1,454,377 research outputs found
On localization properties of Fourier transforms of hyperfunctions
In [Adv. Math. 196 (2005) 310-345] the author introduced a new generalized
function space which can be naturally interpreted as the
Fourier transform of the space of Sato's hyperfunctions on . It was shown
that all Gelfand--Shilov spaces () of
analytic functionals are canonically embedded in . While the
usual definition of support of a generalized function is inapplicable to
elements of and , their
localization properties can be consistently described using the concept of {\it
carrier cone} introduced by Soloviev [Lett. Math. Phys. 33 (1995) 49-59; Comm.
Math. Phys. 184 (1997) 579-596]. In this paper, the relation between carrier
cones of elements of and is
studied. It is proved that an analytic functional is carried by a cone if and only if its
canonical image in is carried by .Comment: 21 pages, final version, accepted for publication in J. Math. Anal.
App
CSD: Discriminance with Conic Section for Improving Reverse k Nearest Neighbors Queries
The reverse nearest neighbor (RNN) query finds all points that have
the query point as one of their nearest neighbors (NN), where the NN
query finds the closest points to its query point. Based on the
characteristics of conic section, we propose a discriminance, named CSD (Conic
Section Discriminance), to determine points whether belong to the RNN set
without issuing any queries with non-constant computational complexity. By
using CSD, we also implement an efficient RNN algorithm CSD-RNN with a
computational complexity at . The comparative
experiments are conducted between CSD-RNN and other two state-of-the-art
RkNN algorithms, SLICE and VR-RNN. The experimental results indicate that
the efficiency of CSD-RNN is significantly higher than its competitors
from dark matter exchange
Hints of lepton flavor violation have been observed by LHCb in the rate of
the decay relative to that of . This can be
explained by new scalars and fermions which couple to standard model particles
and contribute to these processes at loop level. We explore a simple model of
this kind, in which one of the new fermions is a dark matter candidate, while
the other is a heavy vector-like quark and the scalar is an inert Higgs
doublet. We explore the constraints on this model from flavor observables, dark
matter direct detection, and LHC run II searches, and find that, while
currently viable, this scenario will be directly tested by future results from
all three probes.Comment: 6 pages, 6 figures; v2: added references, changed to Majorana dark
matter, direct detection constraints weakened; v3: added references, lepton
flavor constraints weakened by including crossed box diagrams in fig. 1;
published versio
Some aspects of (r,k)-parking functions
An \emph{-parking function} of length may be defined as a sequence
of positive integers whose increasing rearrangement
satisfies . The case
corresponds to ordinary parking functions. We develop numerous properties of
-parking functions. In particular, if denotes the
Frobenius characteristic of the action of the symmetric group
on the set of all -parking functions of length , then we find a
combinatorial interpretation of the coefficients of the power series for any . When ,
this power series is just ; when , we
obtain a dual to -parking functions. We also give a -analogue of this
result. For fixed , we can use the symmetric functions to
define a multiplicative basis for the ring of symmetric functions. We
investigate some of the properties of this basis
Krivine schemes are optimal
It is shown that for every there exists a Borel probability measure
on such that for every
and there exist
such that if is
a random matrix whose entries are i.i.d. standard Gaussian
random variables then for all we have
\E_G[\int_{{-1,1}^{\R^{k}}\times
{-1,1}^{\R^{k}}}f(Gx_i')g(Gy_j')d\mu(f,g)]=\frac{}{(1+C/k)K_G}, where
is the real Grothendieck constant and is a universal
constant. This establishes that Krivine's rounding method yields an arbitrarily
good approximation of
Efficient Simulation for Branching Linear Recursions
We consider a linear recursion of the form where is a
real-valued random vector with ,
is a sequence of i.i.d. copies of ,
independent of , and denotes
equality in distribution. For suitable vectors and
provided the initial distribution of is well-behaved, the process
is known to converge to the endogenous solution of the corresponding
stochastic fixed-point equation, which appears in the analysis of information
ranking algorithms, e.g., PageRank, and in the complexity analysis of divide
and conquer algorithms, e.g. Quicksort. Naive Monte Carlo simulation of
based on the branching recursion has exponential complexity in ,
and therefore the need for efficient methods. We propose in this paper an
iterative bootstrap algorithm that has linear complexity and can be used to
approximately sample . We show the consistency of estimators based on
our proposed algorithm.Comment: submitted to WSC 201
Implicit-Explicit Runge-Kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit
We consider Implicit-Explicit (IMEX) Runge-Kutta (R-K) schemes for hyperbolic
systems with stiff relaxation in the so-called diffusion limit. In such regime
the system relaxes towards a convection-diffusion equation. The first objective
of the paper is to show that traditional partitioned IMEX R-K schemes will
relax to an explicit scheme for the limit equation with no need of modification
of the original system. Of course the explicit scheme obtained in the limit
suffers from the classical parabolic stability restriction on the time step.
The main goal of the paper is to present an approach, based on IMEX R-K
schemes, that in the diffusion limit relaxes to an IMEX R-K scheme for the
convection-diffusion equation, in which the diffusion is treated implicitly.
This is achieved by an original reformulation of the problem, and subsequent
application of IMEX R-K schemes to it. An analysis on such schemes to the
reformulated problem shows that the schemes reduce to IMEX R-K schemes for the
limit equation, under the same conditions derived for hyperbolic relaxation.
Several numerical examples including neutron transport equations confirm the
theoretical analysis
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