Wikipedia sez: Nouns ending in -ius and -ium have a genitive singular in -ī in earlier Latin, which was regularized to -iī in the later language. ... There is no contraction of -iī(s) in plural forms.
@JM Does this integral strike you as familiar? math.stackexchange.com/q/84998/13425 =) I am remembering something like this, but I might be thinking about something else..
@Srivatsan I dimly recall an integral like that. No, not the arithmetic-geometric mean, since that one is a reciprocal square root and not a logarithm...
Hello! Help me please, where can i read about duality between points in R^n and hypersurface's bundles, passing through a common point? Which branch of mathematics works with it?
Won't the TeX in this site render proper quotation marks? See e.g., math.stackexchange.com/q/84642/13425. I tried `` '', but that doesn't work as expected (looks quite ugly).
Well, the map Z -> Z/G is assumed to be a Galois covering, so you'd want Z to be connected and semi-locally simply connected or whatever your favorite name for that property is...
Sorry to ask this again in here but since today have more people, i want to share this question with you, and this eluding me the most recently: is there any way to find the number of real root including the multiplicity of the roots without knowing the actual root and by hand? for example, a cubic polynomial can have value of roots 2,2,3 and the number of the roots is 3
Phd or master? i just want to challenge myself with math but since mathmatician could not really directly get the job, so i like science more than math
@Victor, it's an important step to explain various physical phenomena that didn't have a good model before - there is a gap between the QM model the atom and the statistical outcomes lots of them working together produce in chemistry though.. because such difficult systems of equations would have to be solved
@Victor Nope, you can get those, too... Let me explain:
consider x^3-3x+2
gcd(x^3-3x+2,3x^2-3)=x-1
(x^3-3x+2)/(x-1)=x^2+x-2
Since x^2+x-2 is guaranteed not to have repeated roots, we can apply Sturm which tells us that x^2+x-2 has two real roots (or one positive and one negative, Sturm tells you in any range you want).
Now, we turn to x-1, which contains all the repeated roots of x^3-3x+2
doing the same yields 1 (positive) real root.
Thus, x^3-3x+2 has one repeated real positive root of order 2 and one negative real root of order 1.
@tb I cheated there a little bit, the integral gets a factor of 1/2 and the range goes from 0 to 4pi, but the integral is the same from 0 to 2pi and 2pi to 4pi so I took the 1/2 to remove 2pi to 4pi
Anyway, I'm looking at this geeky mathy watch, and it's like one of those clocks that has math formulas instead of numbers. I've actually seen these particular formulas before. However, I don't know the syntax behind two of them.
well... there's a fix but quite inconvenient. (put it into the codecogs window, copy the img url, then put the url into the upload>file window here in chat and it will upload the image to imgur and get posted here)
I remember when my first time was a slight sip of vodka. I spit it out everywhere and accused the host of trying to prank me by putting bug spray in a glass. (it was actually vodka though..)
