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Apr
17
comment Two variable function with four different stationary points
effective diet pill, Thank you for your example. I hope that I can find simpler example. I think that we can ask, what happen the stationary point if $D=0$ just like $(0,0)$ is the saddle point of $f(x,y)=x^3-y^3$?
Apr
12
comment Determine the number of zeros in the first quadrant
Just using the quadratic formula and $z=\frac{1}{2}-\sqrt{3}i$ is on the second quadrant
Apr
12
comment Two variable function with four different stationary points
Thanks @Ian Coley
Apr
12
comment Two variable function with four different stationary points
Sorry, it is my typo
Mar
18
comment A function $f:\mathbb{R} \to \mathbb{R}$ with infinite norm but finite weak seminorm
@127.0.9.6. Well, after checking again, we have to restrict $q\geq 1$.
Mar
18
comment A function $f:\mathbb{R} \to \mathbb{R}$ with infinite norm but finite weak seminorm
I really thank you for your help. Could you give the references related to this subject? If it is possible, how do I contact you? This problem related to my thesis. I have added the Dirac delta function that I mentioned as my example. May I modify your example and add it if you give your permission? If I do so, how do I give your credit as personal communication?
May
17
comment Solving $x^{\log(x)}=\frac{x^3}{100}$
why prince Charles?
May
17
comment Limit of $\lim_{x \to 0}\left (x\cdot \sin\left(\dfrac{1}{x}\right)\right)$ is $0$ or $1$?
Your mistake: $\lim_{x\rightarrow 0} \frac{sin(1/x)}{1/x}\neq 1$ but $0$
May
17
comment Two random variable with the same variance and mean
is the identity $E(XY|X)=XE(Y|X)$ easy to prove?
May
15
comment length of sum of two submodule
@rschwieb: But I only prove the cases $K \cap N =\{0\}$
May
15
comment length of sum of two submodule
thanks BenjaLim, i will try work on it. But could we prove this without exact sequence concept, instead of directly from definition of composition series?
May
15
comment length of sum of two submodule
How to show that l((K+N)/N)=l(K+N)-l(N)?
May
12
comment Length of composition series and injective homomorphisms
OK, i get it. The composition series of $N$ is the refinement of the series $f(M_0)\subset ... \subset f(M_n)$, so $l(N) \geq n$.
May
12
comment Length of composition series and injective homomorphisms
@user1. I have explain it in my solution. Read carefully before judging!
May
12
comment Length of composition series and injective homomorphisms
With your argument could we conclude that $l(N)=l(M)$? Since every module have the same length of composition series
May
12
comment Length of composition series and injective homomorphisms
@user1: No, Since M isomorphic to Im f and Im f is submodule of N we have $l(M)=l(im f)\leq l(N)$
Apr
15
comment Integral of bivariate normal distribution function with respect to itself
Could you prove this using elementary calculus like substitution rule and etc
Apr
3
comment Independence of $n$ random variables
sory, typo bigcup and bigcap
Mar
24
comment Finitely generaterd torsion-free module over PID
So how to find an $m'\in M$ such that $\{m'\}$ is a basis for $M$?
Mar
23
comment Quotient Modules of finite rank module
Define $f: M \rightarrow M/T$ by $f(m)=2m+T$ if $m\in S$ and $f(m)=m+T$ if $m \in M \backslash S$, then we have $f$ is a homomorphism with $ker(f)=S$, so $M/S$ and $M/T$ are isomorphic.