94,609 research outputs found
Blaschke's problem for timelike surfaces in pseudo-Riemannian space forms
We show that isothermic surfaces and S-Willmore surfaces are also the
solutions to the corresponding Blaschke's problem for both spacelike and
timelike surfaces in pseudo-Riemannian space forms. For timelike surfaces both
Willmore and isothermic, we obtain a description by minimal surfaces similar to
the classical results of Thomsen.Comment: 10 page
A Note on Pretzelosity TMD Parton Distribution
We show that the transverse-momentum-dependent parton distribution, called as
Pretzelosity function, is zero at any order in perturbation theory of QCD for a
single massless quark state. This implies that Pretzelosity function is not
factorized with the collinear transversity parton distribution at twist-2, when
the struck quark has a large transverse momentum. Pretzelosity function is in
fact related to collinear parton distributions defined with twist-4 operators.
In reality, Pretzelosity function of a hadron as a bound state of quarks and
gluons is not zero. Through an explicit calculation of Pretzelosity function of
a quark combined with a gluon nonzero result is found.Comment: improved explanation, published version in Phys. Lett.
Transverse Momentum Dependent Factorization for Quarkonium Production at Low Transverse Momentum
Quarkonium production in hadron collisions at low transverse momentum
with as the quarkonium mass can be used for probing
transverse momentum dependent (TMD) gluon distributions. For this purpose, one
needs to establish the TMD factorization for the process. We examine the
factorization at the one-loop level for the production of or .
The perturbative coefficient in the factorization is determined at one-loop
accuracy. Comparing the factorization derived at tree level and that beyond the
tree level, a soft factor is, in general, needed to completely cancel soft
divergences. We have also discussed possible complications of TMD factorization
of p-wave quarkonium production.Comment: Title changed in the journal, published versio
Breakdown of QCD Factorization for P-Wave Quarkonium Production at Low Transverse Momentum
Quarkonium production at low transverse momentum in hadron collisions can be
used to extract Transverse-Momentum-Dependent(TMD) gluon distribution
functions, if TMD factorization holds there. We show that TMD factorization for
the case of P-wave quarkonium with holds at one-loop
level, but is violated beyond one-loop level. TMD factorization for other
P-wave quarkonium is also violated already at one-loop.Comment: Published version in Physics Letters B (2014), pp. 103-10
Extension of Hereditary Symmetry Operators
Two models of candidates for hereditary symmetry operators are proposed and
thus many nonlinear systems of evolution equations possessing infinitely many
commutative symmetries may be generated. Some concrete structures of hereditary
symmetry operators are carefully analyzed on the base of the resulting general
conditions and several corresponding nonlinear systems are explicitly given out
as illustrative examples.Comment: 13 pages, LaTe
A refined invariant subspace method and applications to evolution equations
The invariant subspace method is refined to present more unity and more
diversity of exact solutions to evolution equations. The key idea is to take
subspaces of solutions to linear ordinary differential equations as invariant
subspaces that evolution equations admit. A two-component nonlinear system of
dissipative equations was analyzed to shed light on the resulting theory, and
two concrete examples are given to find invariant subspaces associated with
2nd-order and 3rd-order linear ordinary differential equations and their
corresponding exact solutions with generalized separated variables.Comment: 16 page
Time-Dependent Symmetries of Variable-Coefficient Evolution Equations and Graded Lie Algebras
Polynomial-in-time dependent symmetries are analysed for polynomial-in-time
dependent evolution equations. Graded Lie algebras, especially Virasoro
algebras, are used to construct nonlinear variable-coefficient evolution
equations, both in 1+1 dimensions and in 2+1 dimensions, which possess
higher-degree polynomial-in-time dependent symmetries. The theory also provides
a kind of new realisation of graded Lie algebras. Some illustrative examples
are given.Comment: 11 pages, latex, to appear in J. Phys. A: Math. Ge
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