20,965 research outputs found
Multifractal Analysis of The New Level Sets
By an appropriate definition, we divide the irregular set into level sets.
Then we characterize the multifractal spectrum of these new pieces by
calculating their entropies. We also compute the entropies of various
intersections of the level sets of regular and irregular set which is rarely
studied in the literature. Moreover, our conclusions also hold for the
topological pressure. Finally, we consider the continuous case and use our
results to give a description for the suspension flow
Study of the Spin-weighted Spheroidal Wave Equation in the Case of s=3/2
In this paper, we use the means of super-symmetric quantum mechanics to study
of the Spin-weighted Spheroidal Wave in the case of s=3/2. We obtain some
interesting results: the first-five terms of the super-potential, the general
form of the super-potential. The ground eigen-function and eigenvalue of the
equation are also given. According these results, we make use of the shape
invariance property to compute the exited eigenvalues and eigen-functions.
These results help us to understand the Spin-weighted Spheroidal Wave and show
that it is integral.Comment: arXiv admin note: substantial text overlap with arXiv:1011.257
On a C. de Boor's Conjecture in a Particular Case and Related Perturbation
In this paper, we focus on two classes of D-invariant polynomial subspaces.
The first is a classical type, while the second is a new class. With matrix
computation, we prove that every ideal projector with each D-invariant subspace
belonging to either the first class or the second is the pointwise limit of
Lagrange projectors. This verifies a particular case of a C. de Boor's
conjecture asserting that every complex ideal projector is the pointwise limit
of Lagrange projectors. Specifically, we provide the concrete perturbation
procedure for ideal projectors of this type
On the irregular points for systems with the shadowing property
We prove that when is a continuous selfmap acting on compact metric space
which satisfies the shadowing property, then the set of irregular
points (i.e. points with divergent Birkhoff averages) has full entropy.
Using this fact we prove that in the class of -generic maps on
manifolds, we can only observe (in the sense of Lebesgue measure) points with
convergant Birkhoff averages. In particular, the time average of atomic
measures along orbit of such points converges to some SRB-like measure in the
weak topology. Moreover, such points carry zero entropy. In contrast,
irregular points are non-observable but carry infinite entropy
DNS Study on Vorticity Structures in Late Flow Transition
Vorticity and vortex are two different but related concepts. This paper
focuses on the investigation of vorticity generation and development, and
vorticity structure inside/ outside the vortex. Vortex is a region where the
vorticity overtakes deformation. Vortex cannot be directly represented by the
vorticity. Except for those vorticity lines which come from and end at side
boundaries, another type of vorticity, self-closed vorticity lines named
vorticity rings, is numerously generated inside the domain during flow
transition. These new vorticity rings are found around the hairpin vortex heads
and legs. The generation and growth of vorticity rings are produced by the
buildup of the vortices according to the vorticity transport equation. On the
other hand, vortex buildup is a consequence of vorticity line stretching,
tilting and twisting. Both new vorticity and new vortices are generated during
the flow transition. According to the Helmholtz vorticity flux conservation
law, vorticity line cannot be interrupted, started, or ended inside the flow
field, the newly produced vorticity has only one form which is the vorticity
rings. In addition, an interesting finding is that a single hairpin vortex
consists of several types of vorticity lines which could come from the side
boundaries, whole vorticity rings and part of vorticity rings
The Spin-weighted Spheroidal Wave functions in the Case of s=1/2
The spin-weighted spheroidal equations in the case s=1/2 is thoroughly
studied in the paper by means of the perturbation method in supersymmetry
quantum mechanics. The first-five terms of the super-potential in the series of
the parameter beta are given. The general form of the nth term of the
superpotential is also obtained, which could derived from the previous terms
W_{k}, k<n. From the results, it is easy to give the ground eigenfunction of
the equation. Furthermore, the shape-invariance property is investigated in the
series form of the parameter beta and is proven kept in this series form for
the equations. This nice property guarantee one could obtain the excited
eigenfunctions in the series form from the ground eigenfunctions by the method
in supersymmetry quantum mechanics. This shows the perturbation method method
in supersymmetry quantum mechanics could solve the spin-weight spheroidal wave
equations completely in the series form of the small parameter beta
On existence of certain error formulas for a special class of ideal projectors
In this paper, we focus on a special class of ideal projectors. With the aid
of algebraic geometry, we prove that for this special class of ideal
projectors, there exist "good" error formulas as defined by C. de Boor.
Furthermore, we completely analyze the properties of the interpolation
conditions matched by this special class of ideal projectors, and show that the
ranges of this special class of ideal projectors are the minimal degree
interpolation spaces with regard to their associated interpolation conditions
A Circumbinary Disk Model for the Rapid Orbital Shrinkage in Black Hole Low-Mass X-ray Binaries
Several black hole low-mass X-ray binaries (BHLMXBs) show very fast orbital
shrinkage, which is difficult to understand in the standard picture of the LMXB
evolution. Based on the possible detection of a circumbinary (CB) disk in
A0620-00 and XTE J1118+480, we investigate the influence of the interaction
between a CB disk and the inner binary and calculate the evolution of the
binary using the Modules for Experiments in Stellar Astrophysics. We consider
two cases for the CB disk formation in which it is fed by mass loss during
single outburst or successive outbursts in the LMXB. We show that when taking
reasonable values of the initial mass and the dissipating time of the disk, it
is possible to explain the fast orbital shrinkage in the BHLMXBs without
invoking high mass transfer rate.Comment: 17 pages, 9 figures, accepted by Ap
Finite Sets of Affine Points with Unique Associated Monomial Order Quotient Bases
The quotient bases for zero-dimensional ideals are often of interest in the
investigation of multivariate polynomial interpolation, algebraic coding
theory, and computational molecular biology, etc. In this paper, we discuss the
properties of zero-dimensional ideals with unique monomial quotient bases, and
verify that the vanishing ideals of Cartesian sets have unique monomial
quotient bases. Furthermore, we reveal the relation between Cartesian sets and
the point sets with unique associated monomial quotient bases
A Bivariate Preprocessing Paradigm for Buchberger-M\"oller Algorithm
For the last almost three decades, since the famous Buchberger-M\"oller(BM)
algorithm emerged, there has been wide interest in vanishing ideals of points
and associated interpolation polynomials. Our paradigm is based on the theory
of bivariate polynomial interpolation on cartesian point sets that gives us
related degree reducing interpolation monomial and Newton bases directly. Since
the bases are involved in the computation process as well as contained in the
final output of BM algorithm, our paradigm obviously simplifies the computation
and accelerates the BM process. The experiments show that the paradigm is best
suited for the computation over finite prime fields that have many
applications.Comment: 24 pages, 7 figures, submitted to JCA
- β¦