Unity Definition and 125 Threads

I apologize if this is not in the correct section of the forum, but it seems most fitting. In the context of dielectric materials, I am having trouble understanding why in the discussion of the optical properties of magnetized bodies, it is justifiable to assume for light vibrations...

Hi there. I'm wondering if anyone can help. I've got a few past papers I'm working on at the moment and there are a few questions I don't even know where to start with. Here's one: a. Write down the transfer function for a time delay and then evaluate its corresponding frequency response...

Can someone please help a layman understand what this unity means in non-technical language?

[SOLVED] rings with unity Homework Statement Corollary 27.18 (in Farleigh) tells us that every ring with unity contains a subring isomorphic to either Z or some Z_n. Is it possible that a ring with unity may simultaneously contain two subrings isomorphic to Z_n and Z_n with n not equal to m...

all of the electronics textbooks say that you can make a unity gain buffer out of a non inverting amplifier by making R2 = 0 and R1 = infinity. Why does R1 have to be infinite? The TF for a non inverting amp is 1 + r2/r1, so as long as r2 = 0, and R1 should make a unity gain buffer, right...

Over Unity Efficient Pulley? Hi, I have a problem regarding a simple pulley system which seems to have an efficiency of over 100% and I just can't figure out what is going on. Scenario: I have a 5N mass vertically suspended using high tensile flexible steel wire from a simple spring gauge...

Three scientists at the Santa Fe Institute, an interdisciplinary institute in northern New Mexico, took up this question a few years ago and discovered that if you compare elephants to lions to housecats to mice to shrews, you discover that heartbeats vary in a precise mathematical way. The...

Homework Statement I understand how you normalize vectors to unity, but how would you normalize a function to unity? For example, how would you show that the function (2/L)^(1/2) sin(n*pi*x/L) is normalized to unity? You cannot just just take its modulus and set it to one since because x...

what are they exactly?

How do you do these two problems? 1. Find the sum of the 6th roots of unity. 2. Find the product of the 6th roots of unity.

I have an assignment question with a variable capacitor in it and it asks what value of capacitance is necessary to provide "unity power factor overall". This wasnt explained in class, does anyone know what it means?

Homework Statement I need to find the real and imaginary roots of z^4 = -1. The Attempt at a Solution The polar coordinates of -1 are at (-1, pi), (-1, 3pi) etc so if I assume the solutions take the form z = exp[i n theta] then n theta = pi + 2npi This dosen't seem to give the...

I'm having trouble following one step in a proof I'm studying. I'm sure I'm missing something obvious, but I just can't get it to work out (it supposed to be "obvious" which is why they left out the details). Anyway, it's part of a proof showing that if you have a monic polynomial with all...

Does any theory explain all these dualities: Wave/Particle Duality, Space/Time Duality, and Energy/Mass Duality. Does ST or LQG account for all these dualities? What I mean is, can ST or LQG show that these dualities are unified by some deeper physical model? Can any theory show that...

Hi, We are using Varian Unity Inova 500 MHz NMR instrument.When we are taking 31P and 19F spectra we do not use any reference sample as like TMS etc. Our customer says us that they are not interpreting these spectras without reference. Which reference can we use for these spectras and how can...

w_{n} is primitive root of unity of order n, w_{m} is primitive root of unity of order m, all primitve roots of unity of order n are roots of Cyclotomic polynomials phi_{n}(x) which is a minimal polynomial of all primitive roots of unity of order n , similarly, phi_{m}(y) is a minimal...

All right, thanks to everybody's help, I've got the algorithm for determining the nth roots of unity. However, for determining which ones are primitive, I'm still having a little trouble. If n is odd, I can test if (n, k) are coprime. However, for even values of n, it seems that it doesn't...

Does anyone know what a coefficient of order unity is? I'm reading a journal paper and it gives the formula P_{KOZ} \simeq P_1 \left( {\frac{{m_0 + m_1 }}{{m_2 }}} \right)\left( {\frac{{a_2 }}{{a_1 }}} \right)^3 \left( {1 - e_2^2 } \right)^{3/2} and then it says . It's on page 6 of this...

Hello, I got pointed to this forum by OfficeShreder. I have a question I've been puzzling myself over for a while. I am currently trying to implement the "Discrete Weighted Transform". I have reached a step where I need to determine "a primitive Nth root of unity in the appropriate domain"...

Lawmakers oppose political speech, citing "national unity" It seems that a large majority of U.S. lawmakers have become blind to the freedom of political expression - particularly the protection of the unpopular views. It has been repeatedly established in SCOTUS that political descration of...

consider the wave packet psi(x, t=0) = C*exp(i*p0*x/hbar)*exp(-[x]/(2*deltax)) where C is the normalisation constant part a) normalise psi(x) to unity I took Integral from negative infinity to positive infinity of ([psi]^2)dx and got [C]^2 * ( Integral from negative infinity to 0 of...

Prove if a ring has a unity, then it is unique: Here is what I have so far: Proof: Assume there exists a ring R that contains two distinct unity's, call a and b, where a != b. By the definition of a unity, we get ax = xa = x and bx = xb = x for all x != 0 in R. So, ax = xa = bx = xb = x. If...

Q. Fix n>= 1. If the nth roots of 1 are w_0,...,w_(n-1), show that they satisfy: \left( {z - \omega _0 } \right)\left( {z - \omega _1 } \right)...\left( {z - \omega _{n - 1} } \right) = z^n - 1 I tried considering z^n = 1. z^n = e^{i2\pi + 2k\pi i} \Rightarrow z =...

Moller Atomic Hydrogen Generator. Claims to extract zero point energy. http://jlnlabs.imars.com/mahg/tests/mahg2c.htm Lots of neat pics and graphs. Any good science in it?

urgent help needed Can anyone tell me what purpose unity gain buffer amplifiers serve and why do you connect 2 low pass filters of same corner frequency by cascading them using one of these op amp buffers and not directly together. Also can you show me the diagram of this and where the...