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1d
comment How to prove that for all $k\in\mathbb N$, $h(kx)=kh(x)$ and $h(x+y)\le h(x)+h(y)$?
No, it's not. Just wanted to show that the scaling property follows even if $g$ does not have the triangle inequality
1d
comment True/false questions about minimal and characteristic polynomials of a matrix
$f_A$ is the characteristic polynomial? Then your 1. is wrong, cause the polynomial you give has degree 5, but $A$ is a $3$-matrix
1d
comment Sobolev space interpolation
How did you define the norm of $H^s(\mathbf R^d)$ then?
1d
comment Convergence in distribution - X/Y
No. Almost the same argument works for $\Omega = [1,2]$ with the uniform distribution, $X$ the identity, $Y(\omega) = 3-\omega$ and $X_n = Y_n = X$
2d
comment Minimum of the Schatten 1-norm
What type of lower bound do you expect? For $A = B$ (which is possible by your assumptions), you have $\|A-B\|_1 = 0$.
Feb
1
comment Continuous but not compact operator on $L^2(0,\infty)$
Fubini, as I said. For $g(x,y) = \frac 2{x^{3/2}}y^{1/2}|f(y)|^2$, we have $$ \int_0^\infty \int_0^x g(x,y)\, dy \,dx = \int_0^\infty \int_y^\infty g(x,y)\, dx\, dy $$
Feb
1
comment Continuous but not compact operator on $L^2(0,\infty)$
In the line above that I did two steps at once, sry. On one side, we have $$ \int_0^x y^{-1/2}\, dy = 2x^{1/2}$$ giving $$ \int_0^\infty \frac1{x^2} \cdot 2x^{1/2} \int_0^x y^{1/2}|f(y)|^2\, dy\, dx $$ Now we use Fubini.
Feb
1
comment Continuous but not compact operator on $L^2(0,\infty)$
$$\int_y^\infty \frac 2{x^{3/2}}\, dx = \left[-\frac 4{x^{1/2}}\right]_y^\infty = \frac 4{y^{1/2}}$$
Feb
1
comment Homography with line correspondences
Could you provide some context? What is $H$, $\ell_i$, $(\cdot)'$, $x$?
Jan
29
comment What is the primitive function of $xe^{x^2+2x}$?
@AmineMarzouki No. The derivative of $\frac 1{2x+2} \exp(x^2 + 2x)$ is $-\frac 2{(2x+2)^2}\exp(x^2 + 2x) + \exp(x^2 + 2x)$.
Jan
27
comment Show that every algebraic subset of $\Bbb A^2(\Bbb R)$ is equal to $V(F)$ for some $F∈\mathbb R[X,Y]$.
@user152715 Added something.
Dec
22
comment Localization $U^{-1} N$ where $U = R^{\times}$ is the set of nonzero elements of an integral domain.
As $R$ is an integral domain, $R$ does not have zero divisors, hence $ab = 0$ with $a \ne 0$ implies $b = 0$. Now use this for $u'(un'' - u''n) = 0$. And: I did not invert your notation, I corrected your correction: You corrected $(u',n) \sim (u,n)$ to $(u',n) \sim (u,n')$, but the correct thing is $(u',n') \sim (u,n)$. (Think of $(u,n)$ as $\frac un$).
Dec
22
comment Localization $U^{-1} N$ where $U = R^{\times}$ is the set of nonzero elements of an integral domain.
Commutativity ... $R$ is an integral domain ...
Dec
17
comment Prove/Disprove: if REFF of $A,B \in M_{nxn}(\mathbb R)$ is $A_R , B_R$, then REFF of $A+B$ is $(A_R + B_R)$
REFF?${}{}{}{}$
Dec
15
comment Numerical method for SDEs
The wikipedia article you linked gives "Kloeden, P.E., & Platen, E.: Numerical Solution of Stochastic Differential Equations, Springer, 1992.", but also says that the general RK-method cannot be adapted as it is possible with the Euler method
Dec
10
comment Formulating that the universe is finite without establishing an upper limit
Can't you just negate your first formula?
Dec
4
comment Can we always multiply some function that is not differentiable everywhere with function that is to obtain differentiable product?
You are right. So in general, we will have that $g = 0$ on the closure (in $(a,b)$) of the points of non-differentiability of $f$.
Dec
4
comment Is the sum of transcendental and algebraic number transcendental number?
Yes, as the set $\mathbf A := \{x \in \mathbf C: \text{$x$ is algebraic}\}$ is a subfield of $\mathbf C$.
Dec
4
comment Are $A^c$ and $B^c$ homeomorphic?
Then it is a duplicate: math.stackexchange.com/questions/1354119/…
Dec
4
comment Are $A^c$ and $B^c$ homeomorphic?
Added something. If only one of $A$, $B$ is simply connected, $A^c$ and $B^c$ are not homeomorphic.