[Archive!] Pure mathematics, physics, chemistry, etc.: brain-training problems not related to trade in any way - page 351

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Solve a system of equations for positive x, y and z:
x+(1/y)=2-(y-z)^2
y+(1/z)=2-(x-y)^2
z+(1/x)=2-(z-x)^2
 
Mathemat >>:
Решите систему уравнений для положительных x, y и z:
x+(1/y)=2-(y-z)^2
y+(1/z)=2-(x-y)^2
z+(1/x)=2-(z-x)^2

Man, you guys...

The decimal mahas still haven't been solved.

And I haven't heard a word from the procurator.

In the senate...

;)

 
How do you deal with them, the mash-ups, avatara? No universally accepted procedure has been proposed yet. Something concrete still has to come from the requirements for implementations at non-integer periods. So far I do not see anything other than continuity.
And S is unlikely to come here, they are very busy.
 
Mathemat >>:
А как с ними решать, с машками, avatara? Общепринятой всеми процедуры пока не предложено. Что-то конкретное все равно должно исходить из требований к реализациям при нецелых периодах. Я пока ничего окромя непрерывности и не вижу.
А S сюда вряд ли заглянет, сильно занятые оне.

Another clue.

Pure geometry.

Peter has - so he thinks, infallibly.

But if the last value (i-1) is greater than the one added (i) with a remainder and vice versa - it is less, the results must be different.

And he has the same.

;)

----

like series (timeseries) -

6 3 7 5

6 7 3 5...

periood the same 3,333

 
Mathemat >>:
Решите систему уравнений для положительных x, y и z:
x+(1/y)=2-(y-z)^2
y+(1/z)=2-(x-y)^2
z+(1/x)=2-(z-x)^2

x+1/x +y+1/y+z+1/z =6-(y-z)^2-(x-y)^2-(z-x)^2
x+1/x >=2
6-(y-z)^2-(x-y)^2-(z-x)^2 >=6
x=y=z=1

 
Yeah, ihor, right on.
 
avatara >>:

Еще одна подсказка.

Чистая геометрия.

У Петра - так он считает, непогрешимо.

That's a strong one. Just an option. // I've already pestered Alexey in private with my doubts. What is "infallible" here...)))

But if the last value (i-1) is larger than the value added (i) with a remainder and vice versa - it's smaller, the results should be different.

And it is the same.

;)

----

like series (timeseries) -

6 3 7 5

6 7 3 5...

periood is the same 3,333

Explain this one. I don't quite understand.

 
Svinozavr >>:
А вот это поясните. Не вполне понимаю.

mashka is not just an average... eh? ;)

now calculate it for the first row 6 3 7 5

and for the second 6 7 3 5.

I assert (and can show:) that MA/*3.333*/(0) is different for these rows.

If no one is interested in this problem, solve the others next...

I'm already embarrassed.

 
Well, then you can go completely off the deep end if you look at the invariants.
What am I saying? A simple waving machine is invariant with respect to any reshuffle of prices involved in the calculation. In principle, the "fractal" should behave the same. No? OK, justify it then.
It's different for other mash-ups. For a linearly weighted one the invariance of the swing will be with respect to other movements of the settlement prices.
 
Mathemat >>:
Ну можно тогда и совсем в дебри залезть, если смотреть на инварианты.
О чем толкую? Простая машка инвариантна относительно любой перестановки цен, участвующих в расчете. В принципе так же должна вести себя и "фрактальная". Нет? ОК, обоснуй тогда.
Для других машек все по-другому. Для линейно взвешенной инвариантность машки будет относительно других движений расчетных цен.

Not really. It's kind of like a... sliding average. used for time series. Imho. ;)

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