# All Questions

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### Can Watson's Lemma be applied on multiple integrals simultaneously?

I need to calculate the asymptotics of the integral $$\left(\int_0^1 \mathrm e^{-tx} f(t)\right)^j$$ for $x\to\infty$. I suspect (and would like to prove), that this behaves like ...
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### Integrability on R

1) What conditions on the integrand make it integrable over $\mathbb{R}$? I know if a function is continuous and bounded on a closed interval $[-a,a]$ then this is enough for the function to be ...
380 views

### Horizontal translations of piecewise-defined functions

I understand that the graph of a real-valued function $g$ where $g(x)=f(x-h)$ is a horizontal translation of the graph of $f$. But is this true for certain piecewise-defined functions? In particular, ...
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### Norms on Dual Spaces

Suppose that $\varphi$ is a norm on $\mathbb{R}^n$ such that the set $$\varphi_1 = \{x \in \mathbb{R}^n : \varphi(x) = 1 \}$$ is a polyhedron. Let the dual norm $\varphi^*$ be defined as usual: ...
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### Alice and Bob matrix problem.

Alice and Bob play the following game with an $n*n$ matrix, where $n$ is odd. Alice fills in one of the entries of the matrix with a real number. then Bob fills one. Then Alice and so on so forth ...
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### Monotone Subseqences

If limsup$(p_k) \neq \infty$ and liminf$(p_k) \neq -\infty$, prove or disprove that $(p_k)$ has monotone increasing and monotone decreasing sub sequences.
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### finite p-groups admit a central series

If a central series is considered as $$G = G_0 \supset G_1 \supset \cdots \supset G_m = \{1\}$$ such that $$G_{i+1} \triangleleft G_i$$ and $$G_i/G_{i+1} \subset Z(G/G_{i+1})$$ then, Show that finite ...
### What type of question should we use $\binom{n + k - 1}{k - 1}$ and others
I know there are some questions with solutions of the form $\binom{n + k - 1}{k - 1}$ There are also questions with solution of the form $\binom{n + k - 1}{k}$ and there are questions with ...