Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 96

How to define a curve surrounding the origin?

Is there any criteria for stating that a curve is sorrounding the origin?For example:Consider $Bbb D={x^2+y^2-ylesqrt{x^2+y^2}}$, that is in polar coordinates: $Bbb D_{(rho, theta)}={0lethetale2pi,, 0lerhole1+sin{theta}}$.In...

Asked on 11/06/2021 by DOmonoXYLEDyL

3 answer

What would a Cayley table of inverse semigroup look like?

I tried to construct a Cayley table of an algebraic structure called inverse semigroup. No success so far. I just end up with more complicated structure (monoid, group). Thank you...

Asked on 11/06/2021 by Josef Hlava

2 answer

about prisoners and selection of numbers

Each of the three prisoners had a natural number written on their foreheads: 1, 2 or 3. Numbers can be repeated. The prisoners see all numbers except their own....

Asked on 11/06/2021

1 answer

If a sequence $langle a_nrangle$ is such that $a_1a_2=1, a_2a_3=2, ldots$ and $limfrac{a_n}{a_{n+1}}=1.$ Then find $|a_1|.$

Here since $lim frac{a_n}{a_{n+1}}=1.$ So no definite conclusion can be made about the nature of the sequence $langle a_nrangle$. So how can I can proceed to find the...

Asked on 11/06/2021 by Dhrubajyoti Bhattacharjee

2 answer

$F= bigcap_{i=1}^{infty} F_i$ isn't necessarily connected where $F_{i+1} subseteq F_i$ and $F_i subseteq mathbb{R}^2$ are closed and connected

In my attempt, I first show that $F$ is closed, this is since we can write $F= bigcap_{i=1}^{infty} F_i = (bigcup_{i=1}^{infty} F_i^C)^C$ and $bigcup_{i=1}^{infty} F_i^C$ is a...

Asked on 11/06/2021 by Aladin

2 answer

plot of $sin(x) + sin(y)= cos(x) + cos(y)$

I was playing arround with implicit plots of the form $f(x,y) = g(x,y)$, and I noticed that if you plot in the plane the following equation: $sin(x) +...

Asked on 11/06/2021

4 answer

Is it possible to show that the fifth roots of 1 add up to 0 simply by using trigonometric identities?

You can't use geometric sums, minimal polynomials, pentagon, and exact values with radicals. All the five, fifth-roots of unity are :$1,left(cos left(frac{2 pi}{5}right)+i sin left( frac{2pi}{5}right)right),left(cos left(frac{4 pi}{5}right)+i...

Asked on 11/06/2021

5 answer

Convergence of $sumlimits_{n=1}^inftyleft{frac{1cdot 3dots 2n-1 }{2cdot 4dots 2n}cdotfrac{4n+3}{2n+2}right}^2$

Show if the inf series$sumlimits_{n=1}^inftyleft{frac{1cdot3dots2n-1 }{2cdot 4dots2n}cdotfrac{4n+3}{2n+2}right}^2$converges. My thought: When $2n=2^k$, $frac{1cdot 3dots2n-1 }{2cdot 4dots2n}cdot frac{4n+3}{2n+2}approx (1-1/4)^1cdot (1-1/8)^2dots(1-1/(2^k))^{2^{k-2}} approx (1-1/4)^{k-1},$and so the...

Asked on 11/06/2021 by Charlie Chang

3 answer

Stalks of Higher direct images of structure sheaf at smooth points

Let $k$ be a field of Characteristic zero, and we will consider normal separated schemes of finite type over $k$. Let $X$ be such a scheme and...

Asked on 11/06/2021

1 answer

Convolution: Integral vs. Discrete sum

I recently stumbled across a question which really confused my understanding of convolution. It's the relation between the continuous integral and the discrete counterpart I don't get. What I learned...

Asked on 11/06/2021 by pythusiast

1 answer

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