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81.
This paper studies a class of initial-value problems of nonlinear singular discrete systems and obtains the existence theorem of extremal solutions by employing a monotone iterative technique combined with the method of upper and lower solutions. 相似文献
82.
83.
Self-Affine Sets and Graph-Directed Systems 总被引:1,自引:0,他引:1
Abstract. A self-affine set in R
n
is a compact set T with A(T)= ∪
d∈ D
(T+d) where A is an expanding n× n matrix with integer entries and D
={d
1
, d
2
,···, d
N
} ⊂ Z
n
is an N -digit set. For the case N = | det(A)| the set T has been studied in great detail in the context of self-affine tiles. Our main interest in this paper is to consider the
case N > | det(A)| , but the theorems and proofs apply to all the N . The self-affine sets arise naturally in fractal geometry and, moreover, they are the support of the scaling functions in
wavelet theory. The main difficulty in studying such sets is that the pieces T+d, d∈ D, overlap and it is harder to trace the iteration. For this we construct a new graph-directed system to determine whether
such a set T will have a nonvoid interior, and to use the system to calculate the dimension of T or its boundary (if T
o
≠ ). By using this setup we also show that the Lebesgue measure of such T is a rational number, in contrast to the case where, for a self-affine tile, it is an integer. 相似文献
84.
Consider the group of affine transformations of the line. Denote by X and Y the right-invariant vector fields corresponding to the s and t directions, respectively, and let We prove that the first-order Riesz operator is of weak type (1, 1) with respect to left Haar measure. This operator is therefore also bounded on . Our results provide answers, in a particular instance, to the open question of the boundedness of Riesz operators on Lie
groups of exponential growth. The main parts of the proof concern the behaviour of the kernel of the operator at infinity,
and exploit cancellation. A key technique is to use expansion with respect to scales of Haar-like functions.
Received March 16, 1998; in final form June 22, 1998 相似文献
85.
Min-Soo Kim 《Journal of Number Theory》2009,129(9):2166-2179
In this note we give a new proof of Witt's formula for Euler numbers, which are related to some known or new identities involving the Euler numbers. We also obtain a brief proof of a classical result on Euler numbers modulo of two due to M.A. Stern using the approach of p-adic integration, which was recently proved by G. Liu, and Z.-W. Sun. Finally some explicit formulas for Genocchi numbers are proved and applications are given. 相似文献
86.
Erik A. van Doorn Nicky D. van Foreest 《Journal of Computational and Applied Mathematics》2009,233(3):847-851
We establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the decay parameter of a birth-death process (with killing) are displayed. 相似文献
87.
Jiman Zhao 《Bulletin des Sciences Mathématiques》2008,132(5):425
In this paper, we define the Littlewood-Paley and Lusin functions associated to the sub-Laplacian operator on nilpotent Lie groups. Then we prove the Lp (1<p<∞) boundedness of Littlewood-Paley and Lusin functions. 相似文献
88.
A geometrical scheme is proposed that leads to a straightforward generalization of a Skyrme Lagrangian, comprising higher-order terms up to the eighth power in pion fields.Boursière DGRST. 相似文献
89.
Mireille Staschok 《Logica Universalis》2008,2(1):77-85
Three logical squares of predication or quantification, which one can even extend to logical hexagons, will be presented and
analyzed. All three squares are based on ideas of the non-traditional theory of predication developed by Sinowjew and Wessel.
The authors also designed a non-traditional theory of quantification. It will be shown that this theory is superfluous, since
it is based on an obscure difference between two kinds of quantification and one pays a high price for differentiating in
this way: losing the definability between the existence- and all-quantifier. Therefore, a combination of non-traditional predication
and classical quantification is preferred here.
相似文献
90.
Manuel Gutiérrez 《Differential Geometry and its Applications》2009,27(1):146-156
Generalized Robertson-Walker (GRW) spaces constitute a quite important family in Lorentzian geometry, and it is an interesting question to know whether a Lorentzian manifold can be decomposed in such a way. It is well known that the existence of a suitable vector field guaranties the local decomposition of the manifold. In this paper, we give conditions on the curvature which ensure a global decomposition and apply them to several situations where local decomposition appears naturally. We also study the uniqueness question, obtaining that the de Sitter spaces are the only nontrivial complete Lorentzian manifolds with more than one GRW decomposition. Moreover, we show that the Friedmann Cosmological Models admit an unique GRW decomposition, even locally. 相似文献