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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
Jun
29
comment is $(x-6)^2$ in $C_0^2$?
No, in $\mathbb R$ the only compact sets are closed and bounded intervals, i.e. sets of the form $[a,b]$. You should check how the compactness is used in the theorem you are attempting to use, and see if it is really necessary for your purposes. A standard argument when compactness is needed is to multiply the function by a bump function.
Jun
29
revised How Do You Know If Mathematical Definition Matches Up With Reality?
added 20 characters in body
Jun
29
answered is $(x-6)^2$ in $C_0^2$?
Jun
29
answered How to show that a complex-valued function is uniformly continuous?
Jun
29
comment How Do You Know If Mathematical Definition Matches Up With Reality?
@user159813 Community-Wiki.
Jun
29
comment How Do You Know If Mathematical Definition Matches Up With Reality?
This should probably be CW, right?
Jun
29
answered How Do You Know If Mathematical Definition Matches Up With Reality?
Jun
27
comment What is the best way to manipulate algebraic expressions?
What are you solving for, or where are you trying to end up from those starting points?
Jun
27
answered How to calculate the number of lattice points in the interior and on the boundary of these figures with vertices as lattice points?
Jun
26
revised Derive property from continuity - is this proof valid?
added 891 characters in body
Jun
26
comment Derive property from continuity - is this proof valid?
It is possible, I will post a proof now.
Jun
26
answered Derive property from continuity - is this proof valid?