g****g
发帖数: 1828 | 1 In probability theory, the normal (or Gaussian) distribution, is a
continuous probability distribution that is often used as a first
approximation to describe real-valued random variables that tend to cluster
around a single mean value. The graph of the associated probability density
function is “bell”-shaped, and is known as the Gaussian function or bell
curve:[nb 1]
f(x) = \tfrac{1}{\sqrt{2\pi\sigma^2}}\; e^{ -\frac{(x-\mu)^2}{2\sigma^2}
},
where parameter μ is the mean (location of the pe... 阅读全帖 |
|
发帖数: 1 | 2 谁吃饱了撑着
背诵一堆和就业市场无关的数学名词啊
你清醒清醒，好吗
gradient descent
heat equation
wave equation
Euler method
Newton method
convex optimization
eigenvalue problem
normal equations
least square
这些都是跟deep learning有直接关系的知识体系
转行学CS coding
只为找工作的人
99.99%是不会知道这些
是什么东东 |
|
发帖数: 1 | 3 谁吃饱了撑着
背诵一堆和就业市场无关的数学名词啊
你清醒清醒，好吗
gradient descent
heat equation
wave equation
Euler method
Newton method
convex optimization
eigenvalue problem
normal equations
least square
这些都是跟deep learning有直接关系的知识体系
转行学CS coding
只为找工作的人
99.99%是不会知道这些
是什么东东 |
|
z****u
发帖数: 3461 | 4 http://www.ncbi.nlm.nih.gov/pubmed/22401258
Phys Rev Lett. 2012 Feb 17;108(7):078101. Epub 2012 Feb 13.
Shape of a ponytail and the statistical physics of hair fiber bundles.
Goldstein RE, Warren PB, Ball RC.
Source
Department of Applied Mathematics and Theoretical Physics, University of
Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
Abstract
A general continuum theory for the distribution of hairs in a bundle is
developed, treating individual fibers as elastic filaments with ra... 阅读全帖 |
|
c****t
发帖数: 19049 | 5 2011 is shaping up to an amazing year for Speculative Fiction at large not
just Fantasy although that is looking damn good all by itself. My Sci-Fi
list last year was only 7 books long, which grew a little with the year, but
it was so short I combined it with UR and Steampunk picks. This year Sci-Fi
warrants a post all its own with loads of debuts and returning stars. The
people claiming Sci-fi is dying or already dead should shear the wool off
their eyes and see what is brewing.
Science Fictio... 阅读全帖 |
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m********y
发帖数: 45 | 6 I met this kind of problem many times. It mainly
dues to equations. Try double click each equation,
if you can not open one, delete that. Try saving.
Then retype that equation. |
|
p******o
发帖数: 216 | 7 actually it's a truly latex input, but 'word auto correction'. If you want
to input equation with latex input, try MathType 6. Also, the equations
edited by Equation Editor from Office is so ugly and that's why I use
MathType instead. |
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T*******n
发帖数: 493 | 8 \rightarrow is a math mode command, so you can only use it in
an equation, e.g., surrounded by $...$ or \begin{equation}...\end{equation}.
Here you want to say
which can be denoted as $V\rightarrow I$.
Because the $...$ were missing, LaTeX added a $ in front of \rightarrow.
If you ran LaTeX on the command line in Linux or Windows, LaTeX should
have stopped to tell you that it had to add the $; it might not stop if you
ran LaTeX from some kind of integrated editor that throws away LaTeX's
wa |
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T*******n
发帖数: 493 | 9 You can try this:
\usepackage{amsmath,amssymb}
\begin{equation}
x=y\tag*{$\blacksquare$}
\end{equation}
but you'll lose the equation number. |
|
T*******n
发帖数: 493 | 10 If there are n equations in the box, does the whole box get
one single equation number outside the box, or are there n
equation numbers, and are they inside or outside the box? |
|
d******r
发帖数: 6 | 11 double column得文章，一个很长的equation无法通过断行缩短，所以现在希望放在
文章的最下面，占据one column。尝试用
\begin{figure*} [!hbtp]
\begin{equation}
...
\end{equation}
\end{figure*}
结果无论如何调整，图片始终跳到下一页的最顶端，无法放到页末。
各位高手谁给指点一下？ |
|
T*******n
发帖数: 493 | 12 Complete example:
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{alignat}{2}
x &=y && +z \\
x_1 &=y_1 && +z_1
\end{alignat}
\begin{equation}
\text{equations} =
\left\{
\begin{alignedat}{2}
x &=y && +z \\
x_1 &=y_1 && +z_1
\end{alignedat}\right .
\end{equation}
\end{document} |
|
T*******n
发帖数: 493 | 13 \sum, \max, \min, \int, and \lim all behave the same way,
you just need to understand when the subscripts appear
beneath, and when on the side. Generally:
* running text $\sum_x$ => always side
* single-line equation mode $$\sum_x$$ or
\begin{equation}\sum_x\end{equation} => below, except:
* in fractions \frac{\sum_x}{\sum_y} => side
* in super- or subscripts: y^{\sum_x} => side
* in roots \sqrt{\sum_x} => side
* in matrices => side
Basically if \sum and others appear in restricted ve |
|
T*******n
发帖数: 493 | 14 \documentclass{article}
\usepackage{amsmath}
\DeclareMathOperator*{\argmin}{argmin}
\begin{document}
In text $\argmin_{x\in X} \{j | g(X_j) \}$ and in displayed equation
\begin{equation}
\argmin_{x\in X} \{j | g(X_j) \}
\end{equation}
\end{document} |
|
T*******n
发帖数: 493 | 15 Try "gather" instead of "align".
Default behavior of "gather" is to center each equation.
If you already use the "fleqn" document class and amsmath option,
"gather" will left-align each equation instead of centering them.
No & is needed or should be used.
If you have to use "align", try putting the & at the beginning of
each equation, not at the = sign. |
|
T*******n
发帖数: 493 | 16 You can't use \[ ... \] or \begin{equation} ... \end{equation} within "
tabbing".
If you can show what exactly you want aligned I can probably show you
how to do it using equation+split+text. I couldn't figure out what you
wanted because you had a problematic \< in your example.
(\ |
|
N**D
发帖数: 10322 | 17 \begin{equation} \label{Eq:abc}
a + b = c
\end{equation}
...
Equation \ref{Eq:abc} states a very simple fact that... |
|
d*****y
发帖数: 140 | 18 比如\newcommand{myCom}{......}
如果是在 equation/align等环境中就输出"this is an equation"
如果在其他环境或text, table/figure cpation中就输出"this is not an equation"?
要怎么搞？
thx! |
|
s*****g
发帖数: 5159 | 19 For the first questions, use display math, i.e.,put your formula with \max i
n
\[
\]
or
$$
$$
or equation environment. Inline formula cannot display in your expected way.
The second question, used
\begin{equation}
\begin{split}
a & = b\\
c & = d\\
e & = f
\end{split}
\end{equation}
To write consistent formulas, suggestted reading is AMS short math guide, yo
u will find eqnarray is deprecated and no longer necessary to be used. I tri
ed to hint this to my advisor a lot of times but he cannot forg |
|
r*******d
发帖数: 958 | 20 pros:
1) being different，to impress girls
2) if you already have the equations in a latex file, you can grab the
equations directly from there, and save time on retyping equations in ppt
plus you have pretty eqations
3) works on different platforms: windows, Linux, Mac OS
cons:
1) less flexible compared with ppt especially when you have a lot of
pictures and animations |
|
h**r
发帖数: 46 | 21 Solved the problem. Just unpluged the internet cable, and restarted again.
It looks that the system can't stop checking sth about internet connection,
and step forward. I had experienced the similar problem when using word or
origin (have set remote printer and 2 remote folders in the system), if I am
working offline, some of the program functions are very slow, for example,
word equation editor, when I click an equation, it takes quite a long time to
activate equation editor.
So, my system got |
|
l**t
发帖数: 452 | 22 【 以下文字转载自 Software 讨论区,原文如下 】
发信人: leot (leot), 信区: Software
标 题: 问一个MS Word 有关caption和cross reference的问题
发信站: Unknown Space - 未名空间 (Wed Jun 1 21:30:46 2005) WWW-POST
我在每一个eqation的右侧直接（不选中那个公式）加一个equation number.
但是，这样的话，我在文章中间如果用cross reference引用这个equation number,就会
把整个公式都引用出来。
如果先选中公式，然后insert caption, 我只能在这个公式的下一行插入这个equation
number.
这样引用的时候就可以只引用这个eqation number.
问题就是第一个办法的插入时候，word把公式都认为是caption lable and number了。
大家说说怎么办呢？多谢了 |
|
l**********1
发帖数: 5204 | 23 Plus him:
Professor Qian (Q=Ch) received his B.A. in Astrophysics from Peking
University in China in 1982, and his Ph.D. in Biochemistry and Biophysics
from Washington University School of Medicine in St. Louis in 1989.
His current research areas are computaional systems biology at the cellular
level, molecular biophysics, and mathematical biology. These include large-
scale metabolic networks, protein interaction networks and signal
transduction modeling, protein thermodynamics and folding, and... 阅读全帖 |
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s******y
发帖数: 28562 | 24 另外，在我对abbe equation 的理解中，这个公式有两项，一个是视椎角度，
这个就是我说的那个光线弯曲的问题（就是用油当介质可以增加有效的视椎
角度，这个是我给你的第一个回答的意思）。
另外一个是你问的这个n. 这个在物理学的角度可以这样理解，镜头通过介质和
盖薄片在看一个Airy disk的虚像，如果玻璃两侧的介质是一样的话，那么
这个Airy disk 的像的有效半径就应该是lambda/2n。
另外你说的那个abberation correction其实是误会我在说spherical
aberration correction吧？这个和油有关，但是和我所说的那个并不是完全
一会事。有些时候，因为镜头本身不够圆而出现光线折射角度不对的问题的时候，
人们会故意调节油的折射率来引入额外的折射度来纠正这个问题。这个和N.A.
以及我一直说的问题没有关系。我一直强调的就是，在我的印象中（很模糊的，
大学时候学光学得到的印象了，不一定准确）这个N.A.推导的时候是用玻璃
两面介质一样的情况下得到的公式，不可以直接套用不同介质的情况。
我举出这个水溶液中的活体细胞就是为了说明这个事情。... 阅读全帖 |
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s******y
发帖数: 28562 | 25 鉴于你终于同意好好说话了，那么我来指出你为什么是错的吧。 、
我和你吵架的过程吧,主要原因就是因为我们对那个Abbe equation 的不同理解.Abbe
Equation 简单来说,就是用来标示一个显微系统的理论分辨率的方程,大致是 d= lamba
/(2n * sin a). Abbe equation我们在大学的时候学光学的时候学过,推导过程很麻烦,
我早就忘得干干净净.但是其中的物理意义我大致还是记得一点的, sin a这个值大致代
表镜头的有效光学视角, lamba/2n 则是Airy Disk 在某个均匀介质里的尺寸. 这个公
式貌似很简单,但是其中有很多暗藏机关.关键就是,生物学的大部分显微样品不是在均
匀介质里的,而是在样品和成像用的介质之间有一个盖玻片.这个就引入了两个问题,一
个就是盖玻片对光路的折射,另外一个就是盖玻片两侧的介质的不均匀.
你现在做了一个在生物成像里几乎是完全错误的近似，就是你以为镜头和盖玻片的那个
介质是决定系统分辨率的关键。这个在本质上是错的。 而我强调的那个油镜改善光通
路的那一点，反而才是正确的。你可能觉得我是个搞传统生物的人所以一定不... 阅读全帖 |
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s******y
发帖数: 28562 | 26 就说我和另外一位ID吵架的过程吧,主要原因就是因为我们对那个Abbe equation 的不
同理解.Abbe Equation 简单来说,就是用来标示一个显微系统的理论分辨率的方程,大
致是 d= lamba/(2n * sin a). 这个吵起来的过程说起来很好笑,就是到底如何理解其
中的各个不同的项. Abbe equation我们在大学的时候学光学的时候学过,推导过程很麻
烦,我早就忘得干干净净.但是其中的物理意义我大致还是记得一点的, sin a这个值大
致代表镜头的有效光学视角, lamba/2n 则是Airy Disk 在某个均匀介质里的尺寸. 这
个公式貌似很简单,但是其中有很多暗藏机关.
关键就是,生物学的大部分显微样品不是在均匀介质里的,而是在样品和成像用的介质之
间有一个盖玻片.这个就引入了两个问题,一个就是盖玻片对光路的折射,另外一个就是
盖玻片两侧的介质的不均匀. |
|
s******y
发帖数: 28562 | 27 就说我和另外一位ID吵架的过程吧,主要原因就是因为我们对那个Abbe equation 的不
同理解.Abbe Equation 简单来说,就是用来标示一个显微系统的理论分辨率的方程,大
致是 d= lamba/(2n * sin a). 这个吵起来的过程说起来很好笑,就是到底如何理解其
中的各个不同的项. Abbe equation我们在大学的时候学光学的时候学过,推导过程很麻
烦,我早就忘得干干净净.但是其中的物理意义我大致还是记得一点的, sin a这个值大
致代表镜头的有效光学视角, lamba/2n 则是Airy Disk 在某个均匀介质里的尺寸. 这
个公式貌似很简单,但是其中有很多暗藏机关.
关键就是,生物学的大部分显微样品不是在均匀介质里的,而是在样品和成像用的介质之
间有一个盖玻片.这个就引入了两个问题,一个就是盖玻片对光路的折射,另外一个就是
盖玻片两侧的介质的不均匀. |
|
a******a
发帖数: 283 | 28 有个问题需要大牛的智慧。
两个病毒载体，一个是商业卖的做浓度标准曲线（用A序列的primers来测定）；一个是
自己构建的。主要骨架一样，只是我们自己做的除了有A序列之外，还有自己的靶基因B
序列。因此自己构建的载体，除了可以用A序列的primers之外，还可以用B序列的
primers来测浓度。
唯一的问题就是，B序列的测定因为GC成分高，所以primers反应浓度要高于A序列
primers的浓度。
作出来的标准曲线（同一个96孔板），用B序列的primers做的，Ct values要比用A序列
的primers迟上5-6个Ct。作出来的曲线，efficiency （都在90%-100%之间）和R
square（都在0.99以上）都类似。
但是作出来的EQUATION在Y-axis上的截距就不一样，差了有6的样子。这样用B作出来
的equation计算出来的样品浓度就比用A作出来的equation计算出来的样品浓度要高10
倍。
有什么看法吗？
这个B序列的primers反应浓度已经高得太离奇了，2um final concentration，低了就
更加出不了什么好的标准曲线了。... 阅读全帖 |
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D***t
发帖数: 64 | 29 Position description
The successful candidate is expected to lead the development and application
of mathematical models which are required to describe the performance of
equipment and processes in the materials processing industries (chemicals,
petrochemicals, coal, etc.). A majority of the work involves the development
and application of process model libraries and systems modeling frameworks
to support process development and optimization.
Job responsibilities
Projects typically... 阅读全帖 |
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a*******t
发帖数: 867 | 30
Thank you very much.
Yes, I also noticed similar trend with different compounds. One is
hypochlorite solution and another one is a pesticide formulation.
I guess this correlation between ORP and pH (H+) should be guided by some
equations, like Nernst equation? But I do not see the [H+] item in the
equation.
So I guess we have to adjust pH to the same level in order to use the ORP
reading as an indicator of concentration of one compound?
To 疯哥:
高手不敢当。现在棋力下降了。
我作的是环境工程，跟化学有关。但是我的化学基础显然还不够.... |
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H**E
发帖数: 620 | 31 the equation you used was for vertical flow only.
so strictly say, that equation can only apply for vertical(upward) exit
gradient(magnitude).
if you want to consider total exit gradient, you need to decompose the total
exit gradient into horizontal and vertical components.
for horizontal component, the critical exit gradient can no longer
calculated by the equation you mentioned. |
|
f****r
发帖数: 27 | 32 This is wrong. Navier-Stokes equation is the fundamental equation describing
fluid flows (essentially Newton's second law of motion: F=ma) and is valid
for both laminar and turbulent flows. Numerical simulations of turbulence
are challenging, not because of the complexity of the equation, but the
underlying physics. |
|
x********g
发帖数: 595 | 33 When using NDSolve to solve partial differential equations, get the error
message:
"
NDSolve::deqn: Equation or list of equations expected instead of True in the
first argument
" |
|
l*****i
发帖数: 3929 | 34 If you divide c on both sides of your equation, and do some simple math, reg
ard y=pi/(d*a), you will get a very simple equation:
log(exp(-y)+exp(y))-y = 0
Isn't this a very nicely scaled equation in y? Solve it using fzero you get
y = 20.48, then
a = pi/(20.48*d) = 4.4463e+5.
pi/ |
|
l*****i
发帖数: 3929 | 35 just found another thing: how did you get such a strange equation? If you do
what I told you to do, you get the equation in y, but it is equivalent to
exp(-y)+exp(y) = exp(y)
which does not have a solution at all! I suspect something in your original
equation was wrong... |
|
c******k
发帖数: 1140 | 36 I already found this problem either. The good thing is that you give a hint
how to solve this kind of nonlinear equation. Actually I need solve two
nonlinear equations in one group, and there is another parameter b in the
above equation. For simplicity, I just let b=0.
do
original |
|
k*********g
发帖数: 791 | 37 in classical rigid body newtonian mechanics, and in solid mechanics, people
use: lagrangian framework for governing equations;
in fluid mechanics, popele use: eulerian framework for governing equations;
however, it turns out both are subsets & can be united;
the superset is: arbitrary lagrangian eulerian framewrok (ALE);
so, up to here, ALE has nothing to do with moving boundaries & free-surface
flows;
ALE is about how to formulate your equations;
level set is about how to capture moving interfa |
|
c*****a
发帖数: 16 | 38 【 以下文字转载自 Statistics 讨论区 】
发信人: cdsdata (CDS), 信区: Statistics
标 题: Heckman two-step
发信站: BBS 未名空间站 (Sun Jan 20 10:31:48 2013, 美东)
First step: run a probit equation of participation using all the
observations. The estimates of from this probit model are then used to
construct consistent estimates of the inverse Mills ratio term.
Second step: Include the inverse Mills ratio and run the original regression
equation.
Question: do these two equations have to include the SAME control variables
(exce... 阅读全帖 |
|
a*****g
发帖数: 19398 | 39 IL 教师对 PARCC 发表的意见
【注：PARCC是基于Common Core的 Assessment】
Dear ICTM colleagues:
With the recent, extensive field test of PARCC test items now completed and
some sample items posted on the PARCC web site, teachers now have a better s
ense of the kinds of test items that PARCC will be asking. (Practice items
form the Grades 3-8 performance-based tests will be released in Fall 2014.)
I raise here one concern about plans for the performance (open response) ite
ms in the hope of generating some discuss... 阅读全帖 |
|
s*********e
发帖数: 1 | 40 一直有个问题搞不清楚，就是kalman filter 的适用范围。
因为kalman filter 要求给定state equation, 这就代表所有无法得到state equation
的情况无法使用kalman filter.
举个例子， Nitendo 的遥控器（wiimote），用来测量瞬时加速度的工具。但是加速度
是由遥控器持有者人为控制的，这种情况怎样得到相邻两个时刻加速度的关系？如果得
不到，那就说明state equation 无法得到，那么如何使用kalman filter？ |
|
b***y
发帖数: 100 | 41 Thanks a lot for your reply. It is very helpful. I am one more question.
I am doing analysis of a boost. I want to derive a equation that shows how
the inductance value and
the capacitance value effect the output voltage ripple. I know generally,
as I increase the inductance's
value or the capacitance value, the output voltage ripple will decrease.
But I couldn't find a equation
that describe this relationship. Do you know how to derive this equation?
or where I can get this |
|
s***r
发帖数: 40 | 42 Manning's equation was developed based on the force balance of
a control volume in a open channel flow. the tricky part is the
selection of Manning's n value, which is determined by the
channel roughness, bed forms, vegetations and other factors.
So, I guess you are looking for Manning's n values for sheet flow
(> 300 feet) instead of the specific equation for sheet flow in
the similar form as V=1/n*R^(3/2)*S^0.5.
If you have other form of the Manning's equation, please share with
us. But I susp |
|
s*****g
发帖数: 221 | 43 sorry, my question originally is,
I believe The second equation obtained the
Wc fraction based on composite's mass.
because it looks like not convincing (maybe I am wrong).
so I intended to simplify it but gave you the first equation.
my difficulty here is I need a equation to calculate
the Wc fraction based on composite's mass.
but I need to convince the reviewer the eq. is right.
I donot think it is a good idea to deduce it using high school
knowledge(step by step).
so I am asking for a refer |
|
f******r
发帖数: 2975 | 44 Hi Suppose I have 4 equations group
Let K,E,Y,S are integers between 0,...,26
Now I have four equations
K- E = 6 (mod 27)
K - Y = 20(mod 27)
Y - S = 1(mod 27)
S - K = 15(mod 27)
Is there any general solution for such equation group?
For example I have x1,x2,x3,x4,....xn
I have
x1 -x2 =a1 (mod M)
x1 - x2 = a2(mod M)
...
Thanks a lot! |
|
R*********r
发帖数: 1855 | 45 要强调“组”就用system of equations或Simultaneous Equations ，一般情况用
equations也就行了。 |
|
m****n
发帖数: 142 | 46 我不是很清楚您的背景，如果您主要是想学elliptic,Poisson equations的话，Gilbarg&Trudinger的书当然是
这个领域很好的，不过听您的意思，似乎你并不需要那么专门，那么高深的东西。
我主要是搞PDE研究的，我的建议如下：
中文的：吴兰成，陈亚浙的“二阶椭圆型方程与椭圆型方程组”----这本书非常棒！强力推荐！有英文译本，是
Princeton的大牛Alice Chang专门推荐请人翻译的；中文书在网上也可以下载到，呵呵。
英文的：
1，Lin Fanghua& Han Qing: Elliptic Differential Equations.这本书是老林在库朗
所使用的教材编写而成。短小精悍，最重要的内容都讲到了，讲诉极为清晰。最强烈推荐。
2，前面smmartineden推荐的Jurgen Jost的教材，主要以椭圆为主，不过稍显冗长，而且讲得不如老林的书深刻。
3，N.V.Krylov最近写的“Lectures on elliptic equations in Sobolev spaces”。
Krylov和Safanov都是明尼苏达的老毛子大牛 |
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发帖数: 632 | 47 Equations of higher degree
Some of the ideas described here can be generalized to equations of higher
degree. The basic ideas for solving the sextic using Klein's approach to the
quintic were worked out around 1900. For algebraic equations beyond the
sextic, the roots can be expressed in terms of hypergeometric functions in
several variables or in terms of Siegel modular functions.
http://library.wolfram.com/examples/quintic/main.html
示（Klein 和Poincare的结果）（应该是自守函数，如理解有误，请千万不吝指教） |
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B********e
发帖数: 10014 | 48 有朋友发了给我，多谢哈
bbs id也没告诉我，不知道怎么报答/bow
贪心不足，还想求两篇，方便的兄弟们搭把手
1.Kato,T.
Quasi-linear equations of evolution with applications to partial
differential equations
Lecture notes in Math.448.Springer-Verlag, 1975,25-70
2.Kato, T.
Linear evolution equations of hyperbolic type, J.Fac.Sci.Univ.Tokyo,17,(1970
), pp.241-258.
比较老，不一定有，无论如何，多谢了
圣诞快乐！ |
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G********n
发帖数: 615 | 49 这个跟burgers equation似乎有点不一样，
burgers equation里 u_x 的系数是 u，
但是这个方程 u_x 的系数不是 u，
您的意思是可以变换到burgers equation？ |
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