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## What is the optimal direction of constant acceleration for a moving particle to reach a target point in 2D?

A particle in the plane has initial position $P$ and initial velocity $V$. It can accelerate at exactly rate $A$ in any direction $\theta$. What path describes the time-optimal trajectory to a target point, $G$? My intuition leads me to believe there is a single value of $\theta$ that if the particle accelerates in that […]

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## How can FTIR method can be used quantitatively to detect the absorption if I have energies of non-radiant and radiated compounds?

So, I have two spectrums given for compound energies that are non radiant and radiated. Plotting the graph of the spectrum data one can observe that on one spectrum the absorption is greater between non-radiant and radiated compound than for the other. But the absorption rate is shown in relation to other energies, so the […]

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## Is there a way to get relative center of a Rect object in pygame?

Now, suppose I always want to draw a circle at the center of a rect object, now, the problem is: For example, if I do pygame.draw.circle(Surface, BLUE, Surface.rect.center, radius, width=3) This will and does fail because Surface.rect.center is actually the coordinates of the center of the Rect object relative to the (0,0) point -top left […]

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## Save multiple impala-query outputs for use in python (without saving each individual query as a .csv)

I’m running multiple impala queries in a bash script, saving them to variables, printing out results in terminal, and additionally, attempting to save the output tables stored in variables to a .txt file which can then somehow be parsed in python: a=$(impala-shell -q “SELECT 1;”) b=$(impala-shell -q “SELECT 2;”) echo -e “print out result of […]

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## Publishing, Intellectual Copyright

So effectively, I am working on creating my very own TTRPG rulebook based on my own setting and universe. The only question I got is how much of mechanics am I allowed to be inspired by? Effectively, Warhammer 2E was a HUGE inspiration for this. I loved the percentiles, the combat mechanics, how your character […]

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## On a mysterious reference of Grothendieck

These days I found a mysterious page on Google books describing a book entitled On the De Rham cohomology of schemes by Grothendieck, Coates, and Jussila. At once I thought this was an error and Google books had miss-indexed Exposé IX of Dix Exposés sur la Cohomologie de Schémas. However, the references diverge both in […]

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## Construction of a piecewise linear function

Given some continuous probability distribution $\rho$ over $\mathbb{R}^3$-tuples (a, w, b), define the function $y(x) = \int a \max(0, wx+b) \rho(da,dw,db)$. Can we construct a continuous probability distribution $\rho$ s.t. $y$ is a (non-constant) piecewise linear function over $\mathbb R$. Is that possible? A couple things to note here: 1) For discrete or mixed discrete-continuous […]

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## Can a 2014 15″ MBP run 2 external monitors if one is a 4k?

I have a 15″ mid-2014 MBP (NVIDIA GeForce GT 750M 2048 MB). According to https://support.apple.com/kb/SP704?viewlocale=en_US&locale=en_US, it “Simultaneously supports full native resolution on the built-in display and up to 2560 by 1600 pixels on up to two external displays, both at millions of colors”. However, I’m currently running a single 4K monitor at 60 Hz. Given […]