ag.algebraic geometry – Do representations of same dimension implies isomorphic closed orbits?

Let us recall this fact. Let $G$ be a semisimple algebraic group over $mathbb C$ and let $V,V’$ be two irreducible $G$-representations. We denote by $X,X’$ the unique closed $G$-orbits contained in $mathbb P V, mathbb P V’$ respectively. We know that if
mathbb P V supset X cong X’ subset mathbb P V’

as projective $G$-varieties, then $mathbb PV cong mathbb PV’$ as projective spaces. In particular, $dim V=dim V’$.

I want to understand the inverse direction: if I have two irreducible $G$-representations $W,W’$ of the same dimension, should I conclude that the closed $G$-orbits $Y subset mathbb P W, Y’ subset mathbb P W’$ are isomorphic as projective $G$-varieties?

Analytic function on complement of closed unit disk onto open unit disk

Does there exist an analytic function whose domain is the complement of the closed unit disk and whose range is the open unit disk?

finite automata – Why are Regular sets not closed under infinite unions and intersections?

Look at $$ell={a^pmid ptext{ is prime}}.$$

This language obtain from infinite union of
$$bigcup_{igeq 2, itext{ is prime}}^{infty}L_i$$
Where each $L_i={a^imid itext{ is prime}}$ that have one word.

Another example is ${a^nb^nmid ninmathbb{N}}$
That isn’t regular and we can describe it by infinite union of regular languages
$$bigcup_{igeq 1}^{infty}a^ib^i=a^1b^1cupdots.$$ Each $a^ib^i$ is language that have one word.

For intersection, i recommend you read the following link.

How to use the h5p api in D8 [closed]

I can see the list of hooks here but i dont understand how each one gets triggered and what parameters have to be passed.

are there any online examples of how to use this api in D8 ?

audio – Sound doesn’t stream from TV when the lid is closed

When I connect laptop with TV, start playing some video and trying to close the laptop’s lid the sound starts streaming from laptop instead of TV.
I use Type-C – HDMI cable.

Expected result: Sound streams from TV.
Actual result: Sound streams from laptop.

Is there is some workaround for this?

Thanks in advance.

network scanners – is the UDP or TCP protocol best suited for a so called stealth counter scan for open or closed ports

network scanners – is the UDP or TCP protocol best suited for a so called stealth counter scan for open or closed ports – Information Security Stack Exchange

git – Simple Solution – error: RPC failed; curl 92 HTTP/2 stream 0 was not closed cleanly: CANCEL (err 8)

I followed most of the answers but not solved my problem.

In my case, the answer is very simple

I encountered this error when pushing GIT through an ADSL Broadband Wi-Fi network with low signal strength, low stability, and low speed.

I was able to push it very successfully when I pushed it into the GIT through a Fibre Broadband Wi-Fi network with greater signal strength, greater stability, and higher speed.


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assetbundle – How to create closed source Unity bundle

I want to create an asset/bundle that I can drop into projects to get up and running easily. Ideally this bundle would be closed-source so that the code is not accessible, but yet still usable. Is there a way to do this with Unity, or does the way packages work simply mean bundles will always be accessible/browsable for the source code?

I am planning on doing this for a simple 1st person controller, so that I can easily drop it into demo scenes of assets I purchase, to get a quick feel for using them. If possible, I would also distribute this as an asset (likely free, maybe minimal cost). Is there anyway to keep it closed-source, or is this simply not possible?

ct.category theory – when a right lifting property closed under pushouts?

A class of morphisms defined by a right Quillen lifting property (weak orthogonality)
is always closed under pullbacks (limits); under what assumptions will it be closed under pushouts (colimits) ?

More particularly:

Call a morphism $f$ good iff
$f perp C vee D rightarrow top $ whenever
$f perp C rightarrow top $ and $f perp D rightarrow top $,
for arbitrary objects $C$ and $D$; here $top $ denotes the terminal object, and $perp $ denotes the Quillen lifting property (weak orthogonality), i.e. for morphisms $f$ and $g$
$f perp g$ says that $f$ has the right Quillen lifting property with respect to $g$, or, in another terminology, $f$ is right weakly orthogonal to $g$.

Is this a well-known notion ? How can one describe good morphisms,
either in the category of topological spaces or simplicial sets ?

Motivation: in model theory, a number of classes of models with amalgamation property
can be described by a lifting property of form as above
(i.e. $f perp Mlongrightarrow top$), in a certain category extending both that of topological spaces and that of simplicial sets.
Thus it is interesting how to express amalgamation properties
in terms of the morphism on the left. The amalgamation properties are somewhat reminiscent of being closed under pullbacks and limits, hence the question.

reference request – Invariant on C*-algebras-number of closed unbounded derivation it admitted

In working of the unbounded derivation of C*-algebras. I observed the following: For topological manifold $M$, the number of closed, linear independent, unbounded derivation it admitted on $C(M)$ is exactly the dimension of $M$.

Of course this is true for smooth manifold. But I found that it may holds for arbitrary manifold. I try to google it but seems like no positive results. I would like to know if my result is known and well-studied. Thank you in advance.

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