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21.
Papert's (1978) appeal to reconsider the power and possibilities of the aesthetic in mathematics learning is often ignored in mathematics education research. This paper begins with the premise, put forth by Dewey (1934), that the aesthetic structures many dimensions of inquiry and experience. In the same way that using particular paintings, musical compositions, or even everyday experiences has been instrumental to attempts by philosophers to understand the aesthetic dimensions of meaning and experience in artistic domains, I propose that analysing a particular encounter with mathematics may help reveal the nature and role of the often nebulous responses of elegance, beauty, and `fit' to which mathematicians lay claim in their mathematical activity. To achieve this, I draw on and adapt the defining features of the aesthetic character of experience set forth by the aesthetician Beardsley (1982). This, in turn, sheds light on the role thataesthetics can play in mathematical inquiry and experience, and provides initial categories and conjectures that can be used to investigate the potential roles of aesthetics in mathematics learning contexts.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
22.
设f是非常数亚纯函数,g是f的线性微分多项式.a和b是f的两个不同的小函数.本文证明如果f和g几乎CM分担a和b,则f≡g;此外,若f是非常数整函数,且f和f(k)(k≥1)IM分担a和b,b-a≠Peλz,测f≡g. 相似文献
23.
方程w"-w+f(t,w)=O的Dirichlet边值问题的正解存在性与多解性 总被引:1,自引:0,他引:1
姚庆六 《应用泛函分析学报》2002,4(1):4-9
考察了下列常微分方程的Dirichlet边值问题的正解[w″(t)-w(t) f(t,w(t))=0,0≤t≤1 w(0)=w(1)=0建立了n正解的存在性,其中n是一个任意的自然数。 相似文献
24.
MM教育方式下常微分方程教学实验研究 总被引:2,自引:0,他引:2
邹泽民 《玉林师范学院学报》2002,23(3):4-6
研究高师MM教育方式下常微分方程教学实验方案的设计框架、实施措施和效果分析,初步摸索出一条MM方式下“问题探究型”(创设问题情景——巧用思想方法——探究‘自主发现’——推证新知结论——获得‘问题解决’——开发实际应用)的创新教学途径。 相似文献
25.
In this work, the natural convection in a concentric annulus between a cold outer square cylinder and a heated inner circular cylinder is simulated using the differential quadrature (DQ) method. The vorticity‐stream function formulation is used as the governing equation, and the coordinate transformation technique is introduced in the DQ computation. It is shown in this paper that the outer square boundary can be approximated by a super elliptic function. As a result, the coordinate transformation from the physical domain to the computational domain is set up by an analytical expression, and all the geometrical parameters can be computed exactly. Numerical results for Rayleigh numbers range from 104 to 106 and aspect ratios between 1.67 and 5.0 are presented, which are in a good agreement with available data in the literature. It is found that both the aspect ratio and the Rayleigh number are critical to the patterns of flow and thermal fields. The present study suggests that a critical aspect ratio may exist at high Rayleigh number to distinguish the flow and thermal patterns. Copyright © 2002 John Wiley & Sons, Ltd. 相似文献
26.
The angular variations of the five-fold differential cross section obtained by using different wave functions of helium are
compared with experimental data. It is found that in the coplanar geometry two kinematical arrangements, (i) equal energy
sharing between the two ejected electrons with one of them ejected along the momentum transfer direction and the other along
varying direction and (ii) the Bethe ridge condition with fixed sum of ejected electron energies and varying angle between
them, are very sensitive to e-e correlations contained in the target wave function. This comparison has been used to show
that open-shell class of wave functions better incorporate e-e correlations than the closed-shell class. 相似文献
27.
本文对具有有限时滞的泛函微分方程建立了关于依照两种测度的实际稳定性的Razumikhin型判定定理,其中未采用通常的辅助函数,且可运用多个含有状态变量x的部分变元的Lyapunov函数,得出部分变远实际稳定性的判定定理,从而改进了已有的结果。 相似文献
28.
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30.
D.H. Delphenich 《Annalen der Physik》2006,15(3):216-246
Some concepts of real and complex projective geometry are applied to the fundamental physical notions that relate to Minkowski space and the Lorentz group. In particular, it is shown that the transition from an infinite speed of propagation for light waves to a finite one entails the replacement of a hyperplane at infinity with a light cone and the replacement of an affine hyperplane – or rest space – with a proper time hyperboloid. The transition from the metric theory of electromagnetism to the pre‐metric theory is discussed in the context of complex projective geometry, and ultimately, it is proposed that the geometrical issues are more general than electromagnetism, namely, they pertain to the transition from point mechanics to wave mechanics. 相似文献