text:
# Table Formatting with and without threeparttable

I have been trying to generate the attached table in LaTeX. I have done it in two ways and I have query for both. The first way I have not used the threeparttable package and in the second way I have used it. This is because while searching for help adding notes under the table, I came to know about threeparttable and this was almost when I was about to finish the first way.

First I have a general question that how shall I format the text in first column which is not aligned to the left? I mean the text including the following items, (Petroleum, bituminous coal; brown coal etc). I guess there must be a better way of doing this as compared to the way I have done here in both the codes. I used \ to include space until that text is in the position where I want it to be.

In the first code I cant write the second table note in a new line as shown in the original table. Any suggestion for it?

In the second code, I cant draw the \hline after the second table note and above the last line of "Source: Energy Balance....." Any suggestion for it?

Here is the code one:

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{array, multirow}
\usepackage{caption,tabularx,booktabs}

\begin{document}

\begin{table}{\bfseries Primary Energy Consumption}\\[0.1ex]
\setlength{\extrarowheight}{1pt}
\begin{tabular*}{118 mm}{p{40mm}@{\hspace{30mm}} llrr @{}}

\hline
Energy Source &1975 &1980 &1986\\[-0.1ex]
\hline

Total Consumption\\
(in million tons of BCU$^{a}$) of which (percentages) \parbox[t]{15mm} &347.7 &390.2 &285.0\\
\ \ \ \ \ \ \ \ \ \ \ \ \   petroleum &52.1 &47.6 &43.2\\
\ \ \ \ \ \ \ \ \ \ \ \ \   bituminous coal &19.1 &19.8 &20.0 \\
\ \ \ \ \ \ \ \ \ \ \ \ \   brown coal &9.9 &10.0 &8.6 \\
\ \ \ \ \ \ \ \ \ \ \ \ \   natural gas &14.2 &16.5 &15.1 \\
\ \ \ \ \ \ \ \ \ \ \ \ \   nuclear energy &2.0 &3.7 &10.1 \\
\ \ \ \ \ \ \ \ \ \ \ \ \   other$^{b}$ &2.7 &2.4 &3.0 \\ \cline{1-1}

\multicolumn{4}{p{.9\textwidth}}{$^{a}$BCU = Bituminous Coal Unit (1 ton BCU corresponds to the heating equivalent of 1 ton of bituminous coal = 8140 kwh) $^{b}$Wind, water, solar energy, etc.}
\\
\hline

\end{tabular*}\\[0.1ex]

\emph{Source:} Energy Balance Study Group, Essen 1987.

\end{table}

\end{document}

Here is the second code;

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{array, multirow}
\usepackage{caption,booktabs}
\usepackage[flushleft]{threeparttable}

\begin{document}

\begin{table}
\begin{threeparttable}
\caption{Primary Energy Consumption}

\begin{tabular*}{118 mm}{p{40mm}@{\hspace{30mm}} llrr @{}}
\toprule

Energy Source &1975 &1980 &1986\\[-0.1ex]

\midrule

Total Consumption\\
(in million tons of BCU$^{a}$) of which (percentages) \parbox[t]{15mm} &347.7 &390.2 &285.0\\
\ \ \ \ \ \ \ \ \ \ \ \ \   petroleum &52.1 &47.6 &43.2\\
\ \ \ \ \ \ \ \ \ \ \ \ \   bituminous coal &19.1 &19.8 &20.0 \\
\ \ \ \ \ \ \ \ \ \ \ \ \   brown coal &9.9 &10.0 &8.6 \\
\ \ \ \ \ \ \ \ \ \ \ \ \   natural gas &14.2 &16.5 &15.1 \\
\ \ \ \ \ \ \ \ \ \ \ \ \   nuclear energy &2.0 &3.7 &10.1 \\
\ \ \ \ \ \ \ \ \ \ \ \ \   other$^{b}$ &2.7 &2.4 &3.0 \\
\bottomrule

\end{tabular*} %\\[0.1ex]

\begin{tablenotes}

\small
\item $^{a}$BCU = Bituminous Coal Unit (1 ton BCU corresponds to the heating equivalent of 1 ton of bituminous coal = 8140 kwh

\item $^{b}$Wind, water, solar energy, etc.
\end{tablenotes}

\emph{Source:} Energy Balance Study Group, Essen 1987.

\end{threeparttable}

\end{table}
\end{document}

I would do it like this:

% arara: pdflatex

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{caption,booktabs}
\usepackage[flushleft]{threeparttable}
\usepackage{siunitx}

\begin{document}
\begin{table}
\centering
\begin{threeparttable}
\caption[Primary Energy Consumption]{Primary Energy Consumption (\emph{Source:} Energy Balance Study Group, Essen 1987.)}
\begin{tabular}{p{1.5cm}l*{3}{S[table-format=3.1]}} % adapt the tabbing width with the p column!
\toprule
\multicolumn{2}{l}{Energy Source} & {1975} & {1980} & {1986} \\
\midrule
\multicolumn{2}{l}{Total Consumption} & & & \\
\multicolumn{2}{l}{(in million tons of BCU\tnote{a}~)} & 347.7 & 390.2 & 285.0 \\
\multicolumn{2}{l}{of which (percentages)} & & & \\
& petroleum       & 52.1 & 47.6 & 43.2 \\
& bituminous coal & 19.1 & 19.8 & 20.0 \\
& brown coal      & 9.9  & 10.0 & 8.6  \\
& natural gas     & 14.2 & 16.5 & 15.1 \\
& nuclear energy  & 2.0  & 3.7  & 10.1 \\
& other\tnote{b}  & 2.7  & 2.4  & 3.0  \\
\bottomrule
\end{tabular}
\begin{tablenotes}
\small
\item[a] BCU = Bituminous Coal Unit (\SI{1}{\tonne} BCU corresponds to the heating equivalent of \SI{1}{\tonne} of bituminous coal $= \SI{8140}{\kilo\watt\hour}$
\item[b] Wind, water, solar energy, etc.
\end{tablenotes}
\end{threeparttable}
\end{table}
\end{document}

I hope the code is self-explaining.

Edit: Or if you want to have the "(percentages)" aligned to the rows below (thanks to Enrico):

\begin{table}
\centering
\begin{threeparttable}
\caption[Primary Energy Consumption]{Primary Energy Consumption (\emph{Source:} Energy Balance Study Group, Essen 1987.)}
\begin{tabular}{l@{\hspace{.4cm}}l*{3}{S[table-format=3.1]}} % adapt the tabbing width with the \hspace
\toprule
\multicolumn{2}{l}{Energy Source} & {1975} & {1980} & {1986} \\
\midrule
\multicolumn{2}{l}{Total Consumption} & & & \\
\multicolumn{2}{l}{(in million tons of BCU\tnote{a}~)} & 347.7 & 390.2 & 285.0 \\
of which & (percentages) & & & \\
& petroleum       & 52.1 & 47.6 & 43.2 \\
& bituminous coal & 19.1 & 19.8 & 20.0 \\
& brown coal      & 9.9  & 10.0 & 8.6  \\
& natural gas     & 14.2 & 16.5 & 15.1 \\
& nuclear energy  & 2.0  & 3.7  & 10.1 \\
& other\tnote{b}  & 2.7  & 2.4  & 3.0  \\
\bottomrule
\end{tabular}
\begin{tablenotes}
\small
\item[a] BCU = Bituminous Coal Unit (\SI{1}{\tonne} BCU corresponds to the heating equivalent of \SI{1}{\tonne} of bituminous coal $= \SI{8140}{\kilo\watt\hour}$
\item[b] Wind, water, solar energy, etc.
\end{tablenotes}
\end{threeparttable}
\end{table}

• Maybe the first two columns could be specified as l@{ }l and the third row can start with of which & (percentages), so as to get the same alignment as in the OP's image (with better spacing). – egreg Aug 19 '15 at 16:11
• @LariFaRi Thanks. I was not aware of siunitx package but you have introduced it to me. Many Many thanks for the help – Jack Aug 19 '15 at 16:44


text:
[texhax] environment from command

Philip Taylor (Webmaster, Ret'd) P.Taylor at Rhul.Ac.Uk
Sat Nov 20 16:02:12 CET 2010

Barbara Sánta wrote:
> very sorry if I was unundrestandable, you are right, the first and
> third argument is not necessary.
> So transform a \command{arg} into a
> \begin{env}
>     arg
> \end{env}
> with defining env environment. My problem was that I could not find a
>    \newenvironment{env}{\command ?beginning a block? }{ ?end of the block? }
> solution, where ? signs my problem. But Heiko Oberdiek gave a perfect
> solution with a package.

OK, many thanks Barbara : your problem is now a lot clearer.

So in general what can be identified is that it not possible
to treat "arg" as a parameter to \command, as otherwise
catcode changes could not occur in setting up {environment}.
However, for the limits of "arg" to be known, it must be
set off by braces.  So the first thing that comes to mind
is :

\def \command #{whatever}

where the trailing # indicates that \command must be followed
by an open brace (which will later be closed), and \command
takes no parameters so no catcode staticisation has yet
taken place.  \command can therefore be programmed to emit
"\begin {environment} :

\def \command #{\begin {environment}}

The problem is how to insert the \end {environment} once
the closing brace is found.  As Fermat might have said
"I have a really ingenious solution, but this message is
too small to contain it".  In reality, I have to prepare
for guests and don't have time to add the final pieces;
more later, perhaps !

** Phil.

format: plain


text:
[Lemma 2, Nagata-UFD]

Lemma 10.120.7 (Nagata's criterion for factoriality). Let $A$ be a domain. Let $S \subset A$ be a multiplicative subset generated by prime elements. Let $x \in A$ be irreducible. Then

1. the image of $x$ in $S^{-1}A$ is irreducible or a unit, and

2. $x$ is prime if and only if the image of $x$ in $S^{-1}A$ is a unit or a prime element in $S^{-1}A$.

Moreover, then $A$ is a UFD if and only if every element of $A$ has a factorization into irreducibles and $S^{-1}A$ is a UFD.

Proof. Say $x = \alpha \beta$ for $\alpha , \beta \in S^{-1}A$. Then $\alpha = a/s$ and $\beta = b/s'$ for $a, b \in A$, $s, s' \in S$. Thus we get $ss'x = ab$. By assumption we can write $ss' = p_1 \ldots p_ r$ for some prime elements $p_ i$. For each $i$ the element $p_ i$ divides either $a$ or $b$. Dividing we find a factorization $x = a' b'$ and $a = s'' a'$, $b = s''' b'$ for some $s'', s''' \in S$. As $x$ is irreducible, either $a'$ or $b'$ is a unit. Tracing back we find that either $\alpha$ or $\beta$ is a unit. This proves (1).

Suppose $x$ is prime. Then $A/(x)$ is a domain. Hence $S^{-1}A/xS^{-1}A = S^{-1}(A/(x))$ is a domain or zero. Thus $x$ maps to a prime element or a unit.

Suppose that the image of $x$ in $S^{-1}A$ is a unit. Then $y x = s$ for some $s \in S$ and $y \in A$. By assumption $s = p_1 \ldots p_ r$ with $p_ i$ a prime element. For each $i$ either $p_ i$ divides $y$ or $p_ i$ divides $x$. In the second case $p_ i$ and $x$ are associates (as $x$ is irreducible) and we are done. But if the first case happens for all $i = 1, \ldots , r$, then $x$ is a unit which is a contradiction.

Suppose that the image of $x$ in $S^{-1}A$ is a prime element. Assume $a, b \in A$ and $ab \in (x)$. Then $sa = xy$ or $sb = xy$ for some $s \in S$ and $y \in A$. Say the first case happens. By assumption $s = p_1 \ldots p_ r$ with $p_ i$ a prime element. For each $i$ either $p_ i$ divides $y$ or $p_ i$ divides $x$. In the second case $p_ i$ and $x$ are associates (as $x$ is irreducible) and we are done. If the first case happens for all $i = 1, \ldots , r$, then $a \in (x)$ as desired. This completes the proof of (2).

The final statement of the lemma follows from (1) and (2) and Lemma 10.120.5. $\square$

Comment #5106 by anon on

If $x/1\in A[S^{-1}]$ is prime then doesn't ideal correspondence for localizations imply $x \in A$ is prime?

Comment #5313 by on

@#5106. I do not understand your comment.

There are also:

• 9 comment(s) on Section 10.120: Factorization

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).


text:
## Basic College Mathematics (10th Edition)

$4^{2}$ * $2^{2}$ Solve the exponents Prime factorization = 4 * 4* 2 * 2 =64


text:
# A Babel of Languages on CodinGame

TBali
14.9K views

## C#

Let's start our journey by visiting C#. It is not the most-used language as of today, but provides modern features, and is used widely in enterprise application development projects.

### Checking the sample code

Let's see our sample puzzle solution in C#. It is a traditional, imperative programming style approach:

### Looking at the syntax

What does the above code snippet reveal about C#?

• using System; C# provides an extensive standard library, that is split to several namespaces. Here we will use only the very basics, but we still need to reference them.
• class Solution C# is object-oriented. Like in Java, we need to have a class to hold our code, even if we don't really use OOP.
• static void Main(string[] args) Every executable program needs a Main method, which will be called, when the program is started.
• { C# has curly braces to construct a code block, similarly to C and many other languages. Whitespaces are usually have no meaning.
• //... Here we commented out the reading from input stream, and replaced it with a simple assignment.
• string m = "CG";
• C# has a static and strong type system. m is declared as a string and it cannot change its type in this program.
• Also note, that semicolon ; ends each statement.
• string[] c = new string[2] {"00", "0"}; We have a wide range of available data structures. c is declared as an array (vector) holding 2 strings, and it is initialized with some string literals. Actually, there is also a shorter syntax for this line, but we are not codegolfing here... (Note: Codegolfing in C# is futile anyhow, as the language tends to be more verbose than others.)
• var b = ""; Didn't we forget here declaring the type? No, because of type inference, the compiler can deduce from the assignment, that b must be a string.
• foreach (char ch in m)
• we can simply iterate through the characters of a string. foreach is available for all iterable data structures.
• Also note, that the curly braces { and } can be omitted, because we use only a single statement within the loop.
• b += Convert.ToString((int)ch, 2).PadLeft(7, '0'); Several things are happening in this line, so let's go one by one:
• We can concatenate strings with the + operator. + is overloaded, meaning different things if operands are strings or integers.
• There is a shortcut for the combination of an operator and an assignment (here: +=).
• We can explicitly cast between compatible types: (int)ch simply gets the ascii code of the character.
• Convert is a class in the standard library (remember the using System; line above?). Its ToString method can be referenced by dot .. In true OOP, even a simple string is an object. ToString() returns a string, so we can immediately invoke the PadLeft() method of the string class on the result.
• While string literals use double quotes ", character literals are marked with single quotes '.
• string ans = c[b[0] - (int)'0'] + " 0"; the only new thing in this line is referencing an array's elements using square brackets [ ]. Arrays are 0 indexed.
• for (int i = 1; i < b.Length; i++) The typical C-style loop syntax. As a string is an object, we get its length by accessing its Length property, and not by a function call, as for example strlen() would do it in C.
• if (b[i] == b[i - 1])
• The conditional statement is quite straight-forward, using a comparison operator == in the boolean expression.
• The ternary operator ? : could have been also used here, but I wanted to show the traditional if.
• Console.WriteLine(ans); Writing to the console. We will need this a lot on CodinGame! :smiley:

### Other characteristics

While not directly visible from the above code snippet, there are some other important aspects of C# worth noting:

• C# is compiled to an intermediate representation, which will be run by a special virtual machine (Common Language Runtime). Such managed code provides lot of advantages, like preventing many types of coding bugs.
• Just-In-Time compilation improves performance. C# code still runs slightly slower than a native compiled code (such as C++ or Rust), but the disadvantage is not huge, and it is still much faster than an interpreted language (such as Python or PHP).
• C# is now cross-platform. Although developed by Microsoft, it is available not only for Windows. Also, it became an ECMA standard.
• C# uses garbage collection, so you don't have to bother too much about memory management.
• There are many advanced language features we could not address in this intro, such us generics, attributes, delegates, LINQ, etc.

### Checking a different approach

C# is a multi-paradigm language. While its design is heavily OOP focused, you can use it in procedural or in functional style. As an illustration, let's revisit the Chuck Norris puzzle in a quite different way!
(Contributed by Djoums):

• We can see the fluent interface in action here: Method calls can be chained to build a more complex query.
• A Regex (regular expression) is a very concise and efficient way for string manipulation. Its disadvantage is that the resulting code is hard to read/understand without checking the regex pattern.
• new string(...) Constructors are overloaded. Here, we create a string by repeating a character by a specified amount.
• => A lambda expression is used to create an anonymous function that can be passed directly to a method as an argument.

### Coming next...

After C#, let's check briefly another, quite similar language: Java!


text:
## anonymous 3 years ago Why we are using LaTeX?

1. zepdrix

Mainly to format math equations. It makes them a lot easier to read! :) Here's an example: y=((ln x)^2)/((x-1)^2+2) All those extra brackets can be confusing! If I format it in LaTeX, I don't need to worry about the outer brackets because it will be very clear which term is on top of the fraction.$\large y=\frac{(\ln x)^2}{(x-1)^2+2}$

2. anonymous


text:
# How to apply geometric transformations to a parametric plot after it has been built?

Suposing that I have precomputed a parametric plot such as pp = ParametricPlot[{2 Cos[x], 3 Sin[x]}, {x, 0, 2 \[Pi]}], an ellipse, how can I apply rotation and translation transform to it?

What I want to do is to apply rotation and translation transforms to pp and not to change the way it was generated, by changing what is inside the brackets.

Is this possible?

Can anyone tell me how to do this? For example, how can I rotate this ellipse around the origin by 45 degrees, and how can I translate it form the origin to the point (0,10)?

Best Regards.

• I'm tempted to call it a duplicate of: 32468 or 100025. 3D or 2D case does not matter here. More explanation can be found in related: 148412 and 104443. What do you think? – Kuba Dec 21 '17 at 18:24

You can use GeometricTransformation:

GraphicsRow[{
(* rotate *)
pp /. Graphics[prim_,opts__] :> Graphics[
GeometricTransformation[prim, RotationTransform[Pi/4]],
PlotRange->Automatic,opts
],

(* translate *)
pp /. Graphics[prim_,opts__] :> Graphics[
GeometricTransformation[prim, TranslationTransform[{0,10}]],
PlotRange->Automatic,opts
]
}]


text:
Quick Overview

In short, the Hawaiian alphabet only has 13 letters – five vowels and eight consonants. Here’s an easy guide to the Hawaiian alphabet:

Keep in mind that:

1. Each of the five vowels are pronounced with only one sound.
2. All consonants sound as they do in English, except for two, as noted below.

Vowel Pronunciation

A – ah, as in father: e.g aloha
E – a, as in way: e.g nene
I  – ee, as in bee: e.g honi
O – oh, as in no: e.g mahalo
U – oo, as in spoon: e.g kapu

Consonant Pronunciation

H  – As in English
K  – As in English
L  – As in English
M – As in English
N  – As in English                                                                                W – After i and e, it is pronounced v
After u and o, it is pronounced like w
At the start of a word or after a pronounced like w or v
– ‘Okina – a glottal stop (more on this below)

In addition, recall that each letter in the alphabet is pronounced separately. This is true even when there are several vowels in a row.

The most important thing to remember is not to be daunted by the seemingly difficult words. After a lesson in pronunciation (you can use the one below) and some practice, you will become more fluent and natural sooner than you probably expect.


text:
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Name Last modified Size; Parent Directory - 12many/ 2005-04-09 19:47 - a0poster/ 2005-02-01 20:43 - a4/ 2020-11-1 Pastebin is a website where you can store text online for a set period of time. \lst@CCPutMacro\lst@ProcessOther {"2D}{\lst@ttfamily{-{}}{-{}}} Is your package available in the TeX catalogue, so I can use it with TeX package manager? +} Could you please take a look at that? 2014-06-21 CTAN update: matlab-prettifier ; 2014-04-29 New on CTAN: matlab-prettifier; more. If I use normal documentclasses such as book, article or report I do not have any problems in compiling. Thanks! format('rat') This has saved me a lot of time. \end{document}. Thanks for your patience! While it doesn't seem to render on screen, it also doesn't break compilation... @Florian: This is the error: "! The easiest way would be to just put it in the same path as your .tex file . 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text:
# The derivative of $f(x) = \tan x\sec x$ using first principles

I have to find out the derivative of given function by using 'first principle method', but the question has eaten half of my brain, the problem is first principle method. The function is $f(x)= \tan x\sec x$.

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Is this a homework question? The problem likely wants you to find the derivative of the function using the limit definition of the derivative. – JavaMan Jan 4 '13 at 21:48
It is from my test sheet. – Syed Sahl Jan 4 '13 at 21:52
Well, you shouldn't be asking for help if it is on a test... – Zev Chonoles Jan 4 '13 at 21:59
@ZevChonoles Often a "test sheet" is a sheet of problem to review before a test. – Alex Becker Jan 4 '13 at 22:00
@Alex: Hmm, I never heard that term before. Sorry for making that assumption, Syed! – Zev Chonoles Jan 4 '13 at 22:05

Because they are more familiar, we express $f(x)$ in terms of sines and cosines. We get $$f(x)=\frac{\sin x}{\cos^2 x}=\frac{\sin x}{1-\sin^2 x}.$$ Thus $$f'(x)=\lim_{h\to 0} \frac{\frac{\sin(x+h)}{1-\sin^2(x+h)}-\frac{\sin x}{1-\sin^2 x}}{h}.$$ We will need to impose the condition $\sin x\ne \pm 1$. Bring the top to the common denominator $(1-\sin^2(x+h))(1-\sin^2 x)$. Some algebra shows that we want $$\lim_{h\to 0}\frac{1+\sin(x+h)\sin x}{(1-\sin^2(x+h))(1-\sin^2 x)} \frac{\sin(x+h)-\sin x}{h}.$$

Now copy the standard first principles argument that shows that $\lim_{h\to 0}\frac{\sin(x+h)-\sin x}{h}=\cos x$. The limits of the remaining terms are easy to compute.

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But that's what I have. – André Nicolas Jan 4 '13 at 23:08
My shift key sticks. So I end up having 62 fairly often instead of ^2. – André Nicolas Jan 4 '13 at 23:14
I have a similar problem! (different key, but same sort of sticky-key problem!) – amWhy Jan 4 '13 at 23:15

Hint: I will map out the approach and see if you can follow it.

Definition: The derivative of the function $f: \mathbb{R} \rightarrow \mathbb{R}$ at a value $x = a$, if it exists, is $$\displaystyle \lim_{h \rightarrow 0} = \large \frac{f(a + h) - f(a)}{h}$$

So, you have $f(x) = \tan(x) \sec(x)$

Let $u(x) = \tan(x)$ and $v(x) = sec(x)$?

Using first principles, you can derive the equation $f'(x)$ for $f(x) = u(x)v(x)$, because we have:

$$\displaystyle \lim_{h \rightarrow 0} = \large \frac{f(a + h) - f(a)}{h} = \frac{u(a + h)v(a + h) - u(a)v(a)}{h}$$

After expanding this and taking the limit, we see that it reduces to $f'(x) = u'(x)v(x) + u(x)v'(x)$.

Do you see that this is the product rule? Do you follow this? Can you actually derive it?

Now, we need $u'(x)$ and $v'(x)$ for $\tan(x)$ and $sec(x)$ and here we will make use of first principles again for those derivatives.

Find the derivative of $\tan(x)$ using first principles.

Using the identity $\sin(A)\cos(B) - \cos(A)\sin(B) = \sin(A-B)$, we find

$\tan(x+h) - \tan(x)$

$= \large \frac{\sin(x+h)}{\cos(x+h)} - \frac{\sin(x)}{\cos(x)}$

$= \large \frac{\sin(x+h)\cos(x)-\cos(x+h)\sin(x)}{\cos(x+h)\cos(x)}$

$= \large \frac{\sin(x+h-x)}{\cos(x+h)\cos(x)}$

$= \large \frac{\sin(h)}{\cos(x+h)\cos(x)}$

$\Rightarrow \large \frac{\tan(x+h) - \tan(x)}{h} = \frac{\sin(h)}{h}[\frac{1}{\cos(x+h)\cos(x)}]$

$\Rightarrow \large \displaystyle \lim_{h \rightarrow 0} \frac{\tan(x+h) - \tan(x)}{h} = \frac{1}{\cos^{2}(x)} = \sec^{2}(x)$

Can you finish it off? Hint: Find the derivative of $\sec(x)$ using first principles and then use the product rule we derived above.

The final result should be: $$f'(x) = \sec(x) (\tan^{2}(x) + \sec^{2}(x))$$

Regards

-


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espressomd-users
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## Re: [ESPResSo-users] Bjerrum Length for Explicit Solvent

 From: Peter Košovan Subject: Re: [ESPResSo-users] Bjerrum Length for Explicit Solvent Date: Sun, 6 Oct 2013 11:22:38 +0200

Dear all,

first of all, thanks for the stimulating discussion. Especially for the remark by Marcus about the need to distinguish the "bjerrum" parameter of Espresso and the physical parameter "Bjerrum length". Just to keep the terminology clear, even though this may seem obvious to many, I add, that it is not the full potential of mean force but the electrostatic contribution to it.

I think Stefan is right that the Bjerrum length is defined as
$$\nabla^2 \Phi = - 4 \pi l_B \rho$$
for two point charges in a dielectric continuum. If we add some excluded volume or polarizability to our point charges, the Bjerrum length becomes ion-specific even in a dielectric continuum. We should observe this when we try to measure the potential of mean force due to electrostatic interactions in an implicit solvent in Espresso where we set the bjerrum parameter to the same value but use polarizable ions.

Similar trouble arises when we use point charges but replace the continuum solvent with an explicit one. We can measure the dielectric constant epsilon_model of our solvent model. This will probably differ from the experimental value epsilon_exp since the model is not exact.

To my understanding, the solution is to adjust our bjerrum parameter such that
1/epsilon_exp = 1/(epsilon_model * epsilon_bjerrum) where epsilon_bjerrum is obtained by substituting the value of bjerrum parameter we provided to Espresso into the common formula for Bjerrum length.

To this end, I do not see inconsistency between what Stefan and Marcus have written.

Btw: does anyone know how users of other software deal with the problem that epsilon_model does not match epsilon_exp? Do they use corrections to epsilon similar to what I described or simply ignore the difference?

With regards,

peter

2013/10/6 Stefan Kesselheim
Hi,
thanks for you long mail Marcus! I'm however not sure that your our conceptions fit..

You say, that the Bjerrum length is the distance where the potential of mean force of two ions in water equals k_B T.
But this would mean, that the Bjerrum length ion (pair) specific. Would that be exactly what we want?

To my understanding the Bjerrum length is a definition with which we theory and simulation guys can write
$$\nabla^2 \Phi = - 4 \pi l_B \rho$$
so that we have single variable determining the strength of electrostatics at a given temperature.

So who is right? It's sunday morning her, and my books don't know about the Bjerrum length.
Cheers
Stefan

On Oct 6, 2013, at 4:07 AM, Markus Deserno <address@hidden> wrote:

> Folks,
>
> this is a beautiful example of the confusion that arises if one does not
> distinguish between the physics one wants to describe and the computer
> variables one types into one's favorite simulation engine.
>
> The Bjerrum length is the distance at which the electrostatic part of the
> free energy of interaction between two unit charges is equal to the thermal
> energy. I concede that my previous email didn't have the important word "free"
> in it. But anyways, this is how it is defined, and no computer simulation
> software in the world will change that. Whether one uses implicit solvent
> or explicit solvent, at the end of the day, it must be true that if you put
> two unit charges at that distance into your simulation, their potential of
> mean force in that solvent is equal to the thermal energy.
>
> Now, in ESPResSo the Bjerrum length is apparently used as an input
> parameter for electrostatics. That is partially convenient, but also partially
> confusing. Stefan is right that if you use an implicit solvent water model,
> you would type in 7 Angstrom at that point, while if you have an explicit
> water model there, there is no need to account for a dielectric constant,
> since it will be created explicitly by the solvent. Electrostatic interactions
> then don't have a dielectric permittivity in them, and one can account that
> by using a value for the Bjerrum length corresponding to vacuum, and
> that is about 56nm (not Angstrom!). But that only means that the parameter
> in the script is set to that value. The Bjerrum length in your simulation should
> be 7A. If it is not, you are simply not simulating water. (In fact, it probably
> is not, since hardly any model is perfect in giving the right dielectric constant,
> and you certainly wouldn't know just by guessing it.)
>
> I also disagree that it's impossible to measure the Bjerrum length. Of course
> it is possible. All you need to do is to measure the potential of mean force
> between two unit charges in your system as a function of distance, and look
> for the distance where it is equal to the thermal energy. This has been done.
> As Stefan suggests, you could alternatively calculate the dielectric constant
> of your system and calculate the Bjerrum length from there.
>
> So again: My main point here is: Please don't lose the physics out of sight.
> It is all fair and square if your simulating day in and day out to think about
> the values of your input parameters. But it is all too easy to forget that the
> value of the input parameters and the physical meaning of the things they
> are supposed to represent are not necessarily the same. I have witnessed
> too often to count that people waste weeks of research by that. In this case:
> Yes, if you want to simulate an explicit water model, you cannot set the value
> of the Bjerrum length input parameter in the Espresso Script to 7 Angstrom.
> And yet, that does not mean that suddenly the Bjerrum length is different.
> It means that the physics is the same but the model is different, and what
> is called "Bjerrum length" in the input script is no longer the Bjerrum length.
> ESPResSo was developed in a time where nobody wanted to simulate
> explicit water with it, and hence it was natural to call the strength parameter
> of the electrostatic interaction the Bjerrum length, since people always used
> implicit models. Now that explicit models are used as well, you simply have
> to jury-rig the code and make it do what you want. You crank up the input
> parameter of the Bjerrum length to its vacuum value. But that doesn't mean
> that the value of the Bjerrum length depends on the model. The Bjerrum
> length is a physics concept and must be model independent. Instead, the
> input parameters of the model must be adapted such as to reflect the right
> physics. Sadly, the input parameters were given physical names, and this
> now may or may not cause confusion.
>
> To be fair: Jezreel probably asked about the input parameter in the first
> place. But the language was confusing. Maybe I'm just a bit too pedantic
> to point all of this out, but in my experience it is helpful to keep a very clean
> line between the physics one wishes to describe and how to algorithmically
> implement this. Using a clear language is never a mistake.
>
> Best,
>
> Markus Deserno
>
>
> --
> Dr. Markus Deserno                    ++1-412-268-4401 (office)
> Associate Professor of Physics        ++1-412-681-0648 (fax)
> Carnegie Mellon University    ++1-412-268-8367 (Amanda Bodnar)
> 5000 Forbes Avenue                    www.cmu.edu/biolphys/deserno/
> Pittsburgh, PA 15213, USA     address@hidden
>
> On Oct 5, 2013, at 9:19 PM, Jezreel Castillo <address@hidden> wrote:
>
>> Thank you very much. It has been very informative.
>>
>> Respectfully,
>> Jezreel
>>
>>
>> On Sun, Oct 6, 2013 at 12:33 AM, Stefan Kesselheim <address@hidden> wrote:
>> Dear Jezreel, Marcus and Espressis,
>>
>> On Oct 5, 2013, at 6:20 PM, Markus Deserno <address@hidden> wrote:
>>
>> > Jezreel,
>> >
>> > the Bjerrum length is the distance at which two unit charges experience
>> > an electrostatic interaction energy equal to the thermal energy. For water,
>> > this is about 7 Angstrom, independent of whether the solvent is treated
>> > explicitly or implicitly. It would be rather unphysical if this physical quantity
>> > depended on the way you implement a solvent in your computer program.
>> > It is rather the other way around: Whatever you do to your computer model,
>> > you must make sure that physical parameters are reproduced, and the
>> > Bjerrum length is one such.
>>
>> I'm not sure if should agree on that. When you create a solvent model with dipoles, partial charges, or whatever you do not know its dielectric constant. You know however the dielectric constant of the medium, you embed it in, typically this is vacuum. In vacuum at room temperature the Bjerrum length is around 56 Angstrom. This is the number you would put into you electrostatics algorithm.
>> The dielectric constant of the medium is a result of a simulation, and can be used to define (!) a Bjerrum length in the medium.
>> I think this is important: l_B is not the distance where the electrostatic energy is unity, but the distance at which it would be unity, if the medium were a homogeneous dielectric with the measured dielectric constant. This also means: there is no way of measuring the Bjerrum length, except for in vacuum.
>> If you treat a solvent implicitly, the Bjerrum length is an input parameter, of course.
>>
>> To make an example: If you want say TIP3P water in Espresso, you create all particles and bonds and such things, and use the vacuum Bjerrum length for the electrostatics algorithm. You can measure a dielectric constant and from that determine the Bjerrum length of the solution. Next you can create an implicit solution model, where you plug in the Bjerrum length you have obtained before, and compare its properties to the original explicit model.
>>
>> I hope I caused not more confusion and that that helps.
>> Cheers
>> Stefan
>>
>>
>

--
Dr. Peter Košovan

Departmtent of Physical and Macromolecular Chemistry
Faculty of Science, Charles University in Prague, Czech Republic

Katedra fyzikální a makromolekulární chemie
Přírodovědecká fakulta Univerzity Karlovy v Praze

www.natur.cuni.cz/chemistry/fyzchem/
Tel. +420221951290
Fax +420224919752


text:
# 27

Warning: this post is moderately technical and very theoretical.

Problem 1: there are five apples on a plate. If you and your friend each eat an apple from the plate, how many apples are left?

Problem 2: what is 5 - 1 - 1?

Word problems are harder than number problems. (Source: every elementary school ever.) This isn’t just true of elementary school students; writing a program which can solve problem 2 is much easier than writing a program which can solve problem 1. Why?

Applying math in the real world requires a recognition/pattern-matching step. We have to notice that some structure in the real world can be represented by mathematical objects, like numbers or functions. In many (most?) cases, that’s the hardest step - figuring out how to translate our own internal world-models into math is more difficult than the math itself.

Unfortunately, the way math is done today often makes the problem harder rather than easier. We usually use definitions and axioms optimized for brevity and elegant proofs, not optimized for ease of recognition in the real world. This post asks: what if our mathematical foundations were optimized from the start for ease of recognition in the hands of AI? In particular, we’ll use the definition of numbers as an example.

## Example: Natural Numbers

The usual way mathematicians construct numbers from first principles goes something like this. We have a number 0, and every number x has a “successor” S(x). So, we have numbers 0, S(0), S(S(0)), S(S(S(0))), ... and we usually use the shorthand notation 1 = S(0), 2 = S(S(0)), 3 = S(S(S(0))), etc. A few more axioms guarantee that these numbers are all distinct (i.e. we don’t have S(S(S(0))) = 0) and there aren’t any “extra” numbers (i.e. numbers which can’t be reached by counting up from 0). There’s various different flavors of this construction in different areas - e.g. we can perform the construction starting from set theory, or from lambda calculus, or from category theory - but they all do basically the same thing.

In some sense, this construction seems to capture the essence of the principle of induction: if a statement like “x is bamfoozled” is true for x = 0, and “x is bamfoozled” implies “S(x) is bamfoozled” (a.k.a. “x+1 is bamfoozled”), then all numbers are bamfoozled. The successor construction provides the minimum framework needed for the principle of induction to work. From a pattern-recognition standpoint: if our goal were to recognize anywhere the principle of induction can be applied, then the successor construction provides a pretty good set of criteria to look for.

Alas, most applications of numbers do not involve induction in any obvious way - not even implicitly. If I say “there are three apples on a plate”, how does that involve induction? Sure, we could formulate it in inductive terms: I could imagine that I started with an empty plate, then put an apple on the plate, then put another apple on the plate, then put another apple on the plate, and wound up with my actual three-apple plate. But I don’t think humans actually think about “three apples on a plate” that way, and I don’t think that would be a very useful design for an AI thinking about “three apples on a plate”.

More generally: any application of natural numbers can be formulated in successor terms. There’s always some isomorphism between any-other-number-formulation and the successor formulation. But when we use the successor formulation, most of the work is in finding those isomorphisms. Instead, we’d like to load more of the work into the definition of numbers. Make the definition do most of the pattern-matching work, so we don’t need complicated case-by-case isomorphisms.

What would that look like?

First pass: our “definition” should be some kind of pattern-template - conceptually similar to a regex. The user (whether human or AI) would match that template against their world-model to recognize numbers. Exactly what it looks like would depend on the kind of world-model we want to match the template against.

As a very toy example, imagine that our “world-model” is just a string, and we want to define the number 3 as a (python) regex. A natural candidate would be

(?P<object>.+)(?P=object)(?P=object)

This regex will match any string which contains (at least) three nonoverlapping copies of the same substring. Each different way of picking three identical “objects” (i.e. nonoverlapping substrings) out of the “world-model” will produce a different match - i.e. a different “three copies of an object”.

That’s a decent definition of “three” in the context of simple string-worlds. But to define “numbers” - i.e. all the numbers - we’d either have to specify each number individually, or use something like the successor construction to specify how-to-construct each number. Neither of those quite seems to capture the underlying idea of “numbers”. In any particular application of numbers (i.e. numbers in the abstract, not just a particular number like three), we’d likely need complicated isomorphisms from our-definition-of-numbers to something-in-our-world-model. For instance, what if we want to talk about general theorems about prime numbers? To do that, we need a general definition of “numbers”, not just case-by-case patterns for each individual number.

To put it differently: the question of “does the number three appear in this situation?” is different from “are numbers relevant in this situation?”. Our regex above would be an ok (though not spectacular) first pass at the former question, but it doesn’t really do any good for the latter question.

## A Better (But Still Not Great) Answer

Let’s change up the question a bit. The key problem is not to recognize any particular number in the wild, but rather to recognize situations where “using numbers” is potentially useful at all.

Rather than pattern-matching against a world model, we’ll pattern-match against a query on a world-model. Rather than looking at apples on a plate and recognizing that there’s three of them, we take some question about apples on a plate (e.g. “will I need to buy more apples before next Thursday?”) and recognize that the number of apples is useful for answering that question.

Here’s one approach: we have some query-function f which depends on some variables x, y, z, ... in the world model, and is invariant under reordering the variables - i.e. f(x, y, z, …) = f(z, y, x, …) = f(y, x, …, z) and so forth. That’s the “pattern” which we look for: our query-function does not care about the order of the variables.

How does this lead to numbers? Well, imagine for a moment that the variables are all binary, so our query is something like f(1,1,0,0,0,0,0,1). But we can re-order the inputs without changing the result - so, in particular, we can sort the inputs: f(1,1,0,0,0,0,0,1) = f(0,0,0,0,0,1,1,1). Any inputs which are the same when sorted produce the same answer. In other words, we get the same answer whenever the number of 0’s and number of 1’s is the same. And we can extend this beyond binary: pick any sort-order for the possible variable values, then sort them, and we find that the query-result depends only on how many of each value appears.

Formally: we can define a function COUNTS which counts how many times each value appears in its input. For instance, COUNTS(“yellow”, “yellow”, 0, “yellow”, “cat”) = {0: 1, “yellow”: 3, “cat”: 1}. Then, given any function f(x, y, z, …) which is invariant under reordering its inputs, we can write f(x, y, z, …) = g(COUNTS(x, y, z, …)) for some function g.

To use this to construct numbers, we flip the whole thing around: we define COUNTS as:

• a function for which any f(x, y, z, …) invariant under reordering inputs can be written as f(x, y, z, …) = g(COUNTS(x, y, z, …)) for some g
• … with the constraint that COUNTS itself should be invariant under reordering its inputs

The second piece guarantees that COUNTS is unique up to isomorphism. (If you’ve studied category theory, this definition should set off some pattern-matchers.)

At this point I’m going to hand-wave. There’s still some nontrivial steps to go from COUNTS to individual numbers, but I think we’ve passed the insights relevant to the point I’m trying to make here. So: “numbers” are <handwave> constructed from equivalence classes induced by COUNTS </handwave>.

## What Does This Buy Us?

This definition immediately buys us a very general, powerful pattern-matcher for recognizing situations where numbers might be useful. Intuitively: numbers are useful when we can “swap around” the inputs without changing the answer.

In the apples-on-a-plate example, we might ask a question like “Will I need to buy more apples before next Thursday?”. The answer to this question probably does not change if we swap one of the apples with another, or move them around on the plate so that an empty space is swapped with an apple. So, we expect that the answer depends only on the number of apples on the plate, not on the details of each apple or how they’re arranged. (Or, more generally, the number of each identical-for-purposes-of-the-question apple-type on the plate; e.g. we might want to distinguish small apples from large.)

As we construct more mathematical operations on top of this idea, we gain additional useful pattern-matchers. For instance, here’s a natural way to think about addition: if a function is invariant not only to reordering its inputs, but also to switching any inputs with value “cat” to 2 (or vice versa), then the function depends only on the sum of the number-of-”cat”-inputs and the number-of-2-inputs. Then, when we prove theorems about addition (e.g. x+y = y+x), those theorems automatically apply to a broad range of “queries” without needing any further work to figure out exactly how our definitions map to the situation at hand.

That said, I still think this construction leaves a lot to be desired. In the apples-on-a-plate example, we can think about swapping an apple with a space-where-an-apple-could-be, but what about moving the apples around more generally? It’s not like plates come with designated apple-slots. It feels like there is a still-more-general pattern for recognizing situations where numbers apply, which would give a still-more-general definition of numbers.

Ideally, we’d find some pattern which provably captures all the possible situations where numbers can show up, without any complicated isomorphisms needed. On the other hand, that’s the sort of problem which sounds very likely to run into uncomputability/undecidability problems.

## Summary

Mathematical definitions are usually not optimized for ease of recognizing real-world situations where the concepts apply. Word problems are harder than number problems.

This post talked about defining numbers in a way which would make it easier to automatically recognize situations where numbers apply. In particular, we saw that numbers apply whenever the answer to some question does not depend on swapping around input variables. There are likely more general patterns which could provide even better definitions, but this already buys us a far more widely applicable pattern-matcher than the usual successor construction of numbers.

One final note: this post talked mainly about the kinds of pattern-matchers one could automate, with an eye toward AI. There’s also plenty to be said about formulating mathematical definitions to make it easy for humans to recognize when the concepts apply. For instance, Category Theory Without The Baggage is my own attempt to do this for some building blocks of category theory. More generally, I think broader adoption of a lot of higher math today is limited by unnecessarily abstract, non-intuitive definitions. (Zooming out even further, this is an instance of Interfaces as a Scarce Resource.) There’s probably gains to be had from reformulating these things in ways which make it easier to recognize applications. Even within pure math, the ability to recognize novel ways to use existing theory in different subfields is quite powerful.

Thankyou to Abram for starting a conversation which led to me writing this post.

# 27

Mentioned in
New Comment

This is great!

An idea which has picked up some traction in some circles of pure mathematicians is that numbers should be viewed as the "shadow" of finite sets, which is a more fundamental notion.

You start with the notion of finite set, and functions between them. Then you "forget" the difference between two finite sets if you can match the elements up to each other (i.e if there exists a bijection). This seems to be vaguely related to your thing about being invariant under permutation - if a property of a subset of positions (i.e those positions that are sent to 1), is invariant under bijections (i.e permutations) of the set of positions, it can only depend on the size/number of the subset.

See e.g the first ~2 minutes of this lecture by Lars Hesselholt (after that it gets very technical)

A problem I'm finding with this formulation is that it moves the problem to something that is arguably harder. We've replaced the problem of recognizing numbers with the problem of recognizing sets. The main post does this as well. There's nothing technically wrong with this, but then the immediate question is this: how do we know when sets are useful? If a similar logic applies: how do we create an abstraction of a set from observation(s)? George Cantor, one of the founders of set theory writes,

A set is a gathering together into a whole of definite, distinct objects of our perception [Anschauung] or of our thought—which are called elements of the set.

To gather distinct perceptions together requires unity of apperception or a single 'I think' to be attached to each perception so that they may be brought under a category/set/etc.

Ooh, I like that formulation. It's cleaner - it jumps straight to numbers rather than having to extract them from counts.


text:
# Thread: Rectangular to Polar Form?

1. ## Rectangular to Polar Form?

How do I convert y = x^2 to polar form?

Thank you, I really appreciate it.

2. Originally Posted by iluvmathbutitshard
How do I convert y = x^2 to polar form?

Thank you, I really appreciate it.
Hi iluvmathbutitshard,

Convert $y=x^2$ into polar form.

In this case there really isn’t much to do other than plugging in the formulas for x and y.

$x=r\cos\theta \:\:and\:\:y=r\sin \theta$

$r\sin \theta=(r\cos \theta)^2$

$r^2 \cos^2 \theta=r\sin \theta$

$r\cos^2 \theta=\sin \theta$

$r=\frac{\sin \theta}{\cos^2 \theta}$

3. Thank you for answering. This is actually the answer I got, but does it translate into a different identity? Because the choices I have been given are:
r = cot(theta) csc(theta)
r = tan(theta) sec(theta)
r = tan(theta)
r = cot(theta)

4. Originally Posted by iluvmathbutitshard
Thank you for answering. This is actually the answer I got, but does it translate into a different identity? Because the choices I have been given are:
r = cot(theta) csc(theta)
r = tan(theta) sec(theta)
r = tan(theta)
r = cot(theta)
Yes.

$r=\frac{\sin \theta}{\cos^2 \theta} \Longrightarrow \frac{\sin \theta}{\cos \theta}\cdot \frac{1}{\cos \theta}={\color{red}\tan \theta \sec \theta}$


text:
libTriton  version 0.6 build 1372
SMT Solver Interface

[internal] All information about the SMT solver interface.

# Description

The solver engine is the interface between an SMT solver and Triton itself. All requests are sent to the SMT solver as Triton AST (See: AstContext). The AST representation as string looks like a manually crafted SMT2-LIB script.

Example:

; Declaration of the theory
(set-logic QF_AUFBV)
; Utility function
(define-fun parity ((x!1 (_ BitVec 8))) (_ BitVec 1)
; x ^= x >> 4;
; v &= 0xf;
; return (0x6996 >> v) & 1;
((_ extract 0 0)
(bvlshr
(_ bv27030 16)
((_ zero_extend 8)
(bvand
(bvxor
x!1
(bvlshr x!1 (_ bv4 8)))
(_ bv15 8)))))
)
; Declaration of the free variables
(declare-fun SymVar_0 () (_ BitVec 8))
; Formula
(assert (= (ite ...)))

# C++ example

Let assume that the $$rax$$'s symbolic expression contains a symbolic variable $$x_0 \in X$$ which has been instantiated previously. At this program point, we want that $$rax = 0$$. We first get the symbolic expression id corresponding to the $$rax$$ register, then, its AST. When the AST has been got, we are able to build our constraint such that $$AST_{constraint} = assert(AST_{rax} == 0)$$.

The solver interface triton::API::getModel() gets as parameter a triton::ast::AbstractNode which corresponds to the $$AST_{constraint}$$ and returns a list of triton::engines::solver::SolverModel. Each model for a symbolic variable $$x \in X$$ is represented by a triton::engines::solver::SolverModel. For example, if there are two symbolic variables in your constraint, the triton::API::getModel() function will return a list of two items.

// Get the symbolic id of RAX
auto raxSymId = api.getSymbolicRegisterId(TRITON_X86_REG_RAX);
// Get the full AST of RAX
auto raxFullAst = api.unrollAstFromId(raxSymId);
// Modify the AST of RAX to build the constraint
auto constraint = triton::ast::equal(raxFullAst, triton::ast::bv(0, raxFullAst->getBitvectorSize()));
auto model = api.getModel(constraint);
// Display all symbolic variable value contained in the model
std::cout << "Model:" << std::endl;
for (auto it = model.begin(); it != model.end(); it++) {
std::cout << " - Variable: " << it->getName() << std::endl;
std::cout << " - Value : " << std::hex << it->getValue() << std::endl;
}


text:
Just how can I reactivate a windows service from another location making use of a manuscript?

I have a Python internet application running in a CherryPy web server, which is running as a windows service. I have a set documents to release this application, yet I'm still needing to remote desktop computer in to the web server to reactivate the solution. Exists any kind of means to manuscript this?

I attempted:

psexec \\server "net restart cherrypyservice"

Yet this does not appear to function.

0
2019-05-07 01:42:11
Source Share

If you intend to make use of psexec:

psexec \\Server cmd "/c net stop servicename"
psexec \\Server cmd "/c net start servicename"

Though in this instance, sc is advised. It does every little thing you require if you're mosting likely to fork over.

0
2019-05-12 01:16:43
Source

Using PowerShell Interactively (localy):

get-service $servicename | restart-service  Using PowerShell Interactively (from another location): (gwmi win32_service -computer$comp -Filter "name='$serviceName'").StopService() (gwmi win32_service -computer$comp -Filter "name='$serviceName'").StartService()  In a function (from another location): function restart-remoteservice{ param($servicename,$computer) (gwmi win32_service -computer$computer -Filter "name='$serviceName'").StopService() (gwmi win32_service -computer$computer -Filter "name='\$serviceName'").StartService()
}

0
2019-05-11 22:03:02
Source

Using Russinovich's psservice :

 psservice \\server restart cherrypyservice

0
2019-05-10 15:39:31
Source

shot

psexec \\server net stop cherrypyservice
psexec \\server net start cherrypyservice

0
2019-05-08 22:55:45
Source

you can make use of the sc command - line device yet i do not recognize just how to do it especially in python.

DESCRIPTION : SC is a command line program made use of for connecting with the NT Service Controller and also solutions. USE : sc [command ] [solution name ] ...

  The option  has the form "\\ServerName"
Further help on commands can be obtained by typing: "sc [command]"
Commands:
query-----------Queries the status for a service, or
enumerates the status for types of services.
queryex---------Queries the extended status for a service, or
enumerates the status for types of services.
start-----------Starts a service.
pause-----------Sends a PAUSE control request to a service.
interrogate-----Sends an INTERROGATE control request to a service.
continue--------Sends a CONTINUE control request to a service.
stop------------Sends a STOP request to a service.
config----------Changes the configuration of a service (persistant).
description-----Changes the description of a service.
failure---------Changes the actions taken by a service upon failure.
qc--------------Queries the configuration information for a service.
qdescription----Queries the description for a service.
qfailure--------Queries the actions taken by a service upon failure.
delete----------Deletes a service (from the registry).
create----------Creates a service. (adds it to the registry).
control---------Sends a control to a service.
sdshow----------Displays a service's security descriptor.
sdset-----------Sets a service's security descriptor.
GetDisplayName--Gets the DisplayName for a service.
GetKeyName------Gets the ServiceKeyName for a service.
EnumDepend------Enumerates Service Dependencies.

The following commands don't require a service name:
sc
boot------------(ok | bad) Indicates whether the last boot should
be saved as the last-known-good boot configuration
Lock------------Locks the Service Database
QueryLock-------Queries the LockStatus for the SCManager Database

EXAMPLE : sc start MyService

0
2019-05-08 22:53:55
Source
net stop cherrypyservice
net start cherrypyservice

with whatever remote implementation engine you favor.

0
2019-05-08 22:52:36
Source


text:
Revision history [back]

Hello, @ chicago: This variant working well but it is a little to long for bigger systems. Thank you of coarse. @ DSM: it's really funny. I have read you answer this morning and I didn't known how to use minimize with a system of functions. But I hag a numeric lecture today where we have done this, so now I know, how to use minimize method with a system. The variant with lambda function does not work for me. I get wrong solutions compared with the minimize method.

I think I will use minimize as often as I can ;) Thanks for quick replies.

Hello,

@ chicago: This variant working well but it is a little to long for bigger systems. Thank you of coarse. coarse.

@ DSM: it's really funny. I have read you answer this morning and I didn't known how to use minimize with a system of functions. But I hag a numeric lecture today where we have done this, so now I know, how to use minimize method with a system. system.

The variant with lambda function does not work for me. I get wrong solutions compared with the minimize method.

I think I will use minimize as often as I can ;) Thanks for quick replies.strong text


text:
## Adding content to Page settings rather than Block settings

Question

I have a Gutenberg editor. Some content of the page is global, and not relevant to an individual block. I’d like to add content to the page settings:

I can see how you can add a plugin that creates a secondary sidebar using registerPlugin, however is there a way to hook into and add settings to the Page settings sidebar?

0
4 months 2022-04-06T11:16:22-05:00 0 Answers 0 views 0


text:
Class 10 CBSE Sample Papers – 2021

Class 9-10, JEE & NEET

Central Board of Secondary Education has released the Class 10 CBSE Sample Papers Board Examinations 2021. To give an overview of the actual exam pattern, CBSE has officially published the Sample Paper for Class 10 of all subjects. Also, the marking scheme and answer key for each paper is available.  Due to the coronavirus pandemic, the syllabus for CBSE Class 10 board exams 2021 has been reduced this year. Students and parents can check the sample papers provided below. Please note that the question papers for the board examinations follow the pattern shared in the sample papers. Going through the exam analysis will help students in evaluating their performance.

There are various speculations regarding the next year’s board examinations. The fact that schools across the country continue to remain closed is a matter of concern. To know more watch the full video. Class 10th CBSE Board 2020-21 | Sample Papers Released – Know Revised Exam Pattern | Major Changes We hope that you must have found this page on “Class 10 CBSE Sample Papers – 2021” useful for your exam preparation. Stay tuned for further updates on CBSE and other competitive exams.
Important Formulas of Maths Class 10 | NCERT Chapter 1 to 5 | Download Mind Map

Class 9-10, JEE & NEET

Mind Map covering Important Formulas of Maths Class 10 will help you to learn all the important and key formulae on Fingertips. The given Mind Map covering Following Chapters from Class 10 NCERT:
• Real Numbers
• Polynomial
• Linear Equations in Two Variables
• Arithmetic Progression
Here is the complete revision for Chapter 1-5 of Mathematics Class 10. Watch out the video and Revise five chapters in 1 Shot!!!!
Get Complete Class 10 Video Lectures and Other Study material. Download eSaral APP
CBSE Class 10 Science Practical Sample Papers

Class 9-10, JEE & NEET

How to Prepare for 10th Board Exams in 1 month | Tips and Strategy to score more than 90%

Class 9-10, JEE & NEET

Last minute revision can be very effective to perform outstanding in Board Exams as it will help to recall all your learning and retain the important information. Most of you are enquiring on How to Prepare for 10th Board Exams in 1 month. To help all class 10 students shed off their exam related stress and revise their syllabus effectively, we bring here some important tips shared by the experienced teacher of eSaral. Strategy shared in this video by Ayushi Ma’am will help you polish your preparations in the last one month of Board Exams. If you follow the given tips rigorously, you can be prepared well for your 10th board exams, even with less time left before the examination starts. 10th board is an important milestone in your life. Therefore, you must make it certain to leave no stone unturned to make yourself and your parents proud. At the same time, also take care of your health! Best of Luck!!!

Class 9-10, JEE & NEET

CBSE Date Sheet 2020 for the pending CBSE 10th Exam 2020 has been released by HRD Minister on his twitter handle. Check the exam dates below. The complete list of papers and the new dates are provided below. Central Board of Secondary Education, CBSE Date Sheet 2020 for pending 10th & 12th board exams has been released today. HRD Minister, Ramesh Pokhriyal had confirmed the same on his twitter handle. The date sheet was earlier expected to be released on May 16 but was deferred till May 18. The complete list of subjects along with the dates as per previous date sheet and new date sheet are listed in the table below. The same would be updated once the new exam dates are announced by the HRD Minister.

10th Board Exam Preparation Tips:
• Make your Revision Time table: CBSE ha released Exam dates for Class 10th, so its time to ace up your preparation. Students can plan their revision as per accordance. Students are advised to provide equal time to every subjects to secure good percentage in Board Exams. Also focus on NCERT, as in board Exams questions are asked directly from the textbooks of students.
• Exam will be conducted in the Morning session from 10:30AM to 1:30 AM, so answer sheets will be distributed at 10:00AM and the students will get question paper at 10:15.
• Students will be advised to spent 15 minutes in reading question paper carefully and prepare plan on how to approach Exam papers.
Tip: Once the exam starts, it is advised to begin with the easiest questions and then move forward  towards difficult ones! With this approcah you can save extra time to attempt long questions.
• Don’t take stress stay calm and positive. Even if you don’t know the answers of the questions, don’t stressed out!!!
• Attempt easy questions first, that will help you in building confidence.
Class 12th Date Sheet 2020
All the Best Students!!! Download eSaral APP to prepare for Class 10, 11, 12, JEE, NEET and other Entrance Examinations.
Maharashtra SSC Board Time Table 2020 | Class 10th – Download PDF

Class 9-10, JEE & NEET

## Maharashtra State Board Time Table 2020 Class 10

Maharashtra SSC Board Time Table 2020 has been released on Official Site. The SSC Time table 2020 of Maharashtra mentions about the exam date of each & every subject. Maharashtra Class 10th Board Exams are to be conducted from 3rd March 2020. If you are a student enrolled in schools of Maharashtra Board then download this date sheet pdf form the section below. The date sheet of 2020 is provided here. As can be seen in the SSC Board Time Table 2020, there are not many gaps for the students to prepare; that is so when they have subjects that come one after another in date sheet. Here we have given the time table for class 10th board exam.

### Preparation Tips for Maharashtra State Board Class 10th Examination

• Plan your Study: Firstly, the students should make a proper plan for the examinations.
• Revision: Secondly, after learning anything, the revision is very important. From revision, the candidates will be able to memorize the things properly.
• Previous Year’s Sample Papers: Finally, the students will feel that preparation will be over then they are required to solve the sample papers of the previous year.
In order to appear for the board examination, students need to carry their SSC board hall ticket. Maharashtra SSC Admit Card / Hall Ticket will be released at least before a month and the board officials of Maharastra will dispatch the hall ticket to their respective schools. Candidates can also download their admit card from the official website of Maharashtra board. Students are advised to keep their hall ticket or admit card safely. Click Here to Open Official Site of Maharashtra State Board
Rajasthan Board Class 10th – Syllabus | Timetable | Previous Year Question Papers

Class 9-10, JEE & NEET

If you are looking for Rajasthan Board Class 10th Syllabus and Timetable for Board Exam 2020, then we are here to inform you that as per the news, RBSE will soon release10th Time Table 2020 in a pdf format. Last year RBSE 10th Exam Dates were announced on December 21. So this year we can expect the time table by the end of December. Important dates related Class 10th RBSE 2020 Exams:
 RBSE 12th Exam Date 2020 Important Dates Availability of Time Table 4th week of Dec Start of Examination March 2020 End of Examination March 2020

 Official Website RBSE http://rajeduboard.rajasthan.gov.in/

### SYLLABUS

Rajasthan Board Class 10th SyllabusRBSE Syllabus Class 10th PDF

### RBSE MODEL PAPERS

RBSE 10th Model Papers for the preparation of upcoming board exams will be available soon for download in PDF format. RBSE 10th Model Papers 2020 will release soon.  Board of Secondary Education, Rajasthan has not released the model papers for the 2020 board exams. The board might shortly release the RBSE 10th Model Papers 2020. Till then students can take help of previous Rajasthan Board papers or Model Papers given below. These papers are important resources and important for the preparation of upcoming Rajasthan Board Exams 2020.
 Model Papers Class 10 RBSE (DOWNLOAD PDF) RBSE Class 10 Board Model Paper Science RBSE Class 10 Board-Model Paper Mathematics RBSE Class 10 Board Model Paper Social Science RBSE Class 10 Board Model Paper Hindi RBSE Class 10 Board Model Paper Sanskrit
The above model papers includes blueprint and complete details of question paper design. Each model papers is published by the Board of Secondary Education, Rajasthan itself and also provided with answers to all the questions.

Answers are provided in each model paper itself. With these help of these model papers, students preparing for RBSE 10th board exams will get an idea about the design of the questions paper and will also understand the level of questions which can be asked in upcoming RBSE 10th exams.

### Download eSaral APP and Prepare for JEE and NEET with KOTA’s TOP FACULTIES

Rajasthan Board 10th Science : Last 5 years Question Papers

Class 9-10, JEE & NEET

Rajasthan Board 10th Science – Past 5 Years Question Papers are always considered as the best source to make an effective preparation for the Board Exams. Here you will get the last years’ RBSE (Board of Secondary Education) School Papers of all subjects of Class 10th (English, Mathematics, Science, Social Science, Sanskrit & Hindi).

 RBSE SOCIAL SCIENCE Class 10th Previous Year Question Papers RBSE-Class-10-Board-Paper-2014-Social Science RBSE-Class-10-Board-Paper-2015-Social-Science RBSE-Class-10-Board-Paper-2018-Social-Science

##### RBSE Syllabus Class 10th 2020 👈
Previous Year Question Papers are always considered as the top source to make an effective preparation for the Board Exams. eSaral Provides you last five years’ RBSE (Board of Secondary Education)n Science Question Papers. These papers will act as the practicing tests for class 10th students. Previous year question papers for Rajasthan board are a smart way to prepare for Exams and Score high marks.

Students must solve the previous year question papers for all subjects by setting the conditions like those in the real board exam so that they may get the examination’s experience beforehand. This way they will be able to evade the unnecessary stress and nervousness while writing the exam in the examination hall on the final day.

Students can directly download PDF of last few years’ questions paper of all subjects (Class 10th) from the link provided in the given table below:

 Mathematics  👈

RBSE Previous years question papers are quite useful as they help students familiarize with the design of the paper and the marking system. Practicing the previous year papers helps you get an idea of some important topics and concepts experienced in the board exams. It also helps you review the whole syllabus in a more effective way as well as measures your preparation for the actual exam. Past year question papers help students measure their strengths and weaknesses so that they can focus on weaker sections to progress in them.

Rajasthan Board 10th English : Last 5 years Question Papers

Class 9-10, JEE & NEET

Rajasthan Board 10th English – Past 5 Years Question Papers are always considered as the best source to make an effective preparation for the Board Exams. Here you will get the last years’ RBSE (Board of Secondary Education) School Papers of all subjects of Class 10th (English, Mathematics, Science, Social Science, Sanskrit & Hindi).

 RBSE SOCIAL SCIENCE Class 10th Previous Year Question Papers RBSE-Class-10-Board-Paper-2014-English RBSE-Class-10-Board-Paper-2015-English RBSE-Class-10-Board-Paper-2016-English RBSE-Class-10-Board-Paper-2018-English

##### RBSE Syllabus Class 10th 2020 👈
Previous Year Question Papers are always considered as the top source to make an effective preparation for the Board Exams. eSaral Provides you last five years’ RBSE (Board of Secondary Education) English Question Papers. These papers will act as the practicing tests for class 10th students. Previous year question papers for Rajasthan board are a smart way to prepare for Exams and Score high marks.

Students must solve the previous year question papers for all subjects by setting the conditions like those in the real board exam so that they may get the examination’s experience beforehand. This way they will be able to evade the unnecessary stress and nervousness while writing the exam in the examination hall on the final day.

Students can directly download PDF of last few years’ questions paper of all subjects (Class 10th) from the link provided in the given table below:

 Social Science 👈 Sanskrit 👈 Mathematics  👈

RBSE Previous years question papers are quite useful as they help students familiarize with the design of the paper and the marking system. Practicing the previous year papers helps you get an idea of some important topics and concepts experienced in the board exams. It also helps you review the whole syllabus in a more effective way as well as measures your preparation for the actual exam. Past year question papers help students measure their strengths and weaknesses so that they can focus on weaker sections to progress in them.

Rajasthan Board 10th Social Science : Last 5 years Question Papers

Class 9-10, JEE & NEET

Rajasthan Board 10th Social Science – Past 5 Years Question Papers are always considered as the best source to make an effective preparation for the Board Exams. Here you will get the last years’ RBSE (Board of Secondary Education) School Papers of all subjects of Class 10th (English, Mathematics, Science, Social Science, Sanskrit & Hindi).

 RBSE SOCIAL SCIENCE Class 10th Previous Year Question Papers RBSE-Class-10-Board-Paper-2014-Social Science RBSE-Class-10-Board-Paper-2015-Social-Science RBSE-Class-10-Board-Paper-2018-Social-Science

##### RBSE Syllabus Class 10th 2020 👈
Previous Year Question Papers are always considered as the top source to make an effective preparation for the Board Exams. eSaral Provides you last five years’ RBSE (Board of Secondary Education) Social Science Question Papers. These papers will act as the practicing tests for class 10th students. Previous year question papers for Rajasthan board are a smart way to prepare for Exams and Score high marks.

Students must solve the previous year question papers for all subjects by setting the conditions like those in the real board exam so that they may get the examination’s experience beforehand. This way they will be able to evade the unnecessary stress and nervousness while writing the exam in the examination hall on the final day.

Students can directly download PDF of last few years’ questions paper of all subjects (Class 10th) from the link provided in the given table below:

 English 👈 Sanskrit 👈 Mathematics  👈

RBSE Previous years question papers are quite useful as they help students familiarize with the design of the paper and the marking system. Practicing the previous year papers helps you get an idea of some important topics and concepts experienced in the board exams. It also helps you review the whole syllabus in a more effective way as well as measures your preparation for the actual exam. Past year question papers help students measure their strengths and weaknesses so that they can focus on weaker sections to progress in them.

Rajasthan Board Class 10th Mathematics : Last 5 years Question Papers

Class 9-10, JEE & NEET

Rajasthan Board Class 10th Mathematics – Past 5 Years Question Papers are always considered as the best source to make an effective preparation for the Board Exams. Here you will get the last years’ RBSE (Board of Secondary Education) School Papers of all subjects of Class 10th (English, Mathematics, Science, Social Science, Sanskrit & Hindi).

 RBSE MATHEMATICS Class 10th Previous Year Question Papers RBSE-Class-10-Board-Paper-2014-MATHEMATICS RBSE-Class-10-Board-Paper-2015-MATHEMATICS RBSE-Class-10-Board-Paper-2016-MATHEMATICS RBSE-Class-10-Board-Paper-2017-MATHEMATICS RBSE-Class-10-Board-Paper-2018-MATHEMATICS

##### RBSE Syllabus Class 10th 2020 👈
Previous Year Question Papers are always considered as the top source to make an effective preparation for the Board Exams. eSaral Provides you last five years’ RBSE (Board of Secondary Education) Math Question Papers. These papers will act as the practicing tests for class 10th students. Previous year question papers for Rajasthan board are a smart way to prepare for Exams and Score high marks.

Students must solve the previous year question papers for all subjects by setting the conditions like those in the real board exam so that they may get the examination’s experience beforehand. This way they will be able to evade the unnecessary stress and nervousness while writing the exam in the examination hall on the final day.

Students can directly download PDF of last few years’ questions paper of all subjects (Class 10th) from the link provided in the given table below:

RBSE Previous years question papers are quite useful as they help students familiarize with the design of the paper and the marking system. Practicing the previous year papers helps you get an idea of some important topics and concepts experienced in the board exams. It also helps you review the whole syllabus in a more effective way as well as measures your preparation for the actual exam. Past year question papers help students measure their strengths and weaknesses so that they can focus on weaker sections to progress in them.

Rajasthan Board Class 10th Sanskrit : Last 5 years Question Papers

Class 9-10, JEE & NEET

Rajasthan Board Class 10th Sanskrit – Past 5 Years Question Papers are always considered as the best source to make an effective preparation for the Board Exams. Here you will get the last years’ RBSE (Board of Secondary Education) School Papers of all subjects of Class 10th (English, Mathematics, Science, Social Science, Sanskrit & Hindi).

 RBSE SANSKRIT Class 10th Previous Year Question Papers RBSE-Class-10-Board-Paper-2014-SANSKRIT RBSE-Class-10-Board-Paper-2015-SANSKRIT RBSE-Class-10-Board-Paper-2016-SANSKRIT RBSE-Class-10-Board-Paper-2017-SANSKRIT RBSE-Class-10-Board-Paper-2018-SANSKRIT

##### Rajasthan Board Class 10th SANSKRIT SYLLABUS – RBSE Syllabus Class 10th 2020 👈
Previous Year Question Papers are always considered as the top source to make an effective preparation for the Board Exams. eSaral Provides you last five years’ RBSE (Board of Secondary Education) Sanns Question Papers. These papers will act as the practicing tests for class 10th students. Previous year question papers for Rajasthan board are a smart way to prepare for Exams and Score high marks.

Students must solve the previous year question papers for all subjects by setting the conditions like those in the real board exam so that they may get the examination’s experience beforehand. This way they will be able to evade the unnecessary stress and nervousness while writing the exam in the examination hall on the final day.

Students can directly download PDF of last few years’ questions paper of all subjects (Class 10th) from the link provided in the given table below:

 Science 👈

RBSE Previous years question papers are quite useful as they help students familiarize with the design of the paper and the marking system. Practicing the previous year papers helps you get an idea of some important topics and concepts experienced in the board exams. It also helps you review the whole syllabus in a more effective way as well as measures your preparation for the actual exam. Past year question papers help students measure their strengths and weaknesses so that they can focus on weaker sections to progress in them.

Rajasthan Board Class 10th Hindi: Last 5 years Question Papers

Class 9-10, JEE & NEET

Rajasthan Board Class 10th HINDI Past 5 Years Question Papers are always considered as the best source to make an effective preparation for the Board Exams. Here you will get the last years’ RBSE (Board of Secondary Education) School Papers of all subjects of Class 10th (English, Mathematics, Science, Social Science, Sanskrit & Hindi).

 RBSE HINDI Class 10th Previous Year Question Papers RBSE-Class-10-Board-Paper-2014-HINDI RBSE-Class-10-Board-Paper-2015-HINDI RBSE-Class-10-Board-Paper-2016-HINDI RBSE-Class-10-Board-Paper-2018-Hindi
Previous Year Question Papers are always considered as the top source to make an effective preparation for the Board Exams. eSaral Provides you last five years’ RBSE (Board of Secondary Education) Hindi Question Papers. These papers will act as the practicing tests for class 10th students. Previous year question papers for Rajasthan board are a smart way to prepare for Exams and Score high marks.

Students must solve the previous year question papers for all subjects by setting the conditions like those in the real board exam so that they may get the examination’s experience beforehand. This way they will be able to evade the unnecessary stress and nervousness while writing the exam in the examination hall on the final day.

Students can directly download PDF of last few years’ questions paper of all subjects (Class 10th) from the link provided in the given table below:

RBSE Previous years question papers are quite useful as they help students familiarize with the design of the paper and the marking system. Practicing the previous year papers helps you get an idea of some important topics and concepts experienced in the board exams. It also helps you review the whole syllabus in a more effective way as well as measures your preparation for the actual exam. Past year question papers help students measure their strengths and weaknesses so that they can focus on weaker sections to progress in them.

How to Prepare for Class 10 Board Exams

Class 9-10, JEE & NEET

In this video we will learn How to prepare for class 10 board exams. This video is an interview of Class 10 CBSE Boards 2018 Topper Nandini Garg. Nandini scored 499 marks out of 500 in 2018 CBSE Boards exams. She scored 100/100 in English, Math, Science and Social Studies and scored 99/100 in Hindi paper. Who can give tips on preparation of boards exam other then CBSE Topper herself. In this post you will find list of 5 videos where Nandini explains how one should prepare for boards and how to prepare for each subject.

## How to Prepare for Class 10 Board Exams

Inthis video you will find general tips for the exam preparation. These tips are applicable for your overall preparation.

## How to Prepare for Science

Now lets get started with our subjectwise strategies. First we will cover up Class 10 Science.

## How to Prepare for Mathematics

In this video we will discuss how to ge 100/100 in math exam.

## How to Prepare for Social Science

This is the pain area for most of the class 10 students. We will see what Nandini did in Social Studies exam that fetched her unbelievable 100/100 in Social Studies.

## How to Prepare for English and Hindi

It is said that no one scores 100/100 in language paper. But beyond everyones expectation Nandini scored 100/100 in English exam. She revels her secrets and also discusses do’s and dont’s in Hindi Exam.

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text:
# Polynomial ring/Field/Degree/Simple rules/Fact/Proof/Exercise

Let ${\displaystyle {}K}$ be a field and let ${\displaystyle {}K[X]}$ be the polynomial ring over ${\displaystyle {}K}$. Prove the following properties concerning the degree of a polynomial:
1. ${\displaystyle {}\operatorname {deg} \,(P+Q)\leq \max\{\operatorname {deg} \,(P),\,\operatorname {deg} \,(Q)\}\,,}$
2. ${\displaystyle {}\operatorname {deg} \,(P\cdot Q)=\operatorname {deg} \,(P)+\operatorname {deg} \,(Q)\,.}$


text:
# How to linearize a max min objective function?

Let us suppose that I have a $$\max \min$$ objective function that only depends on one set of variables:

$$\underset{x}\max \underset{y}\min dy$$

Associated with the linear set of constraints and right size real matrices and vectors $$A, B, b$$ and $$d$$:

$$Ax + By\le b$$

$$(n,m)\in \mathbb N^2$$.

$$x\in \{0,1\}^n$$

$$y\in \{0,1\}^m$$

Meaning that the model tries to chose the values of $$x$$ so that $$\underset{y}\min dy$$ is maximized.

Is it possible to linearize this objective function to get an ILP or a MILP at the end?