not be lowered in order to achieve the uniqueness. Especially, the 2D micropolar equations with the standard Laplacian dissipation, namely $\alpha=\beta=1$ have a unique weak solution for $(u_0, w_0)\in B^0_{2,1}$. The proof involves the construction of successive approximation sequences and extensive {\it a priori} estimates in Besov space settings.
In this work, we present the first results of an ongoing survey to search for planetary nebulae (PNe) around hot subdwarf stars (sdOs). Deep images and intermediate-resolution long-slit spectra of RWT 152, the only confirmed PN+sdO system in the northern hemisphere, as well as preliminary results for other sdO+PN candidate are presented.
The Kochen-Specker theorem theoretically shows evidence of the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments by using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantum contextuality, by using spin-path entanglement in a single neutron system. Here entanglement is achieved not between different particles, but between degrees of freedom, i.e., between spin and path degree of freedom. Appropriate combinations of the spin analysis and the position of the phase shifter allow an experimental verification of the violation of an inequality of the Kochen-Specker theorem. The observed value of (2.291 +/- 0.008), which is above the threshold of 1, clearly shows that quantum mechanical predictions cannot be reproduced by noncontextual hidden variable theories.
We provide a consistent reduction to five dimensions of the system of D3-branes at Calabi-Yau singularities coupled to D7-branes with world-volume gauge flux. The D3-branes source the dual to would-be conformal quiver theories. The D7-branes, which are homogeneously distributed in their transverse directions, are dual to massless matter in the fundamental representation at finite (baryon) density. We provide the five-dimensional action and equations of motion, and discuss a few sub-truncations. The reduction can be used in the study of transport properties and stability of D3-D7 charged systems.
Let $M$ be a compact 1-manifold. Given a continuous function $g:M\to \mathbb R_+$ we consider the following ordinary differential equation: $\|\dot{f}(t)\|=g(t)$, where $f:M\to \mathbb R^2$. We construct a probability measure on the space of almost everywhere differentiable solutions of this differential equation and study this measure. A solution of this equation can be viewed as an isometric immersion of a compact 1-manifold into $\mathbb R^2$. Nash's convergence technique in the proof of isometric $C^1$-immersion theorem plays an important role in the construction.
Context. The binary B5V star BD+31?643 exhibits a disk-like structure detected at optical wavelengths. Even though the feature is well centered on the star, it has been argued, based on Spitzer observations, that the feature is a filament not directly associated to the binary star. Aims. The purpose of the present paper is to investigate whether polarization imaging may provide evidence either for or against the disk hypothesis. In addition, we aim at clarifying whether there might be any additional close companion to the binary star. Methods. We used the coronagraph PolCor in its polarization mode in combination with an EMCCD camera allowing short unit exposure times. As a result of shift-and-add and frame selection, the spatial resolution is improved compared to traditional CCD imaging. In order to possibly reveal an additional stellar companion, we used high resolution spectroscopy in the optical and high spatial resolution imaging in the near-IR. Results. The disk/filament is much better seen in polarization; it is narrow and a line drawn along the ridge passes within a second of arc from the star. The degree of polarization is high (?50% after correction for the extended component of the reflection nebula) which means that the disk/filament must be approximately at the same distance as the star. Although we confirm that the feature is much brighter south-east than north-west of the star, the evidence that the feature is physically connected to the star is strengthened and suggests that we are witnessing the destruction process of an accretion disk. Our spectroscopy shows that at least one of the stars is a spectroscopic binary. We were, however, not able to spatially resolve any stellar component in addition to the two well separated stars.
Short (inner) bars of sub-kiloparsec radius have been hypothesized to be an important mechanism for driving gas inflows to small scales, thus feeding central black holes. Recent numerical simulations have shown that the growth of central black holes in galaxies can destroy short bars, when the black hole reaches a mass of $\sim 0.1\%$ of the total stellar mass of the galaxy. We study $N$-body simulations of galaxies with single and double bars to track the long-term evolution of the central stellar mass distribution. We find that the destruction of the short bar contributes significantly to the growth of the bulge. The final bulge mass is roughly equal to the sum of the masses of the initial pseudo bulge and short bar. The initially boxy/peanut-shaped bulge of S\'ersic index $n\lesssim1$ is transformed into a more massive, compact structure that bears many similarities to a classical bulge, in terms of its morphology ($n \approx 2$), kinematics (dispersion-dominated, isotropic), and location on standard scaling relations (Kormendy relation, mass-size relation, and correlations between black hole mass and bulge stellar mass and velocity dispersion). Our proposed channel for forming classical bulges relies solely on the destruction of short bars without any reliance on mergers. We suggest that some of the less massive, less compact classical bulges were formed in this manner.
There exists a Hamiltonian formulation of the factorisation problem which also needs the definition of a factorisation ensemble (a set to which factorable numbers, $N'=x'y'$, having the same trivial factorisation algorithmic complexity, belong). For the primes therein, a function $E$, that may take only discrete values, should be the analogous of the energy from a confined system of charges in a magnetic trap. This is the quantum factoring simulator hypothesis connecting quantum mechanics with number theory. In this work, we report numerical evidence of the existence of this kind of discrete spectrum from the statistical analysis of the values of $E$ in a sample of random OpenSSL n-bits moduli (which may be taken as a part of the factorisation ensemble). Here, we show that the unfolded distance probability of these $E$'s fits to a {\it Gaussian Unitary Ensemble}, consistently as required, if they actually correspond to the quantum energy levels spacing of a magnetically confined system that exhibits chaos. The confirmation of these predictions bears out the quantum simulator hypothesis and, thereby, it points to the existence of a liaison between quantum mechanics and number theory. Shor's polynomial time complexity of the quantum factorisation problem, from pure quantum simulation primitives, was obtained.
For schemes X over global or local fields, or over their rings of integers, K. Kato stated several conjectures on certain complexes of Gersten-Bloch-Ogus type, generalizing the fundamental exact sequence of Brauer groups for a global field. He proved these conjectures for low dimensions. We prove Kato's conjecture over number fields. In particular this gives a Hasse principle for function fields F over a number field K, involving the corresponding function fields over all completions of K. We get the same results over global fields K of positive characteristic, for coefficients invertible in K. This was proved earlier by M. Kerz and S. Saito, by another method. Finally we obtain a conjecture of Kato over a finite field, and a generalization to finitely generated fields K, assuming resolution of singularities or that the coefficents are invertible in K. The latter case was again obtained earlier by M. Kerz and S. Saito, by different methods.
In this paper, we extract natural invariants of a singularity by using the Deligne weight filtration on the cohomology of an exceptional fibre of a resolution, and also on the intersection cohomology of the link. Our primary goal is to study and give natural bounds on the weights in terms of direct images of differential forms. These bounds can be made explicit for various standard classes such as rational, isolated normal Cohen-Macaulay and toroidal singularities, and lead to strong restrictions on the topology of these singularities. A secondary goal of this paper is to make the weight filtration, and related constructions, more widely accessible. So we have tried to make the presentation somewhat self contained. This is supersedes our earlier preprint arXiv:0902.4234.
Following recent work of the author, partly in collaboration with T. Dupuy and M. Barrett, we describe arithmetic analogues of some key concepts from Riemannian geometry such as: metrics, Chern connections, curvature, etc. Theorems are stated to the effect that the spectrum of the integers has a non-vanishing curvature.
The observed acceleration of the Universe can be explained by modifying general relativity. One such attempt is the nonlocal model of Deser and Woodard. Here we fix the background cosmology using results from the Planck satellite and examine the predictions of nonlocal gravity for the evolution of structure in the universe, confronting the model with three tests: gravitational lensing, redshift space distortions, and the estimator of gravity $E_G$. Current data favor general relativity (GR) over nonlocal gravity: fixing primordial cosmology with the best fit parameters from Planck leads to weak lensing results favoring GR by 5.9 sigma; redshift space distortions measurements of the growth rate preferring GR by 7.8 sigma; and the single measurement of $E_G$ favoring GR, but by less than 1-sigma. The significance holds up even after the parameters are allowed to vary within Planck limits. The larger lesson is that a successful modified gravity model will likely have to suppress the growth of structure compared to general relativity.