I read in http://www-library.desy.de/preparch/books/vstatmp_engl.pdf page 29 (43 for pdf) that the mean volume is:
<V> = \int_{-\infty}^\infty dr V(r) N(r| r_0,s)
I have two questions.
Q1: why do they take the radius to be from -infinity to +infinity and not from 0 to infinity?
Q2: is there an...
[Moderator's note: thread spun off from post in a different thread quoted below.]
That seems to me a rather extraordinary claim.
Could you demonstrate how for instance cosmological redshift can be explained in a coordinate independent fashion?
Hi there.
I want to compare the mean lifetimes of two particles which decay in a way given by two known reaction formulas, such as
##\rho^0 \rightarrow \pi^+ + \pi^-## and ##\Xi^- \rightarrow \Lambda^0 + \pi^-##
In this case it's easy: since the first one corresponds to a first interaction...
Hi guys. New here.
I'm reading philosophy, and this philosopher uses some mathematics which I am having trouble understanding. I am interested in both an understanding of what the signs mean (in themselves and in this context, please), and why someone regularly chooses to use these functions...
Homework Statement
Excess electrons are placed on a small lead sphere with mass 8.00g so that it's net charge is -3.20x10^-9C (a) Find the number of excess electrons on the sphere. (b) how many excess electrons are there per lead atom? The atomic number of lead is 82, and its atomic mass is...
Homework Statement
Charged pion with average life time $$\tau=10^{-8} sec$$, and mean free path in the water$$\ell=100m$$ falls prependicular to a lake (depth of lake is at $$\ell_0 =30m$$ with velocity $$V=0.9999c$$
What of the next is correct?
1). The particle isn't gona touch the bottom of...
If a top has angular momentum of 12 units and the Earth has angular momentum of 100. Does this mean that Earth is spinning faster than the top since it has more angular momentum? The answer is there at the back of my head but can't articulate it.
The angular momentum is related to the rotation. And when a black hole has angular momentum, it is said that it is a "rotating black hole". But what does it mean? A black hole does not have a conventional surface, like a basketball. How should we interpret that angular momentum?
I asked this...
Homework Statement
If the system is in a state
|ψ> = 1/sqrt(6) |v1> + 1/sqrt(3) |v2> - i/sqrt(2) |v3>
with Hamiltonian satisfying H|vj> = (2-j)a|vj>
Find the mean value of energy <E> and the root mean square deviation √(<E2> - <E>2 ) that would result from making a number of measurements of...
Hello! I am predicting the peak altitude of a model rocket based on some ground tests. I know that Total Force on the rocket=Thrust-mg-kv^2 but am stuck as to which value for 'v' to use? Is it the velocity of the rocket with the effects of gravity and air resistance taken into account or the...
I'm reading, or more like deciphering a book about rocket science (Rocket propulsion and spaceflight dynamics from Cornelisse, Schoyer and Wakker). Most of my math skills are self taught from books and I usually figure things out but this one keeps haunting me.
It's some kind of series...
Homework Statement
[Update: just realized that the LMTD is a temperature difference, so my question was not valid] :P
Calculate the logarithmic mean temperature difference (LMTD) to heat water flowing through a tube from 21 C (Ti) to 40 C (Te) if the tube has a fixed temperature of 45 C (Ts)...
Homework Statement
In regards to linearization of a nonlinear system in differential equations. What does it mean for a linear approximation to be reliable to describe the long term behavior of the non-linear system around the equilibrium point?
Homework Equations
jacobian matrix
The Attempt...
I am trying to find the uncertainty of the mean of 3 values.
These values were calculated from experiments to calculate the enthalpy change of various alcohols.
These values are independent values.
−283 ± 11, −175 ± 9, −282 ± 11
How would I calculate the uncertainty of these values?
Thank you.
Homework Statement
Homework Equations
R2=R1(1+alpha(t2-t1))
The Attempt at a Solution
R1=250/5=50ohms
R2=250/3.91=63.94ohms
R2=R1(1+alpha15degrees(t2-t1))
63.94=50(1+1/254.5(t2-15))
t2=
Now I found this online but the answers provided still don't match, 84.25 being the closest.
When...
I am interested in the calculation of the mean energy value of CMB (Cosmic Microwave Background) photons from which the recombination is performed.
The subject on French Wikipedia says :
"Intuitively, one might say that recombination occurs when energy average of photons is of the order of the...
From my humble (physicist) mathematics training, I have a vague notion of what a Hilbert space actually is mathematically, i.e. an inner product space that is complete, with completeness in this sense heuristically meaning that all possible sequences of elements within this space have a...
Hi,
For a SoC project I am working on I need to select one cell which is most critical.
example, If a bus is going through 1000 stops 1000 times I have mean median mode of delay contribution of that stop compared to the total delay to reach from start to stop point and N (number of times bus...
Homework Statement
(a) Suppose we flip a fair coin until two Tails in a row come up. What is the expected number, NTT, of flips we perform? Hint: Let D be the tree diagram for this process. Explain why D = H · D + T · (H · D + T). Use the Law of Total Expectation
(b) Suppose we flip a fair...
Homework Statement
A right circular cylinder of ##4## cm (inner) radius and ##19.9## cm (inner) length contains ##4 \times 10^{14}## Argon atoms (atomic number ##18##). The cylinder is maintained at room temperature, nominally ##300## K.
(a) Estimate the momentum transfer per square meter per...
Homework Statement
Consider a D dimensional Ising model with N sites, defined by the Hamiltonian $$\mathcal H = -J \sum_{\langle i j \rangle} \sigma_i \sigma_j - h \sum_i \sigma_i$$ where the sum extends over nearest neighbours and each spin variable ##\sigma_i = \pm 1##. For a given spin...
In Bernoulli equation we use pressure energy... Pressure* volume gives the unit of energy... But what does this mean... If someone says it is potential energy per unit volume, then what does datum head refers to?... Please help... Can't go ahead without having thorough knowledge about this..
Homework Statement
Current density is the amount of current per cross sectional of flow. I'm having trouble wrapping my head around this definition. Surface charge or volume charge I understand better since they are almost analogous to the density we all understand (amount of matter/charge...
I have encountered this form of a function: ##f \left(x, y\right)##. Later throughout the discussion, the function was represented as ##f \left(y \right)##. Does this change in representation imply anything? I have been looking through the discussion if ##x## was considered constant, but it...
Homework Statement
I just want to focus on the divergence outside the cylinder (r >R)
Homework Equations
The Attempt at a Solution
For r > R, I said ∇ * E = p/ε
But that's wrong. The answer is ∇ * E = 0
I'm confused because there is definitely an electric field outside the cylinder (r...
I recently stumbled across a chemical equation, which had a symbol I have never seen before.
If anyone can tell me what this symbol means, I would be very grateful.
Here's the equation:
Ca(OH)2(aq) + Na2CO3(s) → CaCO3 ↓ + 2 NaOH(aq)
...and I'd like to know what the "↓" symbol means.
Many...
i know this might seem as a very simple question , but i am confused :
in order to calculate the total number of vacancies we need the total number of atomic sites N , and since N depends on the density of the material , then N refers to the number of atoms , right ? what confuses me is the word...
Homework Statement
Homework Equations
The Quotient rule for calculating the derivative.
The Attempt at a Solution
The derivative f'(x) = (x+5)-(x+3) / (x+5)^2
I tried a previous similar problem but failed as I didn't and still don't know what '' means.
What is the root mean squad (RMS) of a signal (or wave) and why is it important for electrical engineering?
How do you Find it?
What is it used for?
Thank You All
Homework Statement
Page 16 (attached file)
\frac{dH}{dt}|_{t=0} = Δ_{Σ}φ + Ric (ν,ν)φ+|A|^{2}φ
\frac{d}{dt}(dσ_{t})|_{t=0} = - φHdσ
H = mean curvature of surface Σ
A = the second fundamental of Σ
ν = the unit normal vector field along Σ
φ = the scalar field on three manifold M
φ∈C^{∞}(Σ)...
Hello all,
I am trying to remember (I did it in Uni) how to calculate the effective mean radius of an annulus that contains a pattern of holes on a PCD.
Consider the following image (pinched from: https://www.solenoid-valves.com/ ):
If one was to vary the value of PCD, then the effective...
While reading a textbook on viscous flows, I came across the following interpretation of an equation:
where, v is the vertical component of the free stream velocity and y is the vertical distance from the surface of a solid and Re is the reynolds number.
Can someone please help me understand...
Homework Statement
What takes more energy a car going 0 to 60 in 3 seconds or a car going 0 to 60 in 8 seconds.
Homework Equations
1/2 k v ^2
The Attempt at a Solution
I know the answer is they are the same but the power is different. But doesn't the car that goes faster lose more gas. And...
For a bubble in water in equilibrium the supporting forces due to pressure of the gas Pg and vapour Pv in the bubble must equal the crushing forces i.e. the hydrostatic forces Ph and those due to surface tension 2sigma/R0. So we have
##P_{v}+P_{g}=P_{h}+ \frac{2\sigma }{R_{0}}##
Now we apply...
Hi,
In the paper "A triangle-free circle graph with chromatic number 5" from A.A. Ageev, I don't understand what the author mean with the following definition:
Somebody can explain it to me? (I'm not mathematician).
Thanks !
Link to the whole paper...
When people want to find a conserved current which is constructed from a Dirac spinor, they consider the Dirac equation and its "Hermitian conjugate". But the equations they consider are ## (i\gamma^\mu \partial_\mu -m)\psi=0 ## and ##\bar{\psi}(i\gamma^\mu \overleftarrow{\partial_\mu}+m)=0 ##...
Homework Statement
I know that at 18,000 ft. above mean sea level, the atm. pressure ~half of what it is at seal level (760 Torr). The temperature also decreases by 70C.
a. How would this change the speed distribution of the air molecules quanitatively?
b.How would it change the mean free...
Consider the state ##\rho_n## obtained by applying n times the same creation operator on the vacuum and an observable A.
How is ##Tr(\rho_n A)## related to ##Tr(\rho_1 A)## ?
And if ##\rho## is a coherent state?
I'd like to ask what exactly do the results of double slit experiment mean? I must confess that I've read about this mainly in New Age literature where it was used as a "proof" that our consciousness changes reality. I know that Physicists probably don't like such explanations :eek:
So I'd like...
Homework Statement
Homework EquationsThe Attempt at a Solution
I'm working on part a.
The numerical value of Q.
I have an equation stating that Q = ω_0/ϒ.
I don't really know what ϒ is, in other places (http://farside.ph.utexas.edu/teaching/315/Waves/node13.html) it seems like the...
Say that 6V battery is connected to a lamp that takes 3V from each coulomb. Does that mean that the battery can supply 6V or dependent upon the need of components in the circuit ?
Good morning,
I was making some investigation regarding the calculation of mean orbital elements - not osculating.
Is this done simply by fitting (with the best equation) several osculating elements across time, or is there a mathematical approach already settled?
Cheers,
Hello,
I am currently studying how to find the centroid of shapes. And I understand that to find the location of the centroid, we must analyze the distribution of the mass over the x and y-axis (i.e calculating Qx and Qy).
However what baffles me is that, given an L shaped beam, the centroid...