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May
21
comment Chi-Square Computations
stats.stackexchange.com/questions/121662/…
Mar
13
comment Evaluating the integral $\int \frac{1}{x+ \text{ ln }(x)}dx$
wolframalpha.com/input/…
Mar
13
comment The formula of Eclidean distance to a hyperplane.
If you consider $H$ as a hyperplane in $\mathbb{R}^{mn}$ and $X$ and $Y$ are two coordinates (i.e. $X,\,Y\in\mathbb{R}$), then $mn$ real numbers, not just $X$ and $Y$, are necessary to specify a point in $\mathbb{R}^{mn}$.
Mar
12
comment Weaker version of the A.M.-G.M. inequality
Related: mathoverflow.net/questions/122411/…
Mar
12
comment Positive numbers inequality
The above answer can be rescued if you show $\sum iy_i\ge \sum i\cdot\frac1n$ when $0< y_1\le y_2\le \cdots \le y_n$ and $y_1+\cdots+y_n=1$.
Mar
11
comment Positive numbers inequality
Where did you use $y_1\le y_2\le \cdots \le y_n$? and why is $\left(\frac2{n(n+1)}\sum y_i\right)^{\log_2 3}\ge \frac1{n^2}$ (the last inequality)?
Feb
17
comment prove that $f_n = 37111111…111$ is never prime
Try Factor[371], Factor[3711], Factor[37111] etc. (up to $n=10$) with WolframAlpha.
Feb
17
comment common probability
Was your sampling not repeated? The above data only suggest that the data from the lab and that from the field are different. Are there any reasons for believing that they are "same things"?
Feb
14
comment Solving a system of equations with an inequality constraint
What sort of functions are $f_1$, $f_2$ and $f_3$?
Feb
13
comment Model a chemical phenomenom
Yes, periodic boundary conditions are often used in mathematical / physical modeling and are a good starting point.
Feb
12
comment Model a chemical phenomenom
I think the lattice should reflect the actual shape of the receptor, but you could start with a rectangle (if it's 2D) or a cuboid (if it's 3D).
Feb
10
comment Express $\binom{n+2}{k}$ according to $\binom{n}{k}$
Similar question: math.stackexchange.com/questions/649567/…
Feb
5
comment Hard inequality with conditions
Then you can construct a counterexample easily, following the above argument. (such as in the case $b_2/g_2=r_2>1$ and $b_3/g_3=r_3<1$)
Feb
5
comment Find one solution for system of inequalities (if exits)
Thank you, I corrected the note.
Feb
4
comment Find one solution for system of inequalities (if exits)
$A(1)=0.020302010304655=20302010304655/10^{15}$ and not equal to $326/160723$ etc. I don't see why you want to convert a finite decimal to a different rational number (circulating decimal).
Feb
4
comment Find one solution for system of inequalities (if exits)
Really? Even though $0.112843485160579$ was changed to $0.112843485160578$? You might need to refresh the page.
Feb
4
comment Find one solution for system of inequalities (if exits)
Thank you, I changed $A(8)$ to satisfy $A(1)+\cdots+A(8)=1$ and updated the results accordingly.
Feb
4
comment Find one solution for system of inequalities (if exits)
@user64494 I'll check, but I think that can be dealt with without affecting inequality signs.
Nov
18
comment Finding an angle between side and a segment from specified point inside an equilateral triangle
It's simple: note that arc length = angle (in radians) when the radius of the circle is 1 (i.e. unit circle). So when the arc length is $u$, the chord length is $2\sin(u/2)$.
Nov
15
comment Find the line that intercepts the lines $r$ and $s$ and forms congruent angles to the coordinate axes
You're almost done. From the first part of your argument, if you set $\overrightarrow{AB}=(x,\,y,\,z)$, you get $|x|=|y|=|z|$. (The angle is not 45 degrees by the way, but the argument still stands.) Then you have four cases to consider: $x=y=z$, $x=-y=z$, $x=y=-z$, $x=-y=-z$.