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Add smaller Hamiltonian circuits to make bigger one

Is it always possible to generate a Hamiltonian circuit by adding smaller ones? For example, a 8x8 grid can be split into four 4x4 grids, each having a Hamiltonian circuit....

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Mathematics Asked by correaswebert on 2 years ago

One number is removed from the set of integers from $1$ to $n.$ The average of the remaining numbers is $163/4.$ Which integer was removed?

One number is removed from the set of integers from $1$ to $n.$ The average of the remaining numbers is $dfrac{163}4$. Which integer was removed?Source. ...

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Mathematics Asked by Drich1002 on 2 years ago

Is it ever possible to "win" a 50/50 game with a clear goal in mind.

Lets say I have 750 dollars and want at least 1250 dollars at the end of a 50/50 game where I can bet any possible value. Is there any way...

2

Mathematics Asked by Big Altz on 2 years ago

Two sequences $f_n$ and $g_n$ such that $int_{[0,1]}f_n g_n$ does not go to $0$ as $nrightarrowinfty$, with these conditions on $f_n$ and $g_n$

Question: Suppose $f_n, g_n:[0,1]rightarrowmathbb{R}$ are measurable functions such that $f_nrightarrow 0$ a.e. on $[0,1]$ and $sup_nint_{[0,1]}|g_n|dx<infty$.Give an example of two sequences $f_n$ and $g_n$...

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Mathematics Asked on 2 years ago

finding the degree of a zero of a function with given conditions

Let $f$ be a holomorphic function at the unit circular disk and that $f(0)=0$. Now let $f$ be real valued function on the radii $[0,1)$ and...

2

Mathematics Asked by pencil321 on 2 years ago

Should the subsets in this graph theory exercise be finite?

I'm reading Béla Bollobás's Modern Graph Theory and one of the exercises (I.10) says the following:Show that in an infinite graph $G$ with countably many edges there exists a...

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Mathematics Asked by laurencevs on 2 years ago

Inverse Mellin Transform

We all know that the Inverse Mellin Transform is$$left{mathcal{M}^{-1}varphiright}(x) = f(x)=frac{1}{2 pi i} int_{c-i infty}^{c+i infty} x^{-s} varphi(s), mathrm{d}s.$$So what is my problem? I want to calculate...

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Mathematics Asked on 2 years ago

Establishing divisibility by a prime

Let $a,b,c$ belong to ${0,1,....p-1}$, where $p$ is an odd prime. We need to find the number of triplets $(a,b,c)$ such that $a^2-bc$ is divisible...

1

Mathematics Asked on 2 years ago

Flabby representable sheaves

Let $S$ be a scheme. Consider some representable moduli functor $mathcal{M}:(Sch/S)^{op}rightarrow Set$ represented by some scheme $M$. Then for each $Vin (Sch/S)^{op}$, let define$$mathcal{M}^{glob}(V):=text{im}left(mathcal{M}(S)rightarrow...

1

Mathematics Asked on 2 years ago

How fast does $lim_{ t to 0} E left[ |Z|^2 1_{B}(X,X+sqrt{t} Z) right]= E left[ |Z|^2 right] E[1_B(X)]$

Let $X in mathbb{R}^n $ and $Z in mathbb{R}^n $ be two independent standard normal random vectors. We are interested in the following quantity:begin{align}E...

1

Mathematics Asked on 2 years ago

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