Mean Definition and 1000 Threads

What does this mean? " spin +1 ("triplet") and is thus a boson." Hey, Can anyone explain the best they can what the following means? Its in response to a question I asked about a certain substance. " spin +1 ("triplet") and is thus a boson."

Homework Statement The mean of a function is as follows: $${1 \over {a - b}}\int_b^a {f(x)\,dx} $$ So why is the mean of the PDF as follows: $$\int_{ - \infty }^\infty {xf(x)\,dx} $$ I thought it would have been this way: $$\lim \,b \to - \infty \,{1 \over { - b}}\int_b^0...

Hi PF, I have always wondered what was meant when my teachers told me that a vector is the same no matter what coordinate system it is represented in. What is it exactly that is the same? I mean the components change. So the only thing that I can see remains the same is the length of the vector...

What does "phase of the motion in terms of cosine displacement" mean? I'm getting tripped up on the wording of this homework question. Homework Statement Measured acceleration: An accelerometer has measured the simple harmonic motion shown in the image below. Homework Equations You...

Hello! I am using physical data to do an analysis (~30k measurements). These measurements include energies, momenta, angles... of particles. I am calculating a value (call it v) at the end after a lengthy process, and if I introduce all the data into my program I did, the result is v±σ...

Homework Statement Find a function f on [-1,1] such that :- (a) there exists c \in (-1,1) such that f'(c) = 0 and (b) f(a) \neq f(b) for any a\neq b \in [-1,1] Homework Equations Lagrange's Mean Value Theorem (LMVT), which states that if f:[a,b]-->ℝ is a function which is...

I have an exam in introductory nuclear physics coming up in 2 days. I am supposed to present an article which i have already drawn. The article is about heavy ion collisions in the SPS accelerator at CERN. They keep mentioning that the experiment uses Pb + Pb collisions at 158 A*Gev/c beam...

Hello everyone, I am self teaching some elementary notions of differential geometry. Rather, I should say I am concentrating on mean and gaussian curvature concepts related to a physics application I am interested in. I see one has to evaluate an integral that goes as...

The Lorentz factor is used ubiquitously in relativity for transformation between frames and in describing various relationships. Wikipedia describes this as: ---------- The Lorentz factor is defined as: γ = 1/√(1-v2/c2) = 1/√(1-β2) = dt/dτ where: v is the relative velocity between...

Homework Statement This is the full question, but we're only asked to do b. A random variable x has a Weibull Distribution if and only if its probability density is given by f(x) = {kx^(b-a) *exp(-ax^b) for x > 0 } where a and b > 0. a) Express k in terms of a and b. b) Show that u = a^(-1/b)...

Homework Statement If four distinct points on the curve y=2x^4+7x^3+3x-5 are collinear, then find the arithmetic mean of x-coordinates of the aforesaid points. Homework Equations The Attempt at a Solution I think that the four points mentioned must be the roots of the equation.

Hi, can someone please clarify me what does the standard "API Q125" in material designation mean? Does it stand for one particular steel grade or it has something to the with physical properties? And what does this "Q125" exactly means? Thank you. Regards Amy

Homework Statement Let f: R->R be a function which satisfied f(0)=0 and |df/dx|≤ M. Prove that |f(x)|≤ M*|x|. Homework Equations Mean value theorem says that if f is continuous on [a,b] and differentiable on (a,b), then there is a point c such that f'(c)=[f(b)-f(a)]/(b-a). The...

One of the boundary conditions for a homogeneous uniform waveguide is \frac{\partial H_z}{\partial n}=0. What does this mean physically?

What does X'X mean ?

For the Dirichlet problem on a sphere of radius a with the boundary condition $$ u(a,\theta,\phi) = f(\theta,\phi), $$ show that the value of $u$ at the origin $(r = 0)$ is equal to the average value of $f$ over the surface of the sphere. I know that the max and min occur on the boundaries and...

I attached a pdf. The questions are not really what is stumping me. Its the wording of the question I don't understand. When it says, "Assume that 0 < λ < 1. Note that your answers will be in terms of the constant λ." and "Assume that λ > 0. Note that your answers will be in terms of the...

I thought |r| means the positive values of r? Why do they say it means -1<r<1? Also, if |r| means -1<r<1 then why do they say |r|<1 when |r| is already -1<r<1 ?

Hi. Let X_1 and X_2 be independent random variables with mean  μ and variance σ^2. \Theta = ( X_1 + 3X_2 ) /4 a) is it unbiased? b) what is the variance of the estimator? c) what is the mean squared error of the estimator? since there are four things, divided by 4...

I've never seen this notation before. What does the ellipsis right after the first summation mean: \begin{equation} \label{aixi_eq} a_t^* = \arg\max\limits_{a_t}\sum\limits_{o_t r_t} \dots \max\limits_{a_{t+m}}\sum\limits_{o_{t+m} r_{t+m}}[r_t + \dots + r_{t+m}]...

I'm doing a practice problem for my upcoming midterm and am stuck on a question. 3. The number of hurricanes that occur in the caribbean during hurricane season is a random variable, where the mean number of hurricanes occurring is 8, or E(X) = 8, with a standard deviation of 2.83. (a) Find...

f: ℝ^n→ℝ\qquad g: ℝ^n→ℝ^m

What is the statement of the mean square convergence of Fourier series?

Does economic freedom = deregulation?

What about in a ring where we have two binary operations defined. I get super confused when I see someone just switch from something like n*a to a + a + ... + a (n times, where * is the binary operation on the "semigroup" part of the ring, and + is the operation on the "group" part of the ring)...

Hello, Does anyone knows why rigid body does not exist.So in order to know its history which textbook can i refer to ? For example to know classical mechanics properly you have to go to Newtons book known as Principia. In order to know rigid bodies who should we refer.

I'm trying to find out: -Mass (g) of acetic acid per liter of vinegar and -Mass (g) of solution per liter of vinegar I thought mass (g) of solution meant how much acetic acid but apparently not? what does it mean and how do I calculate it? Thanks :)

So I'm trying to come up with 2 exponential function for a question, one we do by hand and one with technology. So on graphmatica, it came up with: y = exp(0.0211x - 28.95) which I have no idea what it means. I thought the equation was supposed to be in y= a*b^x Is it possible to change it...

1. Essentially what I'm trying to do is find the asymptotic distributions for a) Y2 b) 1/Y and c) eY where Y = sample mean of a random iid sample of size n. E(X) = u; V(X) = σ2 Homework Equations a) Y^2=Y*Y which converges in probability to u^2, V(Y*Y)=\sigma^4 + 2\sigma^2u^2 So...

The function for simple harmonic oscillation is: Acos(ωT)+\phi Why is there an angle phi added to the function acos(ωT)?

hello , I don't understand the meaning of the next definition , so , I hope that you can make it easy to understand it for me definition if G is an arbitrary group and ∅≠S⊆G , then ,the symbol (s) will represent the set (S) = ∩ { H∖S ⊆ H : H is a subgroup of G } can you give me some...

Hi all, I got an idea why noise is having a gaussian pdf but didnot understood why it should be having zero mean. Why can't noise contain a dc content. -Devanand T

Homework Statement Let D be a division ring, C its center and let S be a division subring of D which is stabilized by every map x -> dxd-1, d≠0 in D. Show that either S = D or S is a subset of C. 2. The attempt at a solution I haven't actually started working on it yet because I am not...

The universe is expanding, I am told by a friend who is well-trained in such matters, not only in its spatial dimensions, but also in its time dimension. This sort of suggests that there is now more time between the beginning of time and yesterday than there was when it was actually yesterday...

Homework Statement This is Purcell 4.12... Given that conductivity in silicon at 500K is 0.3 sec-1, deduce the mean free time between collisions of an electron. Homework Equations Electron mass is 9.1x10-28 grams (mass of a hole is exactly the same), the charge on an electron is...

Hi guys, I have to find the deviation from the mean for each individual entry of a column of numbers. Any one have any idea how to do this? I'm clueless when it comes to excel

I was assigned a multistep task by my professor so I first made the molecule with ChemDraw, then I ran an optimisation using B3LYP/6-31G. I then ran a frequency scan and checked for any imaginary frequencies. There were no negative frequencies and my understanding is that this means that...

Homework Statement So the question is, given a set of random numbers, find the mean and the value that will be >= 99% of the occurances. So for a set of random numbers between say, 1-100, if the mean is 50, how do I find out what number will be >= 99% of all observations of the time...

Hi, I'm a masters student trying to apply DMFT to problems involving transport in strongly correlated systems. I have a cursory understanding of the physics behind the Hubbard model, which is to say, I have spent some time with it in a quantum many body theory course. However, I now want to...

Homework Statement Prove that the only surfaces with zero mean curvature are either planes or hyperbolic curves with the equation: y = \frac{\cosh (ax+b)}{a} rotating alone the x axis.Homework Equations The Attempt at a Solution I made an attempt by devoting the equation of the surface as r =...

In relational algebra what does "in" mean? For example \sigma_{car IN car}R where R is some relation.

What exactly do the terms "near-field" and "far-field" mean? What exactly do the terms "near-field" and "far-field" mean (especially in the context of the two problems attached)? Other than the confusion about those terminologies, I fully get how to do these problems (1.1 and 1.2). Any...

Hi Guys, I am just starting readings on machine learning and came across ways that the error can be used to learn the target function. The way I understand it, Error: e = f(\vec{x}) - y* Loss: L(\vec{x}) = \frac{( f(\vec{x}) - y* )^2}{2} Empirical Risk: R(f) = \sum_{i=o}^{m} \frac{(...

I'm reading a finance book in which the author proposes to exclude the mean when calculating the variance of returns, because he thinks it's difficult to distinguish the drift of the price from the variance of that time series. So he basically calculates the sample variance like this...

I hope this the right place to ask this question. I appologize if this is in the wrong place. I am not from a probability background. I have tried to search for an answer to my question, but I have not found it in any of the literature which I can understand. I'm not even sure exactly how to...

What does "rest" mean? If I throw a ball straight up, at its highest point, is it momentarily at rest? Its velocity is momentarily 0, but it is still accelerating.

I would like to know what this symbol means:\nVdashSpecifically, in the main result of [link] (Theorem 1, at the top of p.4), it has:\nVdash(n=k=0)

Strictly not so much an academic guidance question, but I don't know where else I can put this. In the U.S., What's the typical letter grade you get if you're around mean in a course in college? From where I'm from, being mean in class equates to a B- or a C+, and I'm just curious to know...

Homework Statement Assume that X is squared-Chi-distributed, which means that the moment generating function is given by: m(t)=(1-2t)^{-k/2} Use the mgf to find E(X) and var(X) The Attempt at a Solution I know that m'(0)=E(X), and m''(0)=var(X). So I find...

Hello Everyone, I have a 5 ampere weighing equipment & need it to ground properly. It is about 80 feet away from soil point. (Direct wire to the equipment will be used & long term connection is required). Manufacturer says that: "There must be a good third wire ground, preferably to a...