soft question – Sustainability of ZBmath unrestricted access

ZBmath (formerly Zentralblatt für Mathematik) will become “Open access” in 2021 (see for instance at EMS site and at FIZ Karlsruhe site). It used to be under paywall, although some partial access was allowed.

My question (which was suggested in the comments of this answer to Is a free alternative to MathSciNet possible?):

What are guarantees (technical and/or legal) that the reviews will remain in unrestricted universal access?

(Concretely, I’d be reluctant to write reviews if ZBmath has the possibility to suddenly turn back to partial paywall in 2030 for whatever reasons, especially if this paywall affects searches for reviews made during the so-called open-access period.)

lighting – how do i answer this question

Two Wedding Videographers will cover a wedding ceremony. Both use a Canon Eos 80D DSLR camera with different lenses. The first videographer used a Canon EF 50mm F / 1.8 lens with aperture settings (ISO: 400, F: 2.8, and SS 1/250) and the second videographer used a Canon EF 18 – 55 kit lens. How is a second videographer change the settings so that they both get the same Normal lighting with the first Videographer if the ISO remains the same at 400 ?

A real analysis question about a proof dealing with supremums

Consider two sets, A & B in the set of real numbers such that A is not a subset of B and B is not a subset of A. If sup(AB) is an element of B and sup(BA) is an element of A, prove that supA = supB.

set theory – A question on the cardinality of subsets of positive integers

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soft question – Tools from other disciplines useful to mathematics research?

Obviously, mathematics provides essential tools for physicists, biologists, economists, engineers and many others to use in their research. Equally obviously, physics, biology, economy and engineering provide the inspiration for research topics and directions in mathematics. But this isn’t what this question is about. Instead, I’m wondering about tools provided to mathematicians by other disciplines.

Are there any examples of tools from another discipline that you personally have used in your mathematical research?

E.g., I find dimensional analysis (as in assigning dimensionfull units to variables) a very useful tool from physics, which can greatly help in finding errors during algebraic manipulation of equations.

pathfinder 1e – question about big cat and thier “standard attack” animal companion

IM playing pathfinder with my friends and IM playing a hunter (ranged build) and I have an animal companion a Big Cat we are currently level 5, and we started at level 4 and IM going to ask something that is troublesome.

How does a “standard attack works?”

Let’s say I move 10 yards and then i want to attack an enemy:

Can I attack with bite and claws?

Only bite?

Only claws?

Do I need to do full round attack to get all 3 attacks?

is there a way to get all attacks in a round?

Any good insight about this and any future tips for big cats?

thanks alot guys!

reference request – A question related to the union-closed sets conjecture

Let $f(n)$ denote the maximum possible cardinality of a collection $mathcal F$ of nonempty sets which is closed under unions ($X,Yinmathcal Fimplies Xcup Yinmathcal F$) and is such that no element belongs to more than $n$ members of $mathcal F$.

It follows from the union-closed sets conjecture that $f(n)le2n-1$. (That’s $2n-1$ instead of $2n$ because I’m omitting the empty set, which seems irrelevant to me.)

However, the upper bound $2n-1$ does not seem to be the best possible in all cases. I may have figured these things wrong, but it seems to me that $f(3)=4$ and $f(5)=8$ and $f(6)=9$. (Of course $f(n)ge2n-1$ if $n=2^k$.)

Question. Is there a conjectured exact value for $f(n)$?

combinatorics – question from Saint Petersburg selection competition of 1989, about determining the difference between the size of two sets $A$ and $B$

I was just trying to do the following question:

We have tickets which are 6-digit numbers from 000000 till 999999. A ticket is considered lucky, if the addition of its first 3 digits is equal to the addition of its last 3. It is considered medium if the addition of its digits is equal to 27. I state that $A$ and $B$ are the are the amounts of lucky and medium tickets correspondingly. Calculate $A-B$.

Despite trying for a lot of time to solve it, I did not succeed and had to look at the solution. The solution goes as follows:

We have that $A-B=0$ from the fact that the correspondence $abcxyzrightarrow abc(9-x)(9-y)(9-z)$ between lucky and medium tickets is (injective-bijective-onebyone I’m not sure what it translates to, I used a translator for this word and these are the terms that came up).

I feel that this is a beautiful solution, however I can’t understand it. Could you please explain to me the thought process and why what the author is saying, holds true?

How do I allow the (Add to cart) only if a person answers a particular question correctly?

I am wanting to make the "add to cart " avaialable only if the person answers a particular correctly.
any help appreciated.

mp.mathematical physics – I have given a link .Please help me with the bonus question there ,the question number 5

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