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《Quaestiones Mathematicae》2013,36(4):347-370
Abstract In this note we obtain some extensions and an approximation of the Lyapunov convexity theorem by means of the bilinear integration of a set-valued function. The integration is performed successively with respect to a non-atomic, a direct sum and a Darboux vector measure. The necessary counterexamples are provided. 相似文献
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Tuomas E. Tahko 《Metaphysica》2011,12(2):151-164
The distinction between a priori and a posteriori knowledge has been the subject of an enormous amount of discussion, but the literature is biased against recognizing the intimate relationship between these forms of knowledge. For instance, it seems to be almost impossible to find a sample of pure a priori or a posteriori knowledge. In this paper, it will be suggested that distinguishing between a priori and a posteriori is more problematic than is often suggested, and that a priori and a posteriori resources are in fact used in parallel. We will define this relationship between a priori and a posteriori knowledge as the bootstrapping relationship. As we will see, this relationship gives us reasons to seek for an altogether novel definition of a priori and a posteriori knowledge. Specifically, we will have to analyse the relationship between a priori knowledge and a priori reasoning, and it will be suggested that the latter serves as a more promising starting point for the analysis of aprioricity. We will also analyse a number of examples from the natural sciences and consider the role of a priori reasoning in these examples. The focus of this paper is the analysis of the concepts of a priori and a posteriori knowledge rather than the epistemic domain of a posteriori and a priori justification. 相似文献
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Kirsty Wilson 《Research in Mathematics Education》2013,15(1):117-132
Spreadsheets use a meaningful algebra-like notation which, research suggests, can support pupils in developing an understanding of variables. This paper discusses the activity of Year 8 pupils who were taught to name a column on a spreadsheet, and who were asked to reflect upon their activity in a stimulated recall interview. More specifically, it considers the pupils' understanding of notation, such as 'A2' and 'm', which they used when constructing spreadsheet formulae. It is suggested that experience of naming columns may help pupils to develop a clearer sense of the notation as a variable, and to make links between their spreadsheet activity and use of standard algebraic notation [1]. 相似文献
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向开南 《数学物理学报(B辑英文版)》2000,20(4)
Let M = (Mt,Ft) be a uniformly integrable continuous martingale with MO = 0. For1 5 p < cot we setIIMllBMO. = '3p II[E[IMoo ~ MTIplFT]]'/Pll.,where the supremum is taken over all stopping times T.Set BMO. = {M: IIMllBMO. < co}. It is well known that BMO. = BMO, (VI S p 5 q).F'urthermore, all 11.llBMO. norms are equivalent andIIi ~~if;llMllBMO. = SUP T P(T < co)i'where the supremum is taken over all stopping times T satisfying P(T < co) > 0. In the laterwe shall simply … 相似文献
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Rulin Shen Changguo Shao Qinhui Jiang Wujie Shi Victor Mazurov 《Monatshefte für Mathematik》2010,160(3):337-341
Let G be a group and τ e (G) the set of numbers of elements of G of the same order. In this paper, by τ e (G), we give a new characterization of A 5, where A 5 is the alternating group of degree 5. We get the theorem following: Theorem. Let G be a group, ${G\cong A_5}$ if and only if τ e (G) = τ e (A 5) = {1, 15, 20, 24}. 相似文献
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This note simplifies Cordoba-Fefferman's proof on the weak boundedness of strong maximal operator M_8 (with respect to dμ) on L(1+log~(+(n-1))L). Some two-weighted boundedness results on L(1+log~(+α)L) of M_8 are investigated. 相似文献
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<正> 对任意实数x,定义‖x‖=max(x-[x],[x]+1-x).设a_1,…,a_(k-1)是互不相等的非零整数,a是适合(a,a_1,…,a_(k-1)=1的正整数,r是正整数.置 相似文献
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本文改进了J .G .Thompson在JournalofCombinatorialTheory ,1 (1 96 6 )中得到的一个有用的引理的结果 . 相似文献
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Spyridon Kamvissis 《数学物理学报(B辑英文版)》2011,31(6):2233-2246
One of the inspirations behind Peter Lax’s interest in dispersive integrable systems, as the small dispersion parameter goes to zero, comes from systems of ODEs discretizing 1-dimensional compressible gas dynamics [17]. For example, an understanding of the asymptotic behavior of the Toda lattice in different regimes has been able to shed light on some of von Neumann’s conjectures concerning the validity of the approximation of PDEs by dispersive systems of ODEs. Back in the 1990s several authors have worked on the long time asymptotics of the Toda lattice [2, 7, 8, 19]. Initially the method used was the method of Lax and Levermore [16], reducing the asymptotic problem to the solution of a minimization problem with constraints (an "equilibrium measure" problem). Later, it was found that the asymptotic method of Deift and Zhou (analysis of the associated Riemann-Hilbert factorization problem in the complex plane) could apply to previously intractable problems and also produce more detailed information. Recently, together with Gerald Teschl, we have revisited the Toda lattice; instead of solutions in a constant or steplike constant background that were considered in the 1990s we have been able to study solutions in a periodic background. Two features are worth noting here. First, the associated Riemann-Hilbert factorization problem naturally lies in a hyperelliptic Riemann surface. We thus generalize the Deift-Zhou "nonlinear stationary phase method" to surfaces of nonzero genus. Second, we illustrate the important fact that very often even when applying the powerful Riemann-Hilbert method, a Lax-Levermore problem is still underlying and understanding it is crucial in the analysis and the proofs of the Deift-Zhou method! 相似文献
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<正> §1.如所周知,黎曼空间中关于平面公理的嘉当(E.Cartan)定理可以拓广到更一般的空间中去,满足平面公理的 m 维黎曼空间在它的每点容有∞~(m-1)张全测地超曲面.柏尔特拉米(Beltrami)给出常曲率空间的另一特征,只有常曲率空间才能与欧氏空 相似文献
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Under the framework of a real Hilbert space, we introduce a new iterative method for finding a common element of the set of solution of a general equilibrium problem and the set of fixed points of a nonexpansive semigroup. Moreover, a numerical example is presented. This example grantee the main result of the paper. 相似文献