Memory – what can be used as a Windows registry equivalent in Android?

I am building an app in Android. Before I had the same app in Windows Mobile, you can imagine why I'm doing it.

In any case, there are some important values ​​(encryption key) that I have to save. It used to be done in the Windows registry, but now I don't know where it would be safe enough to do so.

I don't want to create an SQLite database for this because the key is used to encrypt / decrypt an SQLite database.

I also know there are user preferences that I'm not sure if that would be safe enough.

I am not confident of using internal or external storage as it is.

What would you suggest?

Excel – Google Sheets "array_agg" … or equivalent? (Join Match in Array)

I currently have that

    'Raw Paste'!C2:E, "select C, count(C) where C is not null group by C order by C label count(C) ''"
  ), "WHERE Col2 >= 2")

The second QUERY() This allows me to filter the aggregate function like an SQL HAVING Function…

This is what it does:

Enter image description here

But what I want to do is next to the count, I want a third column that connects the invoice numbers that are contained in the aggregate.

This would be trivial with ARRAY_AGG(C) But Google Sheets isn't that fancy.

I was thinking, maybe with INDEX/MATCH Somehow, but I don't know. I have to put the strings together if an element occurs more than once.

C    D
111  PPP
222  OOO
222  QQQ

Issue I want:

C    D
222  OOO, QQQ

Number theory – Show that two binary quadratic forms are equivalent

In the class we have defined binary square shapes by $ ax ^ 2 + 2bxy + cy ^ 2 $ and their discriminant as $ ac-b ^ 2 $, I'm supposed to show that for a given $ n $ and a prime number $ p $ With $ p equiv 1 pmod 4 $ and $ m ^ 2 = np-1 $ the forms $ f (x, y) = px ^ 2 + 2 frac {m ^ 2} {2} xy ^ 2 + ny ^ 2 $ and $ g (x, y) = x ^ 2 + y ^ 2 $ are equivalent.

If I am not mistaken, it should be enough to find a $ 2 times 2 $ matrix $ A $ so that
$ f (A (x, y)) = g (x, y) $, But I don't see how to find such a matrix. Can you help me?

Is a dedicated video camera cheaper than an equivalent compact camera?

I have a Sony RX100 IV that I use for two things – to take with me on vacation etc. to take photos for Facebook, gatherings and the like (since my cell phone camera is cruel) and also to make videos of me at home.

At home I have good lighting and a good setup, but I really need to be able to film myself from two angles so I can jump between them to make nicer videos.

I tried a 1080p webcam, but the quality is terrible compared to the camera, even though I lit up like on July 4th.

The obvious choice would be to buy another identical camera, but that's a lot of money and I would only use it to make videos (i.e. permanently mounted on a tripod). I wouldn't use most of the functions.

So my two questions are whether I can buy a device that can process the desired part of the video (films at 1080p, although the RX100 IV does 4k) with the same or higher quality, and is cheaper than the cost of the RX100 IV by all photographic skills are sacrificed?

And the second question is, how could I search for such a device? I'm not quite sure what "specs" to watch, although I can probably watch YouTube demos from video cameras.

But more importantly, I'm not sure what to look for on amazon to find the types of devices that can record good 1080p videos, as I've already shown with my logitech webcam that 1080p is in relation to that Quality is pretty insignificant.

If someone wanted a camera like mine, I would say they are looking for "compact cameras". But what would I be looking for if I just wanted video cameras? Possibly camcorders, although they look a little different than Gopro devices / action cameras. They also seem to be very cheap, which makes me think that they are not very good.

Any thoughts are welcome.

sharepoint online – What is the PnP equivalent of Set-SPOSiteGroup?

It is Set-PnPGroup.

Here's an example of how to use it:

 #Config Variables

  $SiteURL = ""

$GroupName="Sales Portal Members"

    #Group owner variable: Can be existing group or user account Email

    $GroupOwner = "Sales Portal Owners" #or

#Connect PNP Online

  Connect-PnPOnline -Url $SiteURL -Credentials (Get-Credential)
 #Set Group Owner
 Set-PnPGroup -Identity $GroupName -Owner $GroupOwner

Please refer to the following URL for details:

Type theory – category-theoretical equivalent

As explained here, simply typed lambda calculation can be viewed as a syntactic language for category theory. My question is, can this modification just as well make it a formal syntactic language for the theory of 2 categories?

Vaguely said: we have a universe $ U $, For each $ X: U $, we do $ X $ into the universe of a simply typed lambda calculation by introducing the necessary rules for type formation. cards $ a rightarrow b $ to the $ a, b: X $ are like maps of objects. I would expect cards $ X rightarrow Y $ to the $ X, Y: U $ correspond to functors in any way. That said, I would expect some kind of correspondence between this setup and certain types of $ 2 $Categories. In this way, I expect that the introduction of a higher universe is like a transition from another universe $ n $-Categories up $ n + 1 $Categories. Has anyone followed such an approach?

For a similar idea applied to homotopy type theory instead, one might expect to get a model for it $ ( infty, 1) $Categories.

SkCanvas.drawArc replacement / equivalent in SkiaSharp99

I port an old platform-specific c ++ app from a third-party provider with SkiaSharp to Xamarin.Forms.

In the old code base of SkCanvas :: drawArcMethod is used very often.
The full signature is:

void SkCanvas::drawArc (
const SkRect &oval,
SkScalar startAngle, 
SkScalar sweepAngle, 
bool useCenter, 
const SkPaint &paint)

Unfortunately, this method does not (yet?) Exist in SkiaSharp. There is a bug in Github for this issue, which has not been noticed since it was created in 2018 (see

Now that I need this method, I wonder what an equivalent replacement would look like.
I know that I can draw a simple arc like this:

public void static DrawArc(this SKCanvas canvas, SKRect r, float startAngle, float sweepAngle, bool useCenter, SKPaint paint)
    var path = new SKPath();
    path.AddArc(r, startAngle, sweepAngle);
    Canvas.DrawPath(path, paint);

The problem is that the code above doesn't take that into account useCenter-boolean. Can someone help me with a solution that takes this jerk into account?

Thank you very much

Number theory – For certain values ​​of arithmetic functions and a known equivalent statement of the Goldbach conjecture

In this article we denote the sum of the divisor functions $ sum_ {1 leq d mid n} d $ how $ sigma (n) $the Eulerian function as a $ varphi (n) $ and the Dedekind psi work as $ psi (n) $, The following statements can easily be derived from (1) using elementary algebra.

These claims then result from the idea of ​​the equivalent statement for the Goldbach conjecture shown in (1) or the online encyclopedia Wolfram MathWorld of title Goldbach's conjecture, this is

The motivation for this article was to evoke different equations with specific values $ f (p ^ { alpha}) $ of arithmetic functions, in our case $ alpha = 1 $ and our arithmetic functions $ f (n) $ are remarkable functions in analytical number theory (in particular, it is known that the Riemann hypothesis can be rewritten in relation to these arithmetic functions).

Claim 1. Assuming the Goldbach conjecture for every positive integer $ m $ There are prime numbers $ p $ and $ q $ so that
$$ left ( frac { varphi (p) + varphi (q)} {2} right) left ( frac { sigma (p) + sigma (q)} {2} right) = m (m + 2) $$
$$ left ( frac { psi (p) + psi (q)} {2} right) left ( frac { sigma (p) + sigma (q)} {2} -2 right) = m (m + 2). $$

Claim 2. According to the previous assertion, one has the assumption of the Goldbach conjecture for every positive integer $ m $ There are prime numbers $ p $ and $ q $ so the integer $ 2m $ can be represented as predetermined values ​​of these arithmetic functions for prime numbers $ p $ and $ q $ how
$$ begin {align}
2m & = -2 + sqrt {4 + ( varphi (p) + varphi (q)) ( sigma (p) + sigma (q))} \
& = -2+ sqrt {4 + ( psi (p) + psi (q)) ( sigma (p) + sigma (q) -4)}.
end {align} $$

Question. Prove or disprove the following assumption (I have done modest experiments, so if you can find a counterexample, I ask as a secondary question whether it is possible to find arbitrarily large counterexamples):

If $ r geq 1 $ and $ s geq 1 $ are positive integers that satisfy the system of equations
$$ left.
begin {array} {l}
left ( frac { varphi (r) + varphi (s)} {2} right) left ( frac { sigma (r) + sigma (s)} {2} right) = M (M + 2) \
left ( frac { psi (r) + psi (s)} {2} right) left ( frac { sigma (r) + sigma (s)} {2} -2 right) = M (M + 2)
end {array}
right } $$

for an integer $ M geq 1 $. then $ r $ and $ s $ are prime numbers.

If you can find counterexamples to previous conjectures, can you prove or disprove that there are arbitrarily large counterexamples? Thank you very much.

So I wonder what can be done to prove it or whether you can refute it because you know a counterexample as a secondary question. I ask if the order of your counterexamples is infinite $ p $ or $ q $ increases.


(1) Richard K. Guy, Unsolved problems in number theory, Section C1 Goldbach's conjecture, in pages 105-107, 2nd ed. New York: Springer-Verlag (1994).

Reference request – What proves that two complicated programs are equivalent?

Suppose I wanted to prove that two programs are equivalent (either rigorous if possible or informal unless). Suppose I have something relatively complex, such as an HTTP server implemented in C and one implemented in Node.js / JavaScript. What can I do to say that "these two are basically the same"? What options do I have? What is possible? What is not possible?

It's been a while since I've been dealing with proving program equivalency (I'm currently connected to it, but I can't read it yet, haha, and it seems like it deals with extremely simple programs like equality checks or basic loops focus, whereas I'm asking for a robust HTTP server).

In essence (I imagine) I want to say that "these two programs in JS and C do the same thing". The "do the same"is obviously vague, but at the same time it means something specific. Every observable result is generally the same on both systems. give or take, So it's like evidence, but without being one Perfect Proof. It's like partial evidence or something.

I would like to be able to say about my programs that "these two implementations are equivalent in every respect". I would probably start by providing measurable guarantees or observations about performance and input / output behavior, and then write some tests and … I don't remember making any statements about the system in any way. Or should I just think that "a working HTTP server is a" in both languages? AXIOM". That would make it easier 🙂 Let's just assume it does the same thing as the other one. But that's a dodge as it feels.

Are you wondering what options I have here? How far can I go theoretically? I am not concerned with how long it would take to implement or define if it took years. I just want to know what is possible to make the statement "These two programs in C and JS are equivalent" stricter and more precise. What techniques / theories / research directions could I look for to make this possible?

I'm simple right now provided They are implicitly the same, so my code can call either the C function or the JS function and know that the ~ overall effect ~ is the same (nebulous, I know, I don't know how to hold it). I'd like to do some math or model testing or program simulations or something like that so I can make it more solid if possible 🙂

This proves at the other end of the spectrum 3 > 2 is synonymous with C and JS. What should I do in this simple case? Copying a string of characters on the way to a full HTTP server in C is a bit more complex than JavaScript, but it is relatively easy. Where do I start to prove these "operations" that are equivalent between the two languages? Or if not "prove", then simply "claim" that they are equivalent.

There's not much here, but this diagram is what I'm basically trying to do:

Enter image description here

On a broader level, the problem seems to be similar … Let's say I want to get a medallion. I can either go to the store and buy one, or print one in 3D. Both "algorithms" (shop visits or 3D printing) differ considerably from each other, but are practically the same. There is no direct way to gradually prove that they are equivalent operationally (as I imagine), but the end result is the same. How would you say this (also here) with severity?