Elementary Definition and 558 Threads

Homework Statement Let G be a group, and H a subgroup of G. Let a and b denote elements of G. Prove the following: 1. ##Ha = Hb## iff ##ab^{-1} \epsilon H##. Homework Equations Let ##e_H## be the identity element of H. The Attempt at a Solution Proof: <= Suppose ##ab^{-1} \epsilon H##. Then...

What causes an elementary particle to "decay" into other elementary particles? And where do these particles come from if they were not part of the original particle?

Homework Statement All context is given here. I am trying to understand a few things about what Morin is doing. 1) How is proving that f(x) is a linear function, which I understand the proof of, relevant to the claim that the torques at the left end cancel? Also, the introduction of the...

To my understanding, a matrix is just a way of representing a system of equations in an organized format. So for example, if we have some system of equations, we can get them into standard form, and translate them into what's known as an augmented matrix. This is similar to using synthetic...

The question is simply posed as " identity the variables as discrete or continuous. 1) Mark of a student in an examination. 2) Family income." What I think: 1) There must be a minimum gap between two possible consecutive marks that the examiner can assign. Eg. Suppose that there are N students...

For example, do electrons, atoms etc. experience gravity? Is this proved by experiment?

Helo, given ##f:R^n\rightarrow R^m## and ##g:R^m\rightarrow R^e## both class ##C^m##. Is the composition ##g\circ f## of class ##C^m## ?.

Homework Statement Lets say you role a single honest dice 12 times. Where succes is either if the die shows 4 og 1 eye. My question is what is the probability of sucess or failure? Homework EquationsThe Attempt at a Solution Is it binomial or conditional probability?

<Moderator's note: Moved from a technical forum and thus no template.> I'm not sure how they got the extra (1/2)mv^2? My question is shown using pink font in the image below as well as my attempt.

My textbook states: "The magnitude of charge of the electron or proton is a natural unit of charge." and then has an explanation that follows. It states, "...The charge on any macroscopic body is always either zero or an integer multiple (negative or positive) of the electron charge." Here is...

My question regards the classic example of trivial vs non-trivial fiber bundles, the 'cylinder' and the 'Mobius band.' I'm using Nakahara's 'Geometry, Topology, and Physics', specifically Example 9.1. Here's the text: Then he says (and this is the bit where he loses me): My questions are: i)...

Hello, So i wonder how elementary particles which are said to have no physical extension on a larger scale are able to form what is known to us as matter? Aka stuff with an observable physical extension.

Homework Statement Calculate the charge on each oil drop and determine the elementary charge on an electron given the following: Voltage (Attached) d (Distance between two charged plates) = 0.10m m (Of the droplet) = 1.57x10^-15 kg g = 9.8 kgm/s^2 Homework Equations q = mg*d / ΔV The Attempt...

Hi all. I'm reviewing my daughter's science homework and I disagree with how things are being presented. I wanted some feedback from everyone here to get a sanity check on my own thinking. The exercise is this: answer whether these properties of matter are either an observable property or a...

I understand that the Standard Model of QFT treats elementary particles like the electron, quark, photon, muon, etc. as point-like objects. But I've also heard that a "point-like particle" is nothing more than an idealization of a particle. Elementary particles can be treated as point-like...

Hello everyone. I'm looking for a book that covers very basic finance stuff, e.g. loans, credit cards, annuities, etc., something on basic accounting like balance sheet would be nice too. Cheers

Could I get recommemdations for textbooks that start by defining cosine and sine using power series and then recover their geometric properties? John Roe's "Elementary Geometry" does that, but it's not in my current university's library.

How do we know the spin of an elementary particle? For example, a fermion has spin 1/2; a photon has spin 1; and even the ficticious graviton has spin 2. How do we know these spins? In other words, how are these spins determined?

I need a better understanding and explanation of how a percussion wave form can move through biological soft tissue. I know that human soft tissue functions microscopically in a fluid environment however I also understand that there are also obstructive forces in the way of a wave moving in a...

Prove that interchange of two rows of a matrix can be accomplished by a finite sequence of elemenatary row operations of the other two types. My proof :- If ##A_k## is to be interchanged by ##A_l## then, ##\displaystyle \begin{align} A_k &\to A_l + A_k \\ A_l &\to - A_l \\ A_l &\to A_k + A_l...

For finding the inverse of a matrix A, we convert the expression A = I A (where I is identity matrix), such that we get I = B A ( here B is inverse of matrix A) by employing elementary row or column operations. But why do these operations work? Why does changing elements of a complete row by...

Do elementary particles have inertial mass in the same way composite objects have? If yes, does it have an impact on the motion or on the forces that act on them?

you know all the things that you are supposed to study before algebra . any good book suggestions ? :nb)

Gluons are often depicted as fundamental particles in the Standard Model. But in looking at their mechanism, it seems they are not really fundamental particles in the sense that they are fundamental, indivisible, building blocks. They are mesons- a composite quark-antiquark pair, where their...

Everything in the universe that has a beginning seems to also have an end. Stars, galaxies, molecules, atoms. But what about elementary particles? In case of heat death would it become a uniform quark soup?

Hi If I have this matrix: \begin{array}{cc}0&1\\1&0\end{array} and I want to find its eigenvectors and eigenvalues, I can try it using the definition of an eigenvector which is: A x = λ x , where x are the eigenvectors But if I try this directly I fail to get the right answer, for example...

Hi, I'm not sure if this idea is something old that's been discussed to death or something I'm not formulating right, but i can't find anything online like what I would expect to. What I mean, is a list or rather a table of all possible elementary particle transformations and couplings from...

The net flux over a closed surface is: Flux = The surface integral of the field E = charge / permitivity in space (Gauss law) The permitivity in space is: 8.85 10-12 Coulombs2/N m 2 So I understand the units of Flux are: Newton meter2/Coulombs Is this correct? I don't understand why in a...

The sum of the $k$ th power of n variables $\sum_{i=1}^{i=n} x_i^k$ is a symmetric polynomial, so it can be written as a sum of the elementary symmetric polynomials. I do know about the Newton's identities, but just with the algorithm of proving the symmetric function theorem, what should we do...

Relativity, Elementary Particles and Black Holes by Thorne & 't Hooft Any idea what this book is and why it is unavailable? Is it a popular science book? I did not know that Thorne and 't Hooft co-authored a book.

Homework Statement Find if a molecule is chiral or not. It is 2-chloropentane Homework Equations IF the mirror image is superimposable to the molecule it is not chiral. The Attempt at a Solution Well I wrote the structural formula in 2D and I thought it was not chiral.(bottom ) But the book...

Homework Statement To find the period of oscillation of the pendulum and the equation of motion. Homework Equations Conservation of energy. Potential energy in a constant field = mgh. Kinetic energy in polar coordinates with r constant = (1/2) m r2 (dΘ2/dt2) The Attempt at a Solution I won't...

Homework Statement Show that elementary row operations don't affect solutions sets in linear systems Homework Equations - The Attempt at a Solution It's pretty easy to come up with a random linear system and perform ERO on them and showing that solutions are not affected, but is there all...

Hi folks, I just want to check if I understand this. We start the calculation using the electric potential energy, which is a continuous function that for every value of the distance r, tells you the value of the potential energy "spent" to get the system to that state. We use this function...

It is a very simple question. If we have an expression like this one: x + y = 2 And we have to differenciate it, there is an algorithm that tells us how to do it. We have to find the relationship between the differentials of the given functions. To find them we have to substract the...

Can we compute the relativistic velocities of 2 photons or 2 neutrinos ? :))

Homework Statement We measure the temperature with a thermometer and we get these results: 3.3 +- 0.1 ºC 3.5 +- 0.1 ºC 3.6 +- 0.1 ºC What is the temperature? Homework Equations Average = Sum of values/amount of measurementes The Attempt at a Solution Well, I calculate the average and I...

What is the rule on the preservation of rank through an elementary operation? I know that rank can never go up, but is there any direct way to determine that it goes down (either than reducing the matrix down to row-echelon form)? Is there a good source that go into the proofs for properties...

Homework Statement ; I plotted a graph of length against 1/frequency,determined the slope,which was the speed of sound. I got stucked in the (b) part,when asked to deduce the end correction from the graph drawn.[/B]Homework EquationsThe Attempt at a Solution ; I attempted using the formula end...

The EM wave and the photon have two degrees of freedom. Their polarization directions and spin states, respectively. But they move in space, too. I mean light has the freedom to go in all directions in space. Like a macroscopic ball in 3-D space, which can go all three directions, if there are...

#1. How many classrooms would be necessary to hold 1,000,000 inflated balloons? (Assume one balloon is about 1 ft3 and a typical classroom is about 30 ft × 45 ft × 15 ft. Round your answer to the nearest number of classrooms.) #2. Approximately how high would a stack of 1 million \$1 bills be...

I was reading this article on Wikipedia about single phase generators and the operation of a basic generator, and I'm having a very difficult time understanding what is meant by cutting lines of force and how the rotating armature being perpendicular to the field cuts zero lines. While when it...

Hello, I hope this is not a stupid question as I am not a physicist. But I was curious about how contenders for the so-called Theory of Everything view the shape of the elementary particles. I know that the basic idea of string theory is related to the shape of elementary particles as one...

According to textbook, elementary reactions have an order of reaction equal to the summation of the stoichiometric coefficients. why is this so? And there is another problem, we can balance an equation in different ways and get different stoichiometric coefficient sets, for rates, which set is...

Homework Statement Suppose A⊂B⊂C. What is A/B, A/C, and A∪B Homework EquationsThe Attempt at a Solution This isn't really a homework question, I am just trying to get some exposure to discrete math before I take it in the fall. The set differences A/B and A/C are both empty sets and the 'or'...

Hello there. I'm attending an introductory course in particle physics. We're supposed to know how to draw first-order tree level Feynman diagrams for simple reactions. I've been struggling to understand the method I should follow in order to correctly draw them. As I understand it now, we can...

Homework Statement Homework Equations sum of torques = 0 The Attempt at a Solution So I tried to put the torques into the equation: Sum torques = mgL - T *sin(theta) * (L-x) = 0. Solving for the T gave me [mgL]/[ (L-x) * sin(theta) ]. This is not an option in the answers. Could anyone...

Homework Statement . Disprove the following statement: There exists integers a, b, c, none divisible by 7, such that 7|a^3 + b^3 + c^3 Homework EquationsThe Attempt at a Solution if 7|a^3 + b^3 + c^3, then a^3 + b^3 + c^3 is congruent to 0(mod 7) if a,b,c are none divisible by 7 then I just...

Homework Statement Disprove the following: There exists a polynomial f(x) with integer coefficients such that f(1) is even and f(3) is odd. Homework EquationsThe Attempt at a Solution It's a little bit intuitive. Proof 1 and 3 have the same parity. They are both odd so if(odd)=odd then...

Homework Statement Proof 2/5*(2^0.5)-1/7 is irrational Homework EquationsThe Attempt at a Solution I did this by splitting the expression and setting contradictions 2/5->rational 2^0.5->irrational Proof first rational times irrational is irrational Proof by contradiction Assume the product...