ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we deal with the calculation of the signed (total) Roman domination numbers, $\gamma_{sR}$ and $\gamma_{stR}$ respectively, on a few classes of planar graphs from the literature. We give proofs for the exact values of the numbers $\gamma_{sR}(A_n)$ and $\gamma_{sR}(R_n)$ as well as the numbers   $\gamma_{stR}(S_n)$ and $\gamma_{stR}(T_n)$. For some other classes of planar graphs, such as $Q_n$, %$S_n"$ and $T_n"$, lower and upper bounds on $\gamma_{sR}$ are calculated and proved. %We give some open problems on the exact values of $\gamma_{sR}$ and $\gamma_{stR}$ for some classes of planar graphs.
We report on large-scale Wang-Landau Monte Carlo simulations of the critical behavior of two spin models in two- (2d) and three-dimensions (3d), namely the 2d random-bond Ising model and the pure 3d Blume-Capel model at zero crystal-field coupling. The numerical data we obtain and the relevant finite-size scaling analysis provide clear answers regarding the universality aspects of both models. In particular, for the random-bond case of the 2d Ising model the theoretically predicted strong universality's hypothesis is verified, whereas for the second-order regime of the Blume-Capel model, the expected $d=3$ Ising universality is verified. Our study is facilitated by the combined use of the Wang-Landau algorithm and the critical energy subspace scheme, indicating that the proposed scheme is able to provide accurate results on the critical behavior of complex spin systems.
In this note we show the existence of at least three nontrivial solutions to the following quasilinear elliptic equation $-\Delta_p u = |u|^{p^*-2}u + \lambda f(x,u)$ in a smooth bounded domain $\Omega$ of $\R^N$ with homogeneous Dirichlet boundary conditions on $\partial\Omega$, where $p^*=Np/(N-p)$ is the critical Sobolev exponent and $\Delta_p u =div(|\nabla u|^{p-2}\nabla u)$ is the $p-$laplacian. The proof is based on variational arguments and the classical concentrated compactness method.
The definition of Komar for the mass of a relativistic source is used as a starting point to introduce volume integrals for Relativistic Multipole Moments (RMM). A certain generalization of the classical Gauss theorem is used to rewrite these multipole moments as integrals over a surface at the infinity. Therefore it is shown that the above generalization leads to Asymptotic Relativistic Multipole Moments (ARMM), recovering the multipoles of Geroch or Thorne, when the integrals are evaluated in asympotically cartesian harmonic coordinates. Relationships regarding the Thorne definition and the classical theory of moments are shown.
We find 3D flavored N=4 Chern-Simons-matter theory, a kind of N=3 SCFT, has a gravity dual AdS4xM7(t1,t2,t3) where three coprime parameters can be read off according to the number and charge of 5-branes in Type IIB setup. Because M7(t1,t2,t3) has been known in literatures as Eschenburg space, we exploit some of its properties to examine the correspondence between two sides.
A few nearby interacting galaxies are known that host elevated number of ultraluminous X-ray sources. Here we report the results of a multiwavelength study of the X-ray source population in the field of the interacting pair of galaxies NGC5774/NGC5775. A total of 49 discrete sources are detected, including 12 ultraluminous X-ray source candidates. X-ray source positions are mapped onto optical and radio images to search for potential counterparts. Twelve sources in the field have optical counterparts. Optical colors are used to differentiate these sources, which are mostly located outside the optical extent of the interacting galaxies, as potential globular clusters (2), one compact blue dwarf galaxy and quasars (5). We obtained optical spectra of two of the latter, which confirm that they are background quasars. We expect 3 background sources in the field of these two galaxies. These results are used to determine the true X-ray population of these two interacting galaxies, which are connected with two bridges. Two high mass X-ray binaries are detected on these two bridges suggesting their formation through the interaction-induced starformation episode.
We give a different approach to the well-known modularity lifting results of Wiles and Taylor. Instead of Taylor-Wiles systems we use a Galois cohomological discovery of R. Ramakrishna. This paper is 2 years older than math.NT/0210296 where another approach to modularity lifting results was presented.
The superspinar proposed by Gimon and Horava is a rapidly rotating compact entity whose exterior is described by the over-spinning Kerr geometry. The compact entity itself is expected to be governed by superstringy effects, and in astrophysical scenarios it can give rise to interesting observable phenomena. Earlier it was suggested that the superspinar may not be stable but we point out here that this does not necessarily follow from earlier studies. We show, by analytically treating the Teukolsky equations by Detwiler's method, that in fact there are infinitely many boundary conditions that make the superspinar stable, and that the modes will decay in time. It follows that we need to know more on the physical nature of the superspinar in order to decide on its stability in physical reality.
Interplay of cotunneling and single-electron tunneling in a thermally isolated single-electron transistor (SET) leads to peculiar overheating effects. In particular, there is an interesting crossover interval where the competition between cotunneling and single-electron tunneling changes to the dominance of the latter. In this interval, the current exhibits anomalous sensitivity to the effective electron temperature of the transistor island and its fluctuations. We present a detailed study of the current and temperature fluctuations at this interesting point. The methods implemented allow for a complete characterization of the distribution of the fluctuating quantities, well beyond the Gaussian approximation. We reveal and explore the parameter range where, for sufficiently small transistor islands, the current fluctuations become gigantic. In this regime, the optimal value of the current, its expectation value, and its standard deviation differ from each other by parametrically large factors. This situation is unique for transport in nanostructures and for electron transport in general. The origin of this spectacular effect is the exponential sensitivity of the current to the fluctuating effective temperature.
This paper has been withdrawn due to upload of another version of it as a new preprint: gr-qc/0404097
Emergent cooperative motions of individual degrees of freedom, i.e. collective excitations, govern the low-energy response of system ground states under external stimulations and play essential roles for understanding many-body phenomena in low-dimensional materials. The hybridization of distinct collective modes provides a route towards coherent manipulation of coupled degrees of freedom and quantum phases. In magnets, strong coupling between collective spin and lattice excitations, i.e., magnons and phonons, can lead to coherent quasi-particle magnon polarons. Here, we report the direct observation of a series of terahertz magnon polarons in a layered zigzag antiferromagnet FePS3 via far-infrared (FIR) transmission measurements. The characteristic avoided-crossing behavior is clearly seen as the magnon-phonon detuning is continuously changed via Zeeman shift of the magnon mode. The coupling strength g is giant, achieving 120 GHz (0.5 meV), the largest value reported so far. Such a strong coupling leads to a large ratio of g to the resonance frequency (g/{\omega}) of 4.5%, and a value of 29 in cooperativity (g^2/{\gamma}_{ph}{\gamma}_{mag}). Experimental results are well reproduced by first-principle calculations, where the strong coupling is identified to arise from phonon-modulated anisotropic magnetic interactions due to spin-orbit coupling. These findings establish FePS3 as an ideal testbed for exploring hybridization-induced topological magnonics in two dimensions and the coherent control of spin and lattice degrees of freedom in the terahertz regime.
Star formation is self-regulated by its feedback that drives turbulence and heats the gas. In equilibrium, the star formation rate (SFR) should be directly related to the total (thermal plus turbulent) midplane pressure and hence the total weight of the diffuse gas if energy balance and vertical dynamical equilibrium hold simultaneously. To investigate this quantitatively, we utilize numerical hydrodynamic simulations focused on outer-disk regions where diffuse atomic gas dominates. By analyzing gas properties at saturation, we obtain relationships between the turbulence driving and dissipation rates, heating and cooling rates, the total midplane pressure and the total weight of gas, and the SFR and the total midplane pressure. We find a nearly linear relationship between the SFR and the midplane pressure consistent with the theoretical prediction.
Fashion products typically feature in compositions of a variety of styles at different clothing parts. In order to distinguish images of different fashion products, we need to extract both appearance (i.e., "how to describe") and localization (i.e.,"where to look") information, and their interactions. To this end, we propose a biologically inspired framework for image-based fashion product retrieval, which mimics the hypothesized twostream visual processing system of human brain. The proposed attentional heterogeneous bilinear network (AHBN) consists of two branches: a deep CNN branch to extract fine-grained appearance attributes and a fully convolutional branch to extract landmark localization information. A joint channel-wise attention mechanism is further applied to the extracted heterogeneous features to focus on important channels, followed by a compact bilinear pooling layer to model the interaction of the two streams. Our proposed framework achieves satisfactory performance on three image-based fashion product retrieval benchmarks.
We give an easy counter-example to Problem 7.20 from C. Villani's book on mass transport: in general, the quadratic Wasserstein distance between $n$-fold normalized convolutions of two given measures fails to decrease monotonically.
The aim of the present paper is to apply the Laguerre polynomials method for the analytical solution of the Altarelli- Martinelli equation. We use this method of the low $x$ gluon distribution to the longitudinal structure function using MRST partons as input. Having checked that this model gives a good description of the data to predict of the longitudinal structure function at leading and next to leading order analysis at low $x$
In this work we introduce a new system of partial differential equations as a simplified model for the evolution of reversible martensitic transformations under thermal cycling in low hysteresis alloys. The model is developed in the context of nonlinear continuum mechanics, where the developed theory is mostly static, and cannot capture the influence of dynamics on martensitic microstructures. First, we prove existence of weak solutions; secondly, we study the physically relevant limit when the interface energy density vanishes, and the elastic constants tend to infinity. The limit problem provides a framework for the moving mask approximation recently introduced by the author. In the last section we study the limit equations in a one-dimensional setting. After closing the equations with a constitutive relation between the phase interface velocity and the temperature of the one-dimensional sample, the equations become a two-phase Stefan problem with a kinetic condition at the free boundary. Under some further assumptions, we show that the phase interface reaches the domain boundary in finite time.
We compute the anomalous dimension of the fermion field with N_f flavours in the fundamental representation of a general Lie colour group in the non-abelian Thirring model at four loops. The implications on the renormalization of the two point Green's function through the loss of multiplicative renormalizability of the model in dimensional regularization due to the appearance of evanescent four fermi operators are considered at length. We observe the appearance of one new colour group Casimir, d_F^{abcd} d_F^{abcd}, in the final four loop result and discuss its consequences for the relation of the Knizhnik-Zamolodchikov critical exponents in the Wess Zumino Witten Novikov model to the non-abelian Thirring model. Renormalization scheme changes are also considered to ensure that the underlying Fierz symmetry broken by dimensional regularization is restored.
In a quantum cosmological model consisting of a Euclidean region and a Lorentzian region, Hartle-Hawking's no-bounary wave function, and Linde's wave function and Vilenkin's tunneling wave function are briefly described and compared with each other. We put a particular emphasis on semiclassical gravity from quantum cosmology and compare it with the conventional quantum field theory in curved spacetimes. Finally, we discuss the recent debate on catastrophic particle production in the tunneling universe between Rubakov and Vilenkin within the semiclassical gravity.
We present very deep CCD spectrum of the bright, medium-excitation planetary nebula NGC 7009, with a wavelength coverage from 3040 to 11000 A. Traditional emission line identification is carried out to identify all the emission features in the spectra, based on the available laboratory atomic transition data. Since the spectra are of medium resolution, we use multi-Gaussian line profile fitting to deblend faint blended lines, most of which are optical recombination lines (ORLs) emitted by singly ionized ions of abundant second-row elements such as C, N, O and Ne. Computer-aided emission-line identification, using the code EMILI developed by Sharpee et al., is then employed to further identify all the emission lines thus obtained. In total about 1200 emission features are identified, with the faintest ones down to fluxes 10^{-4} of H_beta. The flux errors for all emission lines, estimated from multi-Gaussian fitting, are presented. Plots of the whole optical spectrum, identified emission lines labeled, are presented along with the results of multi-Gaussian fits. Plasma diagnostics using optical forbidden line ratios are carried out. Also derived are electron temperatures and densities from the H I, He I and He II recombination spectrum.
We analyse a feature that is detectable at the differential phases of high-resolution spectro-interferometry of Be stars. The origin of this feature (dubbed CQE-PS, Central Quasi Emission Phase Signature) lies in the differential absorption of photospheric radiation by the circumstellar disk, which is spectroscopically detected as a CQE line profile in shell stars. This phenomenon has great diagnostic potential for Be star disks, revealing properties of these disks on the scale of a few stellar radii.
Crystal morphologies are important for the design and functionality of devices based on low-dimensional nanomaterials. The equilibrium crystal shape (ECS) is a key quantity in this context. It is determined by surface energies, which are hard to access experimentally but can generally be well predicted by first-principles methods. Unfortunately, this is not necessarily so for polar and semipolar surfaces of wurtzite crystals. By extending the concept of Wulff construction, we demonstrate that the ECSs can nevertheless be obtained for this class of materials. For the example of GaN, we identify different crystal shapes depending on the chemical potential, shedding light on experimentally observed GaN nanostructures.
We present the main features of the explicitly covariant Light-Front Dynamics formalism and a summary of our recent works on this topic. They concern the bound states of two scalar particles in the Wick-Cutkosky model and of two fermions interacting via the usual OBEP ladder kernels.
Stochastic micromagnetic simulations are employed to study switching in three-dimensional magnetic nanopillars exposed to highly misaligned fields. The switching appears to proceed through two different decay modes, characterized by very different average lifetimes and different average values of the transverse magnetization components.
The analysis of the physical properties of low-redshift Ly$\alpha$ emitters (LAEs) can provide clues in the study of their high-redshift analogues. At $z \sim 0.3$, LAEs are bright enough to be detected over almost the entire electromagnetic spectrum and it is possible to carry out a more precise and complete study than at higher redshifts. In this study, we examine the UV and IR emission, dust attenuation, SFR and morphology of a sample of 23 GALEX-discovered star-forming (SF) LAEs at $z \sim 0.3$ with direct UV (GALEX), optical (ACS) and FIR (PACS and MIPS) data. Using the same UV and IR limiting luminosities, we find that LAEs at $z\sim 0.3$ tend to be less dusty, have slightly higher total SFRs, have bluer UV continuum slopes, and are much smaller than other galaxies that do not exhibit Ly$\alpha$ emission in their spectrum (non-LAEs). These results suggest that at $z \sim 0.3$ Ly$\alpha$ photons tend to escape from small galaxies with low dust attenuation. Regarding their morphology, LAEs belong to Irr/merger classes, unlike non-LAEs. Size and morphology represent the most noticeable difference between LAEs and non-LAEs at $z \sim 0.3$. Furthermore, the comparison of our results with those obtained at higher redshifts indicates that either the Ly$\alpha$ technique picks up different kind of galaxies at different redshifts or that the physical properties of LAEs are evolving with redshift.
The features of correlated Michelson interferometers are for describing the analysis of Einsteinian spacetime models, and the quantum geometries pertinent with descriptions of GR compatible with particle Physics. Such apparati allow for the spectral decomposition of fractional Planck-scale displacements correlations and fractional Plancktime- interval correlations for kinematical investigations in particle Physics on emerging Minkowski background, and for models which admit GR as a limit after cosmological implementations for Poincar\'e particles content.
We propose a learning model for the task of visual storytelling. The main idea is to predict anchor word embeddings from the images and use the embeddings and the image features jointly to generate narrative sentences. We use the embeddings of randomly sampled nouns from the groundtruth stories as the target anchor word embeddings to learn the predictor. To narrate a sequence of images, we use the predicted anchor word embeddings and the image features as the joint input to a seq2seq model. As opposed to state-of-the-art methods, the proposed model is simple in design, easy to optimize, and attains the best results in most automatic evaluation metrics. In human evaluation, the method also outperforms competing methods.
Weakly-bound deformed nuclei have been studied by the Skyrme Hartree-Fock-Bogoliubov (HFB) approach in large coordinate-space boxes. In particular, the box-size dependence of the HFB calculations of weakly-bound deformed nuclei are investigated, including the particle density and pairing density distributions at nuclear surfaces, the near-threshold resonant and continuum quasiparticle spectra, and energetic properties. The box size may have larger influences in pairing properties than in other bulk properties. We demonstrate that large-box calculations of weakly-bound nuclei are important to precisely describe exotic phenomena such as deformed halos and peninsulas of stability beyond drip lines.
We present first-principles calculations of the impact ionization rate (IIR) in the $GW$ approximation ($GW$A) for semiconductors. The IIR is calculated from the quasiparticle (QP) width in the $GW$A, since it can be identified as the decay rate of a QP into lower energy QP plus an independent electron-hole pair. The quasiparticle self-consistent $GW$ method was used to generate the noninteracting hamiltonian the $GW$A requires as input. Small empirical corrections were added so as to reproduce experimental band gaps. Our results are in reasonable agreement with previous work, though we observe some discrepancy. In particular we find high IIR at low energy in the narrow gap semiconductor InAs.
In the context of the quantum mechanical modelling of a measurement process using the Stern-Gerlach setup, we critically examine the relationship between the notion of `distinguishability' of apparatus states defined in terms of the inner product and spatial separation among the emerging wave packets. We show that, in general, the mutual orthogonality of these wave packets does not necessarily imply their unambiguous spatial separation even in the asymptotic limit. A testable scheme is formulated to quantify such departures from `idealness' for a range of relevant parameters.
This paper introduces fractional type evolutionary equations modeling the interaction between short waves and long waves. We consider a fractional Benney type system, which is given by a fractional Schr\"odinger equation coupled with a fractional porous medium equation. Under the assumption of weak coupling or small initial data related to the fractional Schr\"odinger equation, it is proved the existence of weak solutions to the Cauchy problem.
The multiple point principle (MPP) is applied to the non--supersymmetric two-Higgs doublet extension of the Standard Model (SM). The existence of a large set of degenerate vacua at some high energy scale caused by the MPP results in a few relations between Higgs self-coupling constants which can be examined at future colliders. The numerical analysis reveals that these MPP conditions constrain the mass of the SM--like Higgs boson to lie below 180 GeV for a wide set of MPP scales $\Lambda$ and $\tan\beta$.
We derive necessary and sufficient conditions for N=1 compactifications of (massive) IIA supergravity to AdS(4) in the language of SU(3) structures. We find new solutions characterized by constant dilaton and nonzero fluxes for all form fields. All fluxes are given in terms of the geometrical data of the internal compact space. The latter is constrained to belong to a special class of half-flat manifolds.
The interaction between electrons and plasmons in trilayer graphene is investigated within the Overhauser approach resulting in the 'plasmaron' quasi-particle. This interaction is cast into a field theoretical problem, nd its effect on the energy spectrum is calculated using improved Wigner-Brillouin perturbation theory. The plasmaron spectrum is shifted with respect to the bare electron spectrum by $\Delta E(\mathbf{k})\sim 50\div200\,{\rm meV}$ for ABC stacked trilayer graphene and for ABA trilayer graphene by $\Delta E(\mathbf{k})\sim 30\div150\,{\rm meV}$ ($\Delta E(\mathbf{k})\sim 1\div5\,{\rm meV}$) for the hyperbolic linear) part of the spectrum. The shift in general increases with the electron concentration $n_{e}$ and electron momentum. The dispersion of plasmarons is more pronounced in \textit{ABC} stacked than in ABA tacked trilayer graphene, because of the different energy band structure and their different plasmon dispersion.
The third neutrino mixing angle theta13 is the least known one. In this contribution, after a brief discussion of the current efforts to determine the value of this angle better, various astrophysical implications of a non-zero value of theta13 are summarized.