4
votes
2answers
373 views
A question on base change
Let $X$ be a regular integral projective scheme of dimension 1 over a field $k$ (not algebraically closed). Further, assume $X$ satisfies $dim_kH^0(X,\mathscr{O}_X)=1$. Let $\bar{X …
-1
votes
1answer
505 views
Cantor type set?
A $proper$ $subinterval$ of an interval $J$ is a subset and interval each of whose endpoints does not coincide with end points of $J$. Let $A_{0}=[0,1]$ be a subspace of $\mathbb{R …
6
votes
2answers
410 views
What’s the name of this flavor of n-category?
I'm looking for the name of a certain n-category definition. (Someone explained it to me a couple of years ago. I remember the definition, but not the name. Without the name it' …
10
votes
1answer
444 views
Put as many points as possible in an equilateral triangle of side 1 with their minimal distance greater than 1/n
It is known by the pigeon-hole principle that:
If we select $5$ points within an equilateral triangle with side $1$, there must be at least two whose distance apart is less than …
6
votes
3answers
410 views
partitioning the 3-sets of [n]={1,…,n} into families
Let $F_1,...,F_m$ be a partition of the 3-element subsets of $[n]$ into families such that no three subsets in any one family $F_i$ are all contained in one 4-element subset of $[n …
1
vote
2answers
536 views
Counting and summing over solutions of a Diophantine equation
Say I have a Diophantine equation of the form $a_1 x_1 + a_2 x_2 + ... + a_m x_m = n$ such that the $a_is$ are all co-prime to each other. And I also have a function say $f$ which …
1
vote
1answer
202 views
Combinatorics for a stochastic dynamics problem
Suppose we have a circular arrangement (periodic boundaries) with $M$ sites and we want to distribute $N$ particles over these sites such that there are occupation numbers $n_m$ th …
2
votes
2answers
588 views
What $Re(f(z))=c$ can be if $f$ is a holomorphic function ?
Suppose that $f:U\subset\mathbb{C}\to\mathbb{C}$, where $U$ is a region in the complex plane, is a holomorphic function.
Of course, if $c\in\mathbb{R}$ is a regular value for $\t …
0
votes
0answers
400 views
Complete Orthonormal Sequences in Hilbert Space [closed]
Let $H$ be a Hilbert space and $(e_n)_{n=1,2,\ldots}$ be a complete orthonormal sequence in $H$. We want to show that if $a_np=(e_n,f_p)$ then $\sum_{p=1}^{\infty}a_{np} \overline …
5
votes
4answers
1k views
Less-known conjectures of significant influence and the contrary
In mathematics, it is common that theorems/results and problems appearing dull in one generation get revitalized and become the center of research in another one.
Sometimes conjec …
5
votes
0answers
196 views
Dirichlet-to-Neumann map on $C^{k,1}$ domains
I am interested in the mapping properties of the Dirichlet-to-Neumann map (also called the Poincare-Steklov operator) for $C^{k,1}$ domains, between Sobolev spaces on the boundary. …
-1
votes
0answers
269 views
find the root of an equation [closed]
How to find the root of $$(1-x)^{a} - {a \choose 2} x^2=0. $$
Here, $a$ is an integer.
Or can we at least have an approximation of it ?
4
votes
4answers
1k views
Approximation by exponential polynomials
Let $u(t) = \Sigma_{k=1}^n c_k e^{\lambda_k t} (c_k \in \mathbb C, \lambda_k \in \mathbb C) $ be an exponential polynomial of $\underline{order}$ $n$.
Define $E_n$ to be the coll …
7
votes
1answer
494 views
When the Lovász theta-function saturates its upper bound
The Lovász $\vartheta$-function of a graph $G$, $\vartheta(G)$, is well-known to be "sandwiched" between the independence number of the graph, $\alpha(G)$, and the chromatic number …
3
votes
0answers
316 views
Lifting local compactness to a covering space
(I decided to repost this from MathSE, since the question seems to not be as easy as I had thought)
NB: In this question, local compactness is used in its weak form, i.e. in a loc …
