Analysis Seminars @ CUHK Math Dept

12 \frac{1}{2}

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1012 \frac{101}{2} 1012\begin{aligned} \dfrac{101}{2} \end{aligned} exp(iπ)+1=01+1=2\begin{aligned} \exp(i\pi)+1 &= 0\\ 1+1 &= 2 \end{aligned}

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E=mC2 E = m C^2
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    • Summary
      12 \frac{1}{2}

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12 \frac{1}{2}
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12 \frac{1}{2}

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  • 8/17 Tuesday Zoom
    Caiyun Ma

    • Feng, D.-J. Lyapunov exponents for products of matrices and multifractal analysis. I. Positive matrices. Israel J. Math., 2003, 138, 353-376.

    • Summary

      To be announced.
      Just random test... hello world blabla... Σ={1,,m}N \Sigma = \{1,\ldots,m\}^{\mathbb{N}}

      π=3+17+115+11+1292+1f(x)={exp(1(xa)(xb))x(a,b)R0otherwise\begin{aligned} \pi & = 3 + \frac{\displaystyle 1}{\displaystyle 7 + \frac{\displaystyle 1}{\displaystyle 15 + \frac{\displaystyle 1}{\displaystyle 1 + \frac{\displaystyle 1}{\displaystyle 292 + \frac{\displaystyle 1}{\displaystyle \dots }}}}}\\ f(x) & = \begin{cases} \exp(\frac{1}{(x-a)(x-b)}) & x \in (a, b) \subset\mathbb{R} \\ 0 & otherwise \end{cases} \end{aligned}

       Fig 1: continued fraction of Pi
      Fig 1: continued fraction of Pi
      Let (X,B,μ,T) (X, \mathscr{B}, \mu, T) be a measure-preserving system.

  • 8/17 Tuesday Zoom
    Caiyun Ma

  • Summary
    To be announced. Just random test... hello world blabla... Σ={1,,m}N\Sigma = \{1,\ldots,m\}^{\mathbb{N}}

    π=3+17+115+11+1292+1f(x)={exp(1(xa)(xb))x(a,b)R0otherwise\begin{aligned} \pi & = 3 + \frac{\displaystyle 1}{\displaystyle 7 + \frac{\displaystyle 1}{\displaystyle 15 + \frac{\displaystyle 1}{\displaystyle 1 + \frac{\displaystyle 1}{\displaystyle 292 + \frac{\displaystyle 1}{\displaystyle \dots }}}}}\\ f(x) & = \begin{cases} \exp(\frac{1}{(x-a)(x-b)}) & x \in (a, b) \subset\mathbb{R} \\ 0 & otherwise \end{cases} \end{aligned}
     Fig 1: continued fraction of Pi
    Fig 1: continued fraction of Pi

    Let (X,B,μ,T)(X, \mathscr{B}, \mu, T) be a measure-preserving system.

  • Summary
    To be announced. Just random test... hello world blabla... Σ={1,,m}N\Sigma = \{1,\ldots,m\}^{\mathbb{N}}

    π=3+17+115+11+1292+1f(x)={exp(1(xa)(xb))x(a,b)R0otherwise\begin{aligned} \pi & = 3 + \frac{\displaystyle 1}{\displaystyle 7 + \frac{\displaystyle 1}{\displaystyle 15 + \frac{\displaystyle 1}{\displaystyle 1 + \frac{\displaystyle 1}{\displaystyle 292 + \frac{\displaystyle 1}{\displaystyle \dots }}}}}\\ f(x) & = \begin{cases} \exp(\frac{1}{(x-a)(x-b)}) & x \in (a, b) \subset\mathbb{R} \\ 0 & otherwise \end{cases} \end{aligned}
     Fig 1: continued fraction of Pi
    Fig 1: continued fraction of Pi

    Let (X,B,μ,T)(X, \mathscr{B}, \mu, T) be a measure-preserving system.

To be announced. Just random test... hello world blabla... Σ={1,,m}N\Sigma = \{1,\ldots,m\}^{\mathbb{N}}

π=3+17+115+11+1292+1f(x)={exp(1(xa)(xb))x(a,b)R0otherwise\begin{aligned} \pi & = 3 + \frac{\displaystyle 1}{\displaystyle 7 + \frac{\displaystyle 1}{\displaystyle 15 + \frac{\displaystyle 1}{\displaystyle 1 + \frac{\displaystyle 1}{\displaystyle 292 + \frac{\displaystyle 1}{\displaystyle \dots }}}}}\\ f(x) & = \begin{cases} \exp(\frac{1}{(x-a)(x-b)}) & x \in (a, b) \subset\mathbb{R} \\ 0 & otherwise \end{cases} \end{aligned}
 Fig 1: continued fraction of Pi
Fig 1: continued fraction of Pi

Let (X,B,μ,T)(X, \mathscr{B}, \mu, T) be a measure-preserving system. To be announced. Just random test... hello world blabla... Σ={1,,m}N\Sigma = \{1,\ldots,m\}^{\mathbb{N}}

π=3+17+115+11+1292+1f(x)={exp(1(xa)(xb))x(a,b)R0otherwise\begin{aligned} \pi & = 3 + \frac{\displaystyle 1}{\displaystyle 7 + \frac{\displaystyle 1}{\displaystyle 15 + \frac{\displaystyle 1}{\displaystyle 1 + \frac{\displaystyle 1}{\displaystyle 292 + \frac{\displaystyle 1}{\displaystyle \dots }}}}}\\ f(x) & = \begin{cases} \exp(\frac{1}{(x-a)(x-b)}) & x \in (a, b) \subset\mathbb{R} \\ 0 & otherwise \end{cases} \end{aligned}
 Fig 1: continued fraction of Pi
Fig 1: continued fraction of Pi

Let (X,B,μ,T)(X, \mathscr{B}, \mu, T) be a measure-preserving system.