6,401 research outputs found

### On the convergence of harmonic Ritz vectors and harmonic Ritz values

We are interested in computing a simple eigenpair $(\lambda,{\bf x})$ of a
large non-Hermitian matrix $A$, by a general harmonic Rayleigh-Ritz projection
method. Given a search subspace $\mathcal{K}$ and a target point $\tau$, we
focus on the convergence of the harmonic Ritz vector $\widetilde{\bf x}$ and
harmonic Ritz value $\widetilde{\lambda}$. 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
$\angle({\bf x},\mathcal{K})\rightarrow 0$. However, this assumption can not be
guaranteed theoretically for a general matrix $A$, and the Rayleigh quotient
matrix can be singular or near singular even if $\tau$ is not close to
$\lambda$. 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 ${\bf x}$ and $\mathcal{K}$ tends to zero and $\tau$ is
satisfied with the so-called {\it uniform separation condition}, the harmonic
Ritz value converges, and the harmonic Ritz vector converges as
$\frac{1}{\lambda-\tau}$ is well separated from other Ritz values of $(A-\tau
I)^{-1}$ in the orthogonal complement of $(A-\tau I)\widetilde{\bf x}$ with
respect to $(A-\tau I)\mathcal{K}$.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

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

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

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 $\Pi$ in
terms of $\nabla \Pi$ in equations, we show that this upper box dimension is at
most $135/104(\approx1.30)$, which improves the known upper box-counting
dimension $95/63(\approx1.51)$ in Koh et al. [9, J. Differential Equations,
261: 3137--3148, 2016], $45/29(\approx1.55)$ in Kukavica et al. [11,
Nonlinearity 25: 2775-2783, 2012] and $135/82(\approx1.65)$ 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

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

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 $L$-functions of certain elliptic curves

### Heavy and light meson wavefunctions

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 ($m_b\to\infty$)
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 $\bar\Lambda$ and $\delta$. Using
such model, the form factors $F^{B\to\pi}_{+,0,T}$ and $F^{B\to K}_{+,0,T}$ in
large recoil region are studied up to ${\cal O}(1/m_b^2)$ within the $k_T$
factorization approach. On the other hand, we adopt Brodsky-Huang-Lepage (BHL)
prescription for constructing the WFs of the lighter pseudoscalars as $\eta_c$,
D-meson, pion, kaon, $\eta^{(\prime)}$ 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 $B$, 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 $K_T$ Factorization Formulae

Based on the light-cone (LC) framework and the $k_T$ factorization formalism,
the transverse momentum effects and the different helicity components'
contributions to the pion form factor $F_{\pi}(Q^2)$ are recalculated. In
particular, the contribution to the pion form factor from the higher helicity
components ($\lambda_1+\lambda_2=\pm 1$), 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 $k_T$
dependence in the hard amplitude, and that the $k_T$ dependence in LC
wavefunction affects the hard and soft contributions substantially. A model for
the twist-3 wavefunction $\psi_p(x,\mathbf{k_\perp})$ 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 ($\lambda_1+\lambda_2=0$) and the
higher helicity components ($\lambda_1+\lambda_2=\pm 1$) 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 $Q^2\sim 10GeV^2$. 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 $\alpha_s$,
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 $B_c$ Events from BCVEGPY

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 $B_c$ 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

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
$\ell_2$-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
$\ell_2$-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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