integration – can i write this $int_{mathbb{R}^2} psi(textbf{x}) , d^{2}textbf{x} = 2pi int_{0}^{infty} rho , phi(rho), drho $?

If the function $psi$ is isotropic, (i.e. $psi(textbf{x}) = phi(|textbf{x}|)$, where $phi in L^{1}(mathbb{R})$, then can i write
int_{mathbb{R}^2} psi(textbf{x}) , d^{2}textbf{x} = 2pi int_{0}^{infty} rho , phi(rho), drho ,

where $rho=|textbf{x}|$ is the norm of $textbf{x}$ in $mathbb{R}^{2}?$

How can I write the eyes emoji in Skype?

How can I write the eyes emoji in Skype?

I mean this emoji:

enter image description here

While I know that if I write the (eyespeechbubble) I will get this emoji:

enter image description here

So, I would hope for there being a code something like (eye) or (eyes), but I was not able to find one.

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How do I write non-English text on image using php

How do I write non-English text on image using php

Here’s my situation.
Mobile users have an option to switch their keyboards to a different language.
Some users might be using a chinese language keyboard, some might use Italian, some might use Indian hindi, or Indian Bengali etc etc.
Most are using default English keyboard.

Now I want to take the text they entered and put it on an image, as caption.
I know how to do this with English text.
That is no problem.

How do I do it if they are using some other language?
Is there a global font file I can use?

If not, where can I download those language font files which these devices are using?
And most important, how do I find out which language they typed in?

Any help is greatly appreciated.


architecture – What are some of the best tools to write, manage, and validate software configuration?

Let’s say you have a project that relies on user-defined configs which have a lot of parameters and sub-parameters. What’s the best tool to manage this kind of complexity so that the config schemas are:

  • easy to define by the developer
  • easy to set by the end-user to make changes
  • Avoids duplication of any parameters (happens easily when there are too many configs)
  • easy to validate when changes are made

I’m aware of json-schema and it does a pretty decent job. I was reading on jsonnet and sounds like it’ll be better than json-schema. I have also researched a bit on marshmallow and pydantic but I’m not sure these are the tools I’m looking for.

Is there anything out there that is latest and greatest and the most intelligent that I’m unaware of? The project is in python if that makes any difference.

PS: Just to clarify, I’m not looking for config management tools like chef, puppet, or salt.

Write an equation of the perpendicular bisector of the line segment whose endpoints are (-1, 1) and (7, -5) [closed]

I’m in 10th grade Geometry and i’m stuck on this. I’d appreciate all help!

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As I force MMA to write the results in the traditional way?

As I get the output in the form that one writes by hand, I have tried with TraditionalForm, but it does not work

I’ve looked at several answers in the forum but I can’t find any that help

enter image description here

a^(2/3) - a^(1/3) b^(1/3) + b^(2/3) -> Power(a^2, (3)^-1) - Power(ab, (3)^-1) + Power(b^2, (3)^-1)

a^(3/4) - Sqrt(a) b^(1/4) + a^(1/4) Sqrt(b) - b^(3/4) -> Power(a^3, (4)^-1) - Power(a^2 b, (4)^-1) + Power(ab^2, (4)^-1) - Power(b^3, (4)^-1)

a^(4/5) - a^(3/5) b^(1/5) + a^(2/5) b^(2/5) - a^(1/5) b^(3/5) + b^(4/5) -> Power(a^4, (5)^-1)  - Power(a^3 b, (5)^-1) + Power(a^2 b^2, (5)^-1) - Power(ab^3, (5)^-1) + Power(b^4, (5)^-1)

python – How to write elements from a list into a csv with different columns

I have a list for example

('1 sam 2000','2 jack 1232','3 lily 34')

Each element in the list actually contains information for 3 columns and separated by spaces.
These were read from a txt file.

with open('test.txt','r',encoding='utf-8',errors='ignore') as file:
    li = ()
    for i in file:

        i =i.rstrip('n')

Or shall can I simply convert txt into csv ?

plotting – How to properly write multiline text with LaTeX symbol in a frame and with background

I wanted to include a number of text-box with background color white inside a plot. The text inside the box will also have LaTex expressions as well as multiple lines.

Is there any way to include multiline text (including LaTeX symbol) inside a plot?

In addition I want to set frame and background color for the box.
I am currently using Epilog and Prolog to include such text.

  PDF(BinomialDistribution(50, p), k)}, {p, {0.3, 0.5, 0.8}}, {k, 0,50}), 
  Filling -> Axis, 
  FillingStyle -> Automatic,
  Epilog -> Text(Style(ToExpression("\text{E}_{x} \n text2", TeXForm, HoldForm),Bold),{30, 0.13}),
  Prolog -> {Inset(Framed( "E_{x}ntext2" , RoundingRadius -> 5,Background -> White), {45, 0.13})}
(*Prolog -> {Inset(Framed( MaTeX("E_{x}\n text2" ) , RoundingRadius -> 5,Background ->White),{45,0.13})}*)

Option-1 fails writing E_{x} as well as breaking line.
Option-2 fails writing E_{x} but breaks line.
Option-3 is the one I wanted but it fails in breaking line.

Is there any way to achieve this.

Moreover I also wanted to ask, what should one do if one has to include say more that two text boxes?