Factors Definition and 411 Threads

I am curious as to the meaning of, and name given to the phase ##\xi(t)## which may be added as a prefix to the time evolution operator ##\hat{U}(t)##. This phase acts to shift the energy of the dynamical phase ##<{\psi(t)}|\hat{H}(t)|\psi(t)>##, since it appears in the Hamiltonian along the...

I seem to have encountered a situation in which I have a quartic which has solutions, but no factors. The polynomial is: x^4 - 8x^2 + 224x - 160 = 0 I attempted to find the factors for this quartic in the following manor f(x) = x^4 - 8x^2 + 224x - 160 f(1) = (1)^4 - 8(1)^2 + 224(1) - 160...

Hi all, A few basic questions regarding inductors really. I'm just doing a bit of reading into these little beauties and trying to get to grips with the workings. My questions are: 1.) Do inductors generate larger magnetic fields with DC or AC? (Providing the same current and voltage) 2.) If...

I am in the final stages of the project I've been working on: Taking a Dynkin diagram and deriving the structure factors for the Lie algebra it represents. Yay me! However. I am confident in my work but it would still be really nice to be able to check them. Does anyone know where to find a...

I'm confused by the following passage in our book (translated). An alternative too choosing the normed tangent vectors ##\vec e_i = \frac{1}{h_1}\frac{\partial \vec r}{\partial u_i}## with scale factors ##h_i = \left| \frac{\partial \vec r }{\partial u_i} \right| ## is to choose the normal...

So I was trying to understand some Mu charts of Brake pads for cars. I thought that Mu was basically a "calculated, or measured constant " which could be used to compare friction between 2 materials. like a solid iron Rotor, and a brake pad. I was thinking that a simple chart that shows...

Hi all, Has anyone an idea how can we derive the color factor ## C_2## , eq. 27 in http://authors.library.caltech.edu/8947/1/GREprd07.pdf ? ## C_2 ## belongs to the second Feynman diagram in fig. 3 which includes two gluons and 4 octet scalars . Best.

I have some trouble grasping voltage, and why it is defined by V = R * I. 1. If voltage can be seen as some form of electrical potential energy, why does it not increase as the circuit is made longer (in terms of meters). Would a current be as likely to travel in a 0.1 meter circuit as in a...

Hi all, Is there a rule in math or logic that states something like this: When Skill is the Primary factor in determining an outcome, When two opposing people are closer in skill, then smaller factors become more important? Lets say two warriors are battling it out and are close to being...

Hi there, In paper as : http://authors.library.caltech.edu/8947/1/GREprd07.pdf I don't understand the colour factor associated with two gluons and single octet scalar as the first Feynman diagram in fig. 3 ? In eq. 27, this colour factor is given by ## (d^{abc})^2 ## .. so, how did this come...

I now know that an insulator will not only keep heat in but keep heat from being conducted in the first place So my solar still is almost 100% metal including the 2 valves. There is however 1 plastic pipe between the rain collector and the evaporator that is flexible. My solar still has several...

1. solve the problem first finding an integrating factor of susceptible form. y(x+y)dx+(xy+1)dy=0Homework Equations form: M(x,y)dx+N(x,y)dy=0 intigrating factor: eint(1/n(dm/dy-dndx)dx The Attempt at a Solution u(x)=eint(1/(xy+1)(y(x+y)d/dy-(xy+1)d/dx)dx this reduces to eint((x+y)/(xy+1))dx...

Homework Statement I am having a look at drift velocity and i know essentially what it is, and i am now noting down the factors that effect the drift velocity of the charge carriers as i think its a useful thing to know. So, so far i have that the number of charge carriers will effect the...

Homework Statement I found the values ##F_{3\rightarrow(1+2)}=0.32## and ##F_{1\rightarrow3}=0.25## I now want to find ##F_{2\rightarrow3}## Homework Equations Reciprocity relation ##A_iF_{i\rightarrow j}=A_jF_{j\rightarrow i}## The Attempt at a Solution Using the reciprocity relation to find...

Homework Statement Start from the 'relevant equation' below and derive $$ (1) \frac{\partial{\bf{\hat{q}}_{i}}}{{\partial{q}}_{j}}={\hat{q}}_{i}\frac{1}{{h}_{i}} \frac{\partial{h}_{i}}{{\partial{q}}_{j}}, {i}\ne{j}$$ $$ (2) \frac{\partial{\bf{\hat{q}}_{i}}}{{\partial{q}}_{i}}= -\sum...

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >[/color] Hello everybody! I am posting this in hopes of further guidance and help on a high school essay assignment. I am required to make an investigation with an experiment(s) that explores a...

Hi, I want to understand how stress concentration factor or notch factor is considered in FEA method. Lets assume a case of stepped shaft which has got the left end of the shaft fixed with rigid wall and the other end being pulled by an axial load. In the case of conventional calculation...

Homework Statement Let f(n) denote the number of unique prime factors of some positive integer n > 1. Prove that f(n) \in \mathcal{O}\left(\dfrac{\log n}{\log \log n}\right) Homework EquationsThe Attempt at a Solution Since every prime number except 2 is prime, an upper bound on the number...

I have come across a question in my explorations of recursive tilings using Gaussian and Eisenstein Integers. It seems there might be a class of composite numbers which have no factors (divisors) that are co-prime. So, for instance: 10 is composite, but its factors (2 and 5) are co-prime. The...

I've heard of the muons and electrons that constantly hit Earth's surface in cosmic rays coming from extra terrestrial particles that break up in Earth's atmosphere but I was curious what factors played a role in the type of radiation produced from these particles in the atmosphere (i.e. More...

I am confused about the following; where am I going wrong here? 1. (1/2)kT is defined as the average kinetic energy of the molecules of a substance at temperature T, right? 2. You can derive the Boltzmann distribution/Boltzmann factors using (1/2)kT as the kinetic energy, making an argument...

Homework Statement Is it true that for each ##n\geq 2## there are two primes ##p, q \neq 1## that divide every ##\binom{n}{k}## for ##1\leq k\leq n-1##?Examples: For ##n=6: \binom{6}{1}=6; \binom{6}{2}=15; \binom{6}{3}=20; \binom{6}{4}=15; \binom{6}{5}=6.## So we can have ##p=2## and...

So from what I had initially understood, in a conversion problem, you go by whatever number has the smallest SF and round your answer to that number, even if that number is one. In the examples on my homework it seems like my teacher chooses a random number of significant figures for each...

How much should one weigh a grad school's location when choosing? Especially when it means living close to family and friends? If you had a choice between a rank 25-30 school in mathematics with an advisor who isn't famous, but does research which you are very interested in, and the school is...

Looking for researches, articles and experimental values conserning factors which influence to half-life speed for different isotopes.

Homework Statement A number divisible by both 16 and 15 is divisible by at least how many unique integers? Homework Equations Combination formula, nCk = n!/(k!(n-k)!) The Attempt at a Solution I found the prime factorization for 16 and 15, 2x2x2x2x3x5. A number divisible by 16 and 15 must be...

[FONT=Lucida Grande]The number of ways in which the number $27720$ can be split into two factors which are co prime

Hi, I am not a native English Speaker, so some words might not be appropriately used below, but I will try my best to explain what I was thinking about. In general, I have never learned how acoustic waves emerge microscopically. The application of the theoretical knowledge I acquired was always...

I only see positive factors in my book. Example: 2 and 2 are factors of 4. But aren't -2 and -2? Is there some unspoken rule in math that only positive factors count? Thanks!

Having trouble with this problem, appreciate help. Excluding 1 and itself, how many factors does the number 19 x 29 x 59 x 79 have?

Homework Statement the factor affecting sound intensity is amplitude and frequency . why not also the distance from the source (r) , in my opinion, intensity = power/area , so the intensity = power/ 4 pi r ^2 ... so I is inversely proportional to r^2 ... Homework Equations The...

Homework Statement the factor affecting sound intensity is amplitude and frequency . why not also the distance from the source (r) , in my opinion, intensity = power/area , so the intensity = power/ 4 pi r ^2 ... so I is inversely proportional to r^2 ... Homework Equations The...

I am about to install a 625 KVA generator in a place where the ambient temperature is around 60* centigrade. What are the necessary modifications should i do with the generator and the factors to be taken into considerations before installing the generator in the site

I'm trying to factorize this: \(16x^2 -144x+99\) The only factors I can find of ac are: 132,12 which add up to -144 but only if both are negative and we need opposing signs to get the -144. I've used an online factor calculator and can't seem to find anything there! I'm obviously missing...

Is there a formula or method for determining the time it takes for water to freeze from a certain temperature? What parameters would this rely on?

Homework Statement 1) Equilibrium is achieved in a closed system where metallic Mg can react with HCl(aq) according to the following net chemical equation: Mg(s) + 2 H+(aq) <--> Mg+2(aq)+ H2(aq) A sodium hydroxide, NaOH(s), pellet is added to this system. What happens to the concentration...

I want to know what factors influence the bond enthalpy of a covalent bond and how do those factors influence the bond strength.

Homework Statement \displaystyle{\int}\dfrac{x}{\sqrt{x^2+x+1}}~dx = \displaystyle{\int}\dfrac{(x+\frac 1 2)-\frac 1 2}{\sqrt{(x+\frac 1 2)^2+(\frac {\sqrt 3} 2)^2}}~dx Homework Equations Given. The Attempt at a Solution The solution is given, but I'm not sure how it was...

Hi. I was reading Griffiths page 289 and I wasn't sure how the transition from Eq. (8.45) to (8.46) was allowed. What bothers me is factoring out the "color factors" since the c's are vectors, and generally the elements of these color factors are matrices. For example, how is it allowed to pull...

First of all, pardon me for my poor English, which is even worse for mathematics. As an answer to my question, I think it does have all the factors n has. But I can't write mathematical proof of it, and so I can't make that statement. It's probably easy. I can write that in the opposite...

Hi guys, I'm currently writing a document about decoherence and I'm trying to make a point about phase factors and how they are altered by an interaction with a surrounding environment. However, i don't want to only state this, i want to show it through basic QM. Is it possible to say the...

While investigating Coulomb's Law, I created a graph of F-1/2 vs. r to display results. The gradient of this graph is much steeper than it should be. What factors could affect the electrostatic force to make this happen? Any suggestions would be greatly appreciated! (The experiment...

Hi everyone, I have been studying transmission lines and it got me thinking. If we have a series circuit which has two equal length transmission lines with the same Zo but with different velocity factors how does this effect the wave velocity through the circuit? Do the waves travel...

Homework Statement In my ODE class, we learned how to solve first order ordinary differential equations which are not exact yet but exact after multiplying by the right integrating factor. The integrating factor we learned about take one of the five forms: f(x), f(y), f(xy), f(x/y), and...

Hello I am having a hard time understanding which factors should be taken into account and which ones should not be taken into account when calculating probability. I have the following situation: Last night I played FIFA12 on xbox live against an unknown opponent. He challenged me to a...

I need to measure a magnetic field of Frequency of around 130KHz in all 3 X,Y,Z axis. I have a plan to make 3 coils perpendicular to each other and measure voltages from each coil in Oscilloscope channel. As per Faraday's law of induction. I could measure (dB/dt) as follows. V = - N A...

I'm currently doing a spectroscopy lab where you use a scintillator and Cs-137 to obtain a Cs-137 spectrum. I calibrated this spectrum using the known gamma energy for Cs-137 at 662 Kev at the photo peak. I am now trying to use this calibration for a Co-60 spectrum. The problem is that when I...

Homework Statement The problem: Derive (3.3) without reference to (2.3) or (2.1). (2.1): F/P = (1 + i)^n (2.3): F/A = [(1 + i)^n – 1]/i (3.3): (F/A, i%, n) = (F/A, i%, n_1) + (F/P, i%, n_1) + (F/P, i%, n_1 + 1) + . . . + (F/P. i%, n – 1) (n > n_1) The solution (which also...

Show that for $a >0$ and $b \ge 0$, $$\int_{0}^{\infty} e^{-a^{4}x^{2}(x^{2}-6b^{2})} \cos \Big(4a^{4}bx(x^{2}-b^{2}) \Big) \ dx = \frac{e^{a^{4}b^{4}}}{4a} \Gamma \left( \frac{1}{4} \right) $$

Homework Statement what factors affect the size of the pressure at a point in a static fluid? Homework Equations The Attempt at a Solution