# All Questions

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### Maximum order of a sum of functions

I'm being introduced to the Big-O notation via Susanna Epp's Discrete Mathematics with Appplications 3rd edition. The following defintion is stated on page 519: Let f and g be real-valued functions ...
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### 'Odd' Odd ratio question

Assuming Intervention group to be mothers having c-section and control group to be mothers having natural birth. Also, the numerical data is as follows: ...
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### Tensor products

I'm trying to get my head round tensor products of vector spaces (I'm happy to see arguments in a more general setting, though). I am concerned principally with two statements: i) If $U,V,W$ are ...
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### Show that if $f^{-1}((\alpha, \infty))$ is open for any $\alpha \in \mathbb{R}$, then $f$ is lower-semicontinuous.

I've tried looking for this question on this site, but I can't seem to find it. But if anyone can direct me to it, that would be great. But i'll pose my question in the mean time. As the title ...
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### Analysis Problem: Prove $f$ is bounded on $I$

Let $I=[a,b]$ and let $f:I\to {\mathbb R}$ be a (not necessarily continuous) function with the property that for every $x∈I$, the function $f$ is bounded on a neighborhood $V_{d_x}(x)$ of $x$. Prove ...
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### Van Der Waerden Theorem [closed]

Can someone explain me what's the meaning of the term "l-equivalent" in the following paper: http://www.math.ucsd.edu/~ronspubs/74_01_van_der_waerden.pdf ? I saw the definition at the first lines, ...
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### How do I find if $\frac{e^x}{x^3} = 2x + 1$ has an algebraic solution?

Is there some way of solving $$\frac{e^x}{x^3} = 2x + 1$$ non-numerically? How would I go about proving if there exists a closed form solution? Similarly how would I go about proving if there exists ...
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### Computing angle

See the drawing for the situation. Given lenghts a, b and c and also L, but k and angle alpha are unknown. How to compute this angle alpha? I know it is possible to compute if we first compute k in ...
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### Gradient of a Mahalanobis distance

Short question: How can I calculate $\dfrac{\partial A}{\partial L}$ where $A = \|Lx\|^2_2= x^TL^TLx$? Is it $\dfrac{\partial A}{\partial L}=2Lx^tx$? Long question: I want to calculate the ...
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### $\mathbb{Z}_{3}\times\mathbb{Z}_{4}$ isomorphic a generated subgroup

I'm trying to prove that the group $\mathbb{Z}_{3} \times \mathbb{Z}_{4}$ is isomorphic to the generated subgroup by $(2,20)$ and $(9,10)$ of $\mathbb{Z}_{12}\times\mathbb{Z}_{40}$ . Here is my ...
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### Proving $(0,1)$ is not countable

Recall that a countable set $S$ implies that there exists a bijection $\mathbb{N} \to S.$ Now, I consider $(0,1).$ I want to prove by contradiction that $(0,1)$ is not countable. First, I assume ...
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### Prove that this sequence does not converge pointwise almost everywhere.

Suppose that $f_n$ is a sequence of real measurable functions on a set $X$ of finite measure, and suppose that there is some $\epsilon$ such that for all $n\geq1$: ...
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### Functions involving infinite set -> infinite set and one-to-one and/or onto

Two true or false questions: $\mathbb{Q}^+$ means the positive rational numbers (no 0) $\mathbb{N}$ means all natural numbers Every function $f\colon \mathbb{Q}^+ \to \mathbb{N}$ is not one-to-one ...
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### A complex function

I just need some help with the penultimate question of my coursework: Let $w=f(z)=\coth(z/2)$. Show that $w=f(z)=h(C) = (C+1)/(C-1)$ where $C=g(z)=e^z$. Find the image of the given points, ...
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### Orthogonality relations of Characters

Could somebody please help me understand the jump from Proposition 10 to Proposition 11 in the following http://www.ms.uky.edu/~pkoester/research/charactersums.pdf Note: The orthogonality relations ...
I'm very interested in the topic of generating functions, so I have two questions: I just realized that when I have exponential generating function for example $F(x)=e^{e^x-1}$, I can take n-th ...
### Why is every meromorphic function on $\hat{\mathbb{C}}$ a rational function?
I know that an analytic function on $\mathbb{C}$ with a nonessential singularity at $\infty$ is necessarily a polynomial. Now consider a meromorphic function $f$ on the extended complex plane ...