## 8 – How to add a secondary Ajax submit to a regular node form?

I’m trying to add an Ajax submit to a regular node edit form (Drupal 9). I’m using Field Groups so that there’s a series of tabs, and I’ve added a pair of “buttons” (Right now they’re just markup `<div>s`, but I could change them to real buttons if that’s recommended) that users can use to move forward and back through the tabs with some Javascript.

The ask now is that each time the tab focus changes, the form is submitted via Ajax.
All the examples I’m finding seem to be doing something other than what I’m after. I’ve seen examples using completely custom forms, loading forms, and altering fields, but nothing that just adds the ability to submit a a regular node form with Ajax.

Things I’ve tried:

• Adding an `#ajax` subarray of various sorts to the buttons and/or the regular submit element. Nothing Ajaxy at all has happened in any of these experiments
• Using Javascript to trigger a click event on the submit, without and without an `#ajax` subarray. All I get is a regular submit with page refresh
• Bypassing all of that just calling `\$.post(\$('#form-id').attr('action'), \$('#form-id').serialize())`. There’s some semblance of Ajax submit going on as my custom `hook_form_alter` gets hit, but the node isn’t saved/updated. I think that’s failing because there’s no proper submit/op value associated with it, and I haven’t been able to figure out how to add/set it.

Can someone point me in the right direction?

## 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.

## decidability – How to determine whether this language is regular?

I’ve encountered this question recently: Given $$Sigma={sigma_1, sigma_2, …, sigma_n}$$ and $$nge 2$$, determine whether the following language is regular or not:
$$L_1={winSigma^*|for 1 le i le n, #_{sigma_1}(w) is even iff i is even }$$
And I need to use the Myhill-Nerode theorem to solve it.
I tried constructing a finite automata that accepts this language but had some troubles with it. I’d really appreciate some help!

## Which of the following languages can be represented by regular expressions?

The set of all words contained in $${0,1}^*$$ that have an even number of 0’s and an odd number of 1’s.

I came to discover that it is possible but not sure how. Can anyone express it in a regular expression?

## database – How to implement notification system based on time that runs in regular intervals

I have a MySQL database with nodeJS server. I want to implement a notification functionality which is as follows. Once a user registers, I want to (inform) send some particular information to the user that runs in fixed time interval. Something like a task management and tracking.
If user A registers at 10am local time, notification must be sent 24 hours after A registers ie (notifications depends upon time that user registers however with a fixed interval). How do I implement this solution. I have looked at jobs in sql and cron jobs in NodeJs however I’m not sure of the approach, any guidance would be appreciated.

P.S. What would be the approach for same problem with mongoDB?

## Is the language regular or not?

The language given is $$L = {w_1 x w_2 mid w1,w2 in {a,b}^* text{ and } x in {a,b}}$$. Is this language regular or not?

Since there is no pattern, so it should be non-regular?

Kindly help!

## pr.probability – Contiguity of uniform random regular graphs and uniform random regular graphs which have a perfect matching

Let us consider $$cal{G}_{_{n,d}}$$ as the uniform probability space of d-regular graphs
on the n vertices $${1, ldots, n }$$ (where $$dn$$ is even). We say that an event $$H_{_{n}}$$ occurs a.a.s. (asymptotically almost surely) if $$mathbf{P}_{_{cal{G}}}(H_{_{n}}) longrightarrow 1$$ as $$n ⟶ infty$$.

Also, suppose $$(cal{G}_{_{n}})_{_{n ≥ 1}}$$ and $$(cal{hat{G}}_{_{n}})_{_{n ≥ 1}}$$ are two sequences of probability spaces such that $$cal{G}_{_{n}}$$ and $$cal{hat{G}}_{_{n}}$$ are differ only in the probabilities. We say that these sequences are contiguous if a sequence of events $$A_{_{n}}$$ is a.a.s. true in $$cal{hat{G}}_{_{n}}$$ if and only if it is true in $$cal{hat{G}}_{_{n}}$$, in which case we write
$$cal{G}_{_{n}} approx cal{hat{G}}_{_{n}}.$$

Thorem. (Bollobas) For any fixed $$d geq 3$$, $$G_{_{n}} ∈ cal{G}_{_{n,d}}$$ a.a.s has a perfect matching.

Using $$cal{G}^p_{_{n,d}}$$ to denote the uniform probability space of d-regular graphs which have a perfect matching on the n vertices $${1, ldots, n }$$, is it true to conclude from the above theorem that $$cal{G}_{_{n,d}} approx cal{G}^p_{_{n,d}}$$?

## If \$f(t,x)in F_q(t)[x]\$ is a Morse function, does this mean splitting field of \$f(t,x)\$ over \$F_q(t)\$ is a regular extension?

One of the classical result of Hilbert says, if $$f$$ is a Morse function, then the splitting field of $$f(X,T)$$ over $$Q(T)$$ is a regular extension with Galois group $$S_n.$$
J. P.Serre- Topics in Galois theory, Theorem 4.4.1

Does the same hold for $$fin F_q(T)(X)$$, function field with positive characteristic?

i.e., if $$f(t,x)in F_q(T)(X)$$ is a Morse function, then does it mean that the splitting field of $$f(X,T)$$ over $$F_q(T)$$ is a regular extension?

Thank you.

## How to use the pumping lemma to show a language is not regular

How can you use pumping lemma to prove that the language H over the alphabet Σ = {L, M, N} is not a regular language? H = {L^o M^p N^q | o, p, q ≥ 0;o ≤ p} ∪ {L^o M^p N^q | o, p, q ≥ 0; p ≤ q} ∪ {L^o M^p N^q |o, p, q ≥ 0; q ≤ I}