Genady

I do not have such equipment. I will keep this possibility in mind, but it will take time to get them to do this check. And cost. There are four lines: from the skimmer, from the main drain, from the vacuum, and the return. Not the first option on my list. Thank you anyway. This was one of the first things I did myself (I am a former SCUBA instructor.) I've just thought of a very simple way to check if the leak is in the pool or in the pipes. I can cover all the inlets and outlets in the pool and see if the leaking stops.

I cannot cover the pool. I can experiment with 'buckets' of different sizes and shapes. I don't think the difference would be so dramatic. If any, I'd expect that relatively shallow buckets heat up and evaporate faster than the much deeper pool. Plus... Buckets have the same or more exposure to the sun. The pool is located on the property in such a way that it is protected from winds. Plus... I am sure that in the last several months I need to add water to the pool about weekly rather than bi-weekly as it used to be for the last 20 years. This was how the project started.

I measure it quite 'scientifically'. I put a backet of water on the pool side and mark the water level in the backet and in the pool. Later, I compare the change of the level between the two. The pool level goes down about twice faster.

I've inspected it on SCUBA vary closely and meticulously. I doubt that I've missed it.

It does. Fresh water is not cheap in Bonaire. It is produced from sea water by reverse osmosis, and we pay by cubic meters consumed. It is pure concrete.

I let it go down to the bottom of the skimmer, with no effect. I don't want it to get any lower.

OK. How do I find / check this?

It's concrete pool, partially in-ground. I SCUBA dove in it to look for cracks. Didn't find any. Not a very fast leak, about 2cm down of the water level a week. This is about twice of a normal evaporation.

Let's start this simple and I will fill in details as needed.

It is an old and well-known problem. What is in it to be discussed here?

One does not need to deal with GR or QM to have meaningful and useful non-commuting operations. They are everywhere. For example, rotations in Euclidean 3D space do not commute.

Knowing this, one can calculate the gas temperature.

What do you mean, temperature of the Sun?

A short Internet search returns many sites explaining how to calculate Jeans length. Just plug in the numbers.

... you quickly die, because your brain will not know how to control functions of your body.

Apparently, an extension K ⊆ L being normal simply means that every irreducible polynomial over K has either all or none of its zeroes in L.

Through mutations and selection.

There is a recent discussion on this here:

Find all subgroups of the group of automorphisms G(L/K) and all corresponding subfields between the fields K and L, where K = Q and L is splitting field of the polynomial f(x) = (x2-2)(x2-5). Each factor of f(x) above is irreducible in K. The first factor has zeroes ±21/2, the second has zeroes ±51/2. Thus L = Q(21/2, 51/2). The order of the group G(L/K) = [L : K] = 4, and it has four automorphisms: s0: 21/2 → 21/2, 51/2 → 51/2 s1: 21/2 → 21/2, 51/2 → -51/2 s2: 21/2 → -21/2, 51/2 → 51/2 s3: 21/2 → -21/2, 51/2 → -51/2. The subgroups are: H0 = {s0}, H1 = {s0, s1}, H2 = {s0, s2}, H3 = {s0, s3}. The subfield corresponding to H0 fixes all elements in L and thus, it is Q(21/2, 51/2). The subfield corresponding to H1 fixes the element 21/2 and thus, it is Q(21/2). The subfield corresponding to H2 fixes the element 51/2 and thus, it is Q(51/2). The subfield corresponding to H3 fixes the element (21/2×51/2) and thus, it is Q(101/2).

Is the extension K ⊆ L normal, where K = Q, L = Q(21/3)? 21/3 is zero of polynomial x3-2, which is irreducible in Q. Other two zeroes of this polynomial are complex and thus ∉ L. Hence, this extension is not normal. Is such extension normal for K = Q(21/2), L = Q(21/4)? 21/4 is zero of polynomial x4-2, which is reducible in K, i.e., x4-2 = (x2 - 21/2)(x2 + 21/2). The first factor has both zeroes in L, while the second does not have any zeroes in L. Hence, this extension is normal.

The same meds as everyone else. You are right about the long-term treatment, but the question was,

We don't know. It's many years now she does not work.

May I offer anecdotal evidence? My wife used to be a psychiatric nurse in NY hospital in Greenwich Village, Manhattan, 30 years ago. You can imagine that they had a lot of emergency homeless patients there. They treated all of them well, in practice.

Let S ⊆ M ⊆ L be field extensions. 1. Let S ⊆ M and M ⊆ L be normal extensions. Is S ⊆ L normal? Not necessarily. Here is an example of it being "abnormal." Let S = Q, M = Q(21/2), L = Q(21/4). Polynomial x2-2 is irreducible over S and has both of its zeroes in M. So, S ⊆ M is normal. Polynomial x2-21/2 is irreducible over M and has both of its zeroes in L. So, M ⊆ L is normal. However, polynomial x4-2 is irreducible over S but has only two of its four zeroes in L. Thus, S ⊆ L is not normal. 2. Let S ⊆ L be normal. Is M ⊆ L normal? Yes. Any polynomial irreducible over M is irreducible over S. If this polynomial has one zero in L it has all zeroes in L, because S ⊆ L is normal. Since it has all its zeros in L, M ⊆ L is normal, too. 3. Let S ⊆ L be normal. Is S ⊆ M normal? Not necessarily. Let S = Q, M = Q(21/4), L = Q(21/4, i). Polynomial x4-2 is irreducible over S and has all its zeros in L. So, S ⊆ L is normal. However, it has only two of its four zeroes in M. Thus, S ⊆ M is not normal.

There is no need in referendums anymore. The data are there, in social media, forums, TV, papers, etc. Everything people talk and write about. All the answers. The tool to collect and summarize these data is also there. It is called, AI. /sarcasm/