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How to write a latex macro to reference a particular time in a set of youtube videos?

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I have a set of educational youtube videos that I want to reference in a document, with links to a particular time in the video. In Python, the code I want would do something like this:

``````links = {
}

def youTubeRef(text:str, ref:str h:int, min:int, sec:int):
return '<a href="{link}">{text}</a>'  # though in latex it would just be a href

``````

Then, in a latex document, I would like to use this like so:

``````Here is youTubeRef{my text}{first}{0}{12}{13}
``````

And the final rendered document would show:

Here is my text

TypeError: ‘NoneType’ object is not iterable using Zonal Statistics

I’m trying do looping zonal statistics to many polygons in a folder, and rasters in aonther folder. Each polygon from a specific folder need to get the mean values from a many rasters from another folders, like slope, standard deviation, etc. But when I run this code the error is:

Traceback (most recent call last):
File “D:/ZONAL1.py”, line 10, in
for shp in shapefiles:
TypeError: ‘NoneType’ object is not iterable

What this means?
My code:

``````import arcpy
import os

arcpy.env.workspace = r'D:pontos_modelagembuffers'
arcpy.env.workspace = r'D:slopes'
arcpy.env.overwriteOutput = True
output = "D:tractebelpontos_modelagembufferdbf"
rasters = arcpy.ListRasters()
shapefiles = arcpy.ListFeatureClasses()
for shp in shapefiles:
for rst in rasters:
table_out = output + "\" + shp + "_Zonal_Est"
arcpy.gp.ZonalStatisticsAsTable_sa(shp,'FID',rst, table_out,"MEAN")
``````

Solve \$1= (x^2+y^2)^{1/2} +((x-1)^2+y^2)^{1/2}.\$

Solve $$1= (x^2+y^2)^{1/2} +((x-1)^2+y^2)^{1/2}$$
for real numbers $$x,y$$. A accept a curve if it is possible or a picture. It may be a cusp.

QGIS – after restarting project WFS Layer only displays after opening attribute table and changing zoom

When i close my project and restart, some WFS Layers are behaving strange. They only display the data after loading/opening attribute table and changing zoom. I’ve tried refreshing with F5 but it is not helping. Any ideas?

Which is the real Euler’s Rotation theorem?

There are two quite different, but useful, theorems related to 3D rotation that are referred to as “Euler’s Rotation Theorem“.

The first definition is given as a quotation in the book by Kuipers

• Any two independent orthonormal coordinate frames can be related by a sequence of rotations (not more than three) about coordinate axes, where no two successive rotations may be about the same axis.

There is a similar, but more pithy definition, from Wolfram MathWorld

• An arbitrary rotation may be described by only three parameters.

This is related to the three-angle representation of an arbitrary rotation by Euler, roll-pitch-yaw, Tati-Bryan angles etc.

The second definition is from Wikipedia

• When a sphere is moved around its centre it is always possible to find a diameter whose direction in the displaced position is the same as in the initial position. (Also given in latin)

This related to the angle-axis representation of an arbitrary rotation. This version of the Rotation Theorem is found in many other places as well, including here on Math Overflow.

Both definitions are related to rotation, and the second at least has a reference to Euler 1776. The first is related to Euler axes and Euler angles, seems like the sort of thing Euler might have figured out, but Kuipers does not provide a reference.

Euler was notorious for not publishing much. Somebody, post Euler, has declared these theorems as Euler’s Rotation Theorem. Which one is it? Is there a more nuanced way to refer to them?

Using Overpass to find intersections with 3 or more links

I’m trying to find all the intersections (nodes) with 3 or more links (ways) in an area as an indicator for walkability. Complete beginner to the Overpass API and this has me pretty stumped. OSM clearly shows which ways are part of a node, suggesting that this should be very doable. Can’t be much more specific as I don’t even know where to start, so thanks in advance for any help!

USN-5931-1 Why is this security patch only for ESM/ Ubuntu Pro

18.04 LTS still has general support until April 2023, the patch for USN-5931-1 was released March 7th 2023. As march is before April, and this is a security patch, this should have been included in support offered via LTS. Why was this decided to be only offered for ESM?

A riddle involving the axiom of choice

So i found a riddle on reddit which is a consequence of the axiom of choice.

There is a house with 100 rooms, and each room contains countably many boxes indexed with the natural numbers. Each box contains a random real number, which is the same over all the rooms (that is, box n contains the same real number in every room).

100 set theorists play a game. Each person will go into a unique room and open as many boxes as they like (perhaps countably many) as long as they leave at least one box in their room unopened. Then, each of them need to pick an unopened box in their room, and guess what real number is inside of it.

In order to win, 99 of them need to guess correctly.

The mathematicians can discuss a strategy beforehand, but after they go into their respective rooms, no more communication is allowed. What is a 100% winning strategy for this seemingly impossible task?

My question is why can the mathematicians agree on a specific representative for each equivalence class? I thought that the axiom of choice guaranteed a choice function existed, but didnt specify it. But for the solution to the riddle, they would need to know what the choice function is. Can someone explain?

problem with Ubuntu Pro blocked my pc

I am user of Bodhi 18.04 LTS Bionic 32 bit wich based on Ubuntu.I update to nvidia-304 and now i can’t enter on my Bodhi os. because it’s show me Ubuntu Pro at the beginning.After insert my password and Token, he show me the error:

WARNING:root:failed to process /proc/version_signature.

Anyone have solution to help me ?

Exponentials of stochastic band matrices

This may be a duplicate, but I’ve done some searching and I can’t find exactly this problem setting, probably due to not knowing the right terminology for how to refer to the transition matrix.

I’m considering absorbing random walks $${X_t}$$ which have symmetric transition probabilities inside a window of size $$k$$. For example, on $${0, 1, 2, dots, 100}$$, with $$k=3$$ if $$X_t = 5$$
begin{align*} P[X_{t+1} = 4] &= P[X_{t+1} = 6]\ P[X_{t+1} = 3] &= P[X_{t+1} = 7]\ P[X_{t+1} = 2] &= P[X_{t+1} = 8]\ end{align*}

When the walk is within $$k$$ of the endpoint, the allowable transitions are truncated on both sides, e.g. if $$X_t = 1$$, $$P[X_t = 3] = 0$$.

I wanted to figure out the probability of the walk being absorbed at the upper endpoint, so I did some numerical experiments with walks on the integers from 0-100.
I calculated $$T^n$$ for the transition matrix $$T$$ and a large $$n$$. I then looked at $$(T^n)_{i, 100}$$ to see the probability of being absorbed at 100. It appears that the value is always equal to $$i/100$$, regardless of how I set the transition distribution or window-size.

The transition matrix for a walk on the integers in $$[0, N]$$ has the following properties:

1. $$T$$ is (row) stochastic
2. $$T$$ is a band matrix with upper and lower band size $$k$$
3. $$T_{i, j} = 0$$ if $$|i – j| > max (i, N – i)$$
4. $$T_{i,i + r} = T_{i, i – r}$$ (this is the main property I don’t know the name of)
5. $$T_{0, 0} = T_{1, 1} = 1$$

I would like a proof or counterexample of the following statement:
$$begin{equation*} limlimits_{n to infty} (T^n)_{i, N} = i/N end{equation*}$$

If the statement above is true, is it still true if the transition distributions are no longer left-right symmetric, but it’s still the case that $$E[X_{t + 1}] = X_t$$?

trouble with writing negative fractional exponential

Code:

``````begin{equation*}
v_o = (v_i - V_D) e^-frac{ t}{tau}
end{equation*}
``````

What I want:

What I am getting:

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