Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 83

Evaluating $I=oint frac{cos(z)}{z(e^{z}-1)}dz$ along the unit circle

Evaluate the following along the unit circle:$$I=oint frac{cos(z)}{z(e^{z}-1)}dz$$I tried doing it by $$f(z)=frac{cos(z)}{e^{z}-1}$$ Then the integral would be: $$I=2pi if(0)$$ The problem is that $f(0)$...

Asked on 11/16/2021 by random name

1 answer

product of sums: $R_{XX}(t_1, t_2) = cos(t_2 - t_2) + cos t_1 cos t_2$

starting with this: $$R_{XX}(t_1, t_2) = 2 cos t_1 cos t_2 + sin t_1 sin t_2$$ The textbook say it should be reducible to this form: $$R_{XX}(t_1, t_2)...

Asked on 11/16/2021 by pico

1 answer

Canonical connection form on 2-dim surface and Gaussian Curvature

Let M be a 2-dimensional Riemannian manifold. Let $X_1,X_2$ be an orthonormal frame (w.r.t Riemannian metric) in an open set $U$. Let $(omega_1,omega_2)$ be the dual coframe...

Asked on 11/16/2021

0 answer

Toeplitz Kernel Question

$$newcommand{kern}{operatorname{Ker}}$$When looking at a Toeplitz Operator (on $mathbb{H}^2(mathbb{C^+}))$ with unimodular symbol, $phi=e^{i psi}$, what can we say about $kern T_{phi}$ when $$limsup_{x rightarrow -infty} psi...

Asked on 11/16/2021 by Sean Nemetz

0 answer

In a quiz with 13 people, what are the probabilities that exactly 12, exactly 11 and exactly 10 people answer correctly?

A group of 13 people, p1, p2, p3, ... , p13 answers the same question. The probability that a person answers correctly are known but differs between the people. For...

Asked on 11/16/2021 by motch

1 answer

Looking for the proof of theorem 5.2.11 of Casella, Berger, Statistical Inference

Theorem 5.2.11 Suppose $X_1,dots, X_n$ is a random sample from a pdf or pmf $f(xmid theta)=h(x)c(theta)exp(sum_{i=1}^kw_i(theta)T_i(x))$ is in exponential family. Define statistics $T_i=sum_it_i(X_j)$ where $i=1,dots, k$....

Asked on 11/16/2021 by user45765

0 answer

Hopf surface as an elliptic surface over $mathbb{P}^1$

I saw that the (primary) Hopf surface is an elliptic surface over $mathbb{P}^1$. I want to see why. What I am thinking is by the Hopf fibration $S^1to...

Asked on 11/16/2021 by 6666

0 answer

Is this probabilistic proof for Brocard's Conjecture flawed?

Brocard's conjecture is the assertion that there are at least four primes between consecutive prime squares, for primes greater than 2. In notation, $pi(p_{n+1}^{2})-pi(p_{n}^{2})ge4$for $ngt1$(so ...

Asked on 11/16/2021 by Sneezeburgers

1 answer

Given $Tin mathcal{L}(V)$ which has $n$ eigenvalues in $K$. Show that if there is a $kin mathbb{N}$ with $T^{k+1}=T$ then T is diagonalizable.

I am thinking about the following problem:Let $V$ be an $n$-dimensional vector space over $K$ and let $T:Vrightarrow V$ be an endomorphism which has $n$...

Asked on 11/16/2021

1 answer

Is this set of linear maps valid?

Notation: The set of all linear maps from a vector space $V$ to a vector space $W$ (over a field $mathbb{F}$) is denoted $mathcal{L}(V, W)$.The question...

Asked on 11/16/2021 by gorgonolo

2 answer

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