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Your search keyword '"Sheng You Wen"' showing total 4 results
Start Over Author "Sheng You Wen" Topic mathematical analysis
4 results on '"Sheng You Wen"'

1. A remark on singularity of homeomorphisms and Hausdorff dimension

Author

Sheng-you Wen and Chun Wei

Subjects
Essential singularity, Pure mathematics, Mathematics::Dynamical Systems, Singularity theory, General Mathematics, Mathematical analysis, Mathematics::General Topology, Isolated singularity, Homeomorphism, Set (abstract data type), Singularity, Hausdorff dimension, Mathematics::Metric Geometry, Unit interval, Mathematics
Abstract

We prove that there is a homeomorphism of the unit interval onto itself that is so singular that it maps some set $E$ of $\dim_HE=0$ onto a set $F$ of $\dim_H[0,1]\setminus F=0$.

Published
2016

2. A 1 weights and d-homogeneous measures on ahlfors d-regular space

Author

Zhi Xiong Wen, Sheng You Wen, and Yu Xia Dai

Subjects
Combinatorics, Homogeneous, Applied Mathematics, General Mathematics, Mathematical analysis, Regular space, Derivative, Absolute continuity, Space (mathematics), Measure (mathematics), Mathematics
Abstract

Let X be an Ahlfors d-regular space and m a d-regular measure on X. We prove that a measure µ on X is d-homogeneous if and only if µ is mutually absolutely continuous with respect to m and the derivative Dmµ(x) is an A1 weight. Also, we show by an example that every Ahlfors d-regular space carries a measure which is d-homogeneous but not d-regular.

Published
2011

3. A remark on singularity of homeomorphisms and Hausdorff dimension.

Author

Chun WEI and Sheng-you WEN

Subjects
*HOMEOMORPHISMS, *FRACTAL dimensions, *MATHEMATICAL mappings, *MATHEMATICAL singularities, *MATHEMATICAL analysis
Abstract

We prove that there is a homeomorphism of the unit interval onto itself that is so singular that it maps some set E of dimH E = 0 onto a set F of dimH[0; 1] \ F = 0. [ABSTRACT FROM AUTHOR]

Published
2016
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4. Gauges for the cookie-cutter sets.

Author

Yu Xia Dai and Sheng You Wen

Subjects
*HAUSDORFF measures, *MATHEMATICAL functions, *EQUATIONS, *NUMERICAL analysis, *MATHEMATICAL analysis
Abstract

Let E be a cookie-cutter set with dim H E = s. It is known that the Hausdorff s-measure and the packing s-measure of the set E are positive and finite. In this paper, we prove that for a gauge function g the set E has positive and finite Hausdorff g-measure if and only if 0 < lim inf t→0 $$ \tfrac{{g(t)}} {{t^s }} $$ < ∞. Also, we prove that for a doubling gauge function g the set E has positive and finite packing g-measure if and only if 0 < lim sup t→0 $$ \tfrac{{g(t)}} {{t^s }} $$ < ∞. [ABSTRACT FROM AUTHOR]

Published
2009
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