Mean Definition and 1000 Threads

I am reading Carroll’s Spacetime and Geometry, and I have seen the word “coupled” used multiple times in seemingly different ways. I have gotten the sense that it means some sort of interaction between particles, but Carroll refers to coupling between matter fields and the curvature of...

Homework Statement We know that $$< (x_1 - x_2)^2 > = \frac{K_bT}{K}$$ $$< (x_2 - x_3)^2 > = \frac{K_bT}{\gamma}$$ What's ##< (x_3 - x_1)^2 >## equal to? Homework EquationsThe Attempt at a Solution I have tried: ##< (x_2 - x_3)^2 > - < (x_1 - x_2)^2 >## but did not get ##< (x_3 - x_1)^2...

while I study in cont. mech. I found this equation and in the index he mention that "the difference between the volume supply and the production phi can be recognized only in relation to the constitutive definition of the material" what does it mean?

Hello, I'm reading a textbook named "Introduction to Rocket Science and Engineering" by Travis S. Taylor. I'm now in a general cosepts about orbits. I have a question, what the book says in here? I can't understand the bold formatted sentence. What the author try to mean? If you can, can you...

What does it mean the word 'Jet' in fluid mechanics, special when it depends on the free surface?!

Homework Statement Homework Equations F=ma=mv/t[/B] The Attempt at a Solution I used the equation F=mv/t, in which I find the change in velocity and change in time before and after the collision. The change in time is t2-t1, but the problem comes when I am calculating the change in...

E=mc^2 Can someone explain this equation to me? Does this mean that energy has mass in the sense that energy will create gravity? For instance, if I have a massless ball and I somehow place (3*10^8)^2 Joules or c^2 joules of electromagnetic energy inside the ball, would that ball now have a...

Let's say I have a system whose time evolution looks something like this: This equation tells me that if I measure energy on it, I will get either energy reading ## E_0 ## or energy reading ## E_1 ## , when I do that, the system will "collapse" into one of the energy eigenstates, ## \psi_0 ##...

A spin quantum number can have a value of 1/2 or -1/2. I assume that the negative means that these two spins are in opposite directions. However, what does the 1/2 mean? Why 1/2, rather than a whole integer? Are there some sort of units associated with this value?

I was reading Fundamentals of Inket Printing and it said the following: "The surface tension in a liquid causes a force to act in the plane of the free surface perpendicularly to a free edge in that surface." Can someone explain to me what this means? What's the direction of the force? I have...

Calculation of probability with arithmetic mean of random variables There are 4 people, each of whom has one deck of cards with 500 cards that are numbered from 1 to 500 with no duplicates. Each person draws a card from his deck and I would like to calculate the probability of the event that...

Hello, Can someone please tell me what the mean rating temperature in the tables provided in ASHRAE fundamentals, ASHRAE standard 90.1&90.2 for chilled water insulation indicates.

Homework Statement Laser probes are being used to examine the states of atoms and molecules at high temporal resolution. A laser operating at a wavelength of 400 nm produces a 1 femtosecond pulse. Compute the mean frequency and frequency spread, ∆ν, of this laser pulse. Homework Equations c =...

Hello I have the exercise below: Consider the function f(x)=1−8x2 on the interval [−5,6]. Find the average or mean slope of the function on this interval, i.e. [f(6)-f(-5)]/[6-(-5)] according to the theorem of laGrange the slope in a continues function which is derivable in an interval...

I know this is kind of a dumb question but please forgive me it's been awhile. Is it enough for a particle to merely "feel" an external force F to state that "F is acting on the particle"? ie if the particle was confined in a potential well and experiences F but does not move. or does...

Problem: We play roulette in a casino. We watch 100 rounds that result in a number between 1 and 36. and count the number of rounds for which the result is odd. assuming that the roulette is fair, calculate the mean and deviation Solution: I understand that the probability - Pr = 0.5. and...

I have the following question and I am struggling to find the right answer. The random variables and are described by a joint PDF which is uniform on the triangular set defined by the constraints 0 <= x <= 1, 0<= theta <= x Find the LMS estimate of theta given that X = x , for in the range...

I was thinking about the fact that space contains all sorts of matter and that these objects have temperatures. But then I read that space itself has a temperature depending on where you are. The cosmic background radiation for example has a temperature of 2.7K. Can someone explain what that...

Homework Statement "Show that if ##P(X=c)>0##, for some ##c\in \mathbb{R}##, then the distribution function ##F_X(x)=P(X\leq x)## is discontinuous at ##c##. Is the converse true?" Homework Equations Continuity of a distribution function: ##\lim_{\epsilon \rightarrow 0}F_X(x+\epsilon)=F_X(x)##...

Homework Statement I read the expression E=fRT/2 where E is internal energy of ideal gas and f is degrees of freedom, and ##V_{rms} = \sqrt{\frac{3RT}{M}}## Since internal energy for an ideal gas is purely kinetic (according to KTG) I can write 1/2 mv^2 = fRT/2. Now H2 is a diatomic molecule...

Homework Statement In Grimaldis discrete math book he asks Determine which of the statements are true which are false: ℚ*∩ ℤ = ℤ Homework EquationsThe Attempt at a Solution he never explained in his book what * represents. I tried google "what does Q* mean in mathematics" and "Q* in...

The Beer-Lambert law gives the intensity of monochromatic light as a function of depth ##z## in the form of an exponential attenuation: $$I(z)=I_{0}e^{-\gamma z},$$ where ##\gamma## is the wavelength-dependent attenuation coefficient. However, if two different wavelengths are present...

Homework Statement Let ##\{a_n\}## be a sequence of positive numbers such that ##\lim_{n\to\infty} a_n = L##. Prove that $$\lim_{n\to\infty}(a_1\cdots a_n)^{1/n} = L$$ Homework EquationsThe Attempt at a Solution Let ##\epsilon > 0##. There exists ##N\in\mathbb{N}## such that if ##n\ge N## then...

Homework Statement Mind mean and STDev of number of quarters someone has on them at one time 0 - 87% 1 - 8% 2 - 3% 3- 1% 4 - 1% The first time I did this I assumed a population but she said that was wrong and not what she was looking for. Here was my new attempt: x^2f(x)= 0(.87) 1(.08) 4(.03)...

I saw this article recently: https://www.sciencedaily.com/releases/2007/08/070827174320.htm It says that "A research team has for the first time ever discovered DNA from living bacteria that are more than half a million years old" Does this mean that this cell hasn't done any divisions since...

I'm currently reading Schwartz's QFT text "Quantum Field Theory and the Standard Model" (although this question does not specifically pertain to this text) and I've got two questions: 1. At the beginning of chapter 6 he talks about how we may consider the system to be non-interacting in...

What does input and output signals mean in terms of circuitry. Is it the current, the voltage, resistance? Also people usually show graphs for AC as Sinusoidal waves or sometimes they show square-waves etc. What are these signals referring to, and what does it mean for signals to have wave like...

Homework Statement Homework Equations Chebyshev's Theorem: The percentage of observations that are within k standard deviations of the mean is at least 100(1 - (1/k2))% Chebyshev's Theorem is applicable to ANY data set, whether skewed or symmetrical. Empirical Rule: For a symmetrical...

What is the difference between: THOMAS' CALCULUS, media UPGRADE (11TH EDITION) [ISBN-13 9780321489876] and THOMAS' CALCULUS (11TH EDITION) [ISBN-13 9780321185587]? could you provide detailed answer please? what does the title-addition "Media Upgrade" mean and what changes does it make on the...

Motion in a straight line has three formulas 1. v = u + at 2. v^2 - u^2 = 2as 3. s = ut + 1/2 at^2 These three formulas are applicable when a is constant. Now my question is 'what does it mean by 'when a is constant'? Could you please explain it?

Griffith says in problem 1.15 the potential energy has an imaginary part. my question is that any real case exists where the part of the potential energy is imaginary?

In the circular motion, What does it mean by this equation s = r.θ?

I have a box with a wall in mid dividing it in 2 sections, and the wall has a hole of diameter d. There is ideal gas in both sections at 150 K in one section and at 300 K in another. How am I supposed to calculate ratio of mean free paths in 2 sections. My attempt: L ~ Volume / Number of...

Homework Statement I've completed this problem and received the below feedback but have gone to a state of complete loss on what to do to amend. Can anyone provide a prompt ? Heat transfer coefficient is correct. But heat transfer rate is wrong - the question says Heat transfer per UNIT...

What does it mean by 1 amu? the mass of a proton or a neutron or an electron? If the mass of O is 16 amu, then what makes 16 amu in O atom? 16 protons or 16 neutrons or 16 electrons?

Homework Statement If, N = n × NA Where N = Number of particles in the substance and n = Amount of substance in moles (mol) and NA = Avogadro Number = 6.022 × 1023 particles mol-1 To find the number of particles, N, in a substance: N = n × NA To find the moles, n, of substance, n = N ÷ NA...

While using L' Hospital's rule in evaluating limits, one comes across limits of the following type: $$\lim_{x \to 0} x \ln x$$ Such limits are generally evaluated by taking ##x## to the denominator and make it ##x^{-1}##. In such a case, an indeterminate form ##\frac{\infty}{\infty}## comes...

My book says If s₁ = s₂ = s, and the body covers equal distance with different speed' Then what does it mean by "the body covers equal distance with different speed'? Could you explain the concept, please?

Homework Statement What does 'dv and dx' mean in f = eta A (dv/dx) in coefficient of viscosity? 2. Homework Equations What does 'dv and dx' mean in f = eta A (dv/dx) in coefficient of viscosity? The Attempt at a Solution As I know v = velocity and x = distance. then what does 'dv' and 'dx'...

(apologies for re-posting, I am unable to find my original thread.) A material which has a Young's modulus of elasticity of 250 GN m-2 and a poisons ratio of 0.32, calculate: (a) the bulk modulus of the material 
 Relevant equation, K=E/3(1-2v) Inputting our known values...

Imagine a gambler playing a casino game with fixed bet, fixed odds, no skill, and a starting bankroll, ##M_0##. She plays until she can no longer afford to bet and records only how many bets she was able to make, ##N_0##, until she could not afford to bet. Each day she goes back to the casino...

Hello! I read from ansys element reference that for solid 65 the key option (1) is used to include or suppress extra deformation shapes. I would like to ask what extra deformation shape mean.

So I'm reading through some stuff trying to learn tensors, and I wanted to stop myself to grasp this concept before I go further. Along the way it was mentioned in one of the sources I'm looking at that other than the dot product and cross product, you could multiply vectors in another way, and...

From this paper, on page 2: https://arxiv.org/pdf/1606.03488.pdf. I know the spectroscopic notation part, but what is the meaning of the symbol after the colon?

Many books sometimes for example define energy as quantity and sometimes as property. Also the definition of energy is the ability to do work or the meter of the ability to do work ? we define for example force as a quantity or as some quality and then we quantify this ?

I'm trying to understand the Schechter function, I read on Wikipedia that the L star term in the function is the 'characteristic galaxy luminosity where the power-law form of the function cuts off'. What does this mean exactly?

If diffraction angle 2θ represents Miller indices, what does intensity represent particularly in the context of quantitative XRD?

Hey! :o Let $D=\left \{x=(x_1, x_2)\in \mathbb{R}^2: x_2>\frac{1}{x_1}, \ x_1>0\right \}$. We have the function $f: D\rightarrow \left (0,\frac{\pi}{2}\right )$ with $f(x)=\arctan \left (\frac{x_2}{x_1}\right )$. I want to show using the mean value theorem in $\mathbb{R}^2$ that for all...

Per Wikipedia (Outer Space) referencing Davies, P. C. W. (1977), "...the mean free path of a photon in intergalactic space is about 10E23 km, or 10 billion light years." Per Lawrence Krauss (1999), it is longer than the size of the visible universe. What is the current thinking about this?

I am studying Quantum Cryptography and I am quite new in Quantum area. I have read an article and I found this confusing statement: My questions: 1. The three stage protocol implementing multiphoton. What is the meaning of coherent states of mean photon number? 2. How to describe the quantum...