## Restriction function as a Morse function

Let $$Sigma$$ be a closed surface smoothly embedded in $$mathbb R^3$$. For any Morse function $$h:mathbb R^3 to mathbb R$$, can we isotope $$Sigma$$ so that the restriction of $$h$$ on $$Sigma$$ is also a Morse function?

## data structures – Why we put restriction on deque(double ended queue)?

The definition of deque says “Deque or Double Ended Queue is a type of queue in which insertion and removal of elements can either be performed from the front or the rear.”

Types of Deque: 1.] Input Restricted Deque: input is restricted at a single end
2.] Output Restricted Deque: output is restricted at a single end

But then why do we put restriction on any one end of deque for insertion/removal, when it is possible to perform both the operations from both the ends ? And then classify them on the basis of this restriction.

## magento2.3 – How can I reduce the Largest Contentful Paint overhead of Magento 2 cookie restriction mode?

Our Google Pagespeed Insights score is suffering due to Largest Contentful Paint when using the Magento 2.3.0 default cookie restriction mode popup. With cookie restriction mode enabled the LCP is showing at over 7 seconds for mobile, the score is close to 3 seconds with cookie restriction disabled (some further minor changes will get LCP below 3s, to the ‘good’ Pagespeed level).

Can anyone suggest how I can reduce the system overhead of the default cookie popup please? For example, can it be preloaded or loaded earlier in the page? Are there any 3rd party extensions which are known to perform much better than the default cookie popup? Would a Magento version upgrade (=> 2.4) help?

Hoping for good news. Thanks…

## As a Green Card holder, can I travel to Iran and come back to the US without restriction?

I am a green card holder and live/work in the US. I want to travel to Iran in July 2021 for a couple of weeks. Am I still exempt from the 14 days quarantine rule in a third country (based on the new restrictions) before entering the US?

## backup – Postgresql dump with data restriction

I’m working on developing a fast way to make a clone of a database to test an application. My database has some specific tables that are quite big (+50GB), but the big majority of the tables only have a few MBs. On my current server, the dump + restore takes some hours. These bigs tables have date fields.

With the context in mind, my question is: Is possible to use some type of restrictions on table rows to select the data that is being dumped? e.g. On table X only dump the rows that date is Y.

If this is a possible show can I do it? if it’s not possible what would be a good alternative?

## Travel restriction to USA from India for a PhD student (with F1 visa)

I am currently a 4th year PhD student (with a valid F1 visa) who came to visit his family in India for a short trip but then due to the unfortunate circumstances, USA put a travel restriction on India. I read the rules carefully but the following concern is not clear to me.

Since I am a PhD student, technically I work every day for the whole year. So the rule says ” if the program begins on or after 1st August, I will be eligible to travel 30 days before that…”

Now I am confused if I am allowed to travel on 1st July (which is a month before 1st August since techincally my program is continuing) or I have to wait till atleast 23 rd July (since the official fall semseter begins on 23rd August)? (I tried to contact consulate on this matter but didn’t get any helpful reply.)

Also in this situation, while traveling, what should I carry as a proof for my starting date of program? Since my i20 is only showing that my program starts on 21st August 2017, so that may not be a best proof for this purpose.

Thank you in advance for any help…

## usa – travel restriction exemption from India to the US on an F1 visa

Because of the high covid case loads in India the US announced travel restrictions between the US ad India. There appear to be exemptions to these restrictions for students on an F1 visa.

It is not clear if this exemption applies immediately, or one month before the start of the fall semester. United airlines support staff says that I may travel, however the international students services organization at my university says that I likely won’t b able to travel.

Which one is true? Where can I find a source that clarifies this?

## category theory – Image of a morphism of sheaves of vector spaces is a sheaf: what are the restriction maps?

Let $$f : mathcal{F} to mathcal{G}$$ be a morphism of sheaves of (complex) vector spaces on a space $$X$$, so $$f$$ is a collection of $$f_U$$ defined on open $$U subset X$$.
The image of $$f$$ is defined in my lectures as as $$mathcal{I}(U) := {a in mathcal{G}(U) : text{ there exists an open cover } U_i text{ of } U text{ s.t. } avert_{U_i} in f(mathcal{F}(U_i))}.$$
I want to show that this is a sheaf, but I am struggling to work with the definition, even with defining what the restriction maps $$rho_{U,V}$$ should do.
I have seen the fact that the category of sheaves of $$mathbb{C}$$-vector spaces is abelian, and in Vakil’s notes he says that

We needn’t worry about restriction maps – they “come along for the ride”.

But when making things concrete, it is hard for me to resolve.
What am I misunderstanding here? I am fairly new to category theory and sheaves, so I would prefer something that uses as little of extra abstract machinery as possible.

## abstract algebra – What primes factor both \$2\$ and \$3\$, with no restriction on the domain?

What numbers (especially primes) factor both $$2$$ and $$3$$ (with no restriction on the domain)? How many answers are there? I’m looking preferably for a prime.

My attempt:

No natural number (other than 1 and themselves), obviously.

Ignore rationals because there are no good answers there.

I had a think about Gaussian integers and figured $$2,3$$ would have to be in unit ratio with each other, which they’re not so I think that rules that out.

That got me to thinking that if $$2,3$$ are primes then I guess they could only be factored by units so either they’re not primes in the domain or there would be a unit ratio between them.

Then I looked at the finite field with four elements. It looks like we can reasonably assign $$2$$ and $$3$$ to numbers, both of which factor both but that’s about as far as I can generalise – and since they are both factored by each other I guess they can’t be considered prime in this context.