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41.
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Hermann G. Burchard † 《Applicable analysis》2013,92(4):309-319
Let SM k be the Polynominal splines of degree n-1, and with K segments. If f∈ C n [a,b],then the distance in the Lp-norm form(0< p ≦ ∞)of from S M k is boundedby M/K n , with a much smaller M than in similar estimates for other processes of approximation. 相似文献
43.
We present a unified framework for constructing the globally convergent algorithms for a broad class of multidimensional coefficient inverse problems arising in natural science and industry. Based on the convexification approach, the unified framework substantiates the numerical solution of the corresponding problem of nonconvex optimization. A globally convergent iterative algorithm for an inverse problem of diffuse optical mammography is constructed. It utilizes the contraction property of a nonlinear operator resulting from applying the convexification approach. The effectiveness of this algorithm is demonstrated in computational experiments. 相似文献
44.
This article studies the existence of viable solutions to the Cauchy problem u′ ∈ ? (t , u) for a.e. t∈ [0,1], u (0)=x 0 ∈ K (a closed subset of R N ) where the nonlinearity ? satisfies a Wintner-type growth condition. 相似文献
45.
Ramesh Kapadia† ‡ 《International Journal of Mathematical Education in Science & Technology》2013,44(4):431-433
We develop one criterion for the selection of the content of a mathematics syllabus. We advocate the importance of the biogenetic law and stress the importance of a historical perspective in mathematical education. 相似文献
46.
R. Butler F. Turner† 《International Journal of Mathematical Education in Science & Technology》2013,44(1):33-49
The rate of convergence of a Fourier‐series representation of a given function depends on the nature of the function and of its derivatives. This is shown by using the graphical outputs of a desk computer for different cases. For full‐range series, the effects of continuity and discontinuity of the function and its first derivatives are shown first. The advantage of half‐range formulae due to the free choice of function in the second half‐range are demonstrated next, along with the importance of choice of sine and cosine series according to the function being represented. Finally, a method is given of modifying the given function in a simple manner whereby a dramatic increase in the rate of convergence of the Fourier series is obtained. Examples of the Gibbs overshoot and its elimination are included. 相似文献
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Weak pullback attractors are defined for non-autonomous difference inclusions and their existence and upper semi continuous convergence under perturbation is established. Unlike strong pullback attractors, invariance and pullback attraction here are required only for (at least) a single trajectory rather than all trajectories at each starting point. The concept is thus useful, in particular, for discrete time control systems. 相似文献
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