Search results for "Mathematica"
showing 10 items of 7971 documents
APPROXIMATION OF BANACH SPACE VALUED NON-ABSOLUTELY INTEGRABLE FUNCTIONS BY STEP FUNCTIONS
2008
AbstractThe approximation of Banach space valued non-absolutely integrable functions by step functions is studied. It is proved that a Henstock integrable function can be approximated by a sequence of step functions in the Alexiewicz norm, while a Henstock–Kurzweil–Pettis and a Denjoy–Khintchine–Pettis integrable function can be only scalarly approximated in the Alexiewicz norm by a sequence of step functions. In case of Henstock–Kurzweil–Pettis and Denjoy–Khintchine–Pettis integrals the full approximation can be done if and only if the range of the integral is norm relatively compact.
Analytic capacity and quasiconformal mappings with $W^{1,2}$ Beltrami coefficient
2008
We show that if $\phi$ is a quasiconformal mapping with compactly supported Beltrami coefficient in the Sobolev space $W^{1,2}$, then $\phi$ preserves sets with vanishing analytic capacity. It then follows that a compact set $E$ is removable for bounded analytic functions if and only if it is removable for bounded quasiregular mappings with compactly supported Beltrami coefficient in $W^{1,2}$.
Holomorphic approximation of ultradifferentiable functions
1981
Introduct ion Let S be a closed subset of some open set in Cn and denote by dT(S) the space of germs of holomorphic functions on (a neighborhood of) S. For a space F(S) of tEvalued (continuous, differentiable etc.) functions on S [containing t~(S)] the problem of holomorphic approximation consists of finding conditions to ensure that the natural mapping Q : e)(S)-~F(S) has dense range with respect to a given topology on F(S). Positive solutions for F = C r, 0_ l . For Q:tP(/3)~O(D)c~C(/3), DCIE n strongly pseudoconvex, proofs were given independently by Henkin [17], Kerzman [21], and Lieb [27], for the case e : (9(/3)~(9(D)c~C~(/3) cf. also [30] and for Sobolev spaces see Bell [3, Sect. 6].…
Sobolev-Poincaré implies John
1995
We establish necessary conditions for the validity of Sobolev-Poincaré type inequalities. We give a geometric characterisation for the validity of this inequality for simply connected plane domains.
Early mathematical skill profiles of prematurely and full-term born children
2017
Abstract Preterm birth is associated with low mathematical skills in children. This study on five-year-old Finnish children investigated whether mathematical skill profiles would differ between prematurely and full-term born children and how such profiles and other cognitive skills would be related. Mathematical skills included digit knowledge, spontaneous focusing on numerosity, arithmetic, counting and geometric skills. The investigated cognitive skills were phonological processing, working memory, instruction comprehension, speeded naming, inhibition and visuomotor skills. The participants were 119 preterm children with birth weight
Individual variance in responsiveness to early computerized mathematics intervention
2015
Abstract We examined the effects of short, intensive computerized intervention in early number skills for kindergarteners with poor addition skills (below 1.5 SD ). The mathematical content of the software was hierarchically organized, starting from one-to-one correspondence, comparing and ordering, and proceeding via number concept and counting to basic addition. The results showed positive within-group effects for basic addition (Wilcoxon ES ( r ) = .59), verbal counting (.56), and the Number Sets Test (.45; see Geary, Bailey, & Hoard, 2009 ). The effects remained stable over a 9-week follow-up period. However, there was no significant between-group difference in terms of gain scores as c…
Development of math anxiety and its longitudinal relationships with arithmetic achievement among primary school children
2019
Abstract The aim of this study is to examine the development of two separable aspects of math anxiety, anxiety about math-related situations and anxiety about failure in math, and their cross-lagged relationship with arithmetic achievement. The mean level of anxiety about math-related situations decreased among second, third, and fourth graders, and the level of anxiety about failure in math declined among third, fourth, and fifth graders. The rank-order of individuals was more stable in arithmetic achievement than in either aspect of math anxiety. Arithmetic achievement predicted later anxiety about failure in math, but neither aspect of math anxiety predicted later achievement. The result…
What Did CS Students Recognize as Study Difficulties?
2019
Computing education research shows substantive interest in novice programming challenges. The present study was rather interested in any phenomena that students would recognize as difficulties during their university studies. The research question was what computing students recognized as their study difficulties after the first year of study. An inductive thematic analysis was applied to the students’ personal writing of the difficulties experienced. The main result categories were independence in new environment, academic requirements, lack of prospects, learning to work, and social integration, which were illustrated by multiple lower level themes. The results inform educators of the wid…
A value for multichoice games
2000
Abstract A multichoice game is a generalization of a cooperative TU game in which each player has several activity levels. We study the solution for these games proposed by Van Den Nouweland et al. (1995) [Van Den Nouweland, A., Potters, J., Tijs, S., Zarzuelo, J.M., 1995. Cores and related solution concepts for multi-choice games. ZOR-Mathematical Methods of Operations Research 41, 289–311]. We show that this solution applied to the discrete cost sharing model coincides with the Aumann-Shapley method proposed by Moulin (1995) [Moulin, H., 1995. On additive methods to share joint costs. The Japanese Economic Review 46, 303–332]. Also, we show that the Aumann-Shapley value for continuum game…
Existence of competitive equilibrium in a non-optimal one-sector economy without conditions on the distorted marginal product of capital
2012
Abstract This paper develops a method for proving the existence of competitive equilibrium in a distorted/non-optimal one-sector economy–a discrete time variant of the Romer model–without conditions on the equilibrium value of the marginal product of capital. Existence is obtained under weaker conditions than in Le Van et al. (2002) . Moreover, we provide an existence result for an economy with a regressive tax studied in Santos (2002) . The proofs rely on ideas of Becker and Boyd (1997) .