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12:00 AM
3
Q: What are some efficient ways to keep a note of results when reading a research article in mathematics?

Praphulla KoushikI learn and produce mathematics. In that process, I had to read quite a number of research articles. Question : What are some efficient ways to keep a note of results when reading a research article in mathematics? I keep a note of definitions (in detail) and results (with out proofs) for...

3
Q: Optimal Poincaré constants under combined boundary and average conditions

DiegoG7Let $\Omega=[0,1]^2$ be the unit square, $\Gamma_1=[0,1]\times\{0;1\}$ its horizontal boundary and $\Gamma_2= \{0;1\}\times[0,1]$ its vertical boundary. I would like to know the optimal Poincaré constants $C$, defined by $$ \forall u\in W^{1,2}(\Omega)\quad \int_\Omega u^2\le C\int_\Omega |\nab...

 
 
3 hours later…
3:08 AM
3
Q: Subring of quaternion algebra

user50139I am following the book Introduction to Quadratic Forms over Fields by T. Y. Lam. In section VI.2, the author proves that, over an arbitrary local field $F$, there is a unique quaternion division algebra, namely $D=\left(\frac{\pi,u}{F}\right)$ where $\pi$ is a uniformizer and $u$ is such that $F...

 
 
5 hours later…
8:01 AM
1
Q: Relation between topological and differentiable Lie group cohomology for unitary modules

Boris BilichIt is well known, that if $V$ is a $C^\infty$ $G$-module, then the differentiable cohomology groups $H^*_{d}(G, V)$ are isomorphic to $H^*(\mathfrak{g}, K, V)$. I am interested if the result can be strengthened to continous cohomology of unitary modules in the following way: Let $V$ be a strongl...

 
 
2 hours later…
10:02 AM
18
Q: Conway's lesser-known results

Joseph O'RourkeJohn Horton Conway is known for many achievements: Life, the three sporadic groups in the "Conway constellation," surreal numbers, his "Look-and-Say" sequence analysis, the Conway-Schneeberger $15$-theorem, the Free-Will theorem—the list goes on and on. But he was so prolific that I bet he estab...

 
 
4 hours later…
1:35 PM
4
Q: Is there a Galois theory for deformations of curves?

Huy DangI have some general questions about the deformations of Galois covers of curves. Suppose we are given a $G$-Galois cover $k[[z]]/k[[x]]$, where $k$ is algebraically closed of characteristic $p>0$. Bertin and Mézard show that the deformation functor $\text{Def}_{G}$ is represented by a versal def...

 
 
3 hours later…
4:29 PM
6
Q: When does $x_n\rightharpoondown 0$ imply $yx_n\to 0$ for all $y$?

Jo JomaxAssume $A$ is an infinite-dimensional C$^*\!$-algebra and $\tau_w$ is the Banach weak topology. I want to know when $A$ has the $\star $-property: $$x_n\to 0 \ (\text{by}\ \tau_w)\ \ \ \ \Longrightarrow \ \ \ \ yx_n\to 0\ (\text{by norm}, \forall y\in A) \ \ \ (\star ) $$ My attempts: Pr...

 
 
2 hours later…
6:08 PM
1
Q: Combinatorial equation system with exponentially many equations in quadratic many variables

Mario KrennA certain question on graph theory (about the existance of graphs with a certain coloring inherited by perfect matchings) can be translated into the satisfiability problem of a certain set of equations (formulated by Michael Engelhardt). Let $X_i $ be indexed by an integer $1\leq i\leq n$, and ...

 

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