10,757 research outputs found
Partition theorems and the Chinese remainder theorem
The famous partition theorem of Euler states that partitions of into
distinct parts are equinumerous with partitions of into odd parts. Another
famous partition theorem due to MacMahon states that the number of partitions
of with all parts repeated at least once equals the number of partitions of
where all parts must be even or congruent to . These partition
theorems were further extended by Glaisher, Andrews, Subbarao, Nyirenda and
Mugwangwavari. In this paper, we utilize the Chinese remainder theorem to prove
a comprehensive partition theorem that encompasses all existing partition
theorems. We also give a natural generalization of Euler's theorem based on a
special complete residue system. Furthermore, we establish interesting
congruence connections between the partition function and related
partition functions
Kaon and pion parton distribution amplitudes to twist-three
We compute all kaon and pion parton distribution amplitudes (PDAs) to
twist-three and find that only the pseudotensor PDA can reasonably be
approximated by its conformal limit expression. At terrestrially accessible
energy scales, the twist-two and pseudoscalar twist-three PDAs differ
significantly from those functions commonly associated with their forms in
QCD's conformal limit. In all amplitudes studied, SU(3) flavour-symmetry
breaking is typically a 13% effect. This scale is determined by nonperturbative
dynamics; namely, the current-quark-mass dependence of dynamical chiral
symmetry breaking. The heavier-quark is favoured by this distortion, for
example, support is shifted to the s-quark in the negative kaon. It appears,
therefore, that at energy scales accessible with existing and foreseeable
facilities, one may obtain reliable expectations for experimental outcomes by
using these "strongly dressed" PDAs in formulae for hard exclusive processes.
Following this procedure, any discrepancies between experiment and theory will
be significantly smaller than those produced by using the conformal-limit PDAs.
Moreover, the magnitude of any disagreement will either be a better estimate of
higher-order, higher-twist effects or provide more realistic constraints on the
Standard Model.Comment: 14 pages, 4 figures, 2 tables. arXiv admin note: text overlap with
arXiv:1406.335
Arithmetic Properties of Andrews' Singular Overpartitions
In a very recent work, G. E. Andrews defined the combinatorial objects which
he called {\it singular overpartitions} with the goal of presenting a general
theorem for overpartitions which is analogous to theorems of Rogers--Ramanujan
type for ordinary partitions with restricted successive ranks. As a small part
of his work, Andrews noted two congruences modulo 3 which followed from
elementary generating function manipulations. In this work, we prove that
Andrews' results modulo 3 are two examples of an infinite family of congruences
modulo 3 which hold for that particular function. We also expand the
consideration of such arithmetic properties to other functions which are part
of Andrews' framework for singular overpartitions
Congruences for rs(n)
AbstractLet rs(n) denote the number of representations of n as the sum of s squares of integers. In this note, we determine r2ks(n) modulo 2k+2 for kβ©Ύ1 and s odd. For general s, we also obtain a congruence for rs(n) modulo 2s. These extend Wagstaff's results (J. Number Theory 127 (2007) 326β329)
Semileptonic Decays of Meson to a P-Wave Charmonium State or
The semileptonic decays of meson to a P-wave charmonium state
or are computed. The results show that the decays
are sizable so they are accessible in Tevatron and in LHC, especially, with the
detectors LHCB and BTeV in the foreseeable future, and of them, the one to the
charmonium state potentially offers us a novel window to see the
unconfirmed particle. In addition, it is pointed out that since the two
charmonium radiative decays have sizable
branching ratios, the cascade decays of the concerned decays and the charmonium
radiative decays may affect the result of the observing the meson through
the semileptonic decays substantially.Comment: 8 pages, 2 figure
- β¦