fractional Definition and 221 Threads

I have heard of such idea: A sphere of fractional dimension 0<s<1 is understood as a probability sphere with probability s to have an electron at a certain position for example the volume of the sphere S^{n-1} in \Re^n has volume Vol(S^{n-1})= (2\Pi^{n/2})/(\Gamma(n/2) and we can...

The following was gathered in an experiment. r(m)----- N1------N2-----N3----N4-------N5---N_avg---delta N 0.001---131------139---175---140-----158----148.6----15.882 0.002----90-------96---102-----87------85----92------6.228 0.003----52-------53----73-----65------55----59.6----8.139...

Hi all, I've been trying to get back into mathematics by teaching myself calculus. I've been starting with the book "Calculus Made Easy" and have been doing fine except for one little thing I encountered on page 57. He shows a mathematical proof of why the derivative of y = x^\frac {1} {2}...

Hello, I have posted a while ago wondering how to make a coil that was tuned to Earth resonance (~7.8 Hz). I realize that the wavelength at that frequency range is ridiculously low and would require an antenna the size of Texas to couple too normally. But I heard something about fractional...

hey there, i'm curious as to why they call it fractional Brownian motion. please don't say its Brownian motion that is fractional :-p many thanks

sooo ... i am kind of clueless about how to determine a linear fractional transformation for a circle that maps on to a line or vice versa ... like i do *kinda* get how to map a circle on to a circle ... or a line on to a line ...

The book and lecture notes do not give a good example of how to solve this type of problem. After writing out f' I don't know how to simplify. Any hints? \begin{array}{l} f(x) = x - 5(x - 1)^{2/5} \\ \\ f'(x) = \frac{{f(x + h) - f(x)}}{h} = \frac{{(x + h) - 5((x + h) - 1)^{2/5} -...

We have been working with Gibbs factors and the grand partition function in my thermodyamics class. There is an example in the text that deals with a system that is either occupied or not occupied (energy = 0 or energy = E). The "fractional occupation" is then defined as the Gibbs factor for...

Perform the idicated operations. Write fractional answers as mixed numbers or as proper fractions reduced to lowest terms. One: -3-(-4)-|4-7| Two: 0.096492 ( Divid) 1.72 Simplify: 3(1-5)-[(1-7)(-5)] -(-{-[-(-64)]}) -|-3+4|+5-7 Evaluate: c-bc if b=-1 and c= -2

So it is well-known that for n=2,3,... the following equation holds \zeta(n)=\int_{x_{n}=0}^{1}\int_{x_{n-1}=0}^{1}\cdot\cdot\cdot\int_{x_{1}=0}^{1}\left(\frac{1}{1-\prod_{k=1}^{n}x_{k}}\right)dx_{1}\cdot\cdot\cdot dx_{n-1}dx_{n} My question is how can this relation be extended to...

Hello all! I was wondering if anyone knew of any good internet leads(besides mathworld, which does not have that much) on the topic of Fractional Differential Equations. I am wanting to investigate Tsallis's Non-Extensive entropy and from what I have come to understand he came to his...

Hi, I've got this particular polynomial a^{3/2}+x^{3/2} and I need to factorize it as far as possible. I've come to the conclusion that there are no factors. Am I wrong?

After esterification, can the ester be separated from other liquids using fractional distillation?

Because I can't write squared, if x is squared, I will just write it like this: xsquared x/x +2 MINUS x/xsquared - 4 = x+3/x+2 I get an LCD for each fracton and then I subtract getting this: xsquared - 2x MINUS x/xsquared - 4 = (x+3)(x-2)/xsquared - 4 What do I do now? If you...

from the expression for a Fractional integral of arbitrary order: D^{-r}=\frac{1}{\Gamma(r)}\int_c^xf(t)(x-t)^{r-1} if we set r=-p then we would have for the Fractional derivative: D^{p}=\frac{1}{\Gamma(-p)}\int_c^xf(t)(x-t)^{-(p+1)} is my definition correct?..i mean if its correct...

Last year I made a more modern version of a QM simulation I did a long long time ago, It makes movies of time evolutions of arbitrary wave functions in a QM harmonical oscillator. (You can see the movies via the links below) http://www.chip-architect.com/physics/gaussian.avi...

hello reader i have a problem understanding the following type of equation. (n+x)/nth root of x n being a fixed numerical value and x being the unknown how would i differentiate such a problem an example of this is: (1+x)/4th root x thank you

...having at least one fixed point. let g be a given function with fixed point p. say g is defined on R though it could be C. here's how we can approximate the fractional iterates of g: expand the series for the nth iterate of g, denoted g^n, about p. g^n(p)=p...

Instead of superstrings having 10 unitary dimensions (6 of compactified space and 3+1 of ordinary spacetime), imagine these 6 compactified spatial dimensions being of fractal value (3/6=1/2) relative to the 3 apparent dimensions of space. This corresponds as a dimensional duality to the 6...

Such as sqrt 5: (2.236067977...) Start with the fractional seeds 2/1, 9/4,... New members are generated (both numerators and denominators) by the rule new member = 4 times the current plus the previous. Which generates the progrssion 2/1, 9/4, 38/17, 161/72, 682/305, 2889/1292...

Has any menaing the use of fractional calculus in..physics?.i have used it several time to quantizy non-polynomial hamiltonians in quantum mechanics...(such us H=p**e e not an integer).but does the fractional calculus have a meaning or utility in physics?..to cancel infinities to calculate...