Mean Definition and 1000 Threads

"One corner short of a pentagon"...What does it mean? Ok I read this phrase somewhere and I have no idea what it means. Apparently it's a North American thing and is something related to someone's personality or stuff like that. Can anyone tell me what it is supposed to mean? Thanks

Homework Statement I am looking at finding the Fourier transform of: f(t)=\exp \left[ \frac{-(t-m)^2}{2 \sigma^2}\right] Homework Equations \hat{f}(t)=\frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{\infty} f(t) e^{-i \omega t} dt The Attempt at a Solution I did it a little differently that my...

I'm looking at a condition in a maths paper that I don't understand, essentially it is: x ∈ R ⊕ R⊥ R is a set I think, but I'm not sure what the perpendicular symbol means. Also am I correct in thinking the circled plus means that x must be in either R or R⊥ (but not both)? Thanks

Homework Statement The proper mean lifetime of a \pi^{+} mesons is 26ns. (a) (i) What is the mean lifetime of \pi^{+} mesons traveling with \beta=\frac{v}{c}=0.73? (ii) What distance is traveled at this velocity during one mean lifetime? (iii) What distance would be traveled in the...

I have seen this word used in every context, is there a solid definition??

Hello all . My questions are : Space/time are any meaning without matter or energy ? Space/time are exist without matter or energy ? We can image space/time without any matter or energy ? These terms are any meaning in physics ?

Cosmic greetings, I am reading up on active galaxies, and 'strong' and 'broad' emission lines are mentioned everywhere, yet no definitions given. Do they mean that the object is emitting energy across a large part of the spectrum, or that it's emitting a lot of energy? Also, I am confused...

Does a di/dt<0 mean an increasing current moving from a lower potential to a higher potential (if we define the direction of current to be the flow of the positive charges)? Similar question with negative current i.e.; dq/dt<0.

Homework Statement 1) Let f be a function differentiable two times on the open interval I and a and b two numbers in I Prove that: \exists c\in]a,b[:\frac{f(b)-f(a)}{b-a}=f'(a)+\frac{b+a}{c}f''(c) 2) Let f be a function differentiable three times on the open interval I and a and b two...

Homework Statement The harmonic mean of the roots of the equation (5+\sqrt{2})x^2-(4+\sqrt{5})x+8+2\sqrt{5}=0 Homework Equations The Attempt at a Solution I know this question is easy but the main problem arises in finding the roots of the above equation. When I use the quadratic...

I have completed bending moment and shear force diagrams and have a question asking for the mean shear stress. I know this is worked out using the formula: tau = F/A. I am unsure of what force to use is it the max shear force on my diagram? My other thought is that it could be an avergae of...

Homework Statement Let f and g be two continuous functions on [a,b] and differentiable on ]a,b[ such that for every x in ]a,b[ : f'(x)<g'(x) Homework Equations Show that f(b)-f(a)<g(b)-g(a) The Attempt at a Solution So I said that there exists a c in ]a,b[ such that f'(c)=(f(b)-f(a))/(b-a)...

if A is a tridiagonal Matrix , what does this mean ? what does tridiagonal mean in matrix ? what is the property which A achieve to be tridiagonal ? what about " dense matrix " and " band matrix " ? what is the meanning in this words ?

Recently I was reading some paper on design surface plasmon polaritons(so called "SPPs") on corrugated surfaces, mainly these two papers listed below: 1.Pendry, J. B., et al. (2004). "Mimicking surface plasmons with structured surfaces." Science 305(5685): 847-848. 2.Garcia-Vidal, F. J...

does the r2s turbo , a 2 stage turbo and a twin turbo mean the same ...well my idea of a 2 stage turbo is that where compression of air takes place in 2 stages ..so does it consist of 2 compressors?

What does the "N" mean in a Cauchy sequence definition? Hi everyone, I have a question regarding Cauchy sequences. I am trying to teach myself real analysis and would appreciate any clarification anyone has regarding my question. I believe I have an intuitive understanding of what a Cauchy...

I'm reading an article about the photo induced ligand loss of metal carbonyl complexes at the moment and here's a bit I'm having trouble getting my head around: Its the wavepacket part that I'm confused about. All I know is that a wavepacket is what you get when you combine multiple sine...

Hi all, I have spent a good half hour searching for the meaning of this, but have only found results for upper-case sigma Ʃ and lower-case sigma σ. Can anyone tell me the meaning of the "word-final" version of sigma, which looks like ζ ? I am trying to evaluate 3ζ(4) but I just need a...

$a,b,c$ are any three positive numbers such that $a+b+c=1$. Prove that $$ab^2c^3 \leq \frac{1}{432}$$

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

I haven't taken the chemistry GRE exam yet, and I certainty don't plan on doing poorly, but part of me wonders if I did do poorly how if would affect my applications. A majority of the places I am applying to do not require it (but "strongly recommend" it). So if you get in the 50th...

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...

Hello Everybody. I have a rather simple question, which still kept me thinking for two hours without any result. If we want to determine the multiplicity in the microcanonical ensemble we just divide the volume of the shell containing the accessible microstates over the volume of one...