Relation Definition and 1000 Threads

Hey! :o Let $K$ be a field. Suppose that there is an element $u\in K$ such that $u^2+1=0$. Show that there is no order relation on $K$ that would make $K$ an ordered field. We have to show that no relation $<$ can exist that satisfies the order axioms, i.e.: Only one of $a < b$, $a = b$, or...

Imagine a Universe where the Hubble parameter is truly a constant, in both space and time. How much smaller would such a Universe be 14 billion years ago compared to today? Using the Hubble parameter in terms of scale factor: ##H(t) = \frac{\dot{a}}{a}## leads to the differential equation...

I've tried to attempt the first part of the problem(spent over an hour on this) as second part could be easily optained with some calculus ,I asked my friend but alas nobody could conjure the solution to this dangerous trigonometric spell. It was just pages and pages of concoction of...

Homework Statement: spin dephasing time Homework Equations: spin relaxation time Hello, i have seen the next equation that relates the spin dephasing time of an ensemble of électrons T2* with the spin relaxation of a single electron T2, and I would like to know how it was deduced/proposed...

1. If a gas is kept at constant pressure of 1 atm & the temp. is raised upto the saturation temprature ( 99.97 C ) and just when Tsat is attained the heat transfer is stopped ( Hin & Hout both are 0 , adiabatic conditions ) . Now # If the adiabatic condition is maintained , then on...

Is E the correct answer because I think angular velocity is independent of mass distribution of the object? Thanks

I figured out that the spring constant is inversely proportional to the natural length, but there’s still an unknown change in a quantity( most likely extension).

Dear Experts, I have read from various sources that the temperature of a gas is related to the "average translational kinetic energy" of a molecule of gas. When there are molecules that support motion other than translational ,which may also have rotational and vibrational motion, How does those...

What relation exists between Bohm's Implicate-Explicate order and De Broglie-Bohm interpretation? If any relation exists at all...

Hello, I am a civil engineer and have been working on concrete creep phenomenon for several years now. After reviewing a large amount of literature on related topics throughout this time, some interesting observations have emerged, and they have formed the idea that the material creep mechanism...

(I'm 16 and german so sorry if my English is a little off) First off, I want to say that the purpose of this post is not to brag about IQ or some other bs like that. So when I was about 7 years old I took an IQ-Test because I was bored of school and another one when I was 12, both at...

Hi When I read the following article: http://nopr.niscair.res.in/bitstream/123456789/14183/1/IJPAP%2050%286%29%20405-410.pdf I tried to convert the value of the conductivity for saline in 500 MHz. At the article, they present the conductivity as ε'' = 70. Which ε'' is the imaginary part of...

Starting from this post, we are able to define the concept of (proper) acceleration or rotation without any reference to something else About this definition which is the physical meaning of gyroscopes axes pointing in three mutually orthogonal spacelike directions ? In other words, from a...

I have a problem that i cannot solve despite my best efforts. I do realize not all information here is relevant, but i still included it so you could get the full picture. Imagining we have a cylinder that is filled with dry air (normal air without water vapor) that has a fixed volume of 8,5...

Mentor Note -- Thread moved from the technical forums, so no Homework Template is shown. So, we've conducted an experiment on resistors in a circuit. The theoretical calculation was based of on E-24 series color band table and the measured resistance of the resistor was measured by a meter...

I began by taking E = mc^2 and E = hf , where h is Planck's constant, and then rewrote E as 1/2mv^2. I rewrote f as c / λ, which made hf become h*c / λ. I then set this expression equal to the Kinetic Energy equation 1/2mv^2, which gave me: 1/2mv^2 = h*c / λ I then replaced c on the...

I have no idea how this dispersion relation was deduced, and also what's the meaning of including plus and minus in the formula.

I tried making B vector in direction of D vector with a minus sign and after doing so I got the answer C vector - D vector= -A vector. But it's given as incorrect. I don't know why. Please explain how other options are correct.

I understand that the work done is Change of Energy. W = ∫xixf F dx = ΔEThe force is gradient of potential energy F = -∇U (For conservative forces of course) from here, we can say that change of potential energy is W: ΔU = -W but also ΔU = -W = ΔE I'm little bit lost here.. Can you help me...

Can someone please explain what the tilde represents? We have had no info on this to date. I know it has to do with an equivalence relation but not sure what it represents on its own as in part (a) of the attached. Just want to make sure I'm clear. Thanks!

I'm trying yo verify the relation \begin{equation} [D_{\mu},D_{\nu}]\Phi=F_{\mu\nu}\Phi, \end{equation} where the scalar field is valued in the lie algebra of a Yang-Mills theory. Here, \begin{equation} D_{\mu}=\partial_{\mu} + [A_{\mu},\Phi], \end{equation} and \begin{equation}...

My simplistic derivation below for a Class A amplifier shows that an AC signal at the input produces DC, fundamental, and 2nd harmonic terms at the output. This seems to contradict most the information I have found on this - which just states that the output is sinusoidal and of the same...

It is common to write e.g photon two point function in terms of manifest transverse and longitudinal form factors with lorentz structure factored out, e.g $$\Pi^{\mu \nu} = (g^{\mu \nu} - q^{\mu} q^{\nu}/q^2)T_T + q^{\mu} q^{\nu}T_L,$$ where mu and nu are polarisation indices. How do I relate...

Homework Statement Prove that the sets ##(S_{\mu\nu})_L## and ##(S_{kl})_R##, where $$ \left( S _ { k \ell } \right) _ { L } = \frac { 1 } { 2 } \varepsilon _ { j k \ell } \sigma _ { j } = \left( S _ { k \ell } \right) _ { R } \quad\text{and}\quad \left( S _ { 0 k } \right) _ { L } = \frac {...

Homework Statement I'm suppose to find the # of ways to climb n stairs if a person can take 1 stair or 2 stairs at a time. The question is: " Find a recurrence relation for the number of ways to climb n stairs if the person climbing the stairs can take one stair or two stairs at a time."...

Hi, my teacher showed us how we can derive de relation between spectral radiance and density of cavity (of a black hole), but I have a doubt. This is the equation of the energy that are coming from definited directions by the intervals of angles θ and Φ with frequency in a determined interval...

<< Mentor Note -- thread moved from the Introductions forum to the technical forums >>[/color] Hello there, This is my first post, I find myself often wondering about the universe and how it works, and there are a couple of things I just can't wrap my head around. According to wikipedia the...

1)* What are sine and cosine functions called in relation to Pi? 2) What is the exponential function called in relation to cosine and sine functions? 3) What are the other smooth, continual nested (or iterative) root functions (that are similar to sine and cosine) called in relation to...

Chemical potential is defined as the change in energy due to change in the number of particles in a system. Let we have a system which is defined by the following Hamiltonian: $$H = -t \sum_i^L c_i^\dagger c_{i+1} + V\sum_i^L n_i n_{i+1} -\mu \sum_i^L n_i$$ where ##c^\dagger (c)## are creation...

Looking into the infinitesimal view of rotations from Lie, I noticed that the vector cross product can be written in terms of the generators of the rotation group SO(3). For example: $$\vec{\mathbf{A}} \times \vec{\mathbf{B}} = (A^T \cdot J_x \cdot B) \>\> \hat{i} + (A^T \cdot J_y \cdot B)...

Homework Statement The capacitance of a spherical condenser is 1uF. If the spacing between the two spheres is 1mm, then what is the radius of the outer sphere Homework Equations [/B] C = 4 pi Epsilon * ab/b-a (for a spherical capacitor) The Attempt at a Solution Given C = 1uF (u = 10^-6) b-a...

As per my intro post, I don’t consider myself to have any science background beyond high school education. In a philosophy thread about time on City-Data Forum, where most of the entries are just general unscientific musings, I saw the following post: “Time is a distance in spacetime: v =x/t...

Homework Statement Ql: Which sound wave will have its crests farther apart from each other - a wave with frequency 100 Hz or a wave with frequency 500 Hz? Homework Equations Frequency= 1/ periodic time The Attempt at a Solution I did it like that: I just found the periodic time for each...

Hi everyone! I'm currently strudying some astrophysical equation of states, some stuff about Fermi's gas and I'm kinda confused about the relation between the energy density and the mass density, $$ \frac{\epsilon}{c^2}=\rho. $$ I don't get why they do not use whole $$...

The Clausius-Clapeyron formula is given by \frac{d P}{d T} = \frac{L}{T \Delta V} where P and T are the pressure and temperature at the boiling point, respectively, and L is the latent heat per mole at the boiling point, and \Delta V is the change in the volume per mole between the gas and...

Homework Statement Theorem: If ##X## is a topological space, each path component of ##X## lies in a component of ##X##. If ##X## is locally path connected, then the components and the path components of ##X## are the same. I need help locating errors in my proof. Please help. Homework...

Homework Statement How to apply constraints in the system to get a relationship between the displacements of block of mass m and pulley of mass M.? Homework Equations ∑T.a= 0 The Attempt at a Solution Assuming tension in both strings to be T . -T × a1 ( for the block) + 2T × a2 ( for the...

When learning about chirality I was very surprised to find that for QED and QCD the decay modes that would produce 2 particles with the same chirality had a Matrix Element of 0, which I took to mean that angular momentum was being conserved. Even the W only decay into RH antiparticles and LH...

Dear all, I'm within my Ph.D. studies in laser engineering and most of the details are rather new to me. Working on short pulse systems, my advisor told me some times about the relation of the output coupler transmissivity and the outcoupled pulse length, but more as a rule of thumb. According...

Homework Statement \sqrt{x-2} = 3 -2\sqrt x Homework EquationsThe Attempt at a Solution Lang says there is no number but i found x = 2.023932257 to work when plugged into a ti84 calculator. Am I wrong somehow? If not, can anyone tell me a book that teaches all of the same material as langs...

Let S = {1,2,5,6 } Define a relation R on S of at least four order pairs, as (a,b)  R iff a*b is even (i.e. a multiply by b is even)

Q: Let S = {1,2,5,6 } Define a relation R on S of at least four order pairs, as (a,b)  R iff a*b is Q: Let S = {1,2,5,6 } Define a relation R on S of at least four order pairs, as (a,b)  R iff a*b is even (i.e. a multiply by b is even)

I'm trying to understand the following derivation. Starting with the one-dimensional equation for a traveling wave ##u = u_0 \exp{[j(\omega t - \beta z)]}## the goal is to derive the phase relation between strain and velocity. The author first derives the relationship between strain and particle...

Homework Statement A vector r has length 21 and direction ratio's 2,-3,6. The direction cosines of r, given that r makes an obtuse angle with x-axis is given by? Homework Equations l/a = m/b =n/c ...(1) (l,m,n are direction cosines, a,b,c are direction ratios l^2 + m^2 + n^2=1...(2) The...

Homework Statement Suppose ##R## and ##S## are relations on a set ##A##. If ##R## and ##S## are transitive, is ##R \cup S## transitive? Why? Homework EquationsThe Attempt at a Solution Suppose that ##a## is an arbitrarily but particularly picked element of ##R \cup S##, then $$a \in R \...

I am studying about dielectric materials and their relaxation properties. There are several ranges of electromagnetic frequencies where different material show different kinds of resonance starting from molecular to atomic motions. Based on the frequency dependence of the imaginary part of the...

Homework Statement Show that if ##\left( \Omega f\right) ^* = -\Omega f ^* ## then ##\left< \Omega \right> = 0 ## for any real function f. where ##\Omega## is an operator Homework Equations It's a self test of the completeness relation --Molecular quantum mechanics (Atkins)-- so the equation...

Homework Statement One of the two glass panes in each window is coated with a transparent electrical conductor. Why does this coating improve the window's insulating ability? Select one: a. The transparent conductor is black in the infrared, with a low-temperature emissivity of almost 1. b...

Hi. I'm reading an introductory text that somehow seems to confuse if ##E^2-(cp)^2=const## means that the left side is invariant (under Lorentz transformations) or conserved (doesn't change in time). As far as I understand it, they only prove Lorentz invariance. Are they both true? If so...

Hi. I've read that there's no Newtonian analogue of the energy-momentum relation $$E^2-(pc)^2=(mc^2)^2\enspace .$$ Why doesn't $$E=\frac{p^2}{2m}$$ qualify as such? There's no rest energy in Newtonian physics anyway.