All Questions

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Convert from one format to other

Sorry for my lack of knowledge but I need help with, it seems, a basic math algebra. I want to know how they got this: $(1 - t)P1 + tP2$ from this: $P1 + t(P2 - P1)$ I did the math and they are ...
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Is $\operatorname{Stab}(\lambda)$ generated by the simple reflections it contains, for $\lambda\in A_0$?

For a finite Weyl group, the stabilizer of an element in the fundamental domain is generated by the simple reflections of the Weyl group that is contains. Does the same still hold for the closure of ...
29 views

To show an entire function is zero

$f$ is entire, satisfying $$|f(z)|\le \frac1{|\text{Re}(z)|}.$$ Show that $f$ is identically zero. It suffices to show boundedness. Since $f$ is bounded on the real line, then if $f$ is ...
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If a conjugacy class intersect with its centralizer what can be said about its elements?

Suppose that $G$ is a finite group and let $x\in G$. If $y\in x^{G}\cap C_{G}(x)$, what can be said about the relationship of $x$ and $y$, or anything about $x$?
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Definition of length of a sequence

In definition $3.11$, the author defined the following rank: If the sets $A$ and $B$ can be separated by a transfinite difference of closed sets, then let $\alpha_1(A,B)$ denote the length of ...
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Clarity on Boolean Algebra and Rings

I'm trying to wrap my head around Abstract Algebra, Boolean rings, and it's a little difficult. So I understand the ring (I believe it's a ring) <ℤ ,x, +, -, 0, 1 > is normal integer arithmetic ...
34 views

How do you find the domain of this function?

$$f(x) = x^2 - 3x$$ My Working : \begin{align} x^2-3x &= 4\\ x(x-3) &= 4\\ x-3 &= 4 \\ x &= 7\\ \end{align} I managed to solve one part of this problem but that one part is ...
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Extending the single parity check code

I recently posted a question if it was possible to extend a code with odd minimum distance in some other way than the single parity check if you want to increment the minimum distance. This question ...
415 views

Solve equation with lower gamma function: $A \gamma(2;x/B)=x$ for $x$

I need to find an expression for $x$ given: $A \gamma(2;x/B)=x$ where $\gamma(a,x)=\int\limits_0^x t^{a-1} e^{-t} \mathrm{d}t$ is the lower incomplete gamma function. $A$ and $B$ are real, positive ...
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Find the limit $\lim_{x\to 0} x^{-3}\int_0^{x^2}\sin{(\sqrt t)}dt$

I use the fundemental theorem of calculus $$\displaystyle\lim_{x\to 0}\frac{\displaystyle\int_0^{x^2}\sin{(\sqrt t)}dt}{x^3}=\frac{F_{(x^2)}-F_{(0)}}{x^3}="\frac{0}{0}"$$ Than apply L'hopital rule ...
24 views

Which probability is greater, given minimal info

which probability is greater, given that $X$ and $Y$ are independant, positive random variables? There is also the option that it's impossible to know as we don't have enough information. I'd ...
20 views

Expressing Tornheim sums in terms of Riemann's Zeta

If $$T(a,b,c)=\sum_{r\geq1}\sum_{s\geq1} \frac{1}{r^as^b(r+s)^c}$$ How to prove that : $$T(3,1,2)=-\frac13 \zeta(6)+\frac{\zeta^2(3)}{2}$$ I tried some algebraic manipulations but did not work. Can ...
19 views

If G and H are two gaphs then what does $G \Delta H$ indicate in graph theory?

I came across this notation in a book titled " Combinatorial Optimization Theory and Algorithms" by Bernhard Korte and Jens Vygen.
27 views

Is the following statement provable?

The statement is: $f$ is a real fucntion on $\mathbb R$. Then if $f'(x)=f(x)$ and $f(0)=1$, then $f(x)\neq 0.$
58 views

Simplification of $(e^{2x}-1)/(e^x-1)$

Why is $$\frac{e^{2x}-1}{e^x-1}$$ equal to $e^x+1$ ?
1k views

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A differential equation (nonlinear First-Order)

how to solve this equation: $(Px-y)(Py+x)=h^2P$ that $P=\frac{dy}{dx}$ and $h$ is a constant.
1k views

Why is the complex plane shaped like it is?

So it's always taken for granted that the real number line is perpindicular to multiples of i, but why is that? Why isn't i just at some non-90 degree angle to the real number line? Could someome ...
8 views

Customer problem in poisson process (two products)

Customers arrive at a shop according to a Poisson process at rate $\lambda$ (/minute), where they choose to buy either product $A$ (with probability p) or product $B$ (with probability $1-p$), ...
22 views

Is $X^p - t\in \mathbb{F}_p (t) [X]$ separable over $\mathbb{F}_p (t)$?

Is $X^p - t\in \mathbb{F}_p (t) [X]$ separable over $\mathbb{F}_p (t)$? I am trying to understand what are in these two structures. My thought is that, if we look at the derivative of $X^p - t$, we ...