22 Result(s)

Article

On multifractal formalism for self-similar measures with overlaps

Let \(\mu \) μ be a self-similar measure generated by an IFS ...

Julien Barral, De-Jun Feng in Mathematische Zeitschrift (2021)

Article

Regularization by Noise for the Point Vortex Model of mSQG Equations

We consider the point vortex model associated to the modified Surface Quasi-Geostrophic (mSQG) equations on the two dimensional torus. It is known that this model is well posed for almost every initial conditi...

De Jun Luo, Martin Saal in Acta Mathematica Sinica, English Series (2021)

Chapter and Conference Paper

Dimension Estimates for C ¹ Iterated Function Systems and C ¹ Repellers, a Survey

In this note we give a survey about some of the results related to fractal dimensions of attractors and ergodic measures of non-linear and non-conformal Iterated Function Systems (IFS) and the repellers of exp...

De-Jun Feng, Károly Simon in Thermodynamic Formalism (2021)

Article

Affine embeddings of Cantor sets and dimension of αβ-sets

Let E,F ⊂ R^d be two self-similar sets, and suppose that F can be affinely embedded into E. Under the assumption that E is dust-like and has a small Hausdorff dimension, we prove the logarithmic commensurability b...

De-Jun Feng, Ying **ong in Israel Journal of Mathematics (2018)

Chapter and Conference Paper

Tiling \(\mathbb{Z}^{2}\) by a Set of Four Elements

A finite subset \(\mathcal{D}\) of \(\mathbb{Z}^{2}\)

De-Jun Feng, Yang Wang in Fractal Geometry and Stochastics V (2015)

Article

Non-conformal Repellers and the Continuity of Pressure for Matrix Cocycles

The pressure function P(A, s) plays a fundamental role in the calculation of the dimension of “typical” self-affine sets, where A = (A ₁, …,A _k )...

De-Jun Feng, Pablo Shmerkin in Geometric and Functional Analysis (2014)

Article

Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients

Combining Le Bris and Lions’ arguments with Ambrosio’s commutator estimate for BV vector fields, we prove in this paper the existence and uniqueness of solutions to the Fokker-Planck type equations with Sobole...

De Jun Luo in Acta Mathematica Sinica, English Series (2013)

Article

Numerical method for optimum motion of undulatory swimming plate in fluid flow

A numerical method for the optimum motion of an undulatory swimming plate is presented. The optimum problem is stated as minimizing the power input under the condition of fixed thrust. The problem is singular ...

Qin-jian Qian 钱勤建, De-jun Sun 孙德军 in Applied Mathematics and Mechanics (2011)

Article

Growth rate for beta-expansions

Let β > 1 and let m > β be an integer. Each \({x\in I_\beta:=[0,\frac{m-1}{\beta-1}]}\) can be represented in the for...

De-Jun Feng, Nikita Sidorov in Monatshefte für Mathematik (2011)

Article

Lyapunov exponents for products of matrices and multifractal analysis. Part II: General matrices

We continue the study in [15, 18] on the upper Lyapunov exponents for products of matrices. Here we consider general matrices. In general, the variational formula about Lyapunov exponents we obtained in part I...

De-Jun Feng in Israel Journal of Mathematics (2009)

Chapter and Conference Paper

The Properties and Application of Target Nearness Degree

In this paper, we point out the insufficiency of balance degree which presented in [6], And introduce the definition of target nearness degree. Some properties of target nearness degree is investigated, and it...

De-jun Peng, Cheng-yi Zhang in Fuzzy Information and Engineering (2009)

Chapter and Conference Paper

Fuzzy Complex Value Measure and Fuzzy Complex Value Measurable Function

Based on the conception of real fuzzy measure. Firstly, the definition of fuzzy complex measure is introduced, the properties of fuzzy complex measure is mainly discussed in details. And gain Some better resul...

Sheng-quan Ma, De-jun Peng, De-yuan Li in Fuzzy Information and Engineering (2009)

Article

When is the union of two unit intervals a self-similar set satisfying the open set condition?

Let U _λ be the union of two unit intervals with gap λ. We show that U _λ is a self-similar set satisfying the open set condition if and only if U ...

De-Jun Feng, Su Hua, Yuan Ji in Monatshefte für Mathematik (2007)

Article

Classification of Refinable Splines

A refinable spline is a compactly supported refinable function that is piecewise polynomial. Refinable splines, such as the well-known B-splines, play a key role in computer aided geometric design. So far all ...

**n-Rong Dai, De-Jun Feng, Yang Wang in Constructive Approximation (2006)

Article

Generation of finite tight frames by Householder transformations

Finite tight frames are widely used for many applications. An important problem is to construct finite frames with prescribed norm for each vector in the tight frame. In this paper we provide a fast and simple...

De-Jun Feng, Long Wang, Yang Wang in Advances in Computational Mathematics (2006)

Article

A Class of Self-Affine Sets and Self-Affine Measures

De-Jun Feng, Yang Wang in Journal of Fourier Analysis and Applications (2005)

Article

On a Statistical Framework for Estimation from Random Set Observations

Using the theory of random closed sets, we extend the statistical framework introduced by Schreiber⁽¹¹⁾ for inference based on set-valued observations from the case of finite sample spaces to compact metric space...

De-Jun Feng, Ding Feng in Journal of Theoretical Probability (2004)

Article

Level set methods based on distance function

Some basic problems on the level set methods were discussed, such as the method used to preserve the distance function, the existence and uniqueness of solution for the level set equations. The main contributi...

Wang De-jun, Tang Yun, Yu Hong-chuan, Tang Ze-sheng in Applied Mathematics and Mechanics (2003)

Article

Lyapunov exponents for products of matrices and multifractal analysis. Part I: Positive matrices

Let (Σ,σ) be a full shift space on an alphabet consisting ofm symbols and letM: Σ→L ⁺(ℝ ^d , ℝ ^d ) be a continuous functi...

De-Jun Feng in Israel Journal of Mathematics (2003)