graphics – How can I make this background white and stop it being “light red” as some kind of default?

This

 Graphics[Square, Background -> Yellow]

yields what it should do, namely:

enter image description here

But when I try to change the background to white, by going

Graphics[Square, Background -> White]

I get this:

enter image description here

Argh! How can I make the background really white? Note that the problem also occurs when I specify white using RGBColor.

What kind of artistic variables are useful for water?

I have tried to implement water by solving the shallow water equations, but it is very complicated, computationally expensive and hard to get right (especially near coastlines) so I was wondering if I could approach the problem from a different direction.

What kind of variables would one want to have to steer how water behaves/looks? I have thought of:

  • wind/water velocity (for visual feedback and boat mechanisms or something)
  • terrain (so it can flow down, creating waterfalls and such)
  • ripples (to make satisfying visuals and maybe cannon mechanics or something)

Do you know more common use cases for water? Maybe I can get away with some model that can churn out beautiful visuals (maybe deep learning based?) instead of solving pdes that diverges for seemingly no reason….

An api for github to get some kind of projects?

I’m trying make an dataset of projetcs from github, with some similarities, like language. The github api got an endpoint to that? Thanks

ag.algebraic geometry – Symmetric matrices of Hyperbolic and elliptic type with certain kind of trace zero

I have been working on a problem related to determinantal varieties in Symmetric matrices. I am stuck at the following point and would like to get some reference/help for the following question.
Let $mathbb{F}_q$ be a finite field with odd characteristic and let $S(2t, m)$ be the set of all $mtimes m$ symmetric matrices over $mathbb{F}_q$ of rank $2t$(even). For some $deltainmathbb{F}_q$ a square (non-square) and $kle m$ let $f^delta_k(X)= X_{11}+cdots+X_{k-1k-1}+delta X_{kk}$. I want to know the cardinality of the following set
$$
{Ain S(2t, m): Atext{ is hyperbolic and }f^delta_k(A=0}.
$$

Here, by hyperbolic $A$ we mean that the corresponding quadric $XAX^T$ is hyperbolic. I am stuck at this point. My approach was to use some induction on $k$. To do so, I was thinking to project a symmetric matrix to an $m-1times m-1$ matrix by deleting its first row and first column. But I have no control over the behavior of the fiber of this map. For example, if we take an $m-1times m-1$ symmetric matrix of rank $2t-2, ;2t-1 or ;2t$ and add a new row and column to obtain a matrix in $S(2t, m)$, what are the odds to get a hyperbolic matrix?

I know this stuff is quite classical and probably this problem is already well understood. But unfortunately, I could not find references that only gives the number of symmetric matrices that are hyperbolic and elliptic.

What kind of polarizer do I get for a wide-angle 65 mm lens?

I have a Nikon D7500 and it came with a cheap XIT wide angle lens. I’m trying to find a polarizer for it but I can’t find any online that are for a 65 mm lens.

This is my first DSLR so I’m still learning how it all comes together.

Can anyone help me understand what size polarizer I need?

What kind of polarized do I get for a wide-angle 65 mm lens?

I have a Nikon D7500 and it came with a cheap XIT wide angle lens; I’m trying to find a polarizer for it but I can’t find any online that are for a 65 mm lens. This is my first DSLR so I’m still learning how it all comes together; can anyone help me understand what size polarizer I need? Thanks!

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Is TCP’s 3-way handshake a kind of mutual authentication?

Is TCP’s 3-way handshake a kind of mutual authentication?

No. It is a weak form of authentication for the client authenticating to the server, but not a form a authentication at all for the other way around.

Can I see it as a way to ensure the source IP in packet’s header is the real source of the packet, so a kind of authentication ?

In all practical cases, yes, you can rely on the source IP in the packet’s header being the real source IP if the sequence number is correct and there is no MITM. Sequence numbers can be anything from 0 to 32^2-1. It is highly unlikely that someone can guess that number faster than the real request can get the correct number.

It seems like you are trying to use the wrong technologies for what you would like. While they may work, there is a reason you don’t use a screwdriver as a hammer. I’d recommend using TLS for mutual authentication with client and server certificates.

gr.group theory – What Kind of Abstract Algebraic Object are they?

Let $A, B$ are subsets of group $G$, where $A cap B =emptyset$.

Consider following: For an unique $alpha in A$, there is an unique $beta in B$, such that $alpha circ beta $ is always a fixed $ gamma in A$ for all $alpha neq gamma , beta$.

It looks like, all $beta in B$ are working as a operator or function, so we can consider the set $B$ (the set of all function or operator) as a single function or operaotr, where $B: A rightarrow A, ; alpha mapsto gamma$.

Question:

What kind of abstract algebraic object are $A$, $B$? Is there anything in the literature exactly or similar?

Notes:

  1. Please consider non-trivial cases, for example, The number of elements in $A, B$ is greater than $3$.

  2. If a specific group is necessary consider Special Linear Group, i.e. $G = SL_2(mathbb Z)$, but I am interested in general case… or where such thing exists!

  3. Please ask for clarification before answering.