Elementary Definition and 558 Threads

I'm a little confused. During Beta(-) radiation, a neutron becomes a proton due to a down quark becoming an up quark. When this happens, a W(-) boson is emitted which almost immediately decays into an electron and an electron antineutrino. A W(+) boson, similarly, is emitted when a down quark...

Homework Statement I am struggling with what seems like a very simple problem from Terrence Tao's Introduction to Measure Theory book (which is available for free online by the way). What I am trying to prove is the following: Give an alternate proof of Lemma 1.1.2(ii) by showing that any two...

Homework Statement the problem is a circuit analysis. I can try to make the circuit but the image i created shows all the resistors and voltage sources. imgurl Find i,v,is,vs Homework Equations \sumloop vi=0 \sumnode ij=0 The Attempt at a Solution I can not make a...

The following question was supposedly given in an admissions test for an elementary school in Hong Kong.

Just refreshing my understanding of measurable cardinals, the first step (more questions may follow, but one step at a time) is to make sure I understand the conditions: one of them is For a (an uncountable) measurable cardinal κ, there exists a non-trivial, 0-1-valued measure μ on P(κ)...

My problem is from Israel Gelfand's Trigonometry textbook. Page 9. Exercise 7: Two points, A and B, are given in the plane. Describe the set of points X such that AX^2+BX^2=AB^2. The attempt at a solution Since problem asked to describe set of points X such that AX^2+BX^2=AB^2, I tried to...

Hi! I've been to the math book listings and there is no such book recommendation on elementary geometry, only the classical geometry of the greeks,I need something that will prepare me for trigonometry can I have suggestions on which book I should use? (Please don't mention Kiselev's Geometry...

Hello everyone, In order to define the eulerian rate deformation tensor, one should first express \dfrac{d}{dt}(\underline{dx}) in gradient velocity terms (denoted \underline{\nabla v} with v equal to the partial time derivative of the geometrical mapping that relates the inital...

how do you find the book "ELEMENTARY ALGEBRA" by Hall and Knight? Is this a good book for a beginner?

I know that if a beam is balanced on a central pivot point with equal weights on either end, the beam will be in equilibrium. If the pivot point were to to be moved to, say, a quarter of the distance from one end, then obviously more weight would be required on the "short" side of the beam to...

Problem 1 Suppose ab=cd, where a, b, c d \in N. Prove that a^{2}+b^{2}+c^{2}+d^{2} is composite. Attempt ab=cd suggests that a=xy, b=zt, c=xz. d=yt. xyzt=xzyt. So (xy)^{2}+(zt)^{2}+(xz)^{2}+(yt)^{2}=x^{2}(y^{2}+z^{2})+t^{2}(z^{2}+y^{2})=(x^{2}+t^{2})(z^{2}+y^{2}) Therefore this is...

Let \zeta(x) be the Zeta function (where, for convenience, x is assumed to be > 1). \zeta(x) = \sum_{k=1}^{\infty}\frac{1}{k^x}Similarly, define the Eta function (alternating Zeta function) by the following series - where again, in this case, we assume x > 1:\eta(x) =...

This is my first time posting anything on the forum so I apologize if I do anything wrong. I have enrolled myself into elementary number theory thinking we would be taught how to do proofs however it is apparently expected that we already know how to do this. And so since I am a beginner at...

Hello all, I was thinking about situations in introductory courses or textbooks where pressure or buoyant forces are suddenly introduced in situations where they become relevant which lead me to think about the consequences of neglected said forces in more elementary problems. I'm curious as...

Hello all, I'm going to begin a PhD program in the fall and likely will be doing research in the world of particle physics. I'm a little rusty on the topic though as my undergrad research experience has been astrophysics, and I did not get a chance to take any classes related to the field other...

I find that in number theory, number theorists (and mathematicians more generally) generally prefer elementary proofs over any other kind of proof. Am I right about this? If so, why is this? Is this something to do with the content of number theory itself? Thanks!

I am trying to self-study some concepts in differential geometry to try to update my knowledge from the old-style index games to something more meaningful. I know that there are many threads that have in some way addressed this, but I am still not understanding it completely. I'm new to this...

We all know that there four fundamental forces in nature, viz. The gravitational force The electromagnetic force The strong nuclear force The weak nuclear force Now also we know that temperature of any system is the average kinetic energy possessed by the particles of the system Now...

Its was proven that one particle can be in two places at once. I found that to be confusing because matter acts in a wave like manner through the transfer of energy. My hypothesis is that the transfer of energy moves in waves effecting more than one particle at once. In light the disperse of...

Hey, does anyone know of a proof that the sinc function Si(x) = \int \frac{\sin x}{x} \, dx is not elementary? Or is it not proven? Thanks

Is the unimolecular elementary step generally more quicker than a two body collision. Also technically how are they possible, if a reaction only occurs when a collision takes place, and since it is one body what can it possibly collide with.

Homework Statement A sinusoidal wave of frequency 50 Hz travels along a string at velocity of 28 m/s. At a given instant the displacement and velocity of a certain point in the string are 24 mm and 1.2 m/s respectively. Taking the certain point and given instant to be x=0, t=0, derive the...

The Maclaurin series expansion for ##(1+z)^\alpha## is as follows: $$(1+z)^\alpha = 1 + \sum_{n=0}^\infty \binom{\alpha}{n}z^n$$ with $$|z|<1$$ What I don't understand is why is ##|z|<1##?

Dummit and Foote (D&F), Ch15, Section 15.1, Exercise 15 reads as follows: ---------------------------------------------------------------------------------------------------- If k = \mathbb{F}_2 and V = \{ (0,0), (1,1) \} \subset \mathbb{A}^2 , show that \mathcal{I} (V) is the...

Dummit and Foote (D&F), Ch15, Section 15.1, Exercise 15 reads as follows: ---------------------------------------------------------------------------------------------------- If k = \mathbb{F}_2 and V = \{ (0,0), (1,1) \} \subset \mathbb{A}^2 , show that \mathcal{I} (V) is the...

(question inspired by a thread on the cosmology subforum) Is there an intuitively simple theoretical reason for the existence of elementary units of charge but not of mass? The parallels between Gauss's law for EM and gravity, the inverse-square law for both, the fact that energy is...

Homework Statement Prove that replacing one equation in a system of linear equations by a non-zero multiple of itself does not change the solution of the system. The Attempt at a Solution I'm still relatively new to proofs, so this is what I have come up with: Let S be a system of...

Homework Statement Two masses of equal mass m are attached by a single spring of sprint constant k, what is the resonant frequency of the system? The Attempt at a Solution I'm not sure how correct it is to treat the two masses on either end as single mass 2m. 2m\ddot{x}=-kx...

1. $|\frac{i(2+i)^3}{(1-i)^2}|$ Is there any way to complete this without expanding the numerator?2. what is the argument of $ -2\sqrt{3}-2i$ I got $r=4$ then $\cos\theta_1 $ $= \frac{-2}{\sqrt{3}{4}}$ and $-2=4\sin\theta_2$ $\theta_1 = \pi - \frac{\pi}{6} = 5\frac{\pi}{6}$ and $\theta_2 =...

The Unruh effect is the fact that an accelerated observer doesn't see vacuum, but a thermal bath of particles with an effective temperature proportional the proper acceleration. The explanations that I've seen for this effect seem very mysterious to me. It seems to involve the fact that the...

Homework Statement A particle moving in one dimensions is in the state |\psi\rangle with position-space wave function \psi(x) = Ae^{−\lambda|x|} where A, λ are positive real constants. a)Normalize the wavefunction. b)Determine the expectation values of x and x^2 Homework Equations...

Greetings, I think this will be a very quick thread. I am new to using Feynman diagrams, and have run into something that I find puzzling. The lowest-order Coulomb interaction Feynman diagram is (image from Wikipedia Moller Scattering article)...

Do Elementary Particles "Jiggle" Like Atoms? Like the question says, if atoms jiggle about because their constituent sub-atomic particles are moving within the atom, is this movement simple orbital/linear displacement or is there also a "jiggling" to it? If there is a "jiggle" or vibration...

Homework Statement OK, a PDE: $$a\frac{\partial u}{\partial t} + b \frac{\partial u}{\partial x} = u$$ we want the general solution. 2. The attempt at a solution So, I'll set up a couple of equations thus: r = m11x + m21t s = m12x + m22t (We have a nice matrix of m here if we...

My question relates to the very origin of the elementary particles. I understand that the Higgs field breaks the mass symmetry of the elementary particles and that the Higgs field-based mass value for each particle is dependent upon the strength of interaction between each elementary particle...

Homework Statement ## \displaystyle \int \frac{dx}{(x^{2}+a^{2})^{3/2}} ## Homework Equations The Attempt at a Solution A substitution does not seem to work. I know that a closed form solution exists however, just curious if it can be done by the standard techniques usually taught...

Homework Statement Surgeons often use a type of "binocular microscope" [that's a word by word translation]. It consists of a 50mm lens close to the patient and a -15mm right in front of the doctor's eye. The distance between the patient and the 50 mm lens is 400mm and the negative lens is...

I could probably find the answer to this problem easily by a quick google search, but I don't want to spoil it. Instead, could someone give me a hint in the right direction? Ok, so it seems to me like a contradiction would work here. It seems like directly proving the existence of an...

Homework Statement http://www.physics.ohio-state.edu/undergrad/greStuff/Problems_2009/Mechanics_4.pdf exercise 83 Homework Equations Conservation of energy?! The Attempt at a Solution Well what I think is that if there is no friction, whenever the initial velocity is >0, the...

I came across the interesting Kummer's Theorem .Does anybody know an elementary proof ?

That's my first question. 2. If that's true, why do they have different masses? 3.Since everything is made of point particles, do the fundamental forces give the actual "size" to the particles? 4.Lastly, if they are all points, is this why matter can be compressed all the way into a...

Hi, I am new to this forum, and to physics in general. I have been reading the basics of General Relativity and Quantum Mechanics but am yet to learn the mathematical side. I am just trying to wrap my head around particle-wave duality and specifically, the wave quantifying of elementary...

Homework Statement 3\sqrt{x}-\sqrt{x+3}>1 Homework Equations The Attempt at a Solution As obvious from the given inequality, x must be greater than zero. Rearranging and squaring both the sides, 9x>1+x+3+2\sqrt{x+3} \Rightarrow 4x-2>\sqrt{x+3} Squaring again, 16x^2+4-16x>x+3...

Hi, I am quite naive in Particle Physics, and I have a question that Can Elementary Particles be related with irreducible representation? Could we say scalar, vector, and spinor are irreducible representation of SO(3)? Thanks a lot! I also wish I could have some reference on...

In the late 80’s and early 90’s there was the idea of ‘calculus reform’ and some emphasis and syllabus changed. The order of doing things in calculus also changed with the advantage of technology. Similarly in linear algebra there was a linear algebra curriculum study group which produced some...

In the late 80’s and early 90’s there was the idea of ‘calculus reform’ and some emphasis and syllabus changed. The order of doing things also changed in calculus with the advantage of technology. Similarly in linear algebra there was a linear algebra curriculum study group which produced some...

I have to teach a course in elementary number theory next academic year. What topics should be included on a first course in this area? What is best order of doing things? The students have a minimum background in proof but this is a second year undergraduate module. I am looking for...

When one says that <\varphi|\psi> is the probability that \psi collapses to \varphi, does this "collapse" necessarily involve a measurement (so that one would have to find the implicit Hamiltonian)? Or does this just exist as part of the evolution of the wave function, perhaps the vacuum energy...

Author: Barrett O'Neill Title: Elementary Differential Geometry Amazon Link: https://www.amazon.com/dp/0120887355/?tag=pfamazon01-20 Prerequisities: Contents:

i) If a wall breaks when it gets hit by a cannonball, did the wall exert an equal and opposite force on the cannonball? ii) Would the force exerted by the cannonball on the wall only be the amount that was needed to break it? iii) Hypothetically, is it possible for the wall to break but...