Search Results

What is missing is that for all $x \in M$ there should be an open neighborhood $U \subseteq M$ of $x$ and a local section $\sigma: U \to P$ of $P$ with $$\sigma(U) \subseteq Q.$$ Why should this exist? … The problem: $b$ has image in $\GL(V)$ and not in $G$. Also a simple example didn't work: Take $M = P$, $G = 1$ and $V = \mathbb{R}$. Then $E = M \times \mathbb{R}$. …

My central question is: What are the key mathematical approaches or open problems in analyzing performance metrics (e.g., outage probability, capacity) for Nakagami-m fading channels, especially in RIS-aided …

Can it be considered research only the research in open problems or it can be considered research also the finding of new formulas, new classes of primes without a context? …

It is open problem if there are only finitely many Wieferich primes and if there are finitely many non-Wieferich primes. Define $W(n)=\frac{2^n+1}{3}$ and $V(n)=2^n+1$. …

In McDuff and Salamon's Introduction to Symplectic Topology, the following open problem is mentioned. … Since another open problem concerning the symplectic topology of Euclidean space was recently resolved, I became curious if any progress has been made on the problem stated above. …

Now the problem. … In particular, $\b(\mathbb{R}) \setminus\iota(\mathbb{R})$ must be closed in $\b(\mathbb{R})$, so $\iota(\mathbb{R})$ must be open. …

$\newcommand\P{\mathbb P} \newcommand\C{\mathbb C}$For a degree 4 curve, the Macaulay quartic curve is the only irreducible space curve (up to isomorphism) for which it remains an open problem to find …

Asking the question I keep in mind by "recent years" something like a dozen years before now, by a "conjecture" something which was known as an open problem for something like at least dozen years before …

Question: I'm asking for a big list of not especially famous, long open problems that anyone can understand. Community wiki, so one problem per answer, please. … Meaning of: long open The problem should occur in the literature or have a solid history as folklore. …

At a workshop it was suggested that it likely remains an open problem whether or not there is a 3- or 2 -piece dissection of a square to an equilateral triangle. …

See here Can you solve the listed smallest open Diophantine equations? … for a version of this question where we only want to check whether any integer solution exists, and here On the smallest open Diophantine equations: beyond Hilbert's 10 problem for a version where we also …

If you have a compact subset $K$ of some open set $\Omega$ I understand your question as : can I find a smooth set $K'$ such that $K\subset K' \subset\Omega$ ? … That's not a real problem : you can replace it by a smooth approximation (or use the regular distance of Stein given in Theorem 2 of his book). …

A topological space $X$ is strongly collectionwise normal if and only if for every open covering $\mathscr{U}$, there exists a refinement $\mathscr{V} \leq \mathscr{U}$ with the following property: if … Bing as a counterexample to a different problem which can also be found in the paper of H. J. Cohen. References Cohen, Herman J., Sur une problème de M. Dieudonné, C. R. Acad. …

\end{cases} $$ In particular, $f=0$ on the nonempty open set $\Om=G_1$. Moreover, it is easy to see that the function $f_0$ is convex on $G_2$. … However, clearly the differentiability of $f$ has hardly anything to do with the essence of this problem. …

constructions based on Sudoku puzzles could be used to obtain any deep results in combinatorics and noted that there were papers of Greenfeld and Tao where Sudoku constructions where employed to resolve several open … problems for higher-dimensional tilings. …