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Jun
26
comment Proving that $\frac{1}{a^2}+\frac{1}{b^2} \geq \frac{8}{(a+b)^2}$ for $a,b>0$
You are trying to prove a sharpening of the inequality in your first formula, not a consequence. How did you prove that result? Maybe a modification works here.
Jun
26
revised Proving that $\frac{1}{a^2}+\frac{1}{b^2} \geq \frac{8}{(a+b)^2}$ for $a,b>0$
edited title
Jun
26
comment prove that $p(n) := n^2 + n + c$ is not prime
What does the assignment say: ¨ Show that that given $c$, $n^2 + n + c$ is never prime"? That is false. Or: "Show that for any given $c$ there is $n$ such that $n^2 + n + c$ is not prime"? That is a true statement.
Jun
26
comment prove that $p(n) := n^2 + n + c$ is not prime
I assume that $c$ is an integer. For $c = 41$, your get a composite number if you set $n = 40$. Can you generalize that trick?
Jun
25
comment Approximate a positive Sobolev function by positive smooth functions
Just add $\frac{1}{k}$ to the functions that were constructed above.
Jun
25
comment Unicity of solution for a parabolic problem?
It's in french.
Jun
25
comment Unicity of solution for a parabolic problem?
Please look at the paper I referenced, or find a textbook that references it.
Jun
25
comment Unicity of solution for a parabolic problem?
You'll need some assumptions for $f$, otherwise it's false. There are counterexamples due to Tychonoff, mathnet.ru/links/1fc4d116bc6753c2908d185847491b01/sm6410.pdf .
Jun
23
comment Mathematical philosophical questions about the general theory of stochastic processes.
This is much better ;)
Jun
21
comment Finding arctan with Euler
Write a function that takes $x$ and $y$ as input and uses only $x$.
Jun
18
answered Show that one cannot make a 8×8 square using 15 T-tetrominoes and 1 square tetromino
Jun
18
answered How do you prove $\sum \frac {n}{2^n} = 2$?
Jun
15
comment The following ODE global existence theorem reference?
@ChrisAl - the solution does not exist globally, only on $[0,1)$.
Jun
15
comment The following ODE global existence theorem reference?
This statement is incorrect. A counterexample is $f(t,x) = x^2, h_C(t) = C^2$. For $y_0 = 1$ the solution is $y(t) = \frac{1}{1-t}$.
Jun
14
comment If the iteration $x^{k+1}=x^k-t_kH_k^{-1}\nabla f(x^k)$ converges superlinearly to a stationary point $x^*\ne x^k$, then $t_k\to 1$
See my edited response.
Jun
14
revised If the iteration $x^{k+1}=x^k-t_kH_k^{-1}\nabla f(x^k)$ converges superlinearly to a stationary point $x^*\ne x^k$, then $t_k\to 1$
Clarified.
Jun
14
answered If the iteration $x^{k+1}=x^k-t_kH_k^{-1}\nabla f(x^k)$ converges superlinearly to a stationary point $x^*\ne x^k$, then $t_k\to 1$
Jun
14
comment $x^3-9x-5=0$, then what is $x^4-18x^3-81x^2-12$
Alternatively, the three numerical zeros of the polynomial $x^3-9x-5$ may be substituted into $x^4-18x^3-81x^2-12$. All three results are negative, so none of the answers is correct.
Jun
8
answered Let the system $Ax=b$ be incompatible. Prove that $C^kx=0, C=[A,b]$ is determined for all $k\in \Bbb{N}$.
Jun
6
reviewed Close Matrix with zeros on diagonal and ones in other places is invertible