Fundamental Definition and 947 Threads

Given a topological space and a group acting on it, the images of a single point under the group action form an orbit of the action. A fundamental domain or fundamental region is a subset of the space which contains exactly one point from each of these orbits. It serves as a geometric realization for the abstract set of representatives of the orbits.
There are many ways to choose a fundamental domain. Typically, a fundamental domain is required to be a connected subset with some restrictions on its boundary, for example, smooth or polyhedral. The images of a chosen fundamental domain under the group action then tile the space. One general construction of fundamental domains uses Voronoi cells.

View More On Wikipedia.org
Recent contents Top users
  1. N

    Calculating Fundamental Frequency of Vibrating String

    Homework Statement Determine fundamental frequency of a vibrating string if two successive harmonics of the string are 180hz and 270hz Homework Equations f=1/t t=1/f The Attempt at a Solution I want to say its just f=1/t for both of them but it seems to easy?no?
  2. J

    Which formulation of Newton's second law is more fundamental?

    Which formulation of Newton's second law is more fundamental?? Hi there! I was Googling for interesting demonstrations in Physics, and I was lucky enough to find very interesting blog. Although it is completely new- the guy is writing it only for two weeks, but it already has a lot of nice...
  3. L

    Changing string length -> changing fundamental freq.

    Homework Statement Don't have the solution, just want to check if I did this properly. A 0.5 m violin string fixed at both ends has its first harmonic or fundamental frequency at 440 Hz. Assuming the string is non dispersive, calculate the length it should have so its new fundamental...
  4. S

    Hi,i want to understand how fundamental group of a closed oriented

    Hi, i want to understand how fundamental group of a closed oriented 3-mfd determines all its homology and cohomology gorups. Please can you help me.
  5. M

    Careers paths of fundamental vs. applied physics

    I have a decision to make in my physics PhD of where to start my research between physics, applied physics, or even ECE/physics. I know that I could always switch fields part way in, but I really don't want to be set back and I want to make the right decision to start with. Anyway, as I am...
  6. M

    Fundamental Theorem of Line Integrals

    If someone could link me to a tutorial on how to put in functions into a post, I would appreciate it, thanks. I am going to be putting in screen shots. Homework Statement http://img864.imageshack.us/img864/1517/scr1305133657.png" http://img864.imageshack.us/img864/1517/scr1305133657.png...
  7. S

    Why is the Fundamental Group of Lens Space L(p,q) Z_p?

    Hi i want to see why the fundamental group of lens space L(p,q) is Z_p. Can you help me?
  8. F

    Which Fundamental Force is Involved?

    Homework Statement Which of the four fundamental interactions is most likely responsible for the following reactions? (a) {}^{16}O\text{ (excited state) }\longrightarrow{}^{16}O\text{ (ground state) }+\gamma (b) {v}_{e}+e\longrightarrow v_{e}+e (c) p+\overline{p} \longrightarrow \gamma +...
  9. K

    How to abelianizing the fundamental group?

    There is a theorem:If |K| is connected,abelianizing its fundamental group gives the first homotopy group of K. How to abelianize a group? And how to understand this theorem more obviously?Can anyone show me an example to see it? I myself will think this problem for more time because I...
  10. F

    Fundamental solutions of the stokes equation.

    Homework Statement Hi, I going through my class notes for a fluids class, specifically fundamental solutions of the Stokes equations. To derive the stresslet and rotlet involves solving the following ui = (1/8*pi*μ)*(∂Gik/∂xj)*Fk*Aj Gik(x) = δij*(1/r)+(xixj/r3) We looked at it in a...
  11. I like Serena

    Is the 5th Fundamental Force Real?

    I'm not sure if this is the right place to post this thread, so if there's a better place I'm all ears. As I understand it the force that holds protons and neutrons together in the nucleus of an atom, is the strong force. But what force is keeping the nucleus from collapsing altogether...
  12. L

    What is the alternative form of the extrinsic curvature in Carroll App D?

    Hi, I'm working through Carroll App D, and trying to show the alternative form of the extrinsic curvature that he says should take a few lines. Starting with K_{\mu\nu}=P^{\alpha}_{\mu}P^{\beta}_{\nu}\nabla_{(\alpha}n_{\beta)} where P is the projection tensor, and n is the normal to the...
  13. R

    Exponential decay question. fundamental

    this is just something has been bugging me for the last few days. it seems like it has a very basic solution. Muons decay randomly, but have a mean lifetime of about 2 us. If I plot the # of muons that decay vs. time (say the axis spans from 0 to 20 us), why is the plot exponential decay...
  14. M

    Do the fundamental forces continue to break down at lower energies?

    First off, I would like to apologize if I'm posting this in the wrong sub-forum. Anyways, I'm sorry if this is an ignorant question, but I am curious as to whether the 4 fundamental forces (electricity and magnetism, gravitation, strong, and weak) would theoretically continue to break down...
  15. J

    Fundamental Theorem Calc: Find f(4) from Integral

    Alright, so in my AP calc class we just got a worksheet and one of the questions i don't undersnat at allll! We have been learning about the Fundamental Theorem of Calculus recently, so I am guessing that is what this is about. Homework Statement Find f(4) if the integral (lower limit = 0 ...
  16. H

    Fundamental theorem of Orthogonality

    Hello there! I have a group represented by the following matricies: \left( \begin{array}{cc} 1 & 0 \\ 0 & 1 \end{array} \right)\] ; 0.5\left( \begin{array}{cc} -1 & \sqrt{3} \\ -\sqrt{3} & -1 \end{array} \right)\] and\quad 0.5 \left( \begin{array}{cc} -1 & -\sqrt{3} \\ \sqrt{3} & -1...
  17. A

    What are the Fundamental Logical Axioms?

    Hi, I've been recently reading about logic. Is there a list of the exact logical axioms underlying all axiomatic systems, postulates and mathematics? Thanks...
  18. D

    Fundamental frequency of a standing wave

    Homework Statement A standing wave is established in a string of length 150 cm fixed at both ends. The string vibrates in four segments when driven at 140 Hz. Find the wavelength in meters. Find the fundamental frequency. Homework Equations L = Nλ v = fλ The Attempt at a...
  19. A

    Fundamental Existence Of Matter/Energy

    the big bang theory suggests that all the matter around us was once infinitely concentrated at some particular high density region...this matter then spread out across the universe following the big bang... but how did this energy/matter come into existence in the first place??..
  20. S

    Proving the Fundamental Theorem of Calculus Twice

    Homework Statement Complete the proof by using the Fundamental Theorem of Calculus TWICE to establish \int_c^d(\int_a^b f _{x}(x,y)dx)dy=...=\int_a^b(\int_{c}^{d}f_{x}(x,y) dy)dx Homework Equations I know that the FTC states that if g(x)=\int_a^x(f), then g'=f The Attempt at a...
  21. E

    Could second and third generation SM particles NOT be fundamental?

    could second and third generation SM particles NOT be fundamental? since they are unstable and rapidly decay, could second and third generation SM particles NOT be fundamental? perhaps as bound states of more fundamental first generation particles? if they are not fundamental, then do we...
  22. N

    Fundamental Theorem of Line Integral question

    The question is suppose that F is an inverse square force field, that is, F(r)=cr/|r^3| where c is some constant. r = xi + yj + zk. Find the work done by F in moving an object from a point P1 along a path to a point P2 in terms of the distances d1 and d2 from those points to the origin...
  23. R

    The fundamental orthogonality theorem

    Homework Statement Hello everyone! I am trying to do my homework and I wonder if any of you knows what ''the fundamental orthogonality theorem'' is...? (my teacher calls it like that) I have googled it but the only thing I could find was orthogonality... I could not find something like ''the...
  24. S

    The Fundamental Theorem of Algebra

    Hi all, I'm currently flicking through and old textbook and came across the following. "Every polynomial of the form , where has n linear factors over C...". What does it mean by http://latex.codecogs.com/gif.latex?a^{n}\neq0? Is this referring to some kind of complex index? This is all that...
  25. Drakkith

    Unifying the Fundamental Forces

    I've read that at certain energy levels the fundamental forces are united or are equal strength. How does the energy level affect the strength of the forces?
  26. R

    Coulombic fundamental force to the Gravitational fundamental force

    Homework Statement Compare the magnitude of the Coulombic fundamental force to the Gravitational fundamental force. Explain similarities/differences between the 2 types of forces. You have 2 protons separated by 1*10^-4 meters. Calculate the gravitational force of attraction between the two...
  27. E

    Field is more fundamental than particles

    A lot of times I read that "Field is more fundamental than particles". This comes from QED. I read some explanations, but I do not understand precisely, what aspect of particles is mentioned. If we say that elementary particles are black holes (let us assume that BH exists smaller than the...
  28. L

    Fundamental Period of f(t) = sin(6t) + cos(8t)

    Homework Statement Let f(t) = sin(6t) + cos(8t). (a) What is the fundamental period of f(t)? T= 2pi/\omega I know the fund. period of sin is pi/3 and cos is pi/4, and the definition of fundamental period saids that f(t + T ) = f(t) for the smallest T in the function, so would pi/4 be my...
  29. L

    What is the fundamental period of the function f(t)= sin6t + cos8t?

    1. what's the fund. period of f(t)= sin6t + cos8t? 2. the fund period of the first term is pi/3, the second pi/4 3. do i just add the 2 fundamental periods up to get the whole fund period? also for the Fourier coefficients of this function, should i use euler's to make it into exponentials...
  30. F

    Fundamental Theorem and Maxima

    Homework Statement Si(x) = \int_{0}^{x}{\frac{sin(t)}{t} dt At what values of x does this function have a local maximum? 2.Solutions [PLAIN]http://img833.imageshack.us/img833/701/27444263.png The Attempt at a Solution So I took the derivative and applying FTC and I got sin(x)/x = 0 sin(x)...
  31. binbagsss

    Is the fundamental frequency of a given swing constant?

    As mass is independent of the period for SHM?
  32. L

    How Does an Electric Circuit Function with a Battery, Wire, and Resistor?

    Homework Statement If I post this question in the wrong section please forgive me and direct me to the correct place. I want to ask about how electric circuit works. Let's use a basic circuit, which has a battery, wire, and resistor, for the problem. From what I learned, the electrons move...
  33. H

    Fundamental Frequency of Vibrating String: From 256Hz to ?Hz

    Homework Statement The fundamental frequency of a vibrating stretched string of length 1.0m is 256Hz.When the string is shortened to 0.4m with the same tension,the fundamental frequency now become how many Hz? Homework Equations The Attempt at a Solution
  34. A

    Who was the first to prove the fundamental theorem?

    Just curious who wrote the first proof of the fundamental theorem of calculus. Thanks.
  35. K

    What's the difference between fundamental particles and composite particles?

    I'm confused, by composite particle we probably mean when we use something to smash it, something new will come up, right? Then what's so different about fundamental particles? For example if we "smash" a electron with a positron, we also get something new--photon. I guess I am making some...
  36. G

    Photon 4-Momentum in SR: Why Must it Transform?

    Why must the 4-momentum for photons p^\mu =(\frac{h\nu}{c},\frac{h\nu}{c} \textbf{e}) transform as a 4-vector in Special Relativity?
  37. V

    One fundamental property of Fourier Series

    Suppose the functions f(t) and g(t) are periodic with periods P and Q, respectively. If the ratio P/Q of their periods is a rational number, show that the sum f(t)+g(t) is a period function. How to prove this?
  38. N

    Tunneling: Can a Particle Appear in the Barrier?

    Hello, I'm following an introductory course in modern physics. So I understand there's a chance the particle appears on the right side of the barrier, and this has been experimentally verified. Now I was wondering: can the particle also appear in the barrier? If so: is this directly...
  39. E

    Curved or non-curved space, what is more fundamental?

    curved or non-curved space, what is more fundamental? By intuition it seems that non-curved space is more fundamental. By general relativity and difeomorphism it seems that no one is more fundamental. But how it is with this?
  40. I_am_learning

    How fundamental is Law of Conservation of Energy?

    Is it just as fundamental as Newtons Law of Motion or it is deeper than that? I mean, is it like- No matter what invention and discoveries you come up in future, no matter which theories fail and which emerge, this Law of Conservation of Energy shall always stand above all.
  41. M

    How can you geometrically see the homotopy between S^n/S^m and S^n-m-1?

    why is S^n/S^m homotopic to S^n-m-1. the book just made this remark how do you see this geometrically. how do you compute fundamental groups of matrices like O(3) and SO(3) or SL(2) and whatnot.
  42. K

    Line Integral Fundamental Theorem

    Homework Statement Use Your Phi(from part 1) and the fundamental theorem of line integrals to evaluate the same line integral. (should get the same answer!) The Attempt at a Solution Phi from part 1: Phi = xy+ y^2 +C The line from before go from (0,2) to (-2,0) r(a) = (0,2)...
  43. C

    Fundamental frequency of a pipe half-filled with water

    Homework Statement A very tall pipe is partially filled as shown. (A vertical pipe is filled with water about halfway, and .85m of air is in the pipe to the open end. The bottom is closed). |**| ^ |**| | |**| .85m |__| _|_ |__| |__| |__| |__| |__| ^^ My attempt at a drawing, where...
  44. M

    Fast Computation of Fundamental Groups: Practical Methods and Tricks

    So I've read through beginning alg topology really fast and there are a lot of theorems and methods for computing fundamental groups but what are the most useful tools? When asked to compute the fundamental group what should one do? try to find a deformation retract and compute the fund group...
  45. B

    Ontoness and Induced Maps on Fundamental Group.

    Hi, everyone: Given a top space X, and a homeo. h: X--->X , we get an induced map (by functoriality ) h_*: Pi_1(X)---> Pi_1(X) . We can also write the map as a map g: Aut(X) --->Hom(Pi_1(X),Pi_1(X)) Is the map g always surjective.? . Almost definitely...
  46. P

    Fundamental doubt on Acceleration.

    Hi Everyone, I have very fundamental question on Acceleration. I can understand that a moving body accelerates or de-accelerate when its velocity goes up and down. But I couldn't understand; when we say a moving body accelrates or de-accelerates when the direction of moving body changes(with...
  47. S

    FTC fundamental theorem of calculus

    FTC "fundamental theorem of calculus Homework Statement Homework Equations FTC The Attempt at a Solution well i have not used FTC in a long time this is from my old lecture notes...how do i show that using FTC(the question show above)
  48. quasar987

    What is the fundamental group of X?

    Compute the fundamental group of the space X:=((S^1\times S^1) \sqcup (S^1\times S^1))/\sim where ~ is the equivalence relation (e^{it},e^{it}) \sim (1,e^{2it}) meaning the diagonal of the first torus is identified and wrapped around twice the second generating circles. Call T_A the...
  49. S

    Fundamental and Adjoint Representation of Gauge Groups

    Basic question, but nevertheless. In a non-Abelian gauge theory, the fermions transform in the fundamental representation, i.e. doublets for SU(2), triplets for SU(3), while the gauge fields transform in the adjoint representation, which can be taken straight from the structure constants of...
  50. O

    Fundamental OFDM question (MATLAB related)

    Upon feeding the IFFT block with the mapped date elements, shouldn't the binary data be upsampled by a sampling frequency that is equal to twice the highest subcarrier frequency (nyquist criterion)? I have written a code for a complete OFDM trasceiver system and I have not upsampled my binary...
Back
Top