6,423 reputation
1929
bio website
location
age
visits member for 2 years, 6 months
seen Jul 24 at 21:40

Jul
14
answered Proving Cauchy inequality involving four expression
Jul
14
comment Proving Cauchy inequality involving four expression
As stated, the inequality you write is not true. For instance, it is false when you take $a = b = c = 1/3$. Perhaps there's a typo, or an extra hypothesis. Do you mean $(a^2 + b^2 + c^2)$ in place of $(a^4 + b^4 + c^4)$?
Jul
13
answered If $f'(x)\cdot x$ goes to zero then $f(2x)-f(x)$ is bounded.
Jul
6
comment Irrational Rotation
@Priyanka: density is a topological property, and all topological properties are preserved under homeomorphism.
Jul
4
answered Irrational Rotation
Jul
2
awarded  Curious
May
6
comment Topology of the tangent bundle of a smooth manifold
@Student: I'm afraid with that topology you would not get a manifold structure on $TM$. Note that the topology you define is not Hausdorff, because if $p\in U$ and $x,y\in \pi^{-1}(p)$, then every open neighborhood of $x$ contains $y$ and vice versa.
May
4
comment Limit conditions of a subharmonic function imply that it is constant
@DanielS.: There is a form of the three circles theorem for subharmonic functions, which is that the function $m(r)$ is a convex function of $\log r$. For a reference, see for instance Hormander's Notions of Convexity Corollary 3.2.22, or just google "three circles theorem subharmonic". To derive the statement you are used to seeing about holomorphic functions, all you have to do is use that for a holomorphic function $f$, we have $\log|f|$ is subharmonic.
Mar
30
accepted Computing the degree of a finite morphism $\mathbb{P}^n\to \mathbb{P}^n$
Mar
30
answered Ring homomorphism with field as image, is the pre-image also a field?
Mar
8
comment Weak derivative: Showing a function is equal to zero a.e.
@Algebra: you can always extend $\phi$ to a function defined on all of $\mathbb{R}$ simply by setting $\phi\equiv 0$ outside of $(a,b)$. This function remains compactly supported and smooth.
Mar
6
comment Closure of an open ball equal to the closed ball
One very common place you find this property is in non-archimedean fields, if you know what those are. For instance, in the $p$-adic numbers $\mathbb{Q}_p$ for $p$ a prime number.
Mar
1
reviewed Approve suggested edit on Finding cosets in $\mathbb{Z}$.
Mar
1
comment How to handle rounding in uneven number bases?
Consider for example the ternary number $11$. The difference between $11$ and $10$ is $11-10 = 1$, whereas the difference between $11$ and $20$ is $20 - 11 = 2$. Thus it would make sense to round down for a number ending in $1$.
Mar
1
reviewed Approve suggested edit on Different methods of evaluating $\int\sqrt{a^2-x^2}dx$:
Mar
1
revised Weak convergence in a Hilbert Space
added extra remark
Mar
1
answered Weak convergence in a Hilbert Space
Mar
1
reviewed Approve suggested edit on minimizing the value of a simple expression
Mar
1
reviewed Reject suggested edit on Limit of $\frac{f'(x)}{g'(x)}$ & $g'(x) \neq 0$ in Hypotheses of L'Hospital's rule.
Mar
1
revised Approximation by a polynomial in $C^1$ norm
Modified tags