2,116 research outputs found
High-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamics
This paper develops the high-order accurate entropy stable finite difference
schemes for one- and two-dimensional special relativistic hydrodynamic
equations. The schemes are built on the entropy conservative flux and the
weighted essentially non-oscillatory (WENO) technique as well as explicit
Runge-Kutta time discretization. The key is to technically construct the
affordable entropy conservative flux of the semi-discrete second-order accurate
entropy conservative schemes satisfying the semi-discrete entropy equality for
the found convex entropy pair. As soon as the entropy conservative flux is
derived, the dissipation term can be added to give the semi-discrete entropy
stable schemes satisfying the semi-discrete entropy inequality with the given
convex entropy function. The WENO reconstruction for the scaled entropy
variables and the high-order explicit Runge-Kutta time discretization are
implemented to obtain the fully-discrete high-order schemes. Several numerical
tests are conducted to validate the accuracy and the ability to capture
discontinuities of our entropy stable schemes.Comment: 26 pages, 14 figure
Convex-constrained Sparse Additive Modeling and Its Extensions
Sparse additive modeling is a class of effective methods for performing
high-dimensional nonparametric regression. In this work we show how shape
constraints such as convexity/concavity and their extensions, can be integrated
into additive models. The proposed sparse difference of convex additive models
(SDCAM) can estimate most continuous functions without any a priori smoothness
assumption. Motivated by a characterization of difference of convex functions,
our method incorporates a natural regularization functional to avoid
overfitting and to reduce model complexity. Computationally, we develop an
efficient backfitting algorithm with linear per-iteration complexity.
Experiments on both synthetic and real data verify that our method is
competitive against state-of-the-art sparse additive models, with improved
performance in most scenarios.Comment: 17 pages, 2 figure
The rate of increase of mean values of functions in weighted Hardy spaces
Let and . For each in the weighted Hardy
space ,\ we show that grows at most like
as .Comment: 5 pages, accepted for publication in Acta Mathematica Vietnamic
Norm-attaining integral operators on analytic function spaces
Any bounded analytic function induces a bounded integral operator
on the Bloch space, the Dirichlet space and respectively. attains
its norm on the Bloch space and for any , but does not attain its
norm on the Dirichlet space for non-constant . Some results are also
obtained for on the little Bloch space, and for another integral operator
from the Dirichlet space to the Bergman space.Comment: 9 page
Analytic version of critical spaces and their properties
In this paper, we establish an analytic version of critical spaces
on unit disc , denoted by
. Further we prove a relation between
and Morrey spaces. By the boundedness of two
integral operators, we give the multiplier spaces of
Strict singularity of Volterra type operators on Hardy spaces
In this paper, we first characterize the boundedness and compactness of
Volterra type operator defined on Hardy spaces . The spectrum of
is also obtained. Then we prove that fixes an isomorphic copy of
and an isomorphic copy of if the operator is not
compact on . In particular, this implies that the strict
singularity of the operator coincides with the compactness of the
operator on . At last, we post an open question for further study.Comment: 9 page
Embedding theorem for Dirichlet type spaces
Using Carleson measure theorem of weighted Bergman spaces, we provide a
complete characterization of embedding theorem for Dirichlet type spaces. As an
application, we study the Volterra integral operator and multipliers for
Dirichlet type spaces
Strict singularity of weighted composition operators on derivative Hardy spaces
We prove that the weighted composition operator fixes an
isomorphic copy of if the operator is not compact
on the derivative Hardy space . In particular, this implies that the
strict singularity of the operator coincides with the
compactness of it on . Moreover, when , we characterize the
conditions for those weighted composition operators on
which fix an isomorphic copy of .Comment: 9 page
Group Sparse Additive Models
We consider the problem of sparse variable selection in nonparametric
additive models, with the prior knowledge of the structure among the covariates
to encourage those variables within a group to be selected jointly. Previous
works either study the group sparsity in the parametric setting (e.g., group
lasso), or address the problem in the non-parametric setting without exploiting
the structural information (e.g., sparse additive models). In this paper, we
present a new method, called group sparse additive models (GroupSpAM), which
can handle group sparsity in additive models. We generalize the l1/l2 norm to
Hilbert spaces as the sparsity-inducing penalty in GroupSpAM. Moreover, we
derive a novel thresholding condition for identifying the functional sparsity
at the group level, and propose an efficient block coordinate descent algorithm
for constructing the estimate. We demonstrate by simulation that GroupSpAM
substantially outperforms the competing methods in terms of support recovery
and prediction accuracy in additive models, and also conduct a comparative
experiment on a real breast cancer dataset.Comment: ICML201
Order boundedness of weighted composition operators on weighted Dirichlet spaces and derivative Hardy spaces
In this paper, we completely characterize the order boundedness of weighted
composition operators between different weighted Dirichlet spaces and different
derivative Hardy spaces.Comment: 9 page
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