共查询到20条相似文献，搜索用时 15 毫秒
1.
Bui Minh Phong 《Acta Mathematica Hungarica》2006,113(1-2):63-71
Summary We prove that if a complex valued completely multiplicative function F and a positive integer ℓ≦5 satisfy the condition F(N) = Uℓ, where Uℓ is the set of all ℓ-th roots of unity, then {F(n+1) F(n) ∣ nε N} = Uℓ. 相似文献
2.
In this paper, we extend the well-known result of Lipschitz approximation of lower semi-continuous functions to a class of lattice valued vector functions. We then use this approximation to get convergence results and we give two applications to the law of large numbers and to an ergodic theorem. 相似文献
3.
利用有限覆盖定理给出了一个命题的初等证明,而《实变函数论》中的一个重要定理可作为该命题的一个直接推论.由此展现作为基础的实数完备性在实分析中的重要地位,也为《实变函数论》课程的部分内容的教学改革提供一种值得探讨的新思路. 相似文献
4.
Christian Richter 《Mathematische Nachrichten》1999,198(1):179-188
The paper deals with the approximation of bounded real functions f on a compact metric space (X, d) by so-called controllable step functions in continuation of [Ri/Ste]. These step functions are connected with controllable coverings, that are finite coverings of compact metric spaces by subsets whose sizes fulfil a uniformity condition depending on the entropy numbers εn(X) of the space X. We show that a strong form of local finiteness holds for these coverings on compact metric subspaces of IRm and Sm. This leads to a Bernstein type theorem if the space is of finite convex information. In this case the corresponding approximation numbers εn(f) have the same asymptotics its ω(f, εn(X)) for f ε C(X). Finally, the results concerning functions f ε M(X) and f ε C(X) are transferred to operators with values in M(X) and C(X), respectively. 相似文献
5.
In this paper, we study a flexible piecewise approximation technique based on the use of the idea of the partition of unity. The approximations are piecewisely defined, globally smooth up to any order, enjoy polynomial reproducing conditions, and satisfy nodal interpolation conditions for function values and derivatives of any order. We present various properties of the approximations, that are desirable properties for optimal order convergence in solving boundary value problems.
AMS subject classification 65N30, 65D05Weimin Han: Corresponding author. The work of this author was partially supported by NSF under grant DMS-0106781.Wing Kam Liu: The work of this author was supported by NSF. 相似文献
6.
Let be an open set and let denote the class of real analytic functions on . It is proved that for every surjective linear partial differential operator and every family depending holomorphically on there is a solution family depending on in the same way such that The result is a consequence of a characterization of Fréchet spaces such that the class of ``weakly' real analytic -valued functions coincides with the analogous class defined via Taylor series. An example shows that the analogous assertions need not be valid if is replaced by another set.
7.
The truncated hierarchical B-spline basis has been proposed for adaptive data fitting and has already drawn a lot of attention in theory and applications.However the stability with respect to the L_p-norm,1≤p∞,is not clear.In this paper,we consider the L_p stability of the truncated hierarchical B-spline basis,since the L_p stability is useful for curve and surface fitting,especially for least squares fitting.We prove that this basis is weakly L_p stable.This means that the associated constants to be considered in the stability analysis are at most of polynomial growth in the number of the hierarchy depth. 相似文献
8.
研究形如的模糊Volterra积分方程整体解的存在性.这里h,k,g是实值函数,f为强模糊Henstock可积的模糊数值函数.所用的方法和工具是利用模糊数值函数的等度可积性和非紧性测度的性质以及广义Darbo不动点定理. 相似文献
9.
In this paper, a hybrid approximation method on the sphere is analysed. As interpolation scheme, we consider a partition of unity method, such as the modified spherical Shepard method, which uses zonal basis functions plus spherical harmonics as local approximants. The associated algorithm is efficiently implemented and works well also when the amount of data is very large, as it is based on an optimized searching procedure. Locality of the method guarantees stability in numerical computations, and numerical results show good accuracy. Moreover, we aimed to discuss preservation of such features when the method and the related algorithm are applied to experimental data. To achieve this purpose, we considered the Magnetic Field Satellite data. The goal was reached, as efficiency and accuracy are maintained on several sets of real data. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
10.
给出了罗尔微分中值定理的三种新的证明方法,其中第二种很简便的方法仅依赖于大家熟知的Heine-Borel有限覆盖定理.由此可见罗尔微分中值定理可以是实数的完备性的直接推论. 相似文献
11.
Map the vertices of a graph to (not necessarily distinct) points of the plane so that two adjacent vertices are mapped at least unit distance apart. The plane‐width of a graph is the minimum diameter of the image of its vertex set over all such mappings. We establish a relation between the plane‐width of a graph and its chromatic number. We also connect it to other well‐known areas, including the circular chromatic number and the problem of packing unit discs in the plane. © 2011 Wiley Periodicals, Inc. J Graph Theory 68: 229‐245, 2011 相似文献
12.
We consider here the morphogenesis (pattern formation) problem for some genetic network models. First, we show that any given spatio‐temporal pattern can be generated by a genetic network involving a sufficiently large number of genes. Moreover, patterning process can be performed by an effective algorithm. We also show that Turing's or Meinhardt's type reaction–diffusion models can be approximated by genetic networks. These results exploit the fundamental fact that the genes form functional units and are organized in blocks. Due to this modular organization, the genes always are capable to construct any new patterns and even any time sequences of new patterns from old patterns. Computer simulations illustrate some analytical results. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
13.
We introduce and study certain classes of optimization problems over the real numbers. The classes are defined by logical means, relying on metafinite model theory for so called R‐structures (see [12, 11]). More precisely, based on a real analogue of Fagin's theorem [12] we deal with two classes MAX‐NPR and MIN‐NPR of maximization and minimization problems, respectively, and figure out their intrinsic logical structure. It is proven that MAX‐NPR decomposes into four natural subclasses, whereas MIN‐NPR decomposes into two. This gives a real number analogue of a result by Kolaitis and Thakur [13] in the Turing model. Our proofs mainly use techniques from [17]. Finally, approximation issues are briefly discussed. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
14.
本文综述了关于熵数和非紧性的测量的插值性质,本文也描述了经典结果及几个非常新的结果。 相似文献
15.
Hoonjoo Kim Sung‐Jin Lee Hae‐Soo Oh 《Numerical Methods for Partial Differential Equations》2003,19(3):399-420
The method of auxiliary mapping (MAM), introduced by Babu?ka and Oh, was proven to be very successful in dealing with monotone singularities arising in two‐dimensional problems. In this article, in the framework of the p‐version of FEM, MAM is presented for one‐dimensional elliptic boundary value problems containing singularities. Moreover, in order to show the effectiveness of MAM, a detailed proof of an error estimate is also presented, which gives a sharp error bound of MAM. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 399–420, 2003. 相似文献
16.
A clique covering of a simple graph G is a collection of cliques of G covering all the edges of G such that each vertex is contained in at most k cliques. The smallest k for which G admits a clique covering is called the local clique cover number of G and is denoted by lcc(G). Local clique cover number can be viewed as the local counterpart of the clique cover number that is equal to the minimum total number of cliques covering all edges. In this article, several aspects of the local clique covering problem are studied and its relationships to other well‐known problems are discussed. In particular, it is proved that the local clique cover number of every claw‐free graph is at most , where Δ is the maximum degree of the graph and c is a constant. It is also shown that the bound is tight, up to a constant factor. Moreover, regarding a conjecture by Chen et al. (Clique covering the edges of a locally cobipartite graph, Discrete Math 219(1–3)(2000), 17–26), we prove that the clique cover number of every connected claw‐free graph on n vertices with the minimum degree δ, is at most , where c is a constant. 相似文献
17.
We study those functions that can be written as a finite sum of periodic integer valued functions. On ℤ we give three different
characterizations of these functions. For this we prove that the existence of a real valued periodic decomposition of a ℤ
→ ℤ function implies the existence of an integer valued periodic decomposition with the same periods. This result depends
on the representation of the greatest common divisor of certain polynomials with integer coefficients as a linear combination
of the given polynomials where the coefficients also belong to ℤ[x]. We give an example of an ℤ → {0, 1} function that has a bounded real valued periodic decomposition but does not have a
bounded integer valued periodic decomposition with the same periods. It follows that the class of bounded ℤ → ℤ functions
has the decomposition property as opposed to the class of bounded ℝ → ℤ functions. If the periods are pairwise commensurable
or not prescribed, then we get more general results.
Supported by OTKA grants T 43623 and K 61908. 相似文献
18.
Many transcendental functions were constructed through finding closed‐form solutions of algebraic or differential equations and become ubiquitous gradually with increasing awareness of applications in specific problems naturally arising from life science. Motivated by Lambert W function, a family of transcendent X functions was introduced recently to express the closed‐form solutions of some nonlinear pharmacokinetic models. Unfortunately, its mathematical properties have not been completely studied. For the purposes of mathematical point of views and the use of wider applications, our objective in this paper is to characterize morphism classification of X functions at the scope of real branches. 相似文献
19.
The principal object of this paper is to present a new approach simultaneously to both nondegenerate and degenerate cases of the matricial Schur problem. This approach is based on an analysis of the central matrixvalued Schur functions which was started in [24]–[26] and then continued in [27]. In the nondegenerate situation we will see that the parametrization of the solution set obtained here coincides with the well‐known formula of D. Z. Arov and M. G. Kre?n for that case (see [1]). Furthermore, we give some characterizations of the situation that the matricial Schur problem has a unique solution (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
20.
In this paper we deal with the hyponormality of Toeplitz operators with matrix‐valued symbols. The aim of this paper is to provide a tractable criterion for the hyponormality of bounded‐type Toeplitz operators (i.e., the symbol is a matrix‐valued function such that Φ and are of bounded type). In particular, we get a much simpler criterion for the hyponormality of when the co‐analytic part of the symbol Φ is a left divisor of the analytic part. 相似文献