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931.
932.
Alec Norton 《Proceedings of the American Mathematical Society》1999,127(10):3111-3118
If is the (unique) minimal set for a diffeomorphism of the circle without periodic orbits, , then the upper box dimension of is at least . The method of proof is to introduce the exponent into the proof of Denjoy's theorem.
933.
Kevin A. Roper Ted J. Suffridge 《Transactions of the American Mathematical Society》1999,351(5):1803-1833
Not many convex mappings on the unit ball in for are known. We introduce two families of mappings, which we believe are actually identical, that both contain the convex mappings. These families which we have named the ``Quasi-Convex Mappings, Types A and B' seem to be natural generalizations of the convex mappings in the plane. It is much easier to check whether a function is in one of these classes than to check for convexity. We show that the upper and lower bounds on the growth rate of such mappings is the same as for the convex mappings.
934.
Robert S. Strichartz 《Transactions of the American Mathematical Society》1999,351(5):1705-1752
For a compact Hausdorff space that is pathwise connected, we can define the connectivity dimension to be the infimum of all such that all points in can be connected by a path of Hausdorff dimension at most . We show how to compute the connectivity dimension for a class of self-similar sets in that we call point connected, meaning roughly that is generated by an iterated function system acting on a polytope such that the images of intersect at single vertices. This class includes the polygaskets, which are obtained from a regular -gon in the plane by contracting equally to all vertices, provided is not divisible by 4. (The Sierpinski gasket corresponds to .) We also provide a separate computation for the octogasket (), which is not point connected. We also show, in these examples, that , where the infimum is taken over all paths connecting and , and denotes Hausdorff measure, is equivalent to the original metric on . Given a compact subset of the plane of Hausdorff dimension and connectivity dimension , we can define the isoperimetric profile function to be the supremum of , where is a region in the plane bounded by a Jordan curve (or union of Jordan curves) entirely contained in , with . The analog of the standard isperimetric estimate is . We are particularly interested in finding the best constant and identifying the extremal domains where we have equality. We solve this problem for polygaskets with . In addition, for we find an entirely different estimate for as , since the boundary of has infinite measure. We find that the isoperimetric profile function is discontinuous, and that the extremal domains have relatively simple polygonal boundaries. We discuss briefly the properties of minimal paths for the Sierpinski gasket, and the isodiametric problem in the intrinsic metric.
935.
Eduardo A. Prado 《Bulletin of the Brazilian Mathematical Society》1999,30(1):31-52
We show in this paper that iff is a quadratic infinitely many times renormalizable polynomial of sufficient high combinatorial type, then: HD (J(f))= inf{: -conformal measure for f} We use Lyubich's construction of the principal nest ([Lyu97]) in order to prove this result.Partially supported by CNP q-Brazil grant # 300534/96-5 相似文献
936.
937.
A Jiménez-Vargas M.G Sánchez-Lirola 《Journal of Mathematical Analysis and Applications》2003,283(2):696-704
Given a topological space T and a strictly convex real normed space X, let be the space of continuous and bounded functions from T into X, with its uniform norm. This paper is devoted to the study of the relation between the fact of T being an F-space and the property that every element in the unit ball of has a representation as a mean of two extreme points. 相似文献
938.
The aim of this paper is to give explicit limit expressions,for diffusion equations involving a small parameter , describingboth nonperiodic homogenization and reduction of dimension.In other words, we give the limit behaviour, when tends tozero, of the diffusion equation in a thin domain, with thicknessof order , when the coefficients of the equation also dependon and may present rapid, nonperiodic oscillations, providedthey satisfy a suitable compensated compactness condition. Weconsider two kinds of reduction of dimension: the case of thinplates (3D 2D) and the case of thin cylinders (3D 1D). Inparticular, we give the limit diffusion equation for laminatedplates. This is completely explicit and requires no specialassumption, except stratification. In the case of thin cylinders,the formulae are less explicit, but we also indicate some simpleapplications. 相似文献
939.
In this paper, we investigate the limiting behavior of increments of the uniform empirical process. More precisely, we are concerned by sets of exceptional oscillation points related to large and small increments. We prove that these sets are random fractals and evaluate their Hausdorff dimensions. This work is a complement to the previous investigations carried out by Deheuvels and Mason(6) where Csörg–Révész–Stute-type increments are studied. 相似文献
940.
In porous electrodes with an immobilized enzyme the substrate must have a high specific surface area, which must be accessible to landing onto it a maximum number of enzyme molecules. These demands are not easy to meet. Conceivable are limiting versions as follows: a stochastic substrate, where substrate particles (SP) are distributed in the volume randomly, and a regular substrate, where SP are distributed strictly regularly. Both versions of the organization of SP have advantages and disadvantages; therefore, in the paper studied is a third, intermediate, version, specifically, substrates with a partially regular structure. Shown is that there exists an optimum of values of fractal dimensionality for a regular base of a substrate, where, by somewhat sacrificing the amount of active enzymes, one can attain a considerable ease of the process of landing enzymes on the surface of a porous substrate. Calculations also show that of practical interest may be a porous substrate with a purely regular structure. 相似文献