# All Questions

389 views

### Analytical geometry - circles

How do you find the point for a circle and find the radius when $x^2$ has a co-efficient?
303 views

### Indices Again - Expressing Negative Fraction Powers as powers of given number

If someone could provide me with a website or link with information about this I'd be grateful but otherwise: I have the number two (with the ability to add a power) and the number ...
424 views

### Help with showing how $\sin\alpha\cos\beta$ $=$ $\frac{1}{2}(\sin (\alpha + \beta) + \sin(\alpha-\beta))$ using Eulers formula.

I need help with understanding how one can rewrite: $\sin\alpha\cos\beta$ to be equal to: $\frac{1}{2}(\sin (\alpha + \beta) + \sin(\alpha-\beta))$ using Eulers formula. I know that it probably ...
422 views

### Prove that a simple graph with $2n$ vertices without triangles has at most $n^2$ lines.

Prove that a simple graph with $2n$ vertices without triangles has at most $n^2$ lines. I've been struggling with this exercise for some time, but I can't come up with a decent proof.
67 views

### Taylor polynomial

I need your help to solve this question. I tried something, but i can't finish my proof. Let $f(x)$ be a differentiable function in $(0, \infty )$, so that $|f'(x)|$ is bounded there. Prove that ...
252 views

### Differential equation initial value problem - hard!!

I have been asked to solve $x' = t/(1 + t^2) - x(t/(1+t^2))$ and determine the maximal interval where the solution exists. I have tried to solve this in many different ways but must be using the ...
392 views

### Binomial random variable with number of trials being a Poisson random variable

Let $Y$ be the number of heads in a an $X$ toss sequence of flipping a coin with probability $p$ of heads. Show that $Y \sim \mathrm{Pois}(p \lambda)$ if $X \sim \mathrm{Pois}(\lambda)$.
256 views

### Kuratowski Definition of Ordered Pairs, ZFC

I came accross the elegant definition given by Kuratowski of an ordered pair which is: $$(x,y) := \{\{x\},\{x,y\}\}$$ and wondered, if the existence of this set presupposes (the axioms of) ZFC?
226 views

### A question on Right half-open Interval topology

Is Right half-open interval topology the same as Sorgenfrey line? I think it is, however I am not sure.
81 views

### Symmetrization of Powersum polynomials

Let $n\in\mathbb{N}$. Then for $i\in\mathbb{N}$ the $i-$th power sum if defined to be $p_i^{(n)}:=\sum_{j=1}^n x_j^i$. Then let $\lambda:=(\lambda_1,\ldots,\lambda_l)$ be a partition of $d$. We can ...
47 views

### Prove that $A^HB^H=(BA)^H$

I want to prove this statement where A and B are matrices and H the Hermitian. Ok, Here is a proof from MathWorld: ...
34 views

98 views

### Does this isomorphism hold?

Proposition: If $B\cong C$ then $\dfrac{A\oplus B}{C} \cong A.$ This is clearly true for vector spaces by counting the dimensions, but I am most interested to see if it holds for groups. What about ...
116 views

### Splitting the action of functionals in duals of Sobolev spaces

Update: After some more thinking and asking I've come to the conclusion that there is no reasonable way to achieve this for all possible $\varphi$ because of the mixed terms. I believe something ...
161 views

### Classical solutions of Neumann Laplacian

I have a question concerning the Neumann Laplacian. Say, we consider a boundary value problem formulated on an interval $\Omega = [0,1]$: -dv'' + cv = r, \quad v'(0) = v'(1) = 0, ...
215 views

### Find $\int e^{-x}\cos x\,dx$ without using complex numbers

$\int e^{-x} \cos{x} dx$ - i know how to solve with Euler complex representation, but can't figure out how to solve with integration by parts or something.
53 views

### Kolmogorov complexity of $n$

I was reading a paper on Kolmogorov complexity, but got stuck on the convergence part. It states that a common form to assign probability to integers $n$ would be $P(n)=A2^{-\log_2^*n}$, where ...
233 views

### Algebraic curves and riemann surfaces

I am a physics undergrad with no formal background in complex analysis. I have done complex analysis at the level of the first 4 chapters (till Complex integration) from Churchill and Brown. I am very ...
232 views

### Find min & max of $a(b-c)^n+b(c-a)^n+c(a-b)^n$ where $a + b+ c =1$

Find min & max of $a(b-c)^n+b(c-a)^n+c(a-b)^n$ where $a + b+ c =1;\ a,b,c\ge0; \ n \in N$ I am really stuck, I don't remember where I read this problem.
78 views

### Cleaning a signal and computing period

I am working with a signal which is a periodic square signal with some kind of noise and some outliers. I would like to know which is the best solution in order to get the period and clean the ...