# All Questions

0answers
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### If the second moments are uniformly bounded, does $Y_n$ converge in $L^2$?

Let $\{X_n\}$ be a pairwise uncorrelated sequence of random variables such that there exists a fixed constant $c>0$ such that $E(X_n^2)\leq c$ for all $n\geq1$. Does it imply that for any ...
0answers
19 views

### How to insert Gothic letters in Word?

I do not manage to find in any of the options provided by Word the real Gothic letters used my German mathematicians in their original works. Noe even under the two "gothic" rubrics. just some sparse ...
0answers
6 views

### Show the following including number of divisors d(n)

I know how to show that $(d ∗ \mu)(n) = 1$ for all n ≥ 1.But.. I have two solutions. Firstly... result is trivial, because $d = 1 ∗ 1$ Secondly We know that both sides are multiplicative. Thus it ...
1answer
4 views

### The Fourier transform of functions with compact support is differentiable.

1) How can I prove that if $f(x)$ is a continous function with compact support (let's say $f(x)=0$ $\forall x\in B(0,R)^c$), then its Fourier transform $\hat{f}(\xi)$ is differentiable? 2) Is there ...
0answers
5 views

### Maximum number of independent parameters for defining a subspace of a vector space

Consider a subspace $W$ in a vector space $V$. The basis of $W$ is a funciton of a set of parameters $\{\alpha_i\}$. What is the maximum number of independent parameters for fully defining the ...
1answer
12 views

### How to find complex coordinates of a square?

If one coordinate is given by: $z_{1}=\frac{3}{2}+\frac{3}{2}i$ and $Re(z_{2})=6,Re(z_{4})=1$. How to find $z_{2},z_{3},z_{4}$ so that $z_{1}z_{2}z_{3}z_{4}$ forms a square in the first quadrant? ...
0answers
8 views

### Are the following logical statements equal? Solution verification

We were requested to rewrite the following statement: $((\phi \rightarrow(\psi \lor \lnot X)) \land (\phi \rightarrow (\psi \land X)))$ Using $\exists, \land, \lnot$ only. My result: ...
0answers
12 views

### If $\sum \|f_n -f \|_{L^1} < \infty$ then $f_n \rightarrow f$ almost uniformly

Consider $(X,m)$ a measure space, $f_n, f : X \rightarrow \mathbb R$ s.t. $\sum_{n=1}^{\infty} \|f_n -f \|_{L^1} < \infty.$ How to show that $f_n \rightarrow f$ almost uniformly? I will have ...
1answer
6 views

### How to express outer sum in a matrix form?

So I have the following equation for a matrix $\mathbf{B}$ given $\mathbf{A}$: $$b_{ij} = \sum_k \sum_l a_{ki} a_{jl}$$ The question is if there is anyway that I can write that one compactly in ...
0answers
6 views

### Can critical point that $f''$ has different sign in its every neighborhood be a local extreme point?

Suppose that $f$ is a second order derivable function on $[0,1)$, and $f'(0)=f''(0)=0$. If for any $\delta>0$ there exits $x_1,x_2\in [0,\delta)$ such that $f''(x_1)>0$ and $f''(x_2)<0$, is ...
0answers
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