Fundamental Definition and 907 Threads

I know of the "result" that if two pointed spaces are homeomorphic, then the group homomorphism induced by such an homeomorphism if actually an isomorphism between the fundamental groups of these pointed spaces. But is there a link between the fundamental groups of homotopy equivalent spaces?

http://img521.imageshack.us/img521/4549/bbav9.png The problem states that it wants the upper and lower estimate of total distance. Therefore, I used rectangles to solve for it. However, let's say I'm working on upper limits. For my initial rectangles, I use the right endpoints, but then it...

http://img527.imageshack.us/img527/8089/fr2rl4.gif I know part a is the fundamental theorem of calculus, but I am not quite sure how to manipulate the integral to find part i or part ii. Part b is again the fundamental theorem of calculus, but I am having a hard time solving for the...

To improve my understanding of physics I was unable find the answer to this question on the web after a lot of searching so I'll try here. let v= net velocity of the x direction and the y direction You take a particle at rest with mass m and you accelerate it to 80% of c in the x...

Homework Statement You blow across the open mouth of an empty test tube and produce the fundamental standing wave of the air column inside the test tube. The speed of sound in air is 344 m/s and the test tube acts as a stopped pipe. If the length of the air column in the test tube is 14.0...

Hello, I need to know the fundamental frequencies of the noble metals "silver, gold, platinum ... etc" .. thank you very much

I have a question that may seem kind of simple, but I would like to hear your thoughts about it. Is there such a thing as a fundamental particle of which all other particles are made of, or even if is even possible for such a thing to actually exist? A particle of continuous matter (no empty...

Homework Statement The frequency of the note f_4 is f_F. If an organ pipe is open at one end and closed at the other, what length must it have for its fundamental mode to produce this note at a temperature of T? ans= v/(4*f_F), where v is the speed of sound in air. Now the part which...

Seems to be isomorphic to Z, but I can't seem to be able to prove it. Am I right? If I am, how do I prove it?

Can someone explain a concept to me? The derivative of an integral ( whose lower limit is a real constant and whose upper limit is the variable x), is the intergrand evaluated at x as per the FTofC. I always thought about this as the limit of the integral as x approached the lower limit becuase...

Hello... I've just recently started studying physics for my A levels and i am finding its concepts very hard to get a handle on :frown: . One major area I am having problems with is my definitions of some of the fundamental properties of electrical circuits. For example i find charge very...

I have a question regarding past thoughts on the fundamental forces of nature. 1) Prior to the unification of the EM force, how many fundamental forces were there thought to be? 2) When did the concept of a force first come to be? 3) How were forces described prior to this time? Where...

This is a question where the answer is given but I don't understand how to derive it. The answer to the homogeneous eq. is: A cosh(x) + B sinh(x) with no explanation of how it is arrived at and the given answer then goes on to describe how the non-homogeneous part is solved. Diff. eq. ...

I heard it suggested that the casmir effect could be related to a 5th fundamental force. I thought it was interesting, but can't explain my reasoning to thinking it was. Why couldn't it be? I almost stutter. Input?

I learned a lot from the discussion of the converse problem, photon absorption. What about this case? Perfectly elastic.

Hello I was thinkng of this question and I found it best expressed in a clear manner in another site. I quote the question and waiting for an asnwer: "Is it a fundamental property of electrons that they can absorb photons? Geometry requires that two points define a straight line. Geometry...

Hello, I have a problem that I am getting stuck simplifying further. The problem asks me to find the integral if it exists using Part 2 of the FTC. I know that the second part of the FTC says:\int_{a}^{b} f(x)dx = F(b) - F(a) Where F is the anti-derivative of f. Here is the problem...

Why the current is fundamental quantity? Why the unit of fundamental quantity current is defined in terms of force?

I hope you can follow my train of thought (I'm not being elitist here, I am open to the possibility that my post may be unintelligible) 1. Velocity is a parallel rate. The distance/time formula with which we are familiar is an expression of the number of meters laid end to end alongside...

When plucking a string on an instrument, are all the overtones heard produced by the string itself (assuming all other strings are muted)? Would plucking the string without muting the others make a significant different? Another thing, why aren't all overtones integer multiples of the...

Evening, Ive been having some trouble with questions about fundamental frequencies and labelling nodes and anti nodes in an air column. for example :a tuning fork is placed above a glass tube and then the sound of the air column is adjusted by raising or lowering the glass tube in the...

Here's one for you. Is there a way of working out what the fundamental frequency of the Earth's crust is? Has anybody done this. And what would happen if we somehow matched this frequency, say by all dancing to a particularly banging dance remix of Electric Light Orchestra's "Mr Blue Sky" all at...

So far, all i can think of is: mass, time, length & charge (maybe?). Temperature isn't even a fundamental unit, since it is a measure of kinetic energy of a particle (1/2*m*vrms^2=3/2*k*T, i think that's right...), am i missing any? If that's all of them, then that's pretty amazing to me.

Hi, Please can someone help me on how to do this exercise. Give a fundamental matrix for the system: {x'(t)=-y(t) {y'(t)=20x(t)-4y(t) the solution is like: {v1(t)=e2t*cos(4t)[1;4]+e2t*sin(4t)[-1;-2], v2(t)=e2t*cos(4t)[1;4]+e2t*sin(4t)[0;-4]} [1;4]...are colunm vectors. IT is just...

Yeah, same as above, Why do fundamental physical forces change their strength with distance? Shouldn't the force be the same everywhere? Why or Why not? :-p (how do you know, and what did you get the answer from) Thanks,

I do not understand what is meant in this question: An open organ pipe has a fundamental frequency of 430 Hz. A closed organ pipe has a fundamental frequency that is the second harmonic of the open organ pipe. What are the lengths of the two pipes? Does the bolded part mean that the...

How could you tell if you had missed one of the natural frequencies when you were finding natural frequencies above the fundamental? thnx a lot

I'm still new to much of this stuff, so I do not claim to be an expert. But I thought I'd still comment. I'm trying to better understand the geometric calculus of David Hestenes: http://modelingnts.la.asu.edu/ A fairly common form for the Fundamental Theorem of Calculus is: \int_S...

Can someone break down these theorems for me please because my book is horrible at explaining them. The examples the book gives shows the initial question but then the answer and none of the steps in between even on the very simple questions. I'm confused. ~Kitty

In https://www.physicsforums.com/showthread.php?t=112890", Space Tiger mentioned the Tully-Fisher relationship for spirals, and the Faber-Jackson relationship, "part of the fundamental plane of elliptical galaxies". Does anyone know of a review article on the extent to which these apply, to...

(that's a 3 on the last integral) http://img131.imageshack.us/img131/2549/jesus1cj.png I need to find which of those are true, now I thought I and III were true for sure. But when I do II with an example f(x) = x^2 I get x^2 - 9, so it's not true right? (I and III are not choices given for the...

I can't get my answer match up with correct answer in the book: i need to find fundamental period of this signal: x(t) = 2 cos(10t + 1) - sin(4t -1) i used formula for cosine Acos(wt + a) = ... that gives two exponentials... so I got pi/10 instead of pi for answer... any help is appreciated

How is the permittivity of free space, \epsilon_0, and the magnetic permeability in vacuum, \mu_o, measured? Thanks

OK, this is more of a spot for an elaboration on a question I just posted in another thread. Not quite duplicating threads, I hope, I just wanted to have this not buried in another spot... So, the question is this: Let's say that we have a smooth manifold \mathcal{M}that may be viewed as a...

We know that there are three fundamental forces: 1. Gravitational Force 2. Strong Nuclear Force 3. Quark-Quark Force (unified by Weak Nuclear and Electromagnetic Force) I've heard about the fourth fundamental force which was found in 1986 and changed the relation: F = G*m*M/R*R to some...

Id like to know if the following argument is valid. Take an arbitrary function f(x). f(x)dx can be thought of an infinitesimal area of a certain form (I emphasise this because I use it later in the argument) determined by the form of the function f(x). Let's denote its integral by Y. \int{...

I am confused with some fundamental things... Does voltage and current go in opposite direction when represented in a drawn circuit? Does current go the way opposite to the actual direction of electrons flow? In an AC signal, for example, a generator is placed at point B and it's...

Howdy all, I've begun to get started in learning about physics, but am still lightyears removed from any of the mathematical aspects of the science. Thus I am now looking to move from themes to numbers (and I'm kinda nervous :rolleyes: lol) Anyway, here's where I'm heading currently...

Question: One of the 63.5-cm-long strings of an ordinary guitar is tuned to produce the note {\rm B_3} (frequency 245 Hz) when vibrating in its fundamental mode. 1. If the tension in this string is increased by 1.0%, what will be the new fundamental frequency of the string? The first part of...

Hello everyone, i have the following problem I'm confused about! Can anyone guide me to what I'm suppose to do? I tried the following but it was wrong, he then told me I can just apply the theorem to |r'(u)| insteed of the stuff under the square root which would be more difficult. This is...

In a book of Introduction to Probability I found this statement: " Let be F(x) = \int_{-\infty}^{x} f(t)dt. Then, by the Fundamental Theorem of Calculus, F'(x) = f(x)." With the minus infinity on the lower limit, it is this a valid aplication of the FTC? Thanks.

Is there a fundamental particle (like a Planck black hole) that has a finite radius?

2 sinusiodal waves are defined y1=2sin(20x-32t) y2=2sin(25x-40t) what is the phase difference between this two waves at point x=5 and t=2s. all length in cm. I sketch the graph y/x and y/t and both have their max amplitude at x=3.2 , and t=3.125s. so what is the different in phase...

Hello. I am in confusion because I cannot understand which formula will be used in this and that derivation,because there are many formulas of physics.Then how we come to know that this specific formula must be used in this derivation It is a great confusion for me. Please solve my problem...

Quick question, what is the approach to this problem? Keep in mind I am supposed to use the Fundamental Theorem of Line Integrals. \int_{C} 2ydx + 2xdy Where C is the line segment from (0,0) to (4,4). Unless I am missing something I need to make that into the form of \vec{F} \cdot...

What is the most fundamental physics that we can observe directly with our senses?

Confusion on just what "fundamental" means I just read the Tao of Physics and I'm slightly confused. Are quarks and leptons fundamental units of matter or are they temporal manifestations of energy with E=mc^2? Is is that all matter is comprised of bundles of energy and that quarks and...

I have my own views on the question of between the two, QM or Relativity, is one more fundamental. It seem that Rel. is based on fundamental principles, i.e. the principle of relativity. As I see it this could never be violated but some of the foundational principles of QM could turn out to be...

A certain pipe produces a fundamental frequency f in air. If the pipe is filled with helium at the same temperature, what fundamental frequency does it produce? (Take the molar mass of air to be M_air, and the molar mass of helium to be M_He). The ratio γ of heat capacities for air (7/5) and...

Over this semester I studied quite a few physiology and anatomy books ranging from the classics of Gray's anatomy, Last's anat, Guyton & Hall's medical physiology and also Lange's histology and Lange's physiology. A word of advice to any premed student buying or reading from these books...