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151.
该文应用Hodge分解定理,得到了非齐次A—调和方程组-Di(A^ij(x,Du)) Difj(i(x)=0,j=1,…,m的很弱解是弱解,进一步,利用Morrey空间法与Campanato空间法以及齐次化方法,作者得出了该方程的很弱解是局部Hoelder连续的,并且得出了Hoelder连续指数μ与λ之间的多值函数关系式. 相似文献
152.
The color of a complex number is defined as the number of vertices of the convex hull of powers of that number. This induces a coloring of the unit disk. The structure of the set of points where the color changes is investigated here. It is observed that there is a connection between this fractal set and some family of trinomial equations. Three algorithms for coloring the unit disk are described, the last one (related to the Farey sequence) arising out of a conjecture. This conjecture is formulated and proved in this presentation. 相似文献
153.
Bernd S. W. Schröder 《Order》1992,9(4):311-319
The following theorem is proved: If Q=L{P
t
tT} is a finite lexicographic sum of posets such that T and all P
t
have the strong fixed point property then Q has the strong fixed point property. Moreover we show the strong fixed point property for two more classes of posets. 相似文献
154.
We establish a result related to a theorem of de Boor and Jia [1]. Their theorem, in turn, corrected and extended a result of Fix and Strang [5] concerning controlled approximation. In our result, the approximating functions are not required to have compact support, but satisfy instead conditions on their behavior at . Our theorem includes some recent results of Jackson [6] and is closely related to the work of Buhmann [2].Communicated by Carl de Boor 相似文献
155.
The approximation order provided by a directed set {S
h
}
h>0 of spaces, each spanned by thehZ
d
-translates of one function, is analyzed. The nearoptimal approximants of [R2] from eachs
h
to the exponential functions are used to establish upper bounds on the approximation order. These approximants are also used on the Fourier transform domain to yield approximations for other smooth functions, and thereby provide lower bounds on the approximation order. As a special case, the classical Strang-Fix conditions are extended to bounded summable generating functions.The second part of the paper consists of a detailed account of various applications of these general results to spline and radial function theory. Emphasis is given to the case when the scale {s
h
} is obtained froms
1 by means other than dilation. This includes the derivation of spectral approximation orders associated with smooth positive definite generating functions. 相似文献
156.
Sharp Remez-, Nikolskii-, and Markov-type inequalities are proved for functions of the form
相似文献
157.
The authors rigorously prove that the exponent for the mean square displacement of self-avoiding random walk on the Sierpinski gasket is
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