6,401 research outputs found

    On the convergence of harmonic Ritz vectors and harmonic Ritz values

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    We are interested in computing a simple eigenpair (λ,x)(\lambda,{\bf x}) of a large non-Hermitian matrix AA, by a general harmonic Rayleigh-Ritz projection method. Given a search subspace K\mathcal{K} and a target point τ\tau, we focus on the convergence of the harmonic Ritz vector x~\widetilde{\bf x} and harmonic Ritz value λ~\widetilde{\lambda}. In [{Z. Jia}, {\em The convergence of harmonic Ritz values, harmonic Ritz vectors, and refined harmonic Ritz vectors}, Math. Comput., 74 (2004), pp. 1441--1456.], Jia showed that for the convergence of harmonic Ritz vector and harmonic Ritz value, it is essential to assume certain Rayleigh quotient matrix being {\it uniformly nonsingular} as (x,K)0\angle({\bf x},\mathcal{K})\rightarrow 0. However, this assumption can not be guaranteed theoretically for a general matrix AA, and the Rayleigh quotient matrix can be singular or near singular even if τ\tau is not close to λ\lambda. In this paper, we abolish this constraint and derive new bounds for the convergence of harmonic Rayleigh-Ritz projection methods. We show that as the distance between x{\bf x} and K\mathcal{K} tends to zero and τ\tau is satisfied with the so-called {\it uniform separation condition}, the harmonic Ritz value converges, and the harmonic Ritz vector converges as 1λτ\frac{1}{\lambda-\tau} is well separated from other Ritz values of (AτI)1(A-\tau I)^{-1} in the orthogonal complement of (AτI)x~(A-\tau I)\widetilde{\bf x} with respect to (AτI)K(A-\tau I)\mathcal{K}.Comment: 14 pages. arXiv admin note: text overlap with arXiv:1512.01584 by other author

    BCVEGPY and GENXICC for the hadronic production of the doubly heavy mesons and baryons

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    Doubly heavy mesons and baryons provide a good platform for testing pQCD. Two generators BCVEGPY and GENXICC for simulating the hadronic production of the doubly heavy mesons and baryons have been developed in recent years. In this talk, we present their main idea and their recent progresses. The dominant gluon-gluon fusion mechanism programmed in those two generators are written based on the improved helicity amplitude approach, in which the hard scattering amplitude are dealt with directly at the amplitude level and the numerical efficiency are greatly improved by properly decomposing the Feynman diagrams and by fully applying the symmetries among them. Moreover, in comparison to the previous versions, we have updated the programs in order to generate the unweighted meson or baryon events much more effectively within various simulation environments. The generators can be conveniently imported into PYTHIA to do further hadronization and decay simulation.Comment: 7 pages, 5 figures. Talk presented at ACAT 2013. References updated and discussions improve

    Itinerant Flat-Band Magnetism in Hydrogenated Carbon Nanotubes

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    We investigate the electronic and magnetic properties of hydrogenated carbon nanotubes using ab initio spin-polarized calculations within both the local density approximation (LDA) and the generalized gradient approximation (GGA). We find that the combination of charge transfer and carbon network distortion makes the spin-polarized flat-band appear in the tube's energy gap. Various spin-dependent ground state properties are predicted with the changes of the radii, the chiralities of the tubes and the concentration of hydrogen (H). It is found that strain or external electric field can effectively modulate the flat-band spin-splitting, and even induce an insulator-metal transition.Comment: 13 pages, 5 figure

    On the box-counting dimension of potential singular set for suitable weak solutions to the 3D Navier-Stokes equations

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    In this paper, we are concerned with the upper box-counting dimension of the set of possible singular points in space-time of suitable weak solutions to the 3D Navier-Stokes equations. By taking full advantage of the pressure Π\Pi in terms of Π\nabla \Pi in equations, we show that this upper box dimension is at most 135/104(1.30)135/104(\approx1.30), which improves the known upper box-counting dimension 95/63(1.51)95/63(\approx1.51) in Koh et al. [9, J. Differential Equations, 261: 3137--3148, 2016], 45/29(1.55)45/29(\approx1.55) in Kukavica et al. [11, Nonlinearity 25: 2775-2783, 2012] and 135/82(1.65)135/82(\approx1.65) in Kukavica [10, Nonlinearity 22: 2889-2900, 2009].Comment: Thanks to referees' crucial comments, we improved the box dimension of potential singular set for suitable weak solutions from 180/131 to 135/104 in this versio

    Characteristics of the Wave Function of Coupled Oscillators in Semiquantum Chaos

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    Using the method of adiabatic invariants and the Born-Oppenheimer approximation, we have successfully got the excited-state wave functions for a pair of coupled oscillators in the so-called \textit{semiquantum chaos}. Some interesting characteristics in the \textit{Fourier spectra} of the wave functions and its \textit{Correlation Functions} in the regular and chaos states have been found, which offers a new way to distinguish the regular and chaotic states in quantum system

    Regulator proofs for Boyd's identities on genus 2 curves

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    We use the elliptic regulator to recover some identities between Mahler measures involving certain families of genus 2 curves that were conjectured by Boyd and proven by Bertin and Zudilin by differentiating the Mahler measures and using hypergeometric identities. Since our proofs involve the regulator, they yield light into the expected relation of each Mahler measure to special values of LL-functions of certain elliptic curves

    Heavy and light meson wavefunctions

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    We present a short review on the properties of heavy and light mesons' light-cone wavefunctions (LCWFs), and their distribution amplitudes (DAs). The B meson LCWFs can be treated by taking the heavy quark limit (mbm_b\to\infty) and by using the heavy quark effective theory. Furthermore, we propose a simple model for the B meson WFs with 3-particle Fock states' contributions, whose behaviors are controlled by two parameters Λˉ\bar\Lambda and δ\delta. Using such model, the form factors F+,0,TBπF^{B\to\pi}_{+,0,T} and F+,0,TBKF^{B\to K}_{+,0,T} in large recoil region are studied up to O(1/mb2){\cal O}(1/m_b^2) within the kTk_T factorization approach. On the other hand, we adopt Brodsky-Huang-Lepage (BHL) prescription for constructing the WFs of the lighter pseudoscalars as ηc\eta_c, D-meson, pion, kaon, η()\eta^{(\prime)} and etc. Such BHL-like model can be conveniently extended to construct the LCWFs for light scalar or vector mesons. Within such model the longitudinal distributions of those WFs are basically determined by a parameter BB, whose value can be determined via a global fit of experimental data.Comment: 15 pages, 12 figures. References updated. To be published in Chinese Science Bulleti

    Pion Electromagnetic Form Factor in the KTK_T Factorization Formulae

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    Based on the light-cone (LC) framework and the kTk_T factorization formalism, the transverse momentum effects and the different helicity components' contributions to the pion form factor Fπ(Q2)F_{\pi}(Q^2) are recalculated. In particular, the contribution to the pion form factor from the higher helicity components (λ1+λ2=±1\lambda_1+\lambda_2=\pm 1), which come from the spin-space Wigner rotation, are analyzed in the soft and hard energy regions respectively. Our results show that the right power behavior of the hard contribution from the higher helicity components can only be obtained by fully keeping the kTk_T dependence in the hard amplitude, and that the kTk_T dependence in LC wavefunction affects the hard and soft contributions substantially. A model for the twist-3 wavefunction ψp(x,k)\psi_p(x,\mathbf{k_\perp}) of the pion has been constructed based on the moment calculation by applying the QCD sum rules, whose distribution amplitude has a better end-point behavior than that of the asymptotic one. With this model wavefunction, the twist-3 contributions including both the usual helicity components (λ1+λ2=0\lambda_1+\lambda_2=0) and the higher helicity components (λ1+λ2=±1\lambda_1+\lambda_2=\pm 1) to the pion form factor have been studied within the modified pQCD approach. Our results show that the twist-3 contribution drops fast and it becomes less than the twist-2 contribution at Q210GeV2Q^2\sim 10GeV^2. The higher helicity components in the twist-3 wavefunction will give an extra suppression to the pion form factor. When all the power contributions, which include higher order in αs\alpha_s, higher helicities, higher twists in DA and etc., have been taken into account, it is expected that the hard contributions will fit the present experimental data well at the energy region where pQCD is applicable.Comment: 4 pages, 2 figures, Prepared for International Conference on QCD and Hadronic Physics, Beijing, China, 16-20 June 200

    A Trick to Improve the Efficiency of Generating Unweighted BcB_c Events from BCVEGPY

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    In the present paper, we provide an addendum to improve the efficiency of generating unweighted events within PYTHIA environment for the generator BCVEGPY2.1 [C.H. Chang, J.X. Wang and X.G. Wu, Comput.Phys.Commun.{\bf 174}, 241(2006)]. This trick is helpful for experimental simulation. Moreover, the BCVEGPY output has also been improved, i.e. one Les Houches Event common block has been added so as to generate a standard Les Houches Event file that contains the information of the generated BcB_c meson and the accompanying partons, which can be more conveniently used for further simulation.Comment: 4 pages, 2 figures. To be published in Computer Physics Communication

    Spectral-graph Based Classifications: Linear Regression for Classification and Normalized Radial Basis Function Network

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    Spectral graph theory has been widely applied in unsupervised and semi-supervised learning. In this paper, we find for the first time, to our knowledge, that it also plays a concrete role in supervised classification. It turns out that two classifiers are inherently related to the theory: linear regression for classification (LRC) and normalized radial basis function network (nRBFN), corresponding to linear and nonlinear kernel respectively. The spectral graph theory provides us with a new insight into a fundamental aspect of classification: the tradeoff between fitting error and overfitting risk. With the theory, ideal working conditions for LRC and nRBFN are presented, which ensure not only zero fitting error but also low overfitting risk. For quantitative analysis, two concepts, the fitting error and the spectral risk (indicating overfitting), have been defined. Their bounds for nRBFN and LRC are derived. A special result shows that the spectral risk of nRBFN is lower bounded by the number of classes and upper bounded by the size of radial basis. When the conditions are not met exactly, the classifiers will pursue the minimum fitting error, running into the risk of overfitting. It turns out that 2\ell_2-norm regularization can be applied to control overfitting. Its effect is explored under the spectral context. It is found that the two terms in the 2\ell_2-regularized objective are one-one correspondent to the fitting error and the spectral risk, revealing a tradeoff between the two quantities. Concerning practical performance, we devise a basis selection strategy to address the main problem hindering the applications of (n)RBFN. With the strategy, nRBFN is easy to implement yet flexible. Experiments on 14 benchmark data sets show the performance of nRBFN is comparable to that of SVM, whereas the parameter tuning of nRBFN is much easier, leading to reduction of model selection time
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