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I don't fully understand the proof in this link on Springer of Lemma 2.2. Why is it that the $i$th and $j$ components of ...
Asked on 01/12/2021
1 answerLet $f: mathbb{R} rightarrow mathbb{R}$ be a smooth function. Consider the partial differential equation:$$frac{partial u}{partial t}+frac{partial f(u(x))}{partial x}+frac{partial^{3} u}{partial x^{3}}=0$$I wish to find the...
Asked on 01/12/2021 by ZeinabQom
1 answerWhat is the smallest sigma value (out of $1sigma$, $2sigma$, $3sigma$, $4sigma$, $5sigma$, $6sigma$) we can use when we want a less than 0.3%...
Asked on 01/12/2021
1 answerI'm having trouble with this problem.$2^n+10n^2 le 12 cdot 2^n, n ge 1$ Here is my process. n = 1, it is true <-- basis step Assume that...
Asked on 01/12/2021 by Guk
4 answerFor the ODE $y’=sqrt y$ and the initial condition $y(0)=0$ the solution is $y=frac{1}{4}x^2$. This doesn’t match the direction field for the ODE. I wondered why this...
Asked on 01/11/2021
3 answerI'm looking for the radius of the sphere of this: $4x^2 + 4y^2 +4z^2 -16x - 24y + 8z= 44$. I have to get it into standard form in...
Asked on 01/11/2021
2 answerTake 2 sets of real numbers:$x_1, x_2, dots, x_n$ and $y_1, y_2, dots, y_m$ such that $prodlimits_{1 le i le n} x_i > prodlimits_{1 le j le...
Asked on 01/11/2021
2 answerLet $$C = { (x,y,z) in mathbb{R}^3 : x^2 + y^2 leq r^2 z^2 text{ and } z > 0 }$$ be a certain convex cone in $mathbb{R}^3$,...
Asked on 01/11/2021 by Eduardo Longa
1 answerLet $n$ be a positive integer.Let $f(n) = lfloorfrac{8n+13}{25}rfloor$ and $g(n) = lfloorfrac{n-17}{25}rfloor$. Now consider $$h(n) = f(n) - lfloorfrac{n - 12 - g(n)}{3}rfloor$$Then...
Asked on 01/11/2021 by Infinity_hunter
1 answerI want to prove that $(mathcal{M}_{mtimes n}(mathbf{R}), ||.||_F)$ is a Banach Space where$A in mathcal{M}_{mtimes n}(mathbf{R})$, the Frobenius norm: $$||A||_F = sqrt{sum_{i = 1}^{m}...
Asked on 01/11/2021 by Dong Le
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