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Systems (or computational) biologist.


Nov
10
comment Show that the value of a definite integral is unity
I posted an answer below.
Nov
10
comment Show that the value of a definite integral is unity
In general: $\int_2^4 \frac{f(x)}{f(x)+f(6-x)}\,dx=1$.
Nov
9
comment Equivalent conditions to $0\leq x+\frac{1}{2}x(1-x)a\leq 1$?
@JavaMan Not necessarily "opening downwards" -- if $a<0$.
Nov
9
comment How can I solve this system?
Plugging the 1st and 2nd equations into the 3rd, we get a quadratic equation for y.
Nov
9
comment How could we find the largest number in the sequence $ \sqrt{50},2\sqrt{49},3\sqrt{48},\cdots 49\sqrt{2},50$?
Note that if the original question is for example $n\sqrt{50-n}$ instead of $n\sqrt{51-n}$, no integer $n$ satisfies the equality of the AM-GM inequality; in that case, a more careful evaluation, such as that used in Jyrki Lahtonen's answer, is needed.
Nov
8
comment Calculating the probability that a cord makes a knot
Thanks so much, that's what I'm looking for. If you post your comment as an answer I'll accept it.
Nov
7
comment Is there a good online dictionary/encyclopedia for mathematics?
If you read Japanese, the most recent (Japanese 4th) edition of the Encyclopedic Dictionary of Mathematics has an accompanying CD-ROM that contains PDF files of the 4th and 3rd (equivalent to English 2nd) edition, which I find extremely convenient. (But of course they are not for free.)
Nov
7
comment Proving a large factorial expression for $1 \le m \le n - 1$
math.stackexchange.com/questions/70190/…
Nov
7
comment Higher order derivative of parameter curves
$\frac{d^2y}{dx^2}=\frac{d}{dx}\left(\frac{dy}{dx}\right)$, and $\frac{d}{dx}(\cdots)=\frac{dt}{dx}\frac{d}{dt}(\cdots)$
Nov
5
comment How to add cosines with different phases using phasors
$\sqrt{14+8\sqrt{2}}$, not $\sqrt{14+\sqrt2}$
Nov
4
comment From given equality find that $p$ for which equality have at least one positive root
(2) has a typo: $\frac{1}{2p}\sqrt{\cdots}$, not $\frac12\sqrt{\cdots}$
Oct
15
comment Population Dynamics model
"Mathematical demography" may be a useful keyword.
Oct
14
comment Filling out an $n \times n$ square grid with $0$s and $1$s
Have you tried solving the case when $n$ is small, e.g. $n=1,2,3,4,5,\ldots$?
Oct
7
comment For which n are there primitive Pythagorean triples with legs of lengths a and a+n?
The title says "primitive", so $GCD(a,n,c)=1$ is assumed?
Oct
6
comment How to visualize the Gaussian curvature of a 3D surface?
graphics.ucsd.edu/~iman/Curvature
Oct
1
comment fractional linear transformations
@Zarrax I see. +1 for your nice argument.
Sep
30
comment fractional linear transformations
Nice argument, but I think it is not immediately clear whether the transformation takes the unit circle to "the whole of" the unit circle.
Sep
30
comment fractional linear transformations
$w=f(z)=(3z+i)/(-iz+3)$ is obviously not equal to $z$. The above is a common procedure for finding the image of a function. Do you understand that $|z|<1$ is equivalent to $|3w-i|<|iw+3|$? Which means, if $|z|<1$, its image $w=f(z)$ must satisfy $|3w-i|<|iw+3|$; and if $w$ satisfies $|3w-i|<|iw+3|$, it must be the image of some $z$ satisfying $|z|<1$. This shows that $\{w\in \mathbb{C}\mid|3w-i|<|iw+3|\}$ is the desired image.
Sep
27
comment Multivariate Taylor Series Derivation (2D)
This is not a rigorous proof: Suppose that one can write $f(x,y)=f(a,b)+A(x-a)+B(y-b)+C(x-a)^2+D(x-a)(y-b)+E(y-b)^2+\cdots$, how can the values $A, B, C, D, E, \dots$ be determined?
Sep
27
comment How to approach mathematical modeling of the human heart problem?
@ChesnokovYuriy Have you already checked "Mathematical Physiology" by Keener & Sneyd? It includes chapters on the human heart (Chapter 12) and can be a good starting point.