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calculus and analysis – Pure functions with derivatives and list elements

I have a list

list = {x, y, z}

and then the following line

D(#, list((2))) &

gives the output

!(
*SubscriptBox(((PartialD)), (list((2))))#1) &

It still works if I apply it to {x,y,z}, but, unfortunately, it no longer continues if I use it inside another function, like

operators(varList_) := 
 Flatten@Table((varList((i)) D(#, varList((i + j))) &), {i, 1, 
    Length(varList)}, {j, 1, Length(varList) - i})

in the sense that

operators({x, y, z})((1))@{x, y, z}

gives

Part::pkspec1: The expression i cannot be used as a part specification.
Part::pkspec1: The expression i+j cannot be used as a part specification.

How shold I write it the right way?

recursion – Find the min in an array and increment it by X with pure functions and no variable

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blockchain – Is it possible to get a monthly “fiat/altcoin allowance” from simply “locking” your Bitcoins in a pure smart contract?

Let’s suppose that Mr. John Doe has somehow managed to accumulate 10 BTC. He holds on to them for dear life as it’s his one and only savings/lifeline. He has essentially zero fiat money. Only a bank account. His coins exist on an encrypted wallet.dat, created on a dedicated computer and redundantly backed up.

John has heard of all this “defi” stuff, but doesn’t understand how it works in practice. He has spent many hours reading and asking questions related to this, but has still not been able to get it all straightened out. He just gets frustrated and irritated trying to make sense of the fuzzy sales talk found on all these slick websites.

Importantly, John has no ability to do “KYC/AML”, and doesn’t trust centralized entities either way. John is fine with providing his full name and bank details to any entity — the only problem is producing a “photo id”, since he hasn’t got one and doesn’t want to ever get one again. This is important to John.

John wishes to somehow get a steady monthly “income” from his ten digital gold bars (Bitcoins, that is), most likely in the form of some sort of “interest”. John is not well educated in economic terms and therefore might not be using the correct financial terms.

Is there some way that John could enter some kind of command into his Bitcoin Core which creates a “smart contract” directly on the Bitcoin blockchain which, in some manner, “locks” the coins from being spent by him, but still doesn’t make him lose control of them (the private keys stay with John)? That is, so that “some other entity” in some way derives value from this so that they will send John some reasonable sum of fiat money to his bank account monthly or yearly?

And if this is possible, how exactly does that other entity derive value from this smart contract if they don’t control John’s coins? They are just “locked” in the sense that John cannot spend them for some pre-determined amount of time, or until both parties agree to dissolve the smart contract. (This is what I’m guessing from my understanding.)

And assuming this is possible, what amount of USD would John get per month from such a setup? Are we talking $1,000 or $100 or even $10? John doesn’t think it’s worth it if it’s less than $1,000, which has become sort of a “Western bare-minimum monthly income” for basic survival. Even if people trust these “smart contracts”, there’s always the risk of a bug or glitch which would make him lose all his hard-earned satoshis. That is a nightmare scenario for John.

In fact, the “monthly allowance” doesn’t necessarily have to be paid in fiat money. It can just as well be Bitcoin or really just any altcoin supported by Bisq, so that John can trade them himself to end up with fiat in the end. If that makes a difference. (Maybe there’s less regulations and legal obstacles for an entity to hand out some weird coin rather than dealing with bank transfers.)

I would highly appreciate if somebody could explain what I’m missing about this, sticking to John in the situation described here.

Please do not redirect this to an existing question; I have more than likely read it and the answers already.

first order logic – Quantifier Elimination Pure Identity Language in Chang

In Model Theory by Chang and Keisler they show quantifier elimination on the theory of the pure identity language. However, I’m confused about the notion of “basic formula” for which any quantified sentence needs to equivalent to a boolean combination of. Atomic formulas are used as these basic formulas for showing QE for the theory of dense linear orders, however the authors note that doing so in the theory of the pure identity language does not permit $forall xy(x equiv y)$ to be expressed as an open formula so the authors add the sentences saying there are at least $n$ distinct elements in the model to their basic formulas. (I believe $n$ is the number of variables being quantified over in the original sentence). The question is, how can we use these sentences for QE when they themselves use quantifiers?

I.e., if $sigma_3$ is the sentence saying there are $3$ distinct elements in our model, how can we perform QE elimination on this sentence?

What sort of task would require programming language instead of pure SQL / SQL procedures

Can someone give me examples of what sorts of tasks are better done in a programming language like Python or Java that can use framework to interface with a database versus pure SQL approach. Do DBA and other people who work alot with database use programming language on their job?

soft question – How difficult will it be to start doing research in pure mathematics in the near future?

I am a first year PhD student in mathematics (complex differential and Kahler Geometry) and the other day I had a thought about the difficulty of starting to do research. This is my first post here but I have some in Math Stack-exchange.

First of all I hope this is the right place to post such a question, if it isn’t let me know and I will move the post immediately.

Being in the first year of my PhD I am in an intensive study phase in order to get to the limits of research and start working on a project with my supervisor. I am noticing, however, that in order to be able to truly understand a problem (which is within the reach of a doctoral student, so excluding complicated problems that have been unsolved for many years e.g. the existence of a complex structure on the six-sphere) it really takes a lot of study and above all a good knowledge of the basics in other nearby fields of mathematics. Just think of Kahler geometry in which you must have good bases of analysis and geometry (sometimes even algebraic if you want to focus on the various notions of stability), or for example also in the low-dimensional differential topology in which you need to have good basics of algebraic topology and differential geometry. Obviously the more one goes on with the years the more this phenomenon, in my opinion, becomes more and more accentuated. On the other hand, however, thanks to technology we have new tools from which to draw/spread the culture and knowledge in pure mathematics (just think of this site), tools that the researchers of 30 years ago did not have.

At this point, thinking in this light, I asked myself a question: how difficult will it be for a master’s degree student to start a PhD in 2050, say? The problems could be two: the first that obviously the research from today to 30 years has gone on and we have gone further and further with knowledge; the second is that university exam programs, to try to cope with the first problematic, are weighed down more and more. The most obvious consequence is that only a few people (the most determined and brilliant) will be able to go ahead and start a research program, or that they will dedicate themselves exclusively to a super specialized topic ignoring everything else (even if I don’t see how it is possible in a subject like mathematics, moreover it would be a real shame).

This talk I am giving is exclusive to pure mathematics research, thus excluding the use of a computer as a means to be able to do research in the strict sense of the term (as for example a particle physicist or an applied mathematician can use it to do numerical simulations).

Having said that, I wanted to know what you thought about it and above all what researchers and/or university professors who have been in this field for many years think about it. I hope I have not asked a question that may be trivial, but rather a food for thought. Thanks for reading.

4.4 kitkat – Custom rom can I trust? Can I install pure android instead?

I have a “galaxy tab E” device, it is old in years, but it is quite new because I don’t use it very often.
The problem is, it has android 4.4.4.
I notice it has a custom rom to install android 7.1.2 Nougat (see this video https://www.youtube.com/watch?v=FmRtueImtlw) It is a rom made by lineage.
First question, can I trust this rom?

Is there a way to install pure android (7.1.2) from google instead? If I download android from google and install it using odin will it work?

Thanks a lot.