Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 45

The importance and applications of order of a group?

Recently, I'm exposed to some exercises and theorems concerning order of a group. For example,If an abelian group has subgroups of orders $m$ and $n$, respectively, then it has...

Asked on 12/08/2021

1 answer

$limlimits_{Rto0^+}intlimits_{x^2+y^2le R^2}e^{-x^2}cos(y)dxdy=?$

$$limlimits_{Rto0^+}intlimits_{x^2+y^2le R^2}e^{-x^2}cos(y)dxdy=?$$ First I want to show $f(x,y)=e^{-x^2}cos(y)$ doesn't go crazy at $(0,0)$ otherwise it is already clearly continuous and bounded. So $$|e^{-x^2}cos(y)|le e^{-x^2}to 1$$ when...

Asked on 12/08/2021

1 answer

What is the difference between ${3 choose 2}$ and ${3 choose 1}{2 choose 1}$?

While choosing 2 from 3, we do ${3 choose 2}$. But what would happen if we do ${3 choose 1}{2 choose 1}$? [Choosing 1 from 3 and again...

Asked on 12/08/2021

3 answer

Computing sparse eigenvectors of psd matrices

Let $A$ be an $m times m$ psd matrix (with $m$ large) and let $s in {0,1,ldots,m}$. Let $mathscr C_s := {v in mathbb R^m...

Asked on 12/08/2021

1 answer

Express the accumulated amount in the bank as an explicit formula

Suppose I earn 500 dollars every month. If I deposit my monthly income fully into the bank, the bank pays interest of 0.25 % per month on the accumulated amount...

Asked on 12/08/2021 by Tay Ivan

0 answer

Which of the following sets of boolean functions is functionally complete?

Let us have two sets of boolean functions: $F_1 = (M setminus T_0) cup (S setminus L)$ $F_2 = (M setminus T_0) cup (L setminus S)$ where ...

Asked on 12/08/2021 by Play4u

1 answer

Find the probability using the formula for the number of permutations with repetitions

A person has forgotten the PIN code for his SIM card, but remembers that it contains three "fives", and one of the numbers is either a "seven" or "eight". What...

Asked on 12/08/2021

2 answer

How to decompose a number sequence into convergent subsequences?

Let ${a_n}$ be a real number sequence. Let $I$ be a subset of $mathbb N_+$, use the symbol ${a_n}_I$ to denote the subsequence of ${a_n}$...

Asked on 12/08/2021 by user779130

1 answer

How to approximate the peak of an epidemic (depending on epidemiological parameters)?

[I posted a follow-up question at MathOverflow.]Numerical solutions of the SEIR equations (describing the spreading of an epidemic disease)$dot{S} = - N$$dot{E} =...

Asked on 12/08/2021

1 answer

Two conditional expectations equal almost everywhere

Suppose $X$ is a continuous random variable. If $mathbb{E}[X,|,mathcal{F}]=mathbb{E}[X,|,mathcal{G}]$ almost everywhere for two sub-sigma algebra $mathcal{F}$ and $mathcal{G}$, does this imply $mathcal{F}$ and $mathcal{G}$...

Asked on 12/08/2021 by yy66yy

1 answer

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