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1.
2.
On <Emphasis Type="Italic">l</Emphasis><Subscript>2,<Emphasis Type="Italic">p</Emphasis></Subscript>-circle numbers 总被引:1,自引:1,他引:0
W.-D. Richter 《Lithuanian Mathematical Journal》2008,48(2):228-234
Circle numbers are defined to reflect the Euclidean area-content and, for p ≠ 2, suitably defined non-Euclidean circumference properties of the l
2,p
-circles, p ∈ [1, ∞]. The resulting function is continuous, increasing, and takes all values from [2, 4].
The actually chosen dual l
2,p
-geometry for measuring the arc-length is closely connected with a generalization of the method of indivisibles of Cavalieri
and Torricelli in the sense that integrating such arc-lengths means measuring area content. Moreover, this approach enables
one to look in a new way into the co-area formula of measure theory which says that integrating Euclidean arc-lengths does
not yield area content except for p = 2.
The new circle numbers play a natural role, e.g., as norming constants in geometric measure representation formulae for p-generalized uniform probability distributions on l
2,p
-circles. 相似文献
3.
Gérard Meurant 《Numerical Algorithms》1997,16(1):77-87
In this paper we consider computing estimates of the norm of the error in the conjugate gradient (CG) algorithm. Formulas
were given in a paper by Golub and Meurant (1997). Here, we first prove that these expressions are indeed upper and lower
bounds for the A-norm of the error. Moreover, starting from these formulas, we investigate the computation of the l
2-norm of the error. Finally, we define an adaptive algorithm where the approximations of the extreme eigenvalues that are
needed to obtain upper bounds are computed when running CG leading to an improvement of the upper bounds for the norm of the
error. Numerical experiments show the effectiveness of this algorithm.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
4.
Andy C. Yau Xuecheng Tai Michael K. Ng 《Computational Optimization and Applications》2011,50(2):425-444
In this paper, we deal with l
0-norm data fitting and total variation regularization for image compression and denoising. The l
0-norm data fitting is used for measuring the number of non-zero wavelet coefficients to be employed to represent an image.
The regularization term given by the total variation is to recover image edges. Due to intensive numerical computation of
using l
0-norm, it is usually approximated by other functions such as the l
1-norm in many image processing applications. The main goal of this paper is to develop a fast and effective algorithm to solve
the l
0-norm data fitting and total variation minimization problem. Our idea is to apply an alternating minimization technique to
solve this problem, and employ a graph-cuts algorithm to solve the subproblem related to the total variation minimization.
Numerical examples in image compression and denoising are given to demonstrate the effectiveness of the proposed algorithm. 相似文献
5.
The main purpose of this paper is to use the strong stability method to approximate the characteristics of the M
2/G
2/1 queue with preemptive priority by those of the classical M/G/1 queue. The latter is simpler and more exploitable in practice. After perturbing the arrival intensity of the priority requests,
we derive the stability conditions and next obtain the stability inequalities with an exact computation of constants. From
those theoretical results, we elaborate an algorithm allowing us to verify the approximation conditions and to provide the
made numerical error. In order to have an idea about the efficiency of this approach, we consider a concrete example whose
results are compared with those obtained by simulation. 相似文献
6.
An additive Schwarz preconditioner for nonconforming mortar finite element discretization of a second order elliptic problem
in two dimensions with arbitrary large jumps of the discontinuous coefficients in subdomains is described.
An almost optimal estimate of the condition number of the preconditioned problem is proved. The number of preconditioned conjugate
gradient iterations is independent of jumps of the coefficients and is proportional to (1+log(H/h)), where H,h are mesh sizes.
AMS subject classification (2000) 65N55, 65N30, 65N22 相似文献
7.
I. A. Al-Subaihi 《Numerical Algorithms》2008,47(1):1-14
There are many applications of fitting circular arcs to data. We have for example, system control, using a computer controlled
cutting machine, approximating hulls of boats, drawing and image techniques. Out of these applications comes the least squares
norm to be the most commonly used criterion. This paper examines how the l
1 norm is used which seems to be more appropriate than the use of least squares in the context of wild points in the data.
An algorithm and different methods to determine the starting points are developed. However, numerical examples are given to
help illustrate these methods.
相似文献
8.
With the objective of generating “shape-preserving” smooth interpolating curves that represent data with abrupt changes in
magnitude and/or knot spacing, we study a class of first-derivative-based -smooth univariate cubic L
1 splines. An L
1 spline minimizes the L
1 norm of the difference between the first-order derivative of the spline and the local divided difference of the data. Calculating
the coefficients of an L
1 spline is a nonsmooth non-linear convex program. Via Fenchel’s conjugate transformation, the geometric dual program is a
smooth convex program with a linear objective function and convex cubic constraints. The dual-to-primal transformation is
accomplished by solving a linear program. 相似文献
9.
By the R-matrix of orthosymplectic quantum superalgebra U
q
(osp(2l+1|2n)) in the vector representation, we establish the corresponding quantum Hopf superalgebra OSP
q
(2l + 1|2n). Furthermore, it is shown that OSP
q
(2l + 1|2n) is coquasitriangular. 相似文献
10.
Pattern formation in associative neural networks is related to a
quadratic optimization problem. Biological considerations imply
that the functional is constrained in the L
\infty norm and in
the L
1 norm. We consider such optimization problems. We derive
the Euler–Lagrange equations, and construct basic properties of
the maximizers. We study in some detail the case where the kernel
of the quadratic functional is finite-dimensional. In this case
the optimization problem can be fully characterized by the
geometry of a certain convex and compact finite-dimensional set. 相似文献
11.
We give a presentation by generators and relations of a certain monoid generating a subgroup of index two in the group Aut(F
2) of automorphisms of the rank two free group F
2 and show that it can be realized as a monoid in the group B
4 of braids on four strings. In the second part we use Christoffel words to construct an explicit basis of F
2 lifting any given basis of the free abelian group Z
2. We further give an algorithm allowing to decide whether two elements of F
2 form a basis or not. We also show that, under suitable conditions, a basis has a unique conjugate consisting of two palindromes.
Mathematics Subject Classification (2000) 05E99, 20E05, 20F28, 20F36, 20M05, 37B10, 68R15 相似文献
12.
Charles Li 《Israel Journal of Mathematics》2009,169(1):341-373
We prove that for a fixed non-archimedean place v of a totally real number field F, the traces of the associated Langlands classes of holomorphic cuspidal representations of GL2(A) with trivial central character and of prime levels is equidistributed with respect to the measure
, where q
v
is the norm of the prime ideal corresponding to v and dμ∞(x)= is the Sato-Tate measure. This generalizes a result of Sarnak [Sa] on the distribution of Hecke eigenvalues of modular forms.
The proof involves establishing a trace formula for the Hecke operators. While not explicit, this trace formula can be used
as a starting point for generalizing the Eichler-Selberg trace formula to totally real number fields. 相似文献
13.
Mikhail Ershov 《Israel Journal of Mathematics》2007,158(1):297-347
Let D be a finite dimensional division algebra over a local field of characteristic p and let SL
1(D) denote the group of elements of reduced norm 1 in D. In this paper we prove that SL
1(D) is finitely presented as a profinite group.
This work is part of the author’s Ph.D. Thesis at Yale University. 相似文献
14.
Matthias Geissert 《Numerische Mathematik》2007,108(1):121-149
In this paper, we present applications of discrete maximal L
p
regularity for finite element operators. More precisely, we show error estimates of order h
2 for linear and certain semilinear problems in various L
p
(Ω)-norms. Discrete maximal regularity allows us to prove error estimates in a very easy and efficient way. Moreover, we also
develop interpolation theory for (fractional powers of) finite element operators and extend the results on discrete maximal
L
p
regularity formerly proved by the author.
The author was supported by the DFG-Graduiertenkolleg 853. 相似文献
15.
W.-D. Richter 《Lithuanian Mathematical Journal》2009,49(1):93-108
For p > 0, the l
n,p
-generalized surface measure on the l
n,p
-unit sphere is studied and used for deriving a geometric measure representation for l
n,p
-symmetric distributions having a density. 相似文献
16.
In 1993, Y. A. Abramovich, C. D. Aliprantis and O. Burkinshaw showed that every continuous operator with modulus on an lp-space (1 ≤ p < ∞) whose modulus commutes with a non-zero positive operator T on lp that is quasinilpotent at a non-zero positive vector x0 has a non-trivial invariant closed subspace. In this paper, it is proved that if
is a collection of continuous operators with moduli on lp that is finitely modulus-quasinilpotent at a non-zero positive vector x
0 then
and its right modulus sub-commutant
have a common non-trivial invariant closed subspace. In particular, all continuous operators with moduli on l
p
whose moduli commute with a non-zero positive operator I on l
p
that is quasinilpotent at a non-zero positive vector x
0 have a common non-trivial invariant closed subspace, so that all positive operators on l
p
which commute with a non-zero positive operator S on l
p
that is quasinilpotent at a non-zero positive vector x
0 have a common non-trivial invariant closed subspace.
This research was supported by the Natural Science Foundation of Hunan Province of P. R. China (04JJ6004), the Foundation
of Education Department of Hunan Province of P. R. China (04C002) and the Natural Science Foundation of P. R. China (10671147).
Received: 4 December 2005 Revised: 19 June 2006 相似文献
17.
Christoph Waldner 《Geometriae Dedicata》2011,151(1):9-25
We study the cohomology of a compact locally symmetric space attached to an arithmetic subgroup of a rational form of a group
of type G
2 with values in a finite dimensional irreducible representation E of G
2. By constructing suitable geometric cycles and parallel sections of the bundle [(E)\tilde]{\tilde{E}} we prove non-vanishing results for this cohomology. We prove all possible non-vanishing results compatible with the known
vanishing theorems regarding unitary representations with non-zero cohomology in the case of the short fundamental weight
of G
2. A decisive tool in our approach is a formula for the intersection numbers with local coefficients of two geometric cycles. 相似文献
18.
Novikov superalgebras are related to quadratic conformal superalgebras which correspond to the Hamiltonian pairs and play
a fundamental role in completely integrable systems. In this note we show that the Novikov superalgebras with A
0 = A
1
A
1 and dim A
1 = 2 are of type N and give a class of Novikov superalgebras of type S with A
0 = A
1
A
1. 相似文献
19.
A. A. Koshelev 《Russian Mathematics (Iz VUZ)》2011,55(6):53-63
We obtain close two-sided estimates for the best approximation of Laplace operator by linear bounded operators on the class
of functions for which the square of the Laplace operator belongs to the L
p
-space. We estimate the best constant in the corresponding Kolmogorov inequality and the error of the optimal recovery of
values of the Laplace operator on functions from this class defined with an error. In a particular case (p = 2) we solve all three problems exactly. 相似文献
20.
We show that for every odd integer p 1 there is an absolute positive
constantcp, so that the maximum cardinality of a set of vectors in Rn
such that the lp distance between
any pair is precisely 1, is at most cp
n log n.
We prove some upper bounds for other lp norms as well. 相似文献