Bernard Pan's user avatar
Bernard Pan's user avatar
Bernard Pan's user avatar
Bernard Pan
  • Member for 3 years, 10 months
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5 votes

Solve the equation $\sqrt{45x^2-30x+1}=7+6x-9x^2$

5 votes
Accepted

Given $X\sim\text{Unif}(0,2\pi)$, find the probability density function of $Y = \sin(X)$

5 votes
Accepted

How to quickly tell this matrix is not rank 1?

4 votes

Matrices and differentiation commute

4 votes
Accepted

Checking if a ring is Artinian.

4 votes
Accepted

Center of $G$ can be infinite Yes/No

4 votes

Any group of order $5^2q^m$ is not simple if both $q$ is a prime and $m$ a positive integer such that $5^2\nmid q^m!$

4 votes

Integral of $\frac{\sin(x)-\cos(x)}{\sqrt{\sin(2x)}}$

4 votes
Accepted

Let $a,b,c$ be integers such that $\gcd(a,6)=3=\gcd(b,6)$. Show that $\gcd(a+b,6)=6$.

3 votes
Accepted

The $2$nd, the $1$st and the $3$rd term of an arithmetic progression form a geometric progression

3 votes
Accepted

Can I compare the cardinality of two uncountable sets

3 votes
Accepted

commutative ring to boolean algebra

3 votes
Accepted

Proving $ax^2+bx+c=a(x-r_1)(x-r_2)$, where the $r_i$ are the roots

3 votes

Proof of $\frac{(n-1)S^2}{\sigma^2} \sim \chi^2_{n-1}$

3 votes
Accepted

Fourier coefficients - can I see them?

2 votes

Show that $\text{ker}(\alpha) \subseteq \text{ker}(\beta\alpha)$. If $\beta$ is one-to-one, show that $\text{ker}(\beta\alpha) =\text{ker}(\alpha) $

2 votes
Accepted

How to know when and where to transpose?

2 votes

Simplification of of Boolean expressions

2 votes

Determine if $\prod\limits_{i=0}^\infty A_i$ countable or uncountable

2 votes
Accepted

Showing that X and Y are not Independent

2 votes
Accepted

Show $K=\{g\in S_4\mid\forall x\in G, (gx)H=xH\}$ is isomorphic to Klein four group

2 votes

Proof for the nature of an eigenvector given a small eigenvalue

2 votes

Is the positive operator $TT^*-T^*T$ on a finite complex inner product space is a zero operator?

2 votes
Accepted

Show that there is a homomorphism with $\operatorname{kernel}(f) \subseteq H$

2 votes
Accepted

Projective groups and retraction definitions in Lyndon & Schupp

2 votes

Given $a_{1} = \frac{1}{2},\;\;a_{n+1} = \frac{a_{n} +3}{4},\;\;n ≥ 1$, find $L = \lim_{n\to \infty} a_{n+1}$.

2 votes
Accepted

Monotonically increasing function and supremes

2 votes
Accepted

simple summation example and simplyfing it

2 votes
Accepted

$C$ is a closed set in $X$, $X$ is $T_4$, show that $C$ is $T_4$

2 votes
Accepted

Is $B$ countable or uncountable?