14,333 research outputs found
Angular Momentum of a Brane-world Model
In this paper we discuss the properties of the general covariant angular
momentum of a five-dimensional brane-world model. Through calculating the total
angular momentum of this model, we are able to analyze the properties of the
total angular momentum in the inflationary RS model. We show that the
space-like components of the total angular momentum of are all zero while the
others are non-zero, which agrees with the results from ordinary RS model.Comment: 8 pages; accepted by Chinese Physics
Angular Momentum Conservation Law for Randall-Sundrum Models
In Randall-Sundrum models, by the use of general Noether theorem, the
covariant angular momentum conservation law is obtained with the respect to the
local Lorentz transformations. The angular momentum current has also
superpotential and is therefore identically conserved. The space-like
components of the angular momentum for Randall-Sundrum models are
zero. But the component is infinite.Comment: 10 pages, no figures, accepted by Mod. Phys. Lett.
Optimal time decay of the non cut-off Boltzmann equation in the whole space
In this paper we study the large-time behavior of perturbative classical
solutions to the hard and soft potential Boltzmann equation without the angular
cut-off assumption in the whole space \threed_x with \DgE. We use the
existence theory of global in time nearby Maxwellian solutions from
\cite{gsNonCutA,gsNonCut0}. It has been a longstanding open problem to
determine the large time decay rates for the soft potential Boltzmann equation
in the whole space, with or without the angular cut-off assumption
\cite{MR677262,MR2847536}. For perturbative initial data, we prove that
solutions converge to the global Maxwellian with the optimal large-time decay
rate of O(t^{-\frac{\Ndim}{2}+\frac{\Ndim}{2r}}) in the
L^2_\vel(L^r_x)-norm for any .Comment: 31 pages, final version to appear in KR
Energy-momentum for Randall-Sundrum models
We investigate the conservation law of energy-momentum for Randall-Sundrum
models by the general displacement transform. The energy-momentum current has a
superpotential and are therefore identically conserved. It is shown that for
Randall-Sundrum solution, the momentum vanishes and most of the bulk energy is
localized near the Planck brane. The energy density is .Comment: 13 pages, no figures, v4: introduction and new conclusion added, v5:
11 pages, title changed and references added, accepted by Mod. Phys. Lett.
Localization of fermionic fields on braneworlds with bulk tachyon matter
Recently, Pal and Skar in [arXiv:hep-th/0701266] proposed a mechanism to
arise the warped braneworld models from bulk tachyon matter, which are endowed
with a thin brane and a thick brane. In this framework, we investigate
localization of fermionic fields on these branes. As in the 1/2 spin case, the
field can be localized on both the thin and thick branes with inclusion of
scalar background. In the 3/2 spin extension, the general supergravity action
coupled to chiral supermultiplets is considered to produce the localization on
both the branes as a result.Comment: 9 pages, no figure
Exploiting the Composite Step Strategy to the BiconjugateA-Orthogonal Residual Method for Non-Hermitian Linear Systems
The Biconjugate A-Orthogonal Residual (BiCOR) method carried out in finite precision arithmetic by means of the biconjugate A-orthonormalization procedure may possibly tend to suffer from two sources of numerical instability, known as two kinds of breakdowns, similarly to those of the Biconjugate Gradient (BCG) method. This paper naturally exploits the composite step strategy employed in the development of the composite step BCG (CSBCG) method into the BiCOR method to cure one of the breakdowns called as pivot breakdown. Analogously to the CSBCG method, the resulting interesting variant, with only a minor modification to the usual implementation of the BiCOR method, is able to avoid near pivot breakdowns and compute all the well-defined BiCOR iterates stably on the assumption that the underlying biconjugate A-orthonormalization procedure does not break down. Another benefit acquired is that it seems to be a viable algorithm providing some further practically desired smoothing of the convergence history of the norm of the residuals, which is justified by numerical experiments. In addition, the exhibited method inherits the promising advantages of the empirically observed stability and fast convergence rate of the BiCOR method over the BCG method so that it outperforms the CSBCG method to some extent
Quantum divide-and-conquer anchoring for separable non-negative matrix factorization
© 2018 International Joint Conferences on Artificial Intelligence. All right reserved. It is NP-complete to find non-negative factors W and H with fixed rank r from a non-negative matrix X by minimizing ||X − WHτ||2F. Although the separability assumption (all data points are in the conical hull of the extreme rows) enables polynomial-time algorithms, the computational cost is not affordable for big data. This paper investigates how the power of quantum computation can be capitalized to solve the non-negative matrix factorization with the separability assumption (SNMF) by devising a quantum algorithm based on the divide-and-conquer anchoring (DCA) scheme [Zhou et al., 2013]. The design of quantum DCA (QDCA) is challenging. In the divide step, the random projections in DCA is completed by a quantum algorithm for linear operations, which achieves the exponential speedup. We then devise a heuristic post-selection procedure which extracts the information of anchors stored in the quantum states efficiently. Under a plausible assumption, QDCA performs efficiently, achieves the quantum speedup, and is beneficial for high dimensional problems
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