ShantanuT01/DACTYL-Pretraining huggingface dataset:
The double zeta function was first studied by Euler in response to a letter from Goldbach in 1742. One of Euler's results for this function is a decomposition formula, which expresses the product of two values of the Riemann zeta function as a finite sum of double zeta values involving binomial coefficients. In this note, we establish a q-analog of Euler's decomposition formula. More specifically, we show that Euler's decomposition formula can be extended to what might be referred to as a ``double q-zeta function'' in such a way that Euler's formula is recovered in the limit as q tends to 1.
In this paper, we will analyse a supersymmetric field theory deformed by generalized uncertainty principle and Lifshitz scaling. It will be observed that this deformed supersymmetric field theory contains non-local fractional derivative terms. In order to construct such deformed N=1 supersymmetric theory, a harmonic extension of functions will be used. However, the supersymmetry will be only preserved for a free theory and will be broken by the inclusion of interaction terms.
It was shown recently that mirror fermions, naturally present in a number of directions for new physics, seem to require an inert scalar doublet in order to pass the electroweak precision tests. This provides a further motivation for considering the inert doublet as a dark matter candidate. Moreover, the presence of extra families enhances the Standard Model Higgs-nucleon coupling, which has crucial impact on the Higgs and dark matter searches. We study the limits on the inert dark matter mass in view of recent Xenon100 data. We find that the mass of the inert dark matter must lie in a very narrow window 74-76 GeV while the Higgs must weigh more than 400 GeV. For the sake of completeness we discuss the cases with fewer extra families, where the possibility of a light Higgs boson opens up, enlarging the dark matter mass window to m_h/2-76 GeV. We find that Xenon100 constrains the DM-Higgs interaction, which in turn implies a lower bound on the monochromatic gamma-ray flux from DM annihilation in the galactic halo. For the mirror case, the predicted annihilation cross section lies a factor of 4-5 below the current limit set by Fermi LAT, thus providing a promising indirect detection signal.
The constraints from the non-observation of neutrinoless double beta decay on the violations of Lorentz invariance (VLI) or violations of the equivalence principle (VEP) have recently been re-examined (hep-ph/9904298) and it was claimed that the constraints are not valid. In this reply we point out that this statement is not correct and prove that the arguments given are wrong.
Altair is the fastest rotating star at less than 10 parsecs from the Sun. Its precise modelling is a landmark for our understanding of stellar evolution with fast rotation, and all observational constraints are most welcome to better determine the fundamental parameters of this star. We wish to improve the seismic spectrum of Altair and confirm the $\delta$-Scuti nature of this star. We used the photometric data collected by the Microvariability and Oscillations of STars (MOST) satellite in the form of a series of Fabry images to derive Altair light curves at four epochs, namely in 2007, 2011, 2012, and 2013. We first confirm the presence of $\delta$-Scuti oscillations in the light curves of Altair. We extend the precision of some eigenfrequencies and add new ones to the spectrum of Altair, which now has 15 detected eigenmodes. The rotation period, which is expected at $\sim$7h46min from models reproducing interferometric data, seems to appear in the 2012 data set, but it still needs confirmation. Finally, Altair modal oscillations show noticeable amplitude variations on a timescale of 10 to 15 days, which may be the signature of a coupling between oscillations and thermal convection in the layer where the kappa-mechanism is operating.The Altair oscillation spectrum does not contain a large number of excited eigenmodes, which is similar to the fast rotating star HD220811. This supports the idea that fast rotation hinders the excitation of eigenmodes as already pointed out by theoretical investigations.
Some changes in a recent convolution formula are performed here in order to clean it up by using more conventional notations and by making use of more referrenced and documented components (namely Sierpi\'nski's polynomials, the Thue-Morse sequence, the binomial modulo~2 transform and its inverse). Several variants are published here, by reading afterwards summed coefficients in another order; the last formula is then turned back from a summation to a new divide-and-conquer recursive formula.
We present the results of a new investigation aimed to identify the pulsational characteristics of the Southern $\beta$ Cephei star ALS 3721. Spectroscopic and multicolour photometric data were acquired at the South African Astronomical Observatory (SAAO), South Africa in 2011. Frequency analysis showed that the oscillations of ALS 3721 could be attributed to the two main frequencies with higher significance. Stellar parameters and projected rotational velocity obtained by the spectra were also used to perform photometric mode identification. In order to determine spherical harmonic degrees ($l$), a principal method was followed by comparing the observed light amplitude ratios in different passbands with those computed from non--adiabatic pulsation models. In general case, therefore, the spherical harmonic degrees corresponding of the frequencies were found in the expected $\beta$ Cephei range.
The Laboratory Astrophysics program employing the Lawrence Livermore National Laboratory (LLNL) Electron Beam Ion Trap (EBIT) has been providing useful atomic data in support of the x-ray missions Chandra and XMM-Newton. Major achievements have been made for Fe L-shell ions in hot, collisional plasmas, relevant to stellar coronae, supernova remnants, elliptical galaxies, and galaxy clusters. Measurements for L-shell ions of other cosmiscally important elements are also required, some of which are in the LLNL EBIT pipeline. On the other hand, data for inner-shelll excited lines relevant to photoionized plasmas near accretion sources are largely lacking. Even the wavelengths of these lines are only poorly known, which severely limits their use for diagnostics, despite the great potential.
We address the problem of classifying complete $\mathbb{C}$-subalgebras of $\mathbb{C}[[t]]$. A discrete invariant for this classification problem is the semigroup of orders of the elements in a given $\mathbb{C}$-subalgebra. Hence we can define the space $\mathcal{R}_{\Gamma}$ of all $\mathbb{C}$-subalgebras of $\mathbb{C}[[t]]$ with semigroup $\Gamma$. After relating this space to the Zariski moduli space of curve singularities and to a moduli space of global singular curves, we prove that $\mathcal{R}_{\Gamma}$ is an affine variety by describing its defining equations in an ambient affine space in terms of an explicit algorithm. Moreover, we identify certain types of semigroups $\Gamma$ for which $\mathcal{R}_{\Gamma}$ is always an affine space, and for general $\Gamma$ we describe the stratification of $\mathcal{R}_{\Gamma}$ by embedding dimension. We also describe the natural map from $\mathcal{R}_{\Gamma}$ to the Zariski moduli space in some special cases. Explicit examples are provided throughout.
We explore the possibility of a structured hadron-quark mixed phase forming in the interior of neutron stars. The quark-meson coupling (QMC) model, which explicitly incorporates the internal quark structure of the nucleon, is employed to describe the hadronic phase, while the quark phase is described by the same bag model as the one used in the QMC framework, so as to keep consistency between the two coexisting phases. We analyze the effect of the appearance of hadron-quark pasta phases on the neutron-star properties. We also discuss the influence of nuclear symmetry energy and the bag constant B in quark matter on the deconfinement phase transition. For the treatment of the hadron-quark mixed phase, we use the energy minimization method and compare it with the Gibbs construction. The finite-size effects like surface and Coulomb energies are taken into account in the energy minimization method; they play crucial roles in determining the pasta configuration during the hadron-quark phase transition. It is found that the finite-size effects can significantly reduce the region of the mixed phase relative to that of the Gibbs construction. Using a consistent value of B in the QMC model and quark matter, we find that hadron-quark pasta phases are formed in the interior of massive stars, but no pure quark matter can exist.
We calculate in (two-loop) chiral perturbation theory the local NN-potentials generated by the three-pion exchange diagrams with one insertion from the second order chiral effective pion-nucleon Lagrangian proportional to the low-energy constants $c_{1,2,3,4}$. The resulting isoscalar central potential vanishes identically. In most cases these $3\pi$-exchange potentials are larger than the ones generated by the diagrams involving only leading order vertices due to the large values of $c_{3,4}$ (which mainly represent virtual $\Delta$-excitation). A similar feature has been observed for the chiral $2\pi$-exchange. We also give suitable (double-integral) representations for the spin-spin and tensor potentials generated by the leading-order diagrams proportional to $g_A^6$ involving four nucleon propagators. In these cases the Cutkosky rule cannot be used to calculate the spectral-functions in the infinite nucleon mass limit since the corresponding mass-spectra start with a non-vanishing value at the $3\pi$-threshold. Altogether, one finds that chiral $3\pi$-exchange leads to small corrections in the region $r\geq 1.4$ fm where $1\pi$- and chiral $2\pi$-exchange alone provide a very good strong NN-force as shown in a recent analysis of the low-energy pp-scattering data-base.
The radio - far infrared correlation is one of the tightest correlations found in astronomy. Many of the models explaining this correlation rely on the association of of global magnetic field strength with gas density. In this letter we put forward that the physical reason for this association lies within the processes of magnetohydrodynamic turbulence.
We are interested in standing waves of a modified Schr\"odinger equation coupled with the Chern-Simons gauge theory. By applying a constraint minimization of Nehari-Pohozaev type, we prove the existence of radial ground state solutions. We also investigate the non-existence for nontrivial solutions.
X-ray amorphous manganese oxides were prepared by reduction of sodium permanganate by lithium iodide in aqueous medium (MnOx-I) and by decomposition of manganese carbonate at moderate temperature (MnOx-C). TEM showed that these materials are not amorphous, but nanostructured, with a prominent spinel substructure in MnOx-C. These materials intercalate lithium with capacities up to 200 mAh/g at first cycle (potential window 1.8-4.3 V) and 175 mAh/g at 100th cycle. Best performances for MnOx-C are obtained with cobalt doping. Potential electrochemical spectroscopy shows that the initial discharge induces a 2-phase transformation in MnOx-C phases, but not in MnOx-I ones. EXAFS and XANES confirm the participation of manganese in the redox process, with variations in local structure much smaller than in known long-range crystallized manganese oxides. X-ray absorption spectroscopy also shows that cobalt in MnOx-C is divalent and does not participate in the electrochemical reaction.
In this work, we have carried on dynamical system analysis of hessence field coupling with dark matter in $f(T)$ gravity. We have analysed the critical points due to autonomous system. The resulting autonomous system is non-linear. So, we have approached via the the theory of non-linear dynamical system.We have noticed very few papers are devoted to this kind of study.Maximum works in literature are done treating the dynamical system as done in linear dynamical analysis, which are unable to predict correct evolution.Our work is totally different from those kind of works.We have used theory of non-linear dynamical system theory,developed till date,in our analysis.This approach gives totally different stable solutions, in contrast what the linear analysis would have predicted. We have discussed the stability analysis in details due to exponential potential through computational method in tabular form and analyzed the evolution of the universe. Some plots are drawn to investigate the behaviour of the system (this plotting technique is different from usual phase plot, and devised by us.). Interestingly, the analysis shows the universe may resemble the `cosmological constant' like evolution (i.e., $\Lambda$CDM model is a subset of the solution set). Also, all the fixed points of our model are able to avoid Big rip singularity.
We define and study a class of fractal dendrites called triangular labyrinth fractals. For the construction, we use triangular labyrinth patterns systems that consist of two triangular patterns: a white and a yellow one. Correspondingly, we have two fractals: a white and a yellow one. The fractals studied here are self-similar, and fit into the framework of graph directed constructions. The main results consist in showing how special families of triangular labyrinth patterns systems, defined based on some shape features, can generate exactly three types of dendrites: labyrinth fractals where are all nontrivial arcs have infinite length, fractals where all nontrivial arcs have finite length, and fractals where the only arcs of finite length are line segments parallel to a certain direction. We also study the existence of tangents to arcs. The paper is inspired by research done on labyrinth fractals in the unit square that have been studied during the last decade. In the triangular case, due to the geometry of traingular shapes, some new techniques and ideas are necessary in order to obtain the results.
We extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic constrained mixed discrete optimization (QCMDO) problem. QCMDO problems are NP-hard, and no efficient classical algorithm for their solution is known. Included in the class of QCMDO problems are combinatorial optimization problems constrained by a linear partial differential equation (PDE) or system of linear PDEs. An essential complication commonly encountered in solving this type of problem is that the linear constraint may introduce many intermediate continuous variables into the optimization while the computational cost grows exponentially with problem size. We resolve this difficulty by developing a constructive mapping from QCMDO to quadratic unconstrained binary optimization (QUBO) such that the size of the QUBO problem depends only on the number of discrete control variables. With a suitable embedding, taking into account the physical constraints of the realizable coupling graph, the resulting QUBO problem can be implemented on an existing AQO. The mapping itself is efficient, scaling cubically with the number of continuous variables in the general case and linearly in the PDE case if an efficient preconditioner is available.
We consider matrix factorizations and homological mirror symmetry on the torus T^2 using a Landau-Ginzburg description. We identify the basic matrix factorizations of the Landau-Ginzburg superpotential and compute the full spectrum, taking into account the explicit dependence on bulk and boundary moduli. We verify homological mirror symmetry by comparing three-point functions in the A-model and the B-model.
The impact of metallicity on the Cepheid Period-Luminosity (P-L) relation is investigated using HST ACS V and I images of M101. Variations in the reddening-free Wesenheit parameter (W), which is employed as a proxy for luminosity, are examined as a function of the radial distance from the center of M101 (and thus metallicity). We determine that there is no dependence of the slope on metallicity. However, the intercept is found to depend on metallicity by -0.33 +/- 0.12 mag/dex and -0.71 +/- 0.17 mag/dex using 2 and 3 sigma rejection criteria, respectively. Sigma-clipping impacts the derived metallicity dependence, and the 2-sigma criterion applied likely mitigates blending, particularly in the crowded inner regions of M101. A metallicity-corrected distance modulus of 28.96 +/- 0.11 for M101 is obtained from 619 Cepheids, a result that agrees with the recently determined SN Ia distance. The metallicity effects described can be bypassed by working at near and mid-infrared wavelengths (e.g., the Carnegie Hubble Program).
Within the framework of non-local time-dependent stellar convection theory, we study in detail the effect of turbulent anisotropy on stellar pulsation stability. The results show that anisotropy has no substantial influence on pulsation stability of g modes and low-order (radial order $n_\mathrm{r}<5$) p modes. The effect of turbulent anisotropy increases as the radial order increases. When turbulent anisotropy is neglected, most of high-order ($n_\mathrm{r}>5$) p modes of all low-temperature stars become unstable. Fortunately, within a wide range of the anisotropic parameter $c_3$, stellar pulsation stability is not sensitive to the specific value of $c_3$. Therefore it is safe to say that calibration errors of the convective parameter $c_3$ do not cause any uncertainty in the calculation of stellar pulsation stability.
In spherically symmetric, static spacetime, we show that only j=1/2 fermions can satisfy both Einstein's field equation and Dirac's equation. It is also shown that neutrinos are able to have effective masses and cluster in the galactic halo when they are coupled to a global monopole situated at the galactic core. Astronomical implications of the results are discussed.
There exist Kruskal like coordinates for the Reissner-Nordstrom (RN) black hole spacetime which are regular at coordinate singularities. Non existence of such coordinates for the extreme RN black hole spacetime has already been shown. Also the Carter coordinates available for the extreme case are not manifestly regular at the coordinate singularity, therefore, a numerical procedure was developed to obtain free fall geodesics and flat foliation for the extreme RN black hole spacetime. The Kottler-Schwarzschild-de Sitter (KSSdS) spacetime geometry is similar to the RN geometry in the sense that, like the RN case, there exist non-singular coordinates when there are two distinct coordinate singularities. There are no manifestly regular coordinates for the extreme KSSdS case. In this paper foliation of all the cases of the KSSdS spacetime by flat spacelike hypersurfaces is obtained by introducing a non-singular time coordinate.
We study the analogues of irreducibility, period, and communicating classes for open quantum random walks, as defined by Attal et al. (J. Stat. Phys., 2012). We recover results similar to the standard ones for Markov chains, in terms of ergodic behavior, decomposition into irreducible subsystems, and characterization of stationary states.
We address the problem of estimating the phase phi given N copies of the phase rotation gate u(phi). We consider, for the first time, the optimization of the general case where the circuit consists of an arbitrary input state, followed by any arrangement of the N phase rotations interspersed with arbitrary quantum operations, and ending with a POVM. Using the polynomial method, we show that, in all cases where the measure of quality of the estimate phi' for phi depends only on the difference phi'-phi, the optimal scheme has a very simple fixed form. This implies that an optimal general phase estimation procedure can be found by just optimizing the amplitudes of the initial state.
Fingerprint classification is an effective technique for reducing the candidate numbers of fingerprints in the stage of matching in automatic fingerprint identification system (AFIS). In recent years, deep learning is an emerging technology which has achieved great success in many fields, such as image processing, natural language processing and so on. In this paper, we only choose the orientation field as the input feature and adopt a new method (stacked sparse autoencoders) based on depth neural network for fingerprint classification. For the four-class problem, we achieve a classification of 93.1 percent using the depth network structure which has three hidden layers (with 1.8% rejection) in the NIST-DB4 database. And then we propose a novel method using two classification probabilities for fuzzy classification which can effectively enhance the accuracy of classification. By only adjusting the probability threshold, we get the accuracy of classification is 96.1% (setting threshold is 0.85), 97.2% (setting threshold is 0.90) and 98.0% (setting threshold is 0.95). Using the fuzzy method, we obtain higher accuracy than other methods.
We conjecture an exact expression for the large deviation function of the stationary state current in the partially asymmetric exclusion process with periodic boundary conditions. This expression is checked for small systems using functional Bethe Ansatz. It generalizes a previous result by Derrida and Lebowitz for the totally asymmetric exclusion process, and gives the known values for the three first cumulants of the current in the partially asymmetric model. Our result is written in terms of tree structures and provides a new example of a link between integrable models and combinatorics.
How to properly understand coronal mass ejections (CMEs) viewed in white-light coronagraphs is crucial to many relative researches in solar and space physics. The issue is now particularly addressed in this paper through studying the source locations of all the 1078 LASCO CMEs listed in CDAW CME catalog during 1997 -- 1998 and their correlation with CMEs' apparent parameters. By manually checking LASCO and EIT movies of these CMEs, we find that, except 231 CMEs whose source locations can not be identified due to poor data, there are 288 CMEs with location identified on the front-side solar disk, 234 CMEs appearing above solar limb, and 325 CMEs without evident eruptive signatures in the field of view of EIT. Based on the statistical results of CMEs' source locations, four physical issues, including (1) the missing rate of CMEs by SOHO LASCO and EIT, (2) the mass of CMEs, (3) the causes of halo CMEs and (4) the deflections of CMEs in the corona, are exhaustively analyzed. It is found that (1) about 32% of front-side CMEs can not be recognized by SOHO, (2) the brightness of a CME at any heliocentric distance is roughly positively correlated with its speed, and the CME mass derived from the brightness is probably overestimated, (3) both projection effect and violent eruption are the major causes of halo CMEs, and especially for limb halo CMEs, the latter is the primary one, (4) most CMEs deflected towards equator near the solar minimum, and these deflections can be classified into three types, the asymmetrical expansion, non-radial ejection, and the deflected propagation.
Here we introduce the concept of special effect curve which permits to study, from a different point of view, special linear systems in P^2, i.e. linear system with general multiple base points whose effective dimension is strictly greater than the expected one. In particular we study two different kinds of special effect: the \alpha-special effect is defined by requiring some numerical conditions, while the definition of h^1-special effect concerns cohomology groups. We state two new conjectures for the characterization of special linear systems and we prove they are equivalent to the Segre and the Harbourne-Hirschowitz ones.