Elementary Definition and 558 Threads

Are there simple analogues of AdS/CFT duality that are understandable without any knowledge of string theory?

Homework Statement Some Transistors of two different kinds (say N and P) are stored in two boxes. You know that there are 6 N's in one box and that 2 N's and 3 P's got mixed in the other box, but you do not know which box is which. You select a box and a transistor from it at random and find...

Sir, I have a tremendous interest in quantum mechanics but I am just an high school graduate, and i don't know anything much in depth, especially the mathematical part. I have just done the basics of calculus but i want to study about quantum mechanics. Basically, i am completely clueless as...

I'd appreciate it if anyone could help me clear up some concepts, the last chapter of one of my math courses is a (highly mysterious) introduction to Hilbert spaces (very very basic): What does it mean for a function to be "square-summable"? Has something to do with the scalar product in...

I'd be grateful to be pointed to some elementary information on the biological shielding in nuclear submarines. (Searching the web did not turn up what I was seeking). I understand that the reactor is somewhere near the centre of the sub, with shielding bulkheads fore and aft of the...

Hello. I am looking for learning materials for the field of number theory. I took a class this semester in number theory and the topic fascinated me, but I don't feel like I learned that much. I am a mathematics minor so I have a very strong background in basic math, abstract/linear algebra, and...

Is there any experimental verification for the fact that elementary particles are point like and have no extension in space or its just an assumption? thanks

Say I am integrating some algebraic function with respect to a variable q. There is also an exp( iq ) in the integral as a factor. There are poles when q takes a certian value as it is in the denominator as q - A, so pole at q = A.I know the poles are in the upper left plane, and lower right ...

Hi Again: Just curious: I know that, given a system of linear equations, ERO's (scaling both sides of an equation, exchanging/swapping rows and adding a multiple of a row to another row) preserve solutions, i.e., if x is a solution to Ax=b, then swapping rows will preserve x as a...

Hello! I asked this question in Physics section but no one replies so i think it is more a chem question. When it is given that the interacting energy between 2 ions in a crystal is U, is the binding energy W(for 1 atom) equal to U? i.e. U=W? I think it's a reasonable guess;but i also...

What would happen if an electron were accelerated in an attempt to collide with an accelerated proton in a particle accelerator? What would happen in a collision between an electron and a neutron?

Hi, Everyone: A question about finding the inverse of a matrix M using elementary row operations (ERO's) E_k (where E_k is either a row-exchange, a scaling of a row by k, or adding the multiple of one row to another row ) to do row-reduction in reduced-row-echelon format, to end...

Suppose I have a 2x2 Hamiltonian describing a conducting channel, as a black box. H_{Rashba}=\sigma_y k_x - \sigma_x k_y and also suppose I have an incident 2x1 wavefunction with up and down spin components, to this black box. What I am trying to do is to write a 2x2 reflection (or...

Can someone give a list of all the pure numbers that relate to elementary particles (such as the fine-structure constant)? How many such numbers are there? Is it likely that more will be discovered? Thanks

While re-reading James Jean's The Mysterious Universe I came across his statement that "the capacity for tying knots is limited to space of three dimensions", in the context of sailor's knots. I'm no mathematician, but understand that mathematical folk regard a knot more generally as a...

"In particle physics, an elementary particle or fundamental particle is a particle believed not to have substructure; that is, it is believed not to be made up of smaller particles." -Wikipedia How does someone ever possibly (LOGICALLY) conclude that a particle is not made up of smaller...

Suppose I have some sinusoidal electromagnetic waves, plane-shaped, moving in a vacuum with frequency f and wavelength \lambda . I want to consider the energy content of a certain volume of space through which they are passing. Let's say it is a cube with side lengths \Delta x where...

Homework Statement I'm supposed to develop an hypothesis about a certain aspect of a snail's behavior and then devise an experiment that would prove or disprove that hypothesis.The Attempt at a Solution Hypothesis: Snails will avoid traveling on hot surfaces. Experiment: Place a snail on a...

I stumbled across this in an obituary article for its author: Prof Chike Obi (1921-2008), reputed to be the first Sub-Saharan African to hold a doctorate in Maths (Cambridge, 1947), later at MIT, returned to Nigeria (Univ of Ibadan) in 1959. He claimed to have discovered an elementary proof...

Homework Statement I can't solve the following problems: 38) Solve y' =y + et from yo =0 by Method 2, where the deposit eT at time T is multiplied by et-T. The total output at time t is y(t) = (Integral)(eT * et-TdT) (The integral goes from 0 to t). Substitute back to check y' =y + et...

I'm sure this integral is easy, but could someone perhaps show the working of: \int e^{i2t} dt between t and 0. I've tried it with trigonometric identities and keep getting lost! Cheers!

I am about to start a mathematics degree and one of the textbooks I have been advised to get is Elementary Linear Algebra with Applications (10th edition) by Howard Anton & Chris Rorres. This book costs about $130 however I have found the 9th edition of the same book for far less. If anyone is...

Homework Statement Prove that ||a|-|b||\leq |a-b| for all a,b in the reals Homework Equations I know we have to use the triangle inequality, which states: |a+b|\leq |a|+|b|. Also, we proved in another problem that |b|\leq a iff -a\leqb\leqa The Attempt at a Solution Using the...

Please teach me this: I wonder whether there exist only quarks(6 quarks) and leptons being really elementary particles. Or there are many another types of particles? Thank you in advance.

Hi, I had a question about irreducible representations and elementary particles... Namely, I've been told by teachers and read in a few texts that particles ARE irreducible representations, and I have never been able to wrap my mind around what that means. Please keep in mind that I am no...

Do you sometimes find learning from more elementary textbooks "stultifying?" And does this sometimes result in exceptionally slow learning when you read the more elementary textbooks, when you feel like you could learn much faster through more advanced textbooks? I'm feeling this effect with...

I'm reading Charles G. Cullens' "Matrices and Linear Transformations" and have a question about one of the examples. Don't worry- I'm self-studying this. Homework Statement This is the section about matrix equivalence- both row and column equivalence. It says "Theorem 1.30 If a sequence of...

Hi, I've received a new accelerometer with a scale factor declared in datasheet as: 800 mV/g @ 1.5g. I googled and searched the forum but still can't fully be sure I understand the accelerometer and its functioning, so please correct me where I'm wrong: One thing that very helped me to get...

Homework Statement I've posted it many months ago.. now i manage to get the answer but I am wondering if anyone has a shorter solution? The question goes like this(without a single omission): Let f(x)=a_0+a_1x+a_2x^2+...+a_nx^n ,where a_0,a_1,a_2,...,a_n are nonnegative integers. If f(1)=8...

So i am almost 3/4 through elementary analysis but i seem to be unable to comprehend the basic definition of convergence of series this is how the defn goes. A sequence (sn) is said to converge to a real number s provided that for each ε > 0 there exists a number N such that n>N implies |sn...

I have looked up what an elementary function is but I'm still stuck with showing that y=abs(x) is one. Can anyone explain how to show this?

Homework Statement We have the decay process: pion --> muon + anti muon neutrion How long does the muon travel before it decays? (the pion is stationary before the decay) The answer is supposed to be d = c * t (m(pi)^2 + m(mu)^2) / (2 m(pi) * m(mu) ) where t is the mean lifetime of the...

I'm still having trouble understanding the connection between a static electric field and harmonic oscillators. I understand that a static electric field can be expressed as a scalar (potential) field, and that through Fourier analysis this scalar field can in turn be expressed as the sum of...

Anyone know where I can find some?

I want to teach myself this, and I have a friend that is captain of his math team to help me, and Physics Forums as well. Please used, I don't plan on selling my gallbladder to buy a math book. They don't have to necessarily be textbooks, just have the same way of teaching (problems to work out...

Homework Statement Let f be a non-zero continuous function. Prove or disprove that there exists a unique, real number, x, such that the integral from 0 to x of f(s) w.r.t. s = pi. Homework Equations If any exist, please let me know. The Attempt at a Solution...

I might have forgotten about it cause I took a similar course two years ago. So I have this assertion: Let F be a C^1 function from R^n to R^n, show that if F is injective, and for each curve \gamma : I\rightarrow R^n Length(\gamma)=Length(F o \gamma) then F is an isometry. So I thought...

Homework Statement If G is a finite group and let H be a normal subgroup of G with finite index m=[G:H]. Show that a^m\in H for all a\in G. Homework Equations order of a group equal the order of element. The Attempt at a Solution no idea.

Hi everyone. I find myself in an unusual position; my training is in philosophy, specifically linguistic philosophy and philosophical logic. A publisher friend of mine has asked me to edit an introductory physics title from a purely conceptual perspective, my knowledge of physics is almost nil...

I know this should be obvious, and I should be ashamed of asking it, but could someone fill in the steps to show that [A,B] = [A-<A>, B-<B>]? Thanks from a non-physicist.

What does it mean for an electromagnetic field to be quantized? If I have a proton at point A, then classical physics tells me that at an electron at point B feels a constant electrical force described by Coulomb's law. If the field is quantized, does this mean that sometimes a force is felt...

Hey guys, below is a small question from introductory measure theory. Maybe be completely wrong on this, so if you could point me in the right direction I'd really appreciate it. Claim: Let B=\mathbb{Q} \cap [0,1] and \{I_k\}_{k=1}^n be a finite open cover for B. Then \sum_{k=1}^n m^*(I_k)...

The ATLAS experiment has recently sent two papers for publication. Both look for evidence of quark substructure, in two different ways. http://arxiv.org/abs/1008.2461" , submitted to Physical Review Letters, looks for an excited quark, and does not see any evidence of one. Based on that...

Hi. I'm new to Group Theory and wanted to see if I had the right train of thought for this problem. Homework Statement Let S be a set with an associative law of composition and with an identity element. Prove that the subset of S consisting of invertible elements is a group. Homework...

Does anyone have any comments or reviews to share on Gareth Jones' Elementary Number Theory? Is it suitable for an introduction to the subject? If not, what is the recommended book?

I have a simple question regarding masses of elementary particles (in string theory). What is the mechanism proposed to explain the tiny but non-zero fermion masses? I know zero masses e.g. due to some symmetry (gauge, conformal) or symmetry breaking (Goldstone bosons). I know the huge...

Elementary question -- Special relativity Hi, I have a really elementary question on the theory of special relativity. Here is an excerpt from the website einstein-online.info that confused me: -- http://www.einstein-online.info/elementary/specialRT/speed_of_light The question is: How do...

I just started reading the introductory section of Spivak's calculus, and it has an introduction about the main mathematical properties; dristributive, associative etc. also how basic operations such as multiplication arises naturally from addition and division from multiplication. What...

Hello, I apologize in advance for the odd nature of this question. Can anyone recommend any renowned old (circa 1900s-1940s) elementary algebra textbooks? I have for a while been searching for some (as a hobby I collect old math texts), but it has been very difficult to determine which were...

Hello I am interested if there is yet a theory that states or has relationships that can be interpreted as stating the age of an elemetary particle. For example, if a neutron just sits around (unbounded) passing the time, does it know that it is not allowed to survive a certain age? This...