962 research outputs found
A map on the space of rational functions
We describe dynamical properties of a map defined on the space
of rational functions. The fixed points of are classified and
the long time behavior of a subclass is described in terms of Eulerian
polynomials
Lambda Polarization in Polarized Proton-Proton Collisions at RHIC
We discuss Lambda polarization in semi-inclusive proton-proton collisions,
with one of the protons longitudinally polarized. The hyperfine interaction
responsible for the - and - mass splittings gives
rise to flavor asymmetric fragmentation functions and to sizable polarized
non-strange fragmentation functions. We predict large positive Lambda
polarization in polarized proton-proton collisions at large rapidities of the
produced Lambda, while other models, based on SU(3) flavor symmetric
fragmentation functions, predict zero or negative Lambda polarization. The
effect of and decays is also discussed. Forthcoming
experiments at RHIC will be able to differentiate between these predictions.Comment: 18 pages, 5 figure
Game saturation of intersecting families
We consider the following combinatorial game: two players, Fast and Slow,
claim -element subsets of alternately, one at each turn,
such that both players are allowed to pick sets that intersect all previously
claimed subsets. The game ends when there does not exist any unclaimed
-subset that meets all already claimed sets. The score of the game is the
number of sets claimed by the two players, the aim of Fast is to keep the score
as low as possible, while the aim of Slow is to postpone the game's end as long
as possible. The game saturation number is the score of the game when both
players play according to an optimal strategy. To be precise we have to
distinguish two cases depending on which player takes the first move. Let
and denote the score of
the saturation game when both players play according to an optimal strategy and
the game starts with Fast's or Slow's move, respectively. We prove that
holds
Upper and Lower Bounds for Weak Backdoor Set Detection
We obtain upper and lower bounds for running times of exponential time
algorithms for the detection of weak backdoor sets of 3CNF formulas,
considering various base classes. These results include (omitting polynomial
factors), (i) a 4.54^k algorithm to detect whether there is a weak backdoor set
of at most k variables into the class of Horn formulas; (ii) a 2.27^k algorithm
to detect whether there is a weak backdoor set of at most k variables into the
class of Krom formulas. These bounds improve an earlier known bound of 6^k. We
also prove a 2^k lower bound for these problems, subject to the Strong
Exponential Time Hypothesis.Comment: A short version will appear in the proceedings of the 16th
International Conference on Theory and Applications of Satisfiability Testin
An Algorithm for Dualization in Products of Lattices and Its Applications
Let \cL=\cL_1×⋅s×\cL_n be the product of n lattices, each of which has a bounded width. Given a subset \cA\subseteq\cL, we show that the problem of extending a given partial list of maximal independent elements of \cA in \cL can be solved in quasi-polynomial time. This result implies, in particular, that the problem of generating all minimal infrequent elements for a database with semi-lattice attributes, and the problem of generating all maximal boxes that contain at most a specified number of points from a given n-dimensional point set, can both be solved in incremental quasi-polynomial time
Systems of Linear Equations over and Problems Parameterized Above Average
In the problem Max Lin, we are given a system of linear equations
with variables over in which each equation is assigned a
positive weight and we wish to find an assignment of values to the variables
that maximizes the excess, which is the total weight of satisfied equations
minus the total weight of falsified equations. Using an algebraic approach, we
obtain a lower bound for the maximum excess.
Max Lin Above Average (Max Lin AA) is a parameterized version of Max Lin
introduced by Mahajan et al. (Proc. IWPEC'06 and J. Comput. Syst. Sci. 75,
2009). In Max Lin AA all weights are integral and we are to decide whether the
maximum excess is at least , where is the parameter.
It is not hard to see that we may assume that no two equations in have
the same left-hand side and . Using our maximum excess results,
we prove that, under these assumptions, Max Lin AA is fixed-parameter tractable
for a wide special case: for an arbitrary fixed function
.
Max -Lin AA is a special case of Max Lin AA, where each equation has at
most variables. In Max Exact -SAT AA we are given a multiset of
clauses on variables such that each clause has variables and asked
whether there is a truth assignment to the variables that satisfies at
least clauses. Using our maximum excess results, we
prove that for each fixed , Max -Lin AA and Max Exact -SAT AA can
be solved in time This improves
-time algorithms for the two problems obtained by Gutin et
al. (IWPEC 2009) and Alon et al. (SODA 2010), respectively
Charge symmetry violation in the parton distributions of the nucleon
We point out that charge symmetry violation in both the valence and sea quark
distributions of the nucleon has a non-perturbative source. We calculate this
non-perturbative charge symmetry violation using the meson cloud model, which
has earlier been successfully applied to both the study of SU(2) flavour
asymmetry in the nucleon sea and quark-antiquark asymmetry in the nucleon. We
find that the charge symmetry violation in the valence quark distribution is
well below 1%, which is consistent with most low energy tests but significantly
smaller than the quark model prediction about 5%-10%. Our prediction for the
charge symmetry violation in the sea quark distribution is also much smaller
than the quark model calculation.Comment: RevTex, 26 pages, 6 PostScript figure
Baryon Magnetic Moments and Proton Spin: A Model with Collective Quark Rotation
We analyse the baryon magnetic moments in a model that relates them to the
parton spins , , , and includes a contribution
from orbital angular momentum. The specific assumption is the existence of a
3-quark correlation (such as a flux string) that rotates with angular momentum
around the proton spin axis. A fit to the baryon magnetic
moments, constrained by the measured values of the axial vector coupling
constants , , yields , , where the error is a theoretical
estimate. A second fit, under slightly different assumptions, gives , with no constraint on . The
model provides a consistent description of axial vector couplings, magnetic
moments and the quark polarization measured in deep
inelastic scattering. The fits suggest that a significant part of the angular
momentum of the proton may reside in a collective rotation of the constituent
quarks.Comment: 16 pages, 3 ps-figures, uses RevTeX. Abstract, Sec. II, III and IV
have been expande
Second moment of the Husimi distribution as a measure of complexity of quantum states
We propose the second moment of the Husimi distribution as a measure of
complexity of quantum states. The inverse of this quantity represents the
effective volume in phase space occupied by the Husimi distribution, and has a
good correspondence with chaoticity of classical system. Its properties are
similar to the classical entropy proposed by Wehrl, but it is much easier to
calculate numerically. We calculate this quantity in the quartic oscillator
model, and show that it works well as a measure of chaoticity of quantum
states.Comment: 25 pages, 10 figures. to appear in PR
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