Extension Definition and 294 Threads

I am trying to work out the efficiency for a self built acrylic bow, but I am having some problems working out a predicted height my arrow will reach. For the experiment i fired the arrow into the air and recorded the height it travelled, I have also recorded the weight of the arrow and the...

Hi, Let E = Q(a), where a is a primitive fifth root of unity. Find a basis for E as a vector space over Q, and express a/a-3 in terms of this basis. I can find a basis for E: {1, a, a^2, a^3}, but am not sure how to express a/a-3 in terms of this basis. Any help much appreciated.

Hey PF gurus! I read that Cayley's theorem can be extended to categories, i.e. that any category with a set of morphisms can be represented as a category with sets as objects and functions as morphisms. I was looking at the construction and for some reason I don't fully understand how they...

Homework Statement Recall that two polynomials f(x) and g(x) from F[x] are said to be relatively prime if there is no polynomial of positive degree in F[x] that divides both f(x) and g(x). Show that if f(x) and g(x) are relatively prime in F[x], they are relatively prime in K[x], where K is an...

Let H, K be finite groups. Instead of asking what groups G there are such that K can be embedded as a normal subroup and G/K is isomorphic with H (the usual extension problem for groups), I've been thinking about the following: Which groups G exist such that H and K can be embedded as (not...

Can someone elaborate? Let I = [0,1], A = {0, 1, 1/2, 1/3, 1/4, \cdots}. Show that the homotopy extension property does not hold on the pair (I, A). Thanks in advance, A

Is cosmology an attempt of the church to highjack science? Is this cosmology the beginning of a new breed of "science" where belief is protected and taught under the name of science?

[SOLVED] extension fields Homework Statement Let F be a field and let E be an extension field of F. Let \alpha be an element of E that is algebraic over E. Is it true that all of the zeros of irr(\alpha,F) are contained in the extension field F(\alpha)? EDIT: I mean algebraic over F Homework...

[SOLVED] extension fields Homework Statement Prove that x^2-3 is irreducible over \mathbb{Q}(\sqrt{2}). EDIT: it should be \mathbb{Q}(\sqrt[3]{2})Homework Equations The Attempt at a Solution So, we want to show that \sqrt{3} and -\sqrt{3} are not expressible as a +b(\sqrt[3]{2})^2...

Is it true that 2z^n(z^n + x^n + y^n) can never be a perfect square if n is a prime greater than 2 and x,y,z are prime to each other?

Structural integrity is a significant matter for aerospace engineers. The Air Force is apparently investigating the possibility that Boeing is liable for the structural "defect" in F-15's. Life extension is a critical matter in aerospace and nuclear industries as highly engineered systems...

Homework Statement 1. A steel bar 375mm long is machined to give a diameter of 75mm for the first 175mm length, a diameter of 45mm for the next 100mm length and a diameter of 37mm for the final 100mm length. Determine: (i) The total extension of the bar when it’s subjected to an axial...

How long could you make/lengthen the telomere of a cell?

Lab stumbles upon "immortal" flesh Could this be used to make other types of cells immortal or does it only work on skin cells? http://abcnews.go.com/Technology/Story?id=119764&page=4

I already know that this is true for galois extensions of Q... how do you extend this result to any finite extension of Q? I was thinking given a finite extension of Q, call it K... find a galois extension that includes the finite extension, call it L... then somehow use the fact that the...

Hi! I'm just reading Wilfrid Hodges's book Logic, chapter 24. Properties of Semantic Entailment. I'm a bit puzzled by the following paragraphs concerning the Extension Theorem: http://i83.photobucket.com/albums/j315/dobry_den/extension_theorem.jpg What if X contains formulae A, A->B and Y...

Hello, I want to extend the wires of my camcorder's focus motor and image stabilization, its about two 2 inches long and I need make them both about 30inches. Would it still work properly especially the image stabilization which calculates and compensates shakes and vibrations quickly, if it...

This is something I've been trying to work on on my own for the past few days but I'm not sure how to approach it. My Question: a. Let E be a Galois extension of a field F with characteristic 0. Prove that there is a unique smallest subfield K such that F \subseteq K \subseteq E , K is...

Let p_1,p_2,...,p_n be distinct primes. Show that [\mathbb{Q}(\sqrt{p_1},\sqrt{p_2},...,\sqrt{p_n} ) : \mathbb{Q}]= 2^n

Homework Statement Let H be all the elements of the alternating group A_4 of exponent 2. Show that A_4 is a split extension of H by \mathbb{Z}_3. Homework Equations None. The Attempt at a Solution I have already shown that H is normal in A_4. I also have the proof of the...

Hi there, I've been asked to prove that (R^2, S^1) has the homtopy extension property and then extend it to the general case: (R^n, S^(n-1)) here's where I've got so far, for (R^2, S^1) Let S^1=A, R^2=X well S^1 is contained in R^2, so by a theorem, if A contained in X, has a mapping...

i am trying to understand why dr/dTau must be negative for a future-directed (physical) observer in the Schwarzschild metric. it says "we also know (e.g. from the Kruskal picture) that the sign of dr/dTau must be negative for a "future-directed" (i.e. physical) observer" i am probably...

I have to prove the map g:torus --> (S^2 3 dimensional sphere of radius 1) is a C infinity map in my assignment. The torus is parameterized as x(u,v)=(3+cos u)(cos v) y(u,v)=(3+cos u)(sin v) z(u,v)=sin u The map g is given by g=[6yz/(x^2+y^2+z^2+8), 3-sqrt(x^2+y^2), -xz/sqrt(x^2+y^2)] I...

http://www.mathphyswiki.com/images/4/41/Latex_extension.xpi It doesn't crash anymore :biggrin: Firefox & windows only, sorry. I have a few more features I hope I can get in today/tomorrow before I take it out of beta. As always, any suggestions would be appreciated - especially on the...

Hi! I assume you all know Fermat's last theorem. Well, has anyone considered the following extension to it? Assuming we're just using integers: We know that x1^n + x2^n = y^n has no solution for n > 2. However, what about this? For which values of k does x1^n+x2^n+...+xk^n = z^n...

Homework Statement "A spring of negligible mass and spring constant 60 N/m is attached to a block of mass 5 kg, which rides on a horizontal surface with a frictional kinetic coefficient of 0.15. A string then goes over a perfect pulley ( no friction or moment of inertia) and attaches to a...

Homework Statement Prove there cannot be an analytic extension containing the unit disk of: f(x) = Series on n from 1 to infinity: x^(n!) Homework Equations Unique Extension theorem, no real explicit equations I can think of. The Attempt at a Solution So far I've proved the...

I've built a horizontal spring launcher, and i need to calculate the extension needed in the spring in order to launch a projectile horizontally to a given distance. The launcher consists of a striker connected to the spring... when the spring is pulled back and let go the strike moves...

LaTeX extension (beta) http://www.mathphyswiki.com/index.php?title=Latex_extension Firefox only, sorry. It's supposed to help with doing latex. Some issues left. It crashes sometimes. I'm taking suggestions on anything, from adding a function to a UI overhaul. I haven't even settled on a...

Homework Statement A winding engine lowers a load of 5 tonne at the rate of 1.4m/s2 for a distance of 10m. Assuming that the load is suspended from a steel rope 12mm in diameter calculate the stress and the extension in the rope after traveling this distance. Assume Esteel=200 GN/m2 and...

I have this file that has no extension (not just bcs it's hidden), so I don't know what to use to open it. Do you guys have any ideas on how to figure out what the file is?

Right now I am in an EE Summer Co-Op with a nice company. They hired me knowing that it was only for my summer break. However, I would like to come back for my 1 month winter break or even next summer's break. How would I go about asking my supervisor for an extension. Although I like...

I'm sure any web developer would appreciate this extension: http://jennifermadden.com/scripts/ViewRenderedSource.html

Take M = Q(i, \sqrt{2} ). Prove that G = Aut(M) is isomorphic to V_4 I have some ideas but I don't know how to justify them: Consider K(i) with K = Q(\sqrt{2}). The the minimal polynomial of i over K equals to X^2 + 1. I know the fact that if x is a zero of a polynomial P and f is an...

I think the heading pretty much says it all! I want to write a python program and I am typing it in Notepad. when I save it, it adds .txt to my filename "myprogram.py". How do I avoid that? (I know, it's a stupid question!) Pat

im tyring a ISP for physics which detrmines were the sprign will land when shot off a frame, with the target being 3 m away we got this formula d (x) = [1/9.8 * k/m ] * x square where x is the extension needed to make it reach d (x) which is 3 m my quesiotn is anyways, does a higher K value...

Does anyone know whether there is a way to change the icons on a mac, in such a way that the changed icon works for all the files of a certain extension? Like, that all the .ppt files have a new icon associated to them. For those who don't know, you can change a single icon by...

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.

There are equivilant definitions of Galois extensions listed here http://mathworld.wolfram.com/GaloisExtensionField.html but I'm confused about the equivilence of 1 and 2. What am I doing wrong here? Take K to be the splitting field of X^4-2 over \mathbb{Q}. This is exactly property 1. But...

Hello all, I was wondering whether there might be anything similar to Thurston's Geometrization Conjecture, except for four manifolds instead of three manifolds. (Essentially, this conjecture (iiuc) states that it is always possible to take an arbitrary 3-manifold and break it up into...

Any help on this would be greatly appreciated. ______ In order to go stop the coaster at the end of its course, a spring has been installed. When the coaster stops, it stands at 2 m from the ground. If the total distance of the ride is 750 m, the friction is 500 N as before, the spring...

It is known that a tensor field is a tensor-valued function T=T(p) whose argument p is a point of some space (or some manifold). However, in physics some tensor fields are produced from other tensor fields, e. g. Lagrangians in physical field theories including tensorial fields...

An extension cord made of two wires of diameter 0.129 cm (no. 16 copper wire) and of length 2.7 m is connected to an electric heater which draws 15.0 A on a 120V line. How much power is dissipated in the cord? Do I just use P=IV? But that leaves a lot of "extraneous" information. My...

Some files ended with *.msi, how to install it ? [?]