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61.
We investigate a boundary-functional problem with transmission conditions for ordinary differential-operator equation in Sobolev spaces with a weight. We prove an isomorphism, coerciveness with respect to the spectral parameter, completeness and Abel basis of a system of root functions of the problem. Obtained results in the article are new even in case of Sobolev spaces without the weight. 相似文献
62.
Allen Leung 《International Journal of Computers for Mathematical Learning》2008,13(2):135-157
What makes Dynamic Geometry Environment (DGE) a powerful mathematical knowledge acquisition microworld is its ability to visually
make explicit the implicit dynamism of thinking about mathematical geometrical concepts. One of DGE’s powers is to equip us
with the ability to retain the background of a geometrical configuration while we can selectively bring to the fore dynamically
those parts of the whole configuration that interest us. That is, we can visually study the variation of an aspect of a DGE
figure while keeping other aspects constant, hence anticipating the emergence of invariant patterns. The aim of this paper
is to expound the epistemic value of variation of the Dragging tool in DGE in mathematical discovery. Functions of variation
(contrast, separation, generalization, fusion) proposed in Marton’s theory of learning and awareness will be used as a framework
to develop a discernment structure which can act as a lens to organize and interpret dragging explorations in DGE. Such a
lens focuses very strongly on mathematical aspects of dragging in DGE and is used to re-interpret known dragging modalities
(e.g., Arzarello et al.) in a potentially more mathematically-relevant way. The exposition will centre about a specific geometrical
problem in which two dragging trajectories are mapped out, consequently resulting in a DGE theorem and a visual theorem. In
doing so, a new spectral dragging strategy will be introduced that literally allows one to see the drag mode in action. A
model for the lens of variation in the form of a discernment nest structure is proposed as a meta-tool to interpret dragging
experiences or as a meta-language to relate different dragging analyses which consequently might give rise to pedagogical
and epistemological implications. 相似文献
63.
64.
《复变函数与椭圆型方程》2012,57(3):229-237
Sharp distortion theorems for close-to-convex functions which satisfy Re ?'(z) > γ are proved using extreme points. 相似文献
65.
本文探讨了单组重复采样设计及配对重复采样设计的检验效能和相应样本含量的估计 ,并在相同检验效能的条件下建立了重复采样资料 (非独立样本 )与单一测量资料 (独立样本 )间样本含量的关系式。以实例分析 ,其结果与实际相符合。 相似文献
66.
We present a systematic identification method for the development of equivalent boundary conditions for turbulent flow simulation over rough walls in engineering applications where the typical roughness involved is known for a given application. After parameterizing the roughness and sampling of the parameter space, numerical simulations or experiences are used to generate a database which is used to identify the coefficients of a polynomial reduced-order model. These laws are parameterized by an a priori length scale for which we propose a new a posteriori criterion. 相似文献
67.
68.
Steklov expansions for a harmonic function on a rectangle are derived and studied with a view to determining an analog of the mean value theorem for harmonic functions. It is found that the value of a harmonic function at the center of a rectangle is well approximated by the mean value of the function on the boundary plus a very small number (often 3 or fewer) of specific further boundary integrals. These integrals are coefficients in the Steklov representation of the function. Similar approximations are found for the central values of solutions of Robin and Neumann boundary value problems. The results follow from analyses of the explicit expressions for the Steklov eigenvalues and eigenfunctions. 相似文献
69.
A general form of Jordan-type double inequality for the generalized and normalized Bessel functions 总被引:1,自引:0,他引:1
Ling Zhu 《Applied mathematics and computation》2010,215(11):3802-3810
In this note, a general form of Jordan-type double inequality involving the generalized and normalized Bessel functions is presented, and then some recent results concerning generalized and sharp work of Jordan’s inequality are extended. At the same time, the applications of the results above give two new infinite series for sinx/x and sinhx/x. 相似文献
70.
Jean-François Babadjian Maria Giovanna Mora 《Journal of Differential Equations》2018,264(8):5109-5151
This work is devoted to establishing a regularity result for the stress tensor in quasi-static planar isotropic linearly elastic – perfectly plastic materials obeying a Drucker–Prager or Mohr–Coulomb yield criterion. Under suitable assumptions on the data, it is proved that the stress tensor has a spatial gradient that is locally squared integrable. As a corollary, the usual measure theoretical flow rule is expressed in a strong form using the quasi-continuous representative of the stress. 相似文献