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 Oct 9 awarded Yearling Oct 4 comment Is a path homotopy equivalence class a path component? Can you define more what $\Omega$ is? Oct 4 comment What is the geometric interpretation of the leading coefficient in a quadratic equation? No. The interpretation of $a$ geometrically is that it impacts the curvature. As far as I know, there is no name which specifically refers to $a$ and also reflects this geometric meaning. If there is one, it would be sufficiently obscure to be relatively useless. Oct 4 comment What is the geometric interpretation of the leading coefficient in a quadratic equation? The sign is the same as the sign of a, so it still determines convexity vs concavity. The number a is directly proportional to the second derivative, so the magnitude directly impacts the curvature as well, and this is the geometric meaning of it. If you're asking for a "name" for a alone, you can call it the leading coefficient (assuming you've written the equation down) or the coefficient of the highest term. Oct 4 answered What are some (previously and currently unsolved) problems providing motivations to study analysis? Oct 4 answered What is the geometric interpretation of the leading coefficient in a quadratic equation? Sep 6 comment Asymptotic behavior of $1/\ln n$ and $e^x-1$ What is the definition of big O that you are using? Normally, this is defined with the limit of a ratio, and this should be a useful way to proceed in both questions. Dec 3 comment Find a value for a number to the power of a complex number Some context would be helpful here in order to present an answer which would most likely agree with your background. Was this a question which came up in a class? If so, what subject? Oct 16 answered Proving Multivairble Limit Exists Oct 13 comment Black-Scholes equation Agreed, I got the same result. Oct 9 awarded Yearling Sep 30 awarded Explainer Jul 18 revised How to calculate the number of lattice points in the interior and on the boundary of these figures with vertices as lattice points? edited body Jul 4 comment How to calculate the number of lattice points in the interior and on the boundary of these figures with vertices as lattice points? @SaaqibMahmuud Which part do you have questions about? Do you understand how to find out how many lattice points are on a line between two specified ones? Jul 2 awarded Curious Jun 29 comment Proving Two sets have same cardinality You haven't said what $f$ is, there's no reason to assume it is injective at all. Certainly not all functions from $B$ to $P(A)$ are injective, so without explicitly constructing the function you cannot complete this proof. Jun 29 comment is $(x-6)^2$ in $C_0^2$? I meant to include: Your book may prove only the compact case (perhaps this is a simplifying assumption in the proof) or perhaps your book later mentions that compactness is not needed. The wikipedia entry for the Feynman-Kac formula also does not seem to include the compactness condition for the initial condition, at least explicitly, but often for applied PDEs compactness is assumed implicitly. An inspection of the proof should indicate if it's really needed. Jun 29 comment is $(x-6)^2$ in $C_0^2$? I believe Feynman-Kac does not require the function to be compact. Often one proves something for compact functions and then generalizes it by an approximation argument. See, for instance, these lecture notes, which include no requirement that $f$ be of compact support. Jun 29 comment How to prove the inequality? Your idea is a good one. If you have tried differentiating $f(x)$, edit your post to include what you got so we can see where you are having trouble. Jun 29 revised is $(x-6)^2$ in $C_0^2$? added 392 characters in body