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Jan
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comment Is there a multiple function composition operator?
Thank you for the answer. I'm not $\LaTeX$-ing this assignment (for reasons that are not relevant). It seems that no such notation exists, then? I was hoping someone could have come across something in a paper they read before.
Jan
8
comment Is there a multiple function composition operator?
Ah, I seem to have found a duplicate. Unfortunately, the answer seems to be negative.
Jan
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revised Is there a multiple function composition operator?
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Jan
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asked Is there a multiple function composition operator?
Nov
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suggested rejected edit on Hölder Condition Implying Uniform Convergence
Nov
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comment Hölder Condition Implying Uniform Convergence
I'm working on the exact same problem (Stein and Shakarchi, Complex Analysis, Ch. 3, Problem 5), and I also don't see why this can be so easily asserted. It's a shame no one answered this yet. I attempted to show as $\epsilon\rightarrow 0^+$ that $g(x\pm i\epsilon)$ is uniformly Cauchy, but this didn't get me anywhere either.
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May
14
comment What are the minimal conditions for the exactness of a 1-form on an open connected subset?
Yes - I mean they still need to be connected, but the paths from $\textbf{a}$ to $\textbf{x}$ are only parallel to the axes in some open set about $\textbf{x}$. If $n$ such paths exist and have the same integrals, one for each dimension, then do we have exactness?
May
14
accepted What are the minimal conditions for the exactness of a 1-form on an open connected subset?
May
14
comment Is there a way in matrix math notation to show the 'flip up-down', and 'flip left-right' of a matrix?
@Spacey no - nothing widely used.
May
14
comment What are the minimal conditions for the exactness of a 1-form on an open connected subset?
I see. Could you please clarify what the minimal condition for exactness is then? It seems that all that's needed is that for every $\textbf{a},\textbf{x}$, that there really only need to be $n$ paths with equivalent integrals, one for each dimension, where the paths don't even need to trace out $\partial\Delta$ fully, but just near $\textbf{x}$.
May
14
comment Is there a way in matrix math notation to show the 'flip up-down', and 'flip left-right' of a matrix?
For a matrix $M$, will $DM$ and $MD$ suffice for up-down and left-right flips, respectively, where $D$ is the unit anti-diagonal matrix?
May
14
asked What are the minimal conditions for the exactness of a 1-form on an open connected subset?
May
10
comment Why does $\exists x\,\ x = x$?
@RickyDemer So, basically, the difference between your formalization and the one in Wikipedia is that there's an additional existential qualifier $\exists\emptyset$ in the Axiom of Infinity?