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HELLO, WORLD!

This is MathJax: $E=mc^2$ and

$$

\begin{equation}

L =

\begin{cases}

1 & \text{if $i = j$ and $deg_j \neq 0 $} \\

stuff & \text{if $(i, j) \in E$} \\

0 & \text{otherwise}

\end{cases}

\end{equation}

$$

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HELLO, WORLD!

This is MathJax: $E=mc^2$ and

$$

\begin{equation}

L =

\begin{cases}

1 & \text{if $i = j$ and $deg_j \neq 0 $} \\

stuff & \text{if $(i, j) \in E$} \\

0 & \text{otherwise}

\end{cases}

\end{equation}

$$

- Get link
- Other Apps

Latin verbs can exhibit their number, person, tense, voice and mood. In this lesson, only present tense indicative mood is considered.

Personal endings of words-o/-m first person singular-mus first person plural-s second person singular-tis second person plural-t third person singular-nt third person plural The present tense: ago

The infinite form: agere

The perfect tense: egi

The supine form: actum

Personal endings of words-o/-m first person singular-mus first person plural-s second person singular-tis second person plural-t third person singular-nt third person plural The present tense: ago

The infinite form: agere

The perfect tense: egi

The supine form: actum

A topelitz matrix is a matrix with form of

$$A=\begin{bmatrix} a & b & c & d & e \\ f & a & b & c & d \\ g & f & a & b & c \\ h & g & f & a & b \\ i & h & g & f & a\end{bmatrix}$$

Generally, the elements are denoted as $a_{i-j}$: $A_{ij}=A_{i+1, j+1}=a_{i-j}$. A circulant matrix is a special kind of Toeplitz matrix where each row vector is rotated one element:

$$C=\begin{bmatrix}c_{0}&c_{n-1}&\dots &c_{2}&c_{1}\\c_{1}&c_{0}&c_{n-1}&&c_{2}\\\vdots &c_{1}&c_{0}&\ddots &\vdots \\c_{n-2}&&\ddots &\ddots &c_{n-1}\\c_{n-1}&c_{n-2}&\dots &c_{1}&c_{0}\\\end{bmatrix}$$

Circulant matrices are closely connected to discrete convolution:

$$y=h\ast x=\begin{bmatrix}h_{1}&0&\cdots &0&0\\h_{2}&h_{1}&&\vdots &\vdots \\h_{3}&h_{2}&\cdots &0&0\\\vdots &h_{3}&\cdots &h_{1}&0\\h_{m-1}&…

$$A=\begin{bmatrix} a & b & c & d & e \\ f & a & b & c & d \\ g & f & a & b & c \\ h & g & f & a & b \\ i & h & g & f & a\end{bmatrix}$$

Generally, the elements are denoted as $a_{i-j}$: $A_{ij}=A_{i+1, j+1}=a_{i-j}$. A circulant matrix is a special kind of Toeplitz matrix where each row vector is rotated one element:

$$C=\begin{bmatrix}c_{0}&c_{n-1}&\dots &c_{2}&c_{1}\\c_{1}&c_{0}&c_{n-1}&&c_{2}\\\vdots &c_{1}&c_{0}&\ddots &\vdots \\c_{n-2}&&\ddots &\ddots &c_{n-1}\\c_{n-1}&c_{n-2}&\dots &c_{1}&c_{0}\\\end{bmatrix}$$

Circulant matrices are closely connected to discrete convolution:

$$y=h\ast x=\begin{bmatrix}h_{1}&0&\cdots &0&0\\h_{2}&h_{1}&&\vdots &\vdots \\h_{3}&h_{2}&\cdots &0&0\\\vdots &h_{3}&\cdots &h_{1}&0\\h_{m-1}&…

Here I present a simple method to calculate the molecular weight distribution of 2nd block by GPC data of preceding block and final di-block copolymer. Assuming that we already have the molecular weight distribution of the preceding block, $P_1(n)$, it is generally that the length of the 2nd block "grow" from the depends on the preceding chain length $n$, therefore, the pdf of the 2 blocks should be a joint pdf $Q(n,…

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ReplyDelete$$ E=mc^2 $$