Formula Definition and 1000 Threads

On page 105 of Peskin and Schroeder's book it says that the integral over ##d^2b## in the expression: $$d\sigma = \left(\Pi_f \frac{d^3 p_f}{(2\pi)^3}\frac{1}{2E_f}\right) \int d^2b\left(\Pi_{i=A,B} \int \frac{d^3 k_i}{(2\pi)^3}\frac{\phi_i(k_i)}{\sqrt{2E_i}} \int \frac{d^3...

So I've observed the animal I am studying dry it's self (a survival mechanism called anhydrobiosis) to avoid freezing (laseration by ice crystals). Life forms given time produce a number of protectants in order to survive. Trehalose a sugar is produced to 2-4%. This will act as an antifreeze to...

I have found various formulations for the Laplacian and I want to check that they are all really the same. Two are from Wikipedia and the third is from Sean Carroll. They are: A Wikipedia formula in ##n## dimensions: \begin{align} \nabla^2=\frac{1}{\sqrt{\left|g\right|}}\frac{\partial}{\partial...

The function should use (r,z,t) variables The domain is (0,H) Since U is not dependent on angle, then theta can be ignored in the expression for Laplacian in cylindrical coordinates(?)

Is everything correct? Percent by mass C = 40.60% Percent by mass H = 5.18% Percent by mass O = 54.22% Empirical formula = ? (unknown) Inverse molar mass C = 1 mol/12.01 g Inverse molar mass H = 1 mol/1.008 g Inverse molar mass O = 1 mol/16.00 g Convert the masses to moles. C = 40.60 g/12.01...

I just finished my freshman year in computer engineering at my college, and after some physics and materials science classes I noticed a pattern. Everybody—at least in my class, I don't about the rest of the world—is just memorizing formulas, myself included. I'm really trying to not just...

Say cell A11 contains the text "power tools". I want B11 to display if A11 contains the word "tools". I choose to use IF() and FIND(). If "tools" does exist it returns "Yes Tools" fine, but if not it returns an error saying FIND() didn't match a value instead of displaying "No Tools". I got...

Hi Guys, I am trying to keep this as simple as possible as I only need a ballpark figure. I am sure there are thousands of other variables which need/could be taken into account, but for this purpose, as simple as could be. A door in my house slams when other doors/windows open. The door is...

Hi everyone. I haven't been here in years, I'm surprised the account still works. Anyway. I have a mathematic thought/question that I really want to learn about. I realize this isn't going to be the easiest thing to explain if it is even possible, so please forgive me. So, What I want to do...

There are an infinite number of natural numbers. Why is that? Well this follows from the following facts: (i) There is at least one natural number. (ii) For each natural number there is a distinct number which is its successor, i.e., for each number $x$ there is a distinct number $y$ such that...

Anyone know what result this article is talking about? https://www.theatlantic.com/science/archive/2019/11/neutrino-oscillations-lead-striking-mathematical-discovery/602128/

Homework Statement: an object has a total mass of 75kg and is stationary, it then ejects as a smaller object to the left with a velocity of(+ve direction)7 ms-1(v2) with a mass of m2 , the original object then recoils backwards to the right (-ve direction) at a velocity of -2 ms-1 and a mass of...

Hi How do I use this formula: ni = (e^(B*(eH-ei))-1)*e^(-0.5772156649..) from this paper? https://ui.adsabs.harvard.edu/abs/2018DDA...49P...2C/abstract According to this site, (n0,n1,n2,n3,n4,n5,n6,n7) = (3,2,1,1,0,0,0,0) for N=7: https://bouman.chem.georgetown.edu/S02/lect21/lect21.htm Does...

I need a citeable source that gives the formula for the Gaussian curvature at a single point of an intrinsically defined Riemannian or Semi-Riemannian manifold given the intrinsic metric tensor and/or Riemann tensor. I've got sources for this already, but I'm not "allowed" to use them for this...

I found equion ##T^{\mu\nu} = \frac{1}{\mu_0} \left[ F^{\mu \alpha}F^\nu{}_{\alpha} - \frac{1}{4} \eta^{\mu\nu}F_{\alpha\beta} F^{\alpha\beta}\right] \,.## from wikipedia page https://en.wikipedia.org/wiki/Electromagnetic_stress–energy_tensor . it's (0,0) component should be electromagnetic...

I do not understand how this formula is derived: Can somebody help me? Source: https://www.corzan.com/en-us/piping-systems/specification/thermal-expansion

Hi I'm looking at David Tong notes on QHE http://www.damtp.cam.ac.uk/user/tong/qhe/two.pdf (page 56), I've attached the relevant screenshot below also. I understand we are working in the interaction picture whereby states evolve via the Unitary Operataor EQ 2.10 in the notes(I think this is...

Trying to calculate the enthalpy of combustion for gasolines with different octane ratings, 95 and 91 gasoline in particular. The thing is, they are mixtures and not compounds. To calculate the enthalpy of combustion, I am trying to find the molecular formula for each of the gasolines, in order...

I drew an illustration to make this easier: Point P is where I wish to find the magnetic flux density H. Given the Biot-Savart formula: $$d\textbf{H} = \frac{I}{4\pi}\frac{d\textbf{l}\times\textbf{R}}{R^2}$$ I can let $$d\textbf{l} = \hat{z}dz$$ and $$\hat{z}dz\times\textbf{R} =...

The circuit to be analyzed is shown below: Since initial conditions are zero (from the instructions) I will use laplace transforms for the cirucit and I will use the MAME method to solve this circuit. The laplace transforms that are required will give me: $$E_g(s) = \frac{10}{s}$$ $$ L_3 =...

Hi, recently I got interested with practical applications of Newton's law of cooling. Its main disadvantage is that one has to measure temperature at some point of time (other than ##t=0##) to obtain solution for any other ##t##. However I've found an online calculator...

I have a little question about converting Velocity formula that is derived as, ##\vec{V}=\frac{d\vec{r}}{dt}=\frac{dx}{dt}\hat{x}+\frac{dy}{dt}\hat{y}+\frac{dz}{dt}\hat{z}## in Cartesian Coordinate Systems ##(x, y, z)##. I want to convert this into Polar Coordinate System ##(r, \theta)##...

I'm trying to determine the force needed for one object to displace another object underwater. Specifically, Object A strikes Object B hard enough to jettison it from the seafloor up to sea level/land, let's say the Pacific coastline. I have a timeframe in mind, density & mass of the two...

##\begin{vmatrix} 1 & 2 & 3 & ... & n \\ 2 & 3 & 4 & ... & 1 \\ 3 & 4 & 5 & ... & 2 \\ {\vdots}& {\vdots}& {\vdots} & {\vdots} & {\vdots} \\ n & 1 & 2 & ... & n-1 \notag \end{vmatrix} = (-1)^{\frac{n(n-1)}{2}}\dfrac{n^n+n^{n-1}}{2}## Consider the 3x3 case. ##\begin{vmatrix} 1 & 2 & 3 \\ 2 & 3...

Hello. My attempt at the solution is as follows: l = 160m Q= 300 ls-1 R= p2/p1= 6+1.01/1.01 = 6.94 (2dp) d = Unknown Pressure drop = 0.3 Bar 0.3 = 800*160*300^2/6.94*d^5.31 0.3 = 1.152x10^10/6.94*d^5.31 0.3 ( 6.94*d^5.31) = 1.152x10^10 6.94*d^5.31 = 1.152x10^10/0.3 d^5.31 =...

Hello, I'm trying to work out the individual steps to get from start: 3y + x = -1 to: 3y = -x -1 to: y = - 1/3x -1/3 Could anyone help me with this! Thank you :-)

Is this the correct symbol to use for average rate of change: \overline{\triangle}=\dfrac{f(b)-f(a)}{b-a}

i have a neobydium magnet of grade n40 , the diameter of magnet is 15mm and thickness is 10 mm , now i want to calculate the pull force between this magnet and a steel plate when there is no gap between them ; & in second case i want to calculate the pull force when i put a 0.15mm copper plate...

Shankar, in the book "Quantum Field Theory and Condensed Matter", at page 328 writes the famous bosonization formula in the form $$\psi_{\pm}(x)=\frac{1}{\sqrt{2\pi\alpha}} e^{\pm i \sqrt{4\pi} \phi_{\pm}(x)}$$ and then writes: "This is not an operator identity: no combination of boson operators...

Suppose we have a light source emitting photons isotropically at a constant rate. Call the rest frame of the source S’ and call the photon-flux-density in this frame ##\sigma ‘##. (I’m treating it as a scalar instead of a vector because I’m assuming the light should travel radially in either...

I had created a formula on arc of a circle...How can I publish it ..So that people see it and decide is it important or not.

I want to render the Earth’s Magnetic field in a software and simulate solar wind electron interaction with it. How do I calculate the magnetic strength and vector orientation at each point around the Earth up to thousands of km? Is there a formula? Or do I need to download a vector field from...

Time it takes from A to travel to B; ##T = \large\frac{Vsinθ}{g}## Max height object can reach, ##h = \large\frac{V^{2} sin⁡2θ}{g}## Time it takes for for B to travel to C; ##T = \large\sqrt\frac{2y_{max}}{g}## What is the proper formula for ##Y_{max}## for this trajectory?

Publication: Rafael G. González-Acuña and Héctor A. Chaparro-Romo, "General formula for bi-aspheric singlet lens design free of spherical aberration," Appl. Opt. 57, 9341-9345 (2018) Open access preprint: arXiv Given one surface of a lens, how does the other surface has to look like to avoid...

From this article : https://arxiv.org/pdf/1611.09787.pdf , I try to deduce the equation that my teacher told me which links 2 quantities : 1) the global number density of galaxies 2) the local number density of galaxies 3) the contrast of Dark matter density The relation that I would like to...

From [b,b^{\dagger}]=I it is easy to see that [b,[b,b^{\dagger}]]=[b^{\dagger},[b,b^{\dagger}]]=0. And from that e^be^{b^{\dagger}}=e^{b+b^{\dagger}}e^{\frac{1}{2}I} Using that I get exp(\beta b^{\dagger}-\beta^*b)=e^{\beta b^{\dagger}}e^{-\beta^*b}e^{-\frac{1}{2}|\beta|^2I}. So...

I ran into this kind of expression for a sum that appears in the theory of 1-dimensional Ising spin chains ##\displaystyle\sum\limits_{m=0}^{N-1}\frac{2(N-1)!}{(N-m-1)!m!}e^{-J(2m-N+1)/kT} = \frac{2e^{2J/kT-J(1-N)/kT}\left(e^{-2J/kT}(1+e^{2J/kT})\right)^N}{1+e^{2J/kT}}## where the ##k## is the...

I am confused as to why the force for T1 in the attached problem is doubled. T1 = 4000 in-lb

Hello everyone. First off, I'm sorry if this post is excessively long, but after tackling this for so many hours I've decided I could use some help, and I need to show everything I did to express exactly what I wish to do. Also, to be clear, this post deals with integration by substitution. Now...

Yeah, not sure what to do

Picture of gondola: Formulae: Initially, I used the equation: I=mr^2 I=(6000)x(3)^2 T=54,000kgm^2 [SIZE=16px][FONT=Noto Sans](but apparently this is incorrect) [SIZE=16px][FONT=Noto Sans]So, basically, I don't know which formula would suit best for the gondola (the picture above). I would...

Well what I did was first use the inverse Fourier transform: $$u(x,t)=\frac{1}{2\pi }\int_{-\infty }^{\infty }\tilde{u}(\xi ,t)e^{-i\xi x}d\xi$$ I substitute the equation that was given to me by obtaining:$$u(x,t)=\frac{1}{2\pi }\left \{ \int_{-\infty }^{\infty}\tilde{f}(\xi)cos(c\xi...

The Swing Weight of a golfclub = m * (r - 14) m = mass of the club in grams r = distance from the top of the shaft to the center of mass of the club in inches 6050 equals the swing weight D-0 But the formula for the angular acceleration of any object spinning around an axis is: ωdot = τ / I In...

The Kloss formula (from Dr. Max Kloss) is apparently widely used in Europe and Russia to approximate the relation between slip and motor torque in a squirrel cage induction motor, but I've never seen it in an American paper or book. Does anyone have a source citation for this?

The result of h from my calculations is equal to about 162321138 when it should be about 400km or 400000m and I don't why.

$$W = - \int _ { a } ^ { b } \vec { F } \cdot d \vec { r }$$ ( The Force here is referring to the applied force, When moving a positive charge towards another positive charge(stationary) / field In this formula why there is a negative sign in the formula? I am not asking the sign of the total...

I have problems deriving a formula in a paper I'm reading for a project. The paper is about putting a number of waveplates in series rotated relatively to each other to form a tuneable broadband waveplate. For the i-th waveplate the jones matrix is given by: $$ J_{i}(\delta_i, \Theta_i)=...

Hi, i have one big problem with this simple formula, i tried many ways and combinations, but nothing worked how i wanted it. Let's assume we have a distance, let's say it's 100000 units of any type, could be virtual since i am trying to program a 3d physics engine. The object pass that...

I want to understand very deeply the meaning of the work integral formula: \int m\frac{d\bar{v}}{dt}d\bar{l} It is not enough for me to know that it was defined in this way, I want to know why it was defined in this way. To start, what is the physical meaning of m\frac{d\bar{v}}{dt}d\bar{l}...