共查询到20条相似文献,搜索用时 31 毫秒
1.
G. F. Hassan 《Mathematical Methods in the Applied Sciences》2012,35(3):286-292
The purpose of this paper is to generalize some theorems on the representation of certain classes of the entire special monogenic functions by inverse and product bases of special monogenic polynomials. We derive bounds for the order of inverse and product bases. Some examples are given showing that the resulting bounds are attainable. Our results improve and generalize some known results in Clifford setting concerning the order of inverse and product bases. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
2.
In this paper, we show that quantum twist maps, introduced by Lenagan-Yakimov, induce bijections between dual canonical bases of quantum nilpotent subalgebras. As a corollary, we show the unitriangular property between dual canonical bases and Poincaré-Birkhoff-Witt type bases under the “reverse” lexicographic order. We also show that quantum twist maps induce bijections between certain unipotent quantum minors. 相似文献
3.
XU Yuesheng & ZOU Qingsong Department of Mathematics Syracuse University Syracuse NY USA Institute of Mathematics Academy of Mathematics System Sciences Chinese Academy of Sciences Beijing China Department of Scientific Computing Computer Science Zhongshan University Guangzhou China 《中国科学A辑(英文版)》2005,48(5):680-702
We construct a tree wavelet approximation by using a constructive greedy scheme (CGS). We define a function class which contains the functions whose piecewise polynomial approximations generated by the CGS have a prescribed global convergence rate and establish embedding properties of this class. We provide sufficient conditions on a tree index set and on bi-orthogonal wavelet bases which ensure optimal order of convergence for the wavelet approximations encoded on the tree index set using the bi-orthogonal wavelet bases. We then show that if we use the tree index set associated with the partition generated by the CGS to encode a wavelet approximation, it gives optimal order of convergence. 相似文献
4.
In prior work [7] we considered networks of agents who have knowledge bases in first order logic, and report facts to their neighbors that are in their common languages and are provable from their knowledge bases, in order to help a decider verify a single sentence. In report complete networks, the signatures of the agents and the links between agents are rich enough to verify any decider?s sentence that can be proved from the combined knowledge base. This paper introduces a more general setting where new observations may be added to knowledge bases and the decider must choose a sentence from a set of alternatives. We consider the question of when it is possible to prepare in advance a finite plan to generate reports within the network. We obtain conditions under which such a plan exists and is guaranteed to produce the right choice under any new observations. 相似文献
5.
In this paper we apply linear control theory to study the effect of various inventory policies on order and inventory variability, which are key drivers of supply chain performance. In particular, we study a two-echelon supply chain with a stationary demand pattern under the influence of three inventory policies: an inventory-on-hand policy that bases orders on the visible inventory at an installation, an installation-stock policy that bases orders on the inventory position (on-hand plus on-order inventory) at an installation, and an echelon-stock policy that bases orders on the inventory position at that installation and all downstream installations. We prove analytically that the inventory-on-hand policy is unstable in practical settings, confirming analytically what has been observed in experimental settings and in practice. We also prove that the installation-stock and echelon-stock policies are stable and analyze their effect on order and inventory fluctuation. Specifically, we show the general superiority of the echelon-stock in our setting and demonstrate analytically the effect of forecasting parameters on order and inventory fluctuations, confirming the results in other research. 相似文献
6.
We formulate and prove a criterion of the equivalence of functional bases of differential invariants of an arbitrary finite
order k for nonconjugate subgroups of the local Lie groups of point transformations. 相似文献
7.
8.
Eugenio Hern��ndez Jos�� Mar��a Martell Maria de Natividade 《Constructive Approximation》2011,33(1):1-14
We study the efficiency of the greedy algorithm for wavelet bases in Lorentz spaces in order to give the near best approximation.
The result is used to give sharp inclusions for the approximation spaces in terms of discrete Lorentz sequence spaces. 相似文献
9.
Molly Maxwell 《Journal of Combinatorial Theory, Series A》2009,116(2):351-378
We define involutively self-dual matroids and prove that an enumerator for their bases is the square of a related enumerator for their self-dual bases. This leads to a new proof of Tutte's theorem that the number of spanning trees of a central reflex is a perfect square, and it solves a problem posed by Kalai about higher dimensional spanning trees in simplicial complexes. We also give a weighted version of the latter result.We give an algebraic analogue relating to the critical group of a graph, a finite abelian group whose order is the number of spanning trees of the graph. We prove that the critical group of a central reflex is a direct sum of two copies of an abelian group, and conclude with an analogous result in Kalai's setting. 相似文献
10.
Ingrid Daubechies 《纯数学与应用数学通讯》1988,41(7):909-996
We construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity. The order of regularity increases linearly with the support width. We start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction. The construction then follows from a synthesis of these different approaches. 相似文献
11.
We consider biquadratic number fields whose maximal orders have power integral bases consisting of units. We prove an effective
and efficient criteria to decide whether the maximal order of a biquadratic field has a unit power integral basis or not.
In particular we can determine all trivial biquadratic fields whose maximal orders have a unit power integral basis. 相似文献
12.
We describe (reduced) Gröbner bases of the ideal of polynomials over a field, which vanish on the set of characterisic vectors of the complete unifom families
. An interesting feature of the results is that they are largely independent of the monomial order selected. The bases depend only on the ordering of the variables. We can thus use past results related to the lex order in the presence of degree-compatible orders, such as deglex. As applications, we give simple proofs of some known results on incidence matrices. 相似文献
13.
Insa and Pauer presented a basic theory of Grbner bases for differential operators with coefficients in a commutative ring and an improved version of this result was given by Ma et al.In this paper,we present an algorithmic approach for computing Grbner bases in difference-differential modules with coefficients in a commutative ring.We combine the generalized term order method of Zhou and Winkler with SPoly method of Insa and Pauer to deal with the problem.Our result is a generalization of theories of Insa and Pauer,Ma et al.,Zhou and Winkler and includes them as special cases. 相似文献
14.
引入偏序半群左基的的概念,给出了一个偏序半群左基的存在性与极大左理想之间的关系。最后还讨论了在什么情况下左基的存在能导出基的存在性。作为应用,本文中所有结论在一靓半群中均成立。 相似文献
15.
Patrick M. Gilmer Gregor Masbaum 《Annales Scientifiques de l'école Normale Supérieure》2007,40(5):815-844
We find explicit bases for naturally defined lattices over a ring of algebraic integers in the SO(3)-TQFT-modules of surfaces at roots of unity of odd prime order. Some applications relating quantum invariants to classical 3-manifold topology are given. 相似文献
16.
The paper is concerned with a construction of new spline-wavelet bases on the interval. The resulting bases generate multiresolution
analyses on the unit interval with the desired number of vanishing wavelet moments for primal and dual wavelets. Both primal
and dual wavelets have compact support. Inner wavelets are translated and dilated versions of well-known wavelets designed
by Cohen, Daubechies, and Feauveau. Our objective is to construct interval spline-wavelet bases with the condition number
which is close to the condition number of the spline wavelet bases on the real line, especially in the case of the cubic spline
wavelets. We show that the constructed set of functions is indeed a Riesz basis for the space L
2 ([0, 1]) and for the Sobolev space H
s
([0, 1]) for a certain range of s. Then we adapt the primal bases to the homogeneous Dirichlet boundary conditions of the first order and the dual bases to
the complementary boundary conditions. Quantitative properties of the constructed bases are presented. Finally, we compare
the efficiency of an adaptive wavelet scheme for several spline-wavelet bases and we show a superiority of our construction.
Numerical examples are presented for the one-dimensional and two-dimensional Poisson equations where the solution has steep
gradients. 相似文献
17.
Summary. Macro-elements of arbitrary smoothness are constructed on Clough-Tocher triangle splits. These elements can be used for solving
boundary-value problems or for interpolation of Hermite data, and are shown to be optimal with respect to spline degree. We
conjecture they are also optimal with respect to the number of degrees of freedom. The construction provides local bases for
certain superspline spaces defined over Clough-Tocher refinements of arbitrary triangulations. These bases are shown to be
stable as a function of the smallest angle in the triangulation, which in turn implies that the associated spline spaces have
optimal order approximation power.
Received November 18, 1999 / Published online October 16, 2000 相似文献
18.
Mortar methods with dual Lagrange multiplier bases provide a flexible, efficient and optimal way to couple different discretization
schemes or nonmatching triangulations. Here, we generalize the concept of dual Lagrange multiplier bases by relaxing the condition
that the trace space of the approximation space at the slave side with zero boundary condition on the interface and the Lagrange
multiplier space have the same dimension. We provide a new theoretical framework within this relaxed setting, which opens
a new and simpler way to construct dual Lagrange multiplier bases for higher order finite element spaces. As examples, we
consider quadratic and cubic tetrahedral elements and quadratic serendipity hexahedral elements. Numerical results illustrate
the performance of our approach.
This work was supported in part by the Deutsche Forschungsgemeinschaft, SFB 404, C12, the Netherlands Organization for Scientific
Research and by the European Community's Human Potential Programme under contract HPRN-CT-2002-00286. 相似文献
19.
In computer aided geometric design (CAGD), Bézier-like bases receive more and more considerations as new modeling tools in
recent years. But those existing Bézier-like bases are all defined over the rectangular domain. In this paper, we extend the
algebraic trigonometric Bézier-like basis of order 4 to the triangular domain. The new basis functions defined over the triangular
domain are proved to fulfill non-negativity, partition of unity, symmetry, boundary representation, linear independence and
so on. We also prove some properties of the corresponding Bézier-like surfaces. Finally, some applications of the proposed
basis are shown. 相似文献
20.
The main goal of this paper is to understand which properties of a basis are important for certain direct and inverse theorems
in nonlinear approximation. We study greedy approximation with regard to bases with different properties. We consider bases
that are tensor products of univariate greedy bases. Some results known for unconditional bases are extended to the case of
quasi-greedy bases. 相似文献