Relation Definition and 1000 Threads

What is the relation between sfc vs rpm in diesel engine and why does it happen like that ? what is relation between air flow vs rpm ??

Homework Statement I'm given a recursive sequence with the following initial terms: ##\begin{matrix} f_0(0)=1&&&f_1(0)=0\\ f_0(1)=2&&&f_1(1)=1 \end{matrix}## Now, I'm asked to justify that we have the following recursive relations: ##\begin{cases} f_0(n)=2f_0(n-1)+f_1(n-1)\\...

What is the Decay Width of a particle and how is it related to the particle's lifetime ?

Homework Statement I want to integrate \int_{0}^{a} xsin\frac{\pi x}{a}sin\frac{\pi x}{a}dxHomework Equations I have the orthogonality relation: \int_{0}^{a} sin\frac{n\pi x}{a}sin\frac{m\pi x}{a}dx = \begin{cases} \frac{a}{2} &\mbox{if } n = m; \\ 0 & \mbox{otherwise.} \end{cases} and...

This thread does justice to a question put forth online several times and, as far as I can tell is only answered in part. I believe this question warrants a distinct and succinct answer. What I'm finding online is summarized below, and as one can see... there is something missing. I've been...

Dear Friends, I carried out an experiment of sudden release of oxygen (open nozzle) from an oxygen cylinder used for medical college and hospitals. I found that pressure drops quite rapidly and cylinder surface cools from outside such that water droplets accumulate on its surface. This...

Homework Statement The Attempt at a Solution I know what relations are individually but what do I do to represent the composition of both? Is it some matrix operation? Would I multiply them, but instead of adding I use the boolean sum?

Does atoms in a crystal have energy states like electronic states? it is according to Einstein relation for harmonic oscillator.E=nhw

Hi guys, I was thinking about the relativistic effects a little bit, and I have a question regarding relative simultaneity. Time dilation and length contraction grow as a function of the speed of the observer, and become noticeable and large on speeds close to the speed of light. By this...

We let C be the set of Cauchy sequences in \mathbb{Q} and define a relation \sim on C by (x_i) \sim (y_i) if and only if \lim_{n\to \infty}|x_n - y_n| = 0. Show that \sim is an equivalence relation on C. We were given a hint to use subsequences, but I don't think they are really necessary...

Digging in the wiki, I found this relation between 'arc-functions' and 'arc-functions-hyperbolics" \\ arcsinh(x)= i \arcsin(-ix) \\ arccosh(x)= i \arccos(+ix) \\ arctanh(x)= i \arctan(-ix) https://it.wikipedia.org/wiki/Funzioni_iperboliche#Funzioni_iperboliche_di_argomento_complesso...

First post here. This question has two parts. (1) Connecting the dots between the Impulse-Momentum Theorem and the Law of Conservation of Momentum and (2) Book recommendations for a more theoretical treatment of classical mechanics? (1) Difficulty reconciling the Impulse-Momentum Theorem...

Hi, I have a few questions regarding the experimental outcome of the stern-gerlach experiment. Let's suppose the following setup: We have a magnetic field whose field-lines point towards the positive z axis and the intensity of that field becomes stronger towards the positive z axis, so there...

Homework Statement a.) Is symmetric and transitive, but not reflective: b.) consists of exactly 8 ordered pairs and is symmetric and transitive: The Attempt at a Solution If the question asks me to define some relation, do I need to define some math property like power of some number or...

Under the effect of an electric and magnetic field the momentum in the Hamiltonian becomes the canonical momentum, p-qA where p is the linear momentum and A is the vector potential so H=(1/2m)(p-qA)^2 + qV where V is the scalar potential. I am trying to find [H,(p-qA)]. My main question arises...

Homework Statement Find ##[L_i,L_j]##. Homework Equations [x_i,p_j] = \delta_{ij}i\hbar The Attempt at a Solution [L_i,L_j] = \epsilon_{ijk}\epsilon_{jlm} [x_jp_k,x_lp_m] = \left( \delta_{jl}\delta_{km} - \delta_{jm}\delta_{kl}\right)[x_jp_k,x_lp_m] = [x_jp_k,x_jp_k] - [x_jp_k,p_kx_j] =...

How to solve this question. Please explain step by step.

I asked this question at AskMrPhysics and received no response so...either it's a really stupid idea/question that doesn't deserve to be answered or no one can help me with a response. I'm hoping that someone here will either let me down gently and tell me to stop asking dumb questions or help...

I have a question about the derivation of the formula for relation between Specific Conductance and Equivalent Conductance i.e. Eq. Conductance = k.V where, k= Specific Conductance ,V=Volume in ml Given link explains the derivation...

Hey again! :p Let $f:[0,+ \infty) \to \mathbb{R}$ strictly increasing and continuous at $[0,+\infty), f(0)=a$(I am not sure,if it is $a$,it could also be $0$ (Blush)) and let $\lim_{x \to +\infty} f(x)=+\infty$.The range of $f$ is $[0,+\infty)$ and the inverse function $f^{-1}:[0,+\infty) \to...

[a, a^{+(n)}] = na^{+(n-1)} 1) What's the name of this relation if it has any? 2) I tried to prove this by induction, I started by saying that for n=1, this holds since [a, a^{+}] = 1 (as we all know and as we can all prove) then I assumed it true for (n-1), but I didn't go too far...

Homework Statement Using the Debye dispersion approximation, calculate the heat capacity of a harmonic, monatomic, 1D lattice. Next, find the temperature dependence in the low temperature limit. (Assume that the longitudinal mode has spring constant CL = C, and the two transverse modes both...

We know how to find S_{x} and S_{y} if we used S_{+} and S_{-}, and after finding S_{x} and S_{y}, we can prove that [S_{x}, S_{y}]= i\hbarS_{z} (Equation 1) and [S_{y}, S_{z}]= i\hbarS_{x} (Equation 2) and [S_{z}, S_{x}]= i\hbarS_{y} (Equation 3) but can we, starting from Equations 1...

According to the theory, E= -dv/dx or E.dx = -dv So if both are positive, the potential drop should increase. But as we know, if a positive charge is placed, as the distance from it keeps on increasing, field strength starts decreasing and potential drop should increase But this is...

Hi, It is a well known fact that in an inverse linear problem low condition numbers have low noise amplification and therefore decrease the error. So I wanted to test this: I draw random (skinny) matrices A, calculate y=A*c where c is a known coefficient vector, add some noise and...

Hi, I have a transitive relation and wana build a complete set of pairs that reflect all (direct/indirect) relations among the pairs. Ex.: suppose I have this relation R = { (1,2), (2,3), (3,5), (5,7), (3,4) } I wana to produce this relation R oper R = { (1,2), (1,3), (1,4), (1,5)...

Hi guys, I'm currently working on a project related to Faraday instability, and I of course came across the dispersion relation for capillary-gravity waves, i.e. ω² = tanh(kh)(gk + σk³/ρ) . Now I would need to numerically solve this relation for the wavenumber k as a function of depth h...

Homework Statement Evaluate the following series ∑u(n) for n=1 → \infty in which u(n) is not known explicitly but is given in terms of a recurrence relation. You should stop the summation when u(n) < 10^(-8) u(n+1) = (u(n-1))^2 + (u(n))2 with u(1) = 0.5, u(2) = 0.6 Note 1:The lecturer...

1-If we had a spherical capacitor and the voltage across it is 1000 V, I need to know the charge on every plate, I know 2 ways to solve this either using C=Q/V or V=Q/r * 1/4ε0∏. So, which one should I use, and why? 2-Another thing, according to hyperphysics the formula for the capacitance of...

Hello! I am interested in knowing the existing relation between the ADM Formalism and the Wheeler-deWitt Equation. From the articles and lectures I was read, I understand that ADM formulation is the Hamiltonian formulation of General Relativity at classical level. Then, the Hamiltonian is...

Homework Statement This is not a homework problem, but a topic in a microeconomics book that I am unclear about. My book argues that the set X = {a, b, c, d} of preferences can be (i) transitive but (ii) incomplete. Is it possible for a similar set of preferences to be (i) complete but (ii)...

Problem: Define $a_n=(1^2+2^2+ . . . +n^2)^n$ and $b_n=n^n(n!)^2$. Recall $n!$ is the product of the first n natural numbers. Then, (A)$a_n < b_n$ for all $n > 1$ (B)$a_n > b_n$ for all $n > 1$ (C)$a_n = b_n$ for infinitely many n (D)None of the above Attempt: The given sequence $a_n$ can be...

Hello. Sorry for being annoying, I've posted like three questions today. But I'm studying nuclear chemistry and still somewhat confused regarding the binding energy and mass defect and their relation with the strong nuclear force.. 1) in this Hank Green video... He says that the mass defect...

I need to know the relation of wave function and vertex function of mesons. Any one give me an explanation of them. Are they same? in some journals their expressions are the same and in other papers the wave function expresses as a function of the vertex function of meson. Which one is the...

Homework Statement Let ##\mathbb{R}^2 = \{Q = (a,b) | a,b\in \mathbb{R}\}##. Prove that if ##q_1 = (a_1,b_1)## and ##q_2=(a_2,b_2)## are equivalent, meaning ##a_1^2+b_1^2 = a_2^2 +b_2^2##, then this gives an equivalence relation on ##\mathbb{R}^2##. What is ##[(1,0)]...

i know the relation between these two. with increase in pressure, the viscosity of liquids (expect water] increases while that of gases is practically independent of pressure. The viscosity of water decreases with increase in pressure. i want to know the reason behind this.

The question assumes that there really exists an objective probability such as disposition or propensity that is an extensive property of a state of affairs. Usually the dissipation of a work potential is associated with the mechanical motion of a system, and work potential is the free...

We say on-shell and off-shell mass of quarks. 1) What is the difference on-shell and off-shell mass of quarks. 2) At lab. center of mass frame for lepton particles p2= -m2. Can we apply this equation for quarks. Thank you!

i heard that aeroplanes are an application of benoulis theorem. Can you please explain it to me.

Homework Statement I don't seem to understand the proper intuition behind the electric field intensity potential difference relation? please can anyone explain it with solid intuition and maybe a good analogy...and can anyone give a short analogy about the concept of electric field...

Homework Statement By considering small changes in enthalpy, and using the central equation, derive the Maxwell relation \left (\frac{\partial S}{\partial V} \right )_{T}= \left (\frac{\partial p}{\partial T} \right )_{V} Homework Equations H=U+pV dU=TdS-pdV The Attempt at a...

Hello! I was playing around with a problem and while I was doing it I noticed a similarity between Cv*T=h by using Celcius and not Kelvin. So if I have a compressed liquid at say 50°C, looking up at a property table I find the hf to be 209.34 kJ/kg (the pressure is considered to be...

I boxed the portion of the solution that I am questioning. How come the number of invalid strings is only 3n-1 - an-1 and not 3(3n-1 - an-1) ? As you can see there are three cases (Which are to the right of the black box) In all the three cases, the portion boxed in red is a string...

I am having difficulty knowing which "cases" include in the recurrence equation. My solution to problem in paint document. Cases 1 - 6: All cases contain strings of length n Let ak represent number of bit string of length k with a pair of consecutive 0s. For cases 1 and 2. an-1, k = n-1. 1...

I'm trying to solve a third order recurrence relation but not sure how. I wrote the characterisitc polynomial and factored it into (x-1)^3. Now what?

In Theodore Frankel's book, "The Geometry of Physics", he observes at page 248 that the covariant derivative of a vector field can be written as $$\nabla_X v = e_iX^j (v^i_{,j} + \omega^i_{jk} v^k)= e_i(dv^i(X) + \omega^i_k(X) v^k) = e_i (dv^i + \omega^i_k v^k)(X)$$ where ##\omega^i_k =...

Hello everyone. I'm am looking for some literature (articles or books) containing information about how is the relation between the liquid water pressure (macroscopic thermodynamic quantity) and it's quantum molecular dynamics (collisions, vibrations, etc.). Like: The pressure increase...

We know that the mass of anybody turns to zero as it gains the velocity of light. From Einstein's Mass-Energy relation, E=mc2 so that, m=E/c2 It is clear that mass is directly proportional to energy. For a body to gain light's speed, we have to apply...

A circuit has n switches, all initially off. In order to be able to flip the ith switch, the (i-1)th switch must be on and all earlier switches off. The first switch can always be flipped. Find a recurrence relation for the total number of times the n switches must be flipped to get the nth...

Find the number of ways to arrange three types of flags on an n foot flag pole: red flags (1 foot high), white flags (1 foot high), blue flags (3 feet high) Find a recurrence relation for this number with one condition that there cannot be three 1 foot flags in a row (regardless of their...