martini
Reputation
53,058
99/100 score
 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.