fractional Definition and 221 Threads

So my question is, if the bulk modulus change by 5%, what is the fractional volume change value? is it times 0.05 or divided by 0.05? or the fractional volume change still the same?

Suppose you have 8-1/3 and want a precise value for it. How would you go about calculating this on a regular scientific calculator. I punched in: 8, then the exponent button, then 1, then negative, then division, and finally 3. The calculator reads "error."

i can't seem to get a handle on this...help :)

Homework Statement The displacement of a particle can be modeled by the function x(t)=\frac{2x-5}{4x^2+2x}, where t is in seconds, x is in meters, and t ∈ [1,10] a) Determine the derivative of the function without using the quotient rule. b) Hence, find exactly when the particle is...

Homework Statement [/B] Having a little trouble solving this fractional inverse Laplace were the den. is a irreducible repeated factor 2. The attempt at a solution tryed at first with partial fractions but that didnt got me anywhere, i know i could use tables at the 2nd fraction i got as...

I have the following function \begin{align*} f(x) &= 6x^5 - 15x^4 + 10x^3 & x &\in [0, 1] \end{align*} and I found that by recursively applying it, that is f(f(x)) etc, I can get new functions with the same s-like shape but steeper slope. I was curious if there was a way to smoothly go from x...

Halo, I was reading about geometry from Tim Gowers book titled "A very brief introduction to mathematics". I came across fractional dimensions and the 4th dimension. The koch snowflake has dimension 1.2 yet he could comfortably drawn it on a 2d page (or is it complete?). Has not he just...

I'm taking an engineering graphics class and I recently learned this rule which states: "When the digit next beyond the last place to be retained is 5, and there are no digits beyond this 5, or only zeros, increase by 1 the digit in the last place retained if it is odd, leave the digit...

See these equations: \left | \frac{d \vec{f}}{d \vec{r}} \right | = \left | \frac{d(f_1,f_2)}{d(x,y)} \right | = \frac{\partial f_1 \wedge \partial f_2}{\partial x \wedge \partial y} = \left | \begin{bmatrix} \frac{\partial f_1}{\partial x} & \frac{\partial f_1}{\partial y} \\ \frac{\partial...

http://math.sfsu.edu/federico/Clase/Math350.S15/linea.JPG 1. Homework Statement The picture below represents the map from a "green projective line" to a "red projective line." It takes the "green points" 1,3,7,-11 to the "red points" 0,6,10,20, respectively as shown by the ruler. Let f be the...

Okay, maybe not really fractional calculus but I don't know what this stands for. Its in the black circle (more like an ellipse though), what does the mu under the natural logarithm mean?

When we calculate fractional uncertainty , we get a percentage of the uncertainty but what does it mean? For example 5% .

So, apparently, it's possible to generalize integration and derivation into non-integer orders. For instance, it's apparently possible to take the 0.5th derivative of a function. What I'm wondering is what would be represented by such an equation? If a derivative represents how a function...

With only only paper & pencil (no calculator or logarithmic tables), figure out which of the following expressions has a greater value: 101/10 or 31/3. Please make use of the spoiler tag and write out your full explanation, not just the answer.

From Abel–Ruffini theorem, we know that, there is no general algebraic solution to polynomial equations of degree five or higher. So there are general solutions for degrees n={1,2,3,4}. Does degree have to be an integer? What about the fractional degrees? Are there general solutions for example...

I started with taking three cases, 1. a=b since a and b are co primes, both will have to be equal to 1 and then we can easily get lhs = rhs. 2. a>b 3.a<b I have no idea as to how to proceed for the second and third cases. Any help would be greatly appreciated.

Homework Statement The problem is defined as below. A/B = x/y ; A/B and x/y are rational numbers. In some equations, we want to find solutions of variable x and y. A, B : given constants. integers. x, y : variables. integers. Homework Equations The Attempt at a Solution

I am learning about statistical design of experiments, and in the process of mathematically rigorizing the concepts behind fractional factorial designs of resolution III, I derived an interesting equation: $$k = \sum_{i=1}^{3}{\lceil{\log_2{k}}\rceil \choose i},$$ for which the solutions $k$...

How does 2^5/2 become 2^2 multiplied by 2^1/2? (The '^' means 'to the power of' so 2 to the power of 5/2. I am not sure how to write this as an exponent as this is my first post.) 2^5/2 = 2^2 × 2^1/2 So 2^2 = 4 and 2^1/2 means Square Root so there is a radical sign, so it becomes √2. I...

i.e., does the set of functions of the form, \{ x^{\frac{n}{m}}\}_{n=0}^{\infty} for some fixed m produce a linearly independent set? Either way, can you give a brief argument why or why not? Just curious :)

Prove the following \int^1_0 \left \{ \frac{1}{x} \right \} \, dx = 1- \gamma

What is the significance/physical interpretation of Fractional Occupation Numbers in DFT?

Can someone explain how these graphs are drawn. How does the value of p/q affect this graph? How does the domain and range change? How are the asymptotes found? The below is an image about what I'm talking about: Here is a question the deals with this type of graph (no idea how to solve it...

Can someone explain the following: How does changing the value of p/q affect the drawing of the graph (so domain/range/shape etc) What makes this graph an odd function? How to work out asymptotes? Heres a picture so you know what I'm referring to: And below is a question dealing with this...

Homework Statement When a photon is emitted from an atom the atom recoils. The kinetic energy of recoil and the energy of photon come from the difference in energies between the states involved in the transition. Suppose a hydrogen atom changes its state from n=3 to n=2. Calculate the...

Homework Statement I'm given two circles in the complex plane. |z|=1 and |z-1|=\frac{5}{2}. The goal is to find a "Linear Fractional Transformation" or Mobius Transformation that makes these two circles concentric about the origin. Homework Equations w=f(z)=\frac{az+b}{cz+d} The...

Homework Statement x/y - y/x ---------- 1/x^2 - 1/y^2 Simplify the compound fractional exponent. Homework Equations The process that you are supposed to use are 1. finding the LCD and combining the expressions in the numerator and then the denominator, making it just a regular...

According to Fractional Calculus, the power rule can be written as (dm/dzm) zn = n!/(n-m)! zn-m For example, (d1/2/dz1/2) z1/2 = (1/2)!/(1/2-1/2)! z0 = (1/2)√π To find the residue of f(z) = f(z)/(z-z0)m at z→z0, the formula is Res(z→z0) f(z) = 1/(m-1)! dm-1/dzm-1 f(z). For...

Couldn't we just say the voltage could be variable, hold that as a constant, and design circuits which could run off completely safe 12v systems? Why not use fractional resistors to get the amperage to an arbitrary value? In other words could you just make a resistor valued at, say, 0.10...

I need to find the derivative of R(t)=5t-3/5 are there any derivative rules I can use for this problem?

Hi all! :D I wasn't really sure where to post this, but Analysis seemed a fair bet. While searching on-line recently, I came across the following expressions for the Fractional Part \{x\} and Floor Function \lfloor x \rfloor respectively: \{x\}=\frac{i\log\left(-e^{-2\pi i...

Hello, I have a problem that has me stumped, please help. Question: Find the equations of the asymptotes of the following fractional functions., and then, draw the graph and label x- and y-axis points of intersection. The equation: y= x/(x + 1) My try at it: I first divided x by (x + 1) to get...

Homework Statement Anand, Bhadkamkar, and Moghe (1995) used a fractional factorial design to determine which of the six possible factors influenced the determination of manganese in cast iron. The six factors and their levels follow: A-Titration speed ; Medium...

\int^1_0 \frac{\log (1+x)}{1+x^2} dx $\log $ is the natural logarithm .

I came up with the following integral I(t,a) = \int^t_0 \frac{\log( x^2+a^2)}{1+x}\, dx http://www.mathhelpboards.com/f28/fractional-logarithm-integral-5457-new/we have an attempt to solve the integral succeeded by chisigma for the particular case I(1,1) , I don't now whether there is a...

Prove the following \int_{0}^{1}\frac{\log(1+x^{2})}{1+x}dx=\frac{3}{4}\log^{2}(2)-\frac{{\pi}^{2}}{48} Good luck with this one ... :)

Hi all, I would like to find the distribution (CDF or PDF) of a random variable Y, which is written as Y=X_1*X_2*...X_N/(X_1+X_2+...X_N)^N. X_1, X_2,...X_N are N i.i.d. random variables and we know they have the same PDF f_X(x). I know this can be solved by change of variables technique and...

Okay so I'm in Calculus 1 and we are working on derivatives. I understand it all but I have been having some trouble with some basic math skills that I cannot remember from high school and I can't seem to find a good tutorial anywhere online. I am having problems with multiplying fractional...

Weinberg's dark matter idea re "fractional cosmic neutrinos" http://arxiv.org/pdf/1305.1971v1.pdf http://arxiv.org/abs/1305.1971 Goldstone Bosons as Fractional Cosmic Neutrinos Steven Weinberg (Submitted on 8 May 2013) It is suggested that Goldstone bosons may be masquerading as fractional...

http://www1.gantep.edu.tr/~physics/media/kunena/attachments/382/chapter2.pdf On page 9 and 10 of the above PDF the method for deriving the fractional energy loss per cycle in a lightly damped oscillator is described. I understand and follow this derivation. What would the derivation...

Homework Statement This is a research problem that I imagine is very similar to a homework problem. I am a PhD student in biology, and I lack the mathematical background needed to make sense of the topic. I would like to find the solution to the fractional differential equation that...

Is it possible that for a random variable X there exist no p in (0,1) so that EX^p < ∞ ? Is there any example?

I was wondering if anyone knows any textbooks that are a good beginners guide for the dynamics (mechanics) using the fractional calculus. I have The Fractional Calculus by Oldham and Spanier but was hoping to find something more rudimentary. Thanks.

Hi everyone! How to solve this: S(n) = { (a+b)/n } + { (2a+b)/n } + { (3a+b)/n } + ... + { (na+b)/n } where {x} represents fractional part of x. a,b,n are natural non-null numbers and (a,n)=1. I don`t need only an answer, i need a good solution. Thanks!

Hi everyone, does anybody now some good pedagogical materials to learn fractional quantum hall effect? I have a book of J.K.Jain, but it seems to me not a good one. Thanks

I'm trying to find the set $\mathscr{F}$ of all linear fractional transformations (l.f.t.) of the unit disc D in itself which map 1 in 1, -1 in -1 and i in -i. By l.f.t. i mean a function$$f(z)=\frac{az+b}{cz+d}$$with $a,b,c,d\in\mathbb C$, $ad-bc\neq0$.I know that this kind of maps sends lines...

I wanted to do a demo of fractional crystallization that would have a nice visual result. I had intended to make a saturated solution of ferric chloride, nickel chloride, and sodium chloride, put the solution in a very broad shallow petri dish, and allow natural evap to produce concentric...

Hi, this seems like the right section to post, I have a few questions, three fractions that I know the answer for but I just can't figure out how they were arrived at (the middle step). The only way I can think of solving them is expanding it all out etc. which would result in a 100 term cubic...

The geometric and physical properties of derivatives and integrals to an integer order are easy to describe, but fractional calculus is obviously present in modern mathematics and physics. That being said, are there a generalizations of the definitions derivatives and integrals that include...

Homework Statement f(x)=x^7/2, Find the derivative Homework Equations f'(a)=limit as x approaches a; ((x+h)-x)/h The Attempt at a Solution limit as h approached 0; ((x+h)^7/2-x^7/2)/h Multiplied by the conjugate with -5/2 as exponent and came up with 2x^5/2, which is incorrect