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0
votes
0answers
10 views
Lattice paths in polytopes
Let $P$ be a polytope in $\mathbb{R}^n$. Let $A_ix = b_i$ be the defining equations of its codimension $1$ faces. Is there an algorithm or some kind of criterion to decide if the lattice points inside ...
0
votes
0answers
6 views
A quaternion x generates a left ideal of rank 2 if and only if x, ix and jx are linearly dependent?
I am trying to understand the construction of Artin and Mumford of a non-rational unirational threefold in ([1], p.90).
Assume $S$ is a smooth projective surface over $\mathbb{C}$ with a smooth ...
0
votes
0answers
9 views
Completude for intermediate logics
Let $IL$ be intuitionist logic and $\mathcal{L}$ be $IL$ enriched by some set of formulas $\Delta$.
It is also true that
$$
IL \vdash \varphi \hspace{10pt} iff \hspace{10pt} \varphi \text{ is valid ...
2
votes
0answers
12 views
Poincare Recurrence by Mean Ergodic Theorem
I have a question regarding a confusion from reading the Princeton Companion to Mathematics on the topic of Ergodics Theorems. It is about proving a stronger version of Poincare Recurrence Theorem ...
2
votes
1answer
19 views
Have this generalization of Indifference graphs been studied before?
Indifference graphs are those graphs $G=(V,E)$ for which there exists a real-valued function $f$ defined on $V(G)$ such that, if $u$ and $v$ are distinct vertices, $|f(u)−f(v)| \lt 1$ if and only if $\...
1
vote
0answers
12 views
For a given Gaussian vector, which rectangular parallelepiped with unit volum has the largest probability?
Let $X$ be a centered Gaussian vector of $\mathbb{R}^n$ and $\Gamma$ its variance matrix. We assume that diagonal coefficients of $\Gamma$ are all equals to 1.
We are looking for a rectangular ...
1
vote
0answers
29 views
Cohen-Macaulay Artin algebras
In http://link.springer.com/chapter/10.1007%2F978-3-0348-8658-1_8#page-1
Auslander and Reiten introduced COhen-Macaulay Artin algebras as a generalisation of Gorenstein algebras. Let X be the full ...
-1
votes
0answers
28 views
Are these examples of retractions and sections correct? [on hold]
In the book “Conceptual Mathematics: A first introduction to categories” (first edition) on page 52 we can see the following (link because I don't have 10 reputation points):
https://i.stack.imgur....
0
votes
0answers
11 views
Evolution equations with convolution coefficients
I'm looking for references about evolution equations with "convolution coefficients", that is to say PDEs that looks like
$$ a(t)*\frac{\partial}{\partial t} u(t) = b(t) * A u(t)$$
where $A$ is a ...
0
votes
0answers
21 views
Find max(x) in the equality [on hold]
for $ x<y<z,x∈z+,y,z∈R+ $
$ \frac{8}{x}-\frac{3}{y}+\frac{5}{z}=\frac{1}{4} $
Find max(x)
.
2
votes
1answer
67 views
Irreducible representations of simple complex groups
Let $G$ be a simple complex algebraic group. What are its complex irreducible finite-dimensional representations?
Before you start voting to close the question, I never said "rational". I am asking ...
0
votes
0answers
32 views
Has the Jacobson/ Baer radical of a group been studied?
On groupprops, the Jacobson or Baer radical of a group $G$ is defined to be the intersection of all maximal normal subgroups of $G$. This is similar to, but distinct from, the Frattini subgroup which ...
0
votes
1answer
71 views
Homological dimensions of tensor products of algebras
Given two finite dimensional algebras $A$ and $B$ over a field. The Gorenstein dimension of an algebra A is defined as the injective dimension of the module A. The finitistic dimension of an algebra A ...
6
votes
0answers
194 views
Computation of $\pi_4$ of simple Lie groups
Below we assume any simple Lie group $G$ to be simply connected.
$\pi_3(G)=\mathbb{Z}$ for any simple Lie group $G$ and there is a uniform proof for that.
Now the textbooks say $\pi_4(G)$ is trivial ...
0
votes
1answer
22 views
Minimal clique decompositions
Let $G=(V,E)$ be a simple, undirected graph. A clique decomposition is a set ${\cal C} \subseteq {\cal P}(V)$ such that
$\emptyset \notin {\cal C}$,
$C\in {\cal C}$ and $x\neq y \in C$ imply that $\{...
