fractional Definition and 206 Threads

Hi I have an orthogonalized rotation matrix -0.500000 -0.866025 0.000000 0.866025 -0.500000 0.000000 0.000000 0.000000 1.000000 for the following unit cell: a b c alpha beta gamma space group 131.760 131.760 120.910...

Please help me understand. It seems to me that the fractional charge of a quark suggests that this is actually the smallest (most fundamental) unit of charge, and that an electron has a combined unit charge.

Homework Statement My textbook states that one of the safety precautions to be taken in the fractional distillation of petroleum(in school laboratory) is using a small flame to heat the rocksil(rocksil is soaked with petroleum),and avoil using stationary flame for heating. Can anyone explain...

Calculate $x$ in $\{x^2\}+\{x\} = 1$ where $\{x\} = $ fractional part of $x$

Hi All, Can anyone walk me through this problem. This is from an old med school entry test. The answer is 81 but I can't work out how the x terms cancel. 3x(3x^ -1/3)^3 Thanks in advance John

Hi, simple question, but difficult to find an answer for me How to integrate sqrt((ax+b)/x) dx ? a,b constants and x variable if it matters, I would be happy if you could solve it just for both a,b >0 Thanks

Hi everyone! This time I have a lesson on word problems, and that is probably my absolute weakest point in math. (In fact, as I write, I'm puzzling over several different problems, but here is the one I'll post for now.) Homework Statement Members of the Computer Club were assessed equal...

Homework Statement find linear fractional transformation that carries circle |z|=1 onto the line Re((1+i)w)=0 Homework Equations linear fractional transformation is of the form az+b/cz+b where ad-bc≠0 The Attempt at a Solution Re((1+i)w)=0 means that the line is just the y axis, but then I...

Hello. I have simple DE y' + p y^(1/2) = q --------------- y'=dy/dt p,q=constant I am confused because I tried bernoulli's method to solve and I think I exploded the universe. Basically, my initial condition of t=0,y=0 made infinity, not right. I'm not sure that method works when there...

Find necessary and sufficient conditions on the real numbers $a$, $b$, $c$, and $d$ such that the fractional linear transformation $$ f(z) = \frac{az + b}{cz + d} $$ maps the upper half plane to itself. I just need some guidance on starting this one since I am not sure on how to begin.

The following comes from the complex analysis text by Joseph Bak: He is trying to determine all conformal mappings f of upper half plane H onto the unit disk. "Let us first assume that f is an LFT and f(a)=0 for Im(a)>0. Then, since the real axis is mapped into the unit circle, it...

Hi everyone, I'm currently looking to solve an equation of the general form: \sqrt{x^2-y^2}+\sqrt{\epsilon x^2-y^2} = \beta. I'm interested in solving this equation for x assuming y>0, \epsilon>1 and \beta \in \mathbb{C}. By squaring the equation twice I can find four potential solutions of...

In the text by Joseph Bak, He is trying to determine all automorphisms of the unit disk such that f(a)=0. He says "let us suppose that this automorphism is a linear fractional transformation. Then it must map the unit circle onto the unit circle. I am asking for help in understanding this...

solved.

HOw to calculate 3*x - x^2

Hi guys, I'm having a bit of trouble splitting the RHS of the following expression into real and imaginary parts: (χ'+iχ")/A = \frac{1}{ω-ω_{0}-iγ/2} (It's to find expressions for absorption coefficient and index of refraction, but that's irrelevant). I've defined a = ω-ω_{0} and b =...

Suppose we have some ODE given by y' = G(x,y)/H(x,y). Let x and y depend on a third variable, t, so that x and y are parametrized in a way. Then applying the chain rule to y' gives \frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}} = \frac{G(x,y)}{H(x,y)} Then comparing the numerators and...

Suppose I have the Laurent series with region of convergence given below: f(z)=\sum_{n=-\infty}^{\infty} a_n z^n,\quad \sqrt{3}<|z|<\sqrt{5} Can I conclude the Laurent-Puiseux series: f(\sqrt{z})=\sum_{n=-\infty}^{\infty} a_n \left(\sqrt{z}\right)^n has a region of convergence...

Can someone explain the logic behind this? For instance if 2 to the 3rd power = 2 x 2 x 2 =8 So 2 to the 3rd power is telling me I have 2 multiplied by itself 3 times. Now how would I solve for 2 to the 1/3rd power? It is telling me I have 2 multiplied by itself 1/3 times but how do you...

hi guys i was wondering how the coordination numbers for the atomic positions of atoms in crystals such as NaCl are derived ...more specifically why is Na at (0,0,0) and Cl at (1/2,1/2,1/2) and not (0,0,0) and (1/4,1/4,1/4) of course this is in fractional coordinates

Fractional Calculus...? What?? I came across this Wiki article a couple of days ago: http://en.wikipedia.org/wiki/Fractional_calculus As a student who just finished an undergrad major in math, the idea of a "fractional derivative" or "fractional integral" is mind blowing! Up until I read...

Does anyone know any applications / uses for fractional derivatives and integrals? I supposed the idea and asked a professor, he tried to explain fractional calculus to me, but I was in calculus 2 at the time... so it was way over my head back then. I asked him what it could be used for and...

Circuit Design for a "fractional"-amplifier Hello all, I am right now in the process of designing a simple device that will help me measure the voltage response of a piezoelectric element attached to a specimen after it has been hit with a projectile. The obvious issue is that the amount...

Straight line, "fractional difference" Homework Statement To set a speed record in measured (straight) distance d, a race car must be driven first in one direction (in time t1) and then in the opposite direction (in time t2). (a) To eliminate the effects of the wind and obtain the car's speed...

Hello, I'm pretty rusty when it comes to rearranging more complex equations and can't seem to remember how to deal with fractions as powers, for example; [1/2] x y^[1/2] = sqrt[[z] over [x y^-1/2]] and [2/3] x y^[-1/3] = sqrt[[z] over [x y^2/3]] I'm trying to solve a similar, but more...

Hello guys :), I have a question which I think is very advanced and weird. But I need the answer for some signal analysis purpose. As we know, the derivative of a sine function, per se, shifts the phase, by Pi/2; i.e., f(x) = A sin (w t) df(x)/dt = A sin (w t + Pi/2) = A cos(w t)...

I am a graduate assistant and was asked a question about FLTs (Mobius Transformations). The student was asked to prove that any FLT can be written as an FLT with determinant 1. However, I can't make sense of that. If I look at the possible Jordan Canonical forms of 2-by-2's, it would seem...

Homework Statement I'm working out a differential equation problem that I am supposed to solve with the formula \mathcal{L}\{t^\alpha\} = \frac{\Gamma{(\alpha + 1)}}{s^{\alpha+1}}. The problem is \mathcal{L}\{t^{\frac{1}{2}}\} (finding the Laplace transform of the given function)...

How would I go about finding the fraction field of Z[1/2]?

1. A light, hollow cone is filled with sand set spinning about a vertical axis through its apex on a frictionless bearing. Sand is allowed to drain slowly through a hole in the apex. Calculate the fractional change in angular velocity when the sand level has fallen to half its original value...

I recently read a paper on fractional derivatives. That is how to take derivatives of fractional order rather than the usual integral order. The paper made perfect sense to me, however I wondered: 1) Are there geometric interpretations of fractional derivatives? Kind of like how first...

Hi everybody! I recently came across the hyperoperation sequence which extends the sequence of operations x+y, x*y, x^y to operations x[n]y, which are recursively defined as "the previous operation applied y times on x". So I asked myself: Can this be generalized to positive rational (or even...

The question is x2/3 - x1/3 - 2 = 0 So the first thing I did was: x2/3 - x1/3 = 2 Then, I put both sides to the power of three, so I got: x2 - x1 = 8 From there I factorized: x (x - 1) =8 And got the answers: x = 8 or x = 9, the book however, says the correct answers are -1 and 8. Any...

Homework Statement Find the area below the graph of f. f(x) = (2x + 5)/[(x + 2)2(x + 3)2] xE [0, 1] Homework Equations I know the area under the graph is the definite integral with upper limit = 1; lower limit = 0. The Attempt at a Solution I have such a hard time evaluating...

Homework Statement Solve the Inequality: (3x-7)/(x+2)<1 Homework Equations The Attempt at a Solution Cross Multiply: x+2>3x-7 Simplify: 9>2x Simplify More: 9/2>x My Answer: (-∞, 9/2) I put this as my answer but the answer is really (-2, 9/2) Can someone explain to me why this is? I know you...

Good day! I have problem: Find all integers for which is fraction (n3+2010)/(n2+2010) equals to integer. I can find 0 and 1 and I tried prove that any integers don't exist, but I didnt contrive it. Could someone help me with it?

Hello all. As I understand it, there's somewhat of a divide in the scientific community (basically between chemists and physicist) around the topic of solutions to the SE (or KS eqn) that give fractional occupations of molecular or KS orbitals. I myself see no physical reason why probability...

Homework Statement I know this is the wrong place. I tired to post in Science materials but it wouldn't let me. Trying to do this in latex t_n = ar^(n-1) t_n=ar^{n-1} Getting weird results. I'm using Chrome on Vista. Its driving me nuts. I'm trying to post questions. Can someone sort me out?

the title says everything. I encountered this term and I wanted to know what fractional calculus is and what it does.

Homework Statement 4 1/(x+1) · 8 1/(x+2) = 9log3 2 Homework Equations n/a - same as 1 The Attempt at a Solution To get rid of the exponents and be able to solve for x, I first took the logarithm with base 4 of all terms: log44 1/(x+1) · log48 1/(x+2) = log49 log3 2 This equals: 1/(x+1)...

I've been toying around with stuff I probably shouldn't be. :biggrin: I've been sketching a graph of y=x^n where n is a rational number (as opposed to an integer). Of course, when I get into the fractional exponents, the negative portion of the curve ends up being imaginary (eg. x=-2,n=2.5...

I have a function f(x) such that f(x) = x^{\frac{a}{b}} where {\frac{a}{b}} is noninteger. Is there an equation to solve this? A series expansion or something? I've looked around and couldn't find anything.

what is d^0.5/(dx)^0.5 {exp(-x)* (x^-1) tks for any help.

It bugs me: is it theoretically possible for orbital angular momentum to take fractional values? Which laws of physics should be changed to get that?

According to the third paragraph over here, http://www.particleadventure.org/quarks.html "Quarks have the unusual characteristic of having a fractional electric charge, unlike the proton and electron, which have integer charges of +1 and -1 respectively." What does the fractional...

Hi all, I have been trying to write code to convert from cartesian to fractional coordinates. I think everything is correct in my code (i have used wikipedia as reference - http://en.wikipedia.org/wiki/Fractional_coordinates), but still, the code doesn't work for some test values. The code is...

Homework Statement My question is simple is there a formula for the bi/tri-nomial expansion of bi/tri-nomials raised to fractional powers. that is, (x^{2}+1)^{1/2} or (x^{2}+x+1)^{1/2} I know pascals triangle for integer exponents but i can't really find anything about fraction...

Homework Statement http://j.imagehost.org/0069/thermo.jpg Homework Equations The Attempt at a Solution OK, so I tried to derive θ in respect to r as in θ(r): \frac{d\theta}{dr} = \frac{-100}{(r - 1)^2} Then, I multiplied both sides of the equation by 'dr', d\theta = \frac{-100}{(r -...

Can someone explain to me as simply as possible why the Laughlin states create energy gaps in the lowest landau level? I am trying to understand for a presentation why the Laughlin states correctly model the QHE effect when the filling factor is a odd fraction (1/3, 1/5, 1/7). As far as I...

I've been day dreaming about this idea for a month or two. There are many hypothesises that describe the universe in some higher number of dimensions. As far as I know, this is always an integer number of dimensions. I've been wondering if it is possible for the universe to have a...