Recent content by fabiancillo

Ok I'll try

I am totally blocked

Hello I have problems with this exercise For the painted area calculate inertias with respect to the x and y axes and the principal inertias Hint: $I_x = \displaystyle\frac{bh^3}{12}$ $I_{xy} = \displaystyle\frac{b^2h^2}{24}$ Thanks

Hello, I have problems with this exercise Let $(X,\mathcal{B} , \mu)$ a measurement space, consider $\bar{\mathcal{B}} = \{ A \subseteq{X} \; : \; A\cap{B} \in \mathcal{B}$ for all that satisfies $\mu(B) < \infty \}$, and for $A \in \bar{\mathcal{B}}$ define $\bar{\mu}(A) = \left \{...

Hello i have problems with this exersice Let $$\{X_{\alpha}\}_{\alpha \in I}$$ a collection of topological spaces and $$X=\prod_{\alpha \in I}X_{\alpha}$$ the product space. Let $$p_{\alpha}:X\rightarrow X_{\alpha}$$, $$\alpha\in I$$, be the canonical projections a)Prove that a sequence...

Hello, I don't know to solve this exercise: Let $\mathcal{B}_\mathbb{R}$ the $\sigma-algebra$ Borel in $\mathbb{R}$ and let $\mu : \mathcal{B}_\mathbb{R} \rightarrow{} \mathbb{R}_{+}$ a finite measure. For each $x \in \mathbb{R}$ define $$f_{\mu} := \mu((- \infty,x]) $$ Prove that: a)...

I understand. Thank you

$R^{\times} = m \in \mathbb{Q} $ such that $p$ does not divide $m$ ?

$p$ does not divide $m$

$1$ ,$-1$ and prime numbers $\neq p$?

I understand but . What are the units of $R$?

Can you explain? Sorry In the exercise I do not know if this happens contains the multiplicative identity of R.

Hello, I don't know to solve this exercise: Let $p \in \mathbb{Z}$ be a prime number. Consider $R = \{m/n \in \mathbb{Q}: p$ does not divide $n \}$ How can I prove that $R $ is a sub-ring of $\mathbb{Q}$? (only the obvious parts) and find the group of units of $R, R^{\times}$I have no idea.How...

a) I think that elementary divisors are $\{2,3,2^2,3,2,3^2 \} $ because is the prime decomposition of ${6,12,18}$. b) elementary divisors are $\{5 ,2 ,2^2, 5, 2, 3, 5, 2^3, 5 \}$ . But I don't use the Chinese remainder theorem to split each factor into cyclic pp-groups, then regroup

Hello I have problems with this exercise Find the elementary divisors and invariant factors of each of the following groups a) $G1= Z_6 \times Z_{12} \times Z_{18}$ , b) $G_2= Z_{10} \times Z_{20} \times Z_{30} \times Z_{40}$Thanks