6
votes
6answers
442 views
Sequences equidistributed modulo 1
Let $\alpha$ be any positive irrational and $\beta$ be any positive real. We have the following results.
H. Weyl (1909): The fractional part of the sequence $\alpha n$ is equidist …
1
vote
1answer
78 views
exceptional divisor on a smooth surface
Let $D=\sum d_iD_i$ be an exceptional divisor on a smooth projective surface $X$.
i.e., the intersection matrix $(D_i.D_j)$ is negative definite.
I have 2 stupid questions.
Fix …
7
votes
0answers
144 views
What are the main structure theorems on finitely generated commutative monoids?
I should read J. C. Rosales and P. A. García-Sánchez's book Finitely Generated Commutative Monoids and L. Redei's book The Theory of Finitely Generated Commutative Semigroups. I h …
0
votes
1answer
56 views
Is there any result concerning on the metric dimension of inverse limit?
To be specific, my question is as follows:
Question: Let X be an inverse limit of compact metric spaces (X_i, d_i), then does it hold
dim(X, d) \leq sup_i {dim (X_i, d_i)} for so …
0
votes
0answers
70 views
Strong convergence in the Bochner space L^p([0,T],X)
Dear mathoverflowers, I have a question concerning the strong convergence in $L^p([0,T],X)$.
Let $X_1,X$ be two Banach spaces such that $X_1\subset X$ with compact embedding. Let …
1
vote
2answers
123 views
A question about large real closed fields
A real closed field can be ordered in one and only one way, and is therefore provided with a unique
order topology. Given any infinite cardinal number k, does there always exist a …
3
votes
2answers
118 views
On finite groups with same complex-valued character table
What are the necessary and sufficient conditions for two finite groups $G$ and $H$
to have same complex-valued character table?
Is there any criterion for which one could know abou …
2
votes
1answer
90 views
Is this cube packing possible?
I know how to pack $5$ unit squares in a square of side length $2+\frac{\sqrt{2}}{2}$. Is there an $\varepsilon>0$ such that there exists a packing of $9$ unit cubes in a cube of …
4
votes
1answer
346 views
Doubt in the proof of Stickelberger’s Theorem
I was going through the proof of Stickelberger's Theorem, as given in the book 'Algebraic Number Theory' by Richard A Mollin, and I am having some problem in understanding the proo …
1
vote
1answer
91 views
Composition in the category quotient
I would like to understand the accounts of P. Gabriel (link text), pag 365, when he shows that the composition of this category is well defined.
Definition: Given a Serre subcateg …
5
votes
1answer
154 views
What is an interpretation of the relation in the cohomology of the pure braid groups?
In 1968, Arnol'd proved that the integral cohomology of the pure braid group $P_n$ is isomorphic to the exterior algebra generated by the collection of degree-one classes $\omega_{ …
2
votes
1answer
144 views
Reference request: Minimal Axiomatizations of PA over (+,x,<=).
Many years ago, when I was still a high school student, I came up with a certain first-order axiomatization of PA over the signature (+, x, ≤). Out of nostalgia, I've decided t …
1
vote
2answers
177 views
The relations between the Perelman’s entropy functional and notions of entropy from statistical mechanics
I am looking for the relations and analogies between the Perelman's entropy functional,$\mathcal{W}(g,f,\tau)=\int_M [\tau(|\nabla f|^2+R)+f-n] (4\pi\tau)^{-\frac{n}{2}}e^{-f}dV$, …
0
votes
0answers
28 views
how to get the class interval given the distribution starts at 1, 3 as the highest value and 0.65 as the lowest? [closed]
Good day. I know getting the class interval given 3 as the highest value and 0.65 as the lowest value is easy. Here's the catch, the distribution of the interval starts at 1 which …
3
votes
1answer
246 views
Differentiable manifolds by Serge Lang question
I have started reading "Introduction to differentiable manifolds" by Serge Lang. In this book, Lang takes a different approach, by immediately introducing manifolds on arbitrary Ba …
