Extension Definition and 294 Threads

A filename extension, file extension or file type is an identifier specified as a suffix to the name of a computer file. The extension indicates a characteristic of the file contents or its intended use. A filename extension is typically delimited from the filename with a full stop (period), but in some systems it is separated with spaces.
Some file systems implement filename extensions as a feature of the file system itself and may limit the length and format of the extension, while others treat filename extensions as part of the filename without special distinction.

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  1. A

    Continuous Extension of Function at Origin: Can f=1?

    How can the function f: ℝ² → ℝ : (x,y) |--> {{x^2+y^2-(x^3y^3)}\over{x^2+y^2}} if (x,y) ≠ (0,0) be defined in the origin so that we get a continuous function?When I take 'x=y' (so (y,y)) and 'y=x' (so (x,x)) I get: {{2-y^4}\over{2}} and {{2-x^4}\over{2}} So for the first one I get '1'...
  2. D

    Angle, range and extension in projectile motion?

    We have a trebuchet which we can adjust the launch angle, and how far the rubber band is pulled back (extension). The rubber band spring constant is constant throughout. I need to find the relationship between the angle of launch and range, and the relationship between the extension and range...
  3. S

    Criteria for extension to cts fn between metric spaces?

    Given metric spaces (X, d_X), (Y, d_Y), and subsets \{ x_1, ..., x_n \}, \{ y_1, ..., y_n \} of X and Y respectively, if I define a function that send x_i to y_i, what are the minimal restrictions we need on X and Y in order for there to exist an extension of that map to a continuous...
  4. M

    Temporal Extension of Quantum Uncertainty (A Theoretical Quantum Fortune Teller)

    Based on the results of every variation of the two-slit experiment so far, the presence or absence of the interference pattern is based on whether or not which-path information can be known or not. The Delayed Choice Quantum Eraser experiment...
  5. A

    Can You Extend a Function Defined on Atomic Sentences to Complex Sentences?

    Homework Statement "Given a function H, assigning a value, 0 or 1, to each atomic sentence, define a sequence ℑ0, ℑ1, ℑ2, ℑ3,... of functions, as follows: ℑ0 is just H. Given a function ℑn, assigning a value, either 0 or 1, to the sentences of degree less than or equal to n, define the...
  6. J

    What Is the Degree of the Splitting Field of x^8 - 2 over Q?

    Homework Statement Find the splitting field of x8 − 2 over Q, including its degreeHomework Equations Degree is multiplicative in tower of fields: F \subset K \subset L [L:F] = [L:K][K:F] Degree of Galois extension is equal to the order of the Galois group [K:F] = |Gal(K/F)| The Attempt at a...
  7. C

    Finding axial extension in steel bar

    Homework Statement A cylindrical steel bar, 20-mm in diameter and 5.0-m in length, is subjected to an axial tensile load of 40-kN applied at the ends of the steel bar. Determine the axial extension, in millimeters, of the steel bar under this loading condition?Homework Equations E=\sigma/e...
  8. A

    Galois Extension of Q isomorphic to Z/3Z

    Hi... How do I construct a Galois extension E of Q(set of rational numbers) such that Gal[E,Q] is isomorphic to Z/3Z. Thanks.
  9. L

    How to calculate wire extension from tension and Young's modulus?

    Homework Statement A wire of diameter 5.0 mm supports a 2.8kg load. (a) Determine the tension in the wire (b) The original length of the wire was 2.0m Calculate its extension when supporting the load. Homework Equations Young's modulus for the material of the wire = 2.0 x 10^7N...
  10. P

    What is the Basis for an Extension Field Adjoined with an Element?

    I am having no luck understanding how to find the basis of a field adjoined with an element. For example Q(sqrt(2)+sqrt(3)) I know that if i take a=sqrt(2)+sqrt(3) that i can find a polynomial (1/4)x^4 - (5/2)x^2 + 1/4 that when evaluated at a is equal to zero. So, from that I know the...
  11. Y

    Why the book call f(x+ct) and f(x-ct) odd extension of D'Alembert Method?

    For wave equation: \frac{\partial^2 u}{\partial t^2} \;=\; c^2\frac{\partial^2 u}{\partial x^2} \;\;,\;\; u(x,0)\; =\; f(x) \;\;,\;\; \frac{\partial u}{\partial t}(x,0) \;=\; g(x) D'Alembert Mothod: u(x,t)\; = \;\frac{1}{2} f(x\;-\;ct)\; +\; \frac{1}{2} f(x\;+\;ct)\; +\; \frac{1}{2c}...
  12. C

    Experimental tests of General relativity vs Cartan extension

    First, if there are tests that have ruled one way or the other, that pretty much ends this discussion. I couldn't find any, but if they exist please point them out here. That leaves the discussion of: 1) How could these been distinguished experimentally, and 2) How precise do tests have...
  13. M

    Galois Extension: Proving L is Galois Over K

    This stuff is killing me... Let K \leq M \leq L be fields such that L is galois over M and M is galois over K. We can extend \phi \in G(M/K) to an automorphism of L to show L is galois over K. I need help filling in the details in why exactly L is galois over K.
  14. P

    Modern Physics - Extension of the Galilean Transformation?

    Homework Statement Conventionally, the Galilean Transformation relates two reference frames that begin at the same location and time with one reference frame moving at a constant velocity {\vec{v}} along a positive {x}-axis (which is common to both reference frames) with respect to the other...
  15. D

    Abstract Algebra: Extension Fields & Complex nth Roots

    Two problems from my abstract algebra class... 1) Let K be the algebraic closure of a fi eld F and suppose E is a field such that  F F \subseteq E \subseteq K. Then is K the algebraic closure of E? 2) Let n be a natural number with n\geq2, and suppose that \omega is a complex nth...
  16. E

    Calculating Tension Required for 4*10^-4m Extension of Steel Wires on a Violin

    Homework Statement The wires on a violin have a cross section of 5.1*10^-7m^2. The wires are put under tension by turning the wooden pegs. The Young Modulus of Steel is 2.0*10^11 Pa. Calculate the tension required to produce an extension of 4*10^-4m. Homework Equations Thats where...
  17. B

    Proving Normal Field Extensions with an Example | Field Extension Normality

    Hi, how can I show that a field extension is normal? Here is a concrete example: L|K is normal, whereas L=\mathbb F_{p^2}(X,Y) and K= \mathbb F_p(X^p,Y^p) . p is a prime number of course. I have to show that every irreducible polynomial in K[X,Y] that has a root in L...
  18. O

    How Can We Prove the Extension of Bezout's Identity?

    As a consequence of Bezout's identity, if a and b are coprime there exist integers x and y such that: ax + by = 1 The extension states that, if a and b are coprime the least natural number k for which all natural numbers greater than k can be expressed in the form: ax + by Is a+b-1...
  19. C

    Can Q(sqrt a + sqrt b) be equal to Q(sqrt a, sqrt b) in abstract algebra?

    field extension question (abstract algebra) Homework Statement For any positive integers a, b, show that Q(sqrt a + sqrt b) = Q(sqrt a, sqrt b). Homework Equations The Attempt at a Solution i proved that [Q(sqrt a):Q] for all n belonging to Z+ is 2 whenever a is not a perfect...
  20. F

    I'm learning about relativity and, by extension, the classic

    I'm learning about relativity and, by extension, the classic Michelson-Morley setup. I cannot see why a "fringe effect" was expected and could use some discussion. Here is my reasoning. Firstly we imagine the light signal to propagate from the SM (silvered mirror, in the "center") to M1 and...
  21. F

    Is the field extension normal?

    I've been asked to find out if some field extensisons are normal. I want to know if I'm thinking about these in the right way. For Q(a):Q I first find the minimal polynomial for a in Q[a]. Then I look at all zeros of that polynomial. If all of the zeros are in Q(a) the extension is...
  22. Mentallic

    Australian HSC maths extension 2 test question

    Homework Statement This question is from the Australian HSC maths extension 2 test. Q8b) Let n be a positive integer greater than 1. The area of the region under the curve y=1/x from x=n-1 to x=n is between the areas of two rectangles. Show that...
  23. Mentallic

    Australian HSC mathematics extension 2 exam Polynomial

    Homework Statement This problem is from the Australian HSC mathematics extension 2 exam. Q6b) It states: b) Let P(x)=x^3+qx^2+qx+1, where q is real. One zero of P(x) is -1 i) Show that if \alpha is a zero of P(x) then \frac{1}{\alpha} is a zero of P(x) ii) Suppose that \alpha is a...
  24. R

    Cauchy Integral Extension Complex Integrals

    Homework Statement Allow D to be the circle lz+1l=1, counterclockwise. For all positive n, compute the contour integral. Homework Equations int (z-1/z+1)^n dz The Attempt at a Solution I know to use the extension of the CIF. Where int f(z)/(z-zo)^n+1 dz = 2(pi)i*...
  25. B

    Does Spring Length Affect Its Extension?

    Consider a sping of length, L m and spring constant K N/m. If a force of F N is applied, we will expect the spring to be extended by x m. So The variables(F,K,x) can be combined to formed an equation, known as the hookes law i.e F=Kx. Does the length of spring have any effect on the extension...
  26. L

    Method of image charges: any extension for oscillating fields?

    I was wondering if the "Method of image charges" could be extended even partly or approximately to oscillating charges. I am not considering nearly-static problems, but really radiating problems. After all, the Poisson equation and the wave equation are rather close ! Therefore, I thought...
  27. L

    Points, extension, time, waves and many times (help )

    Points, extension, time, waves and many times (help!) I have posted this on another forum. Please I am not a spammer, I just mean to find the best informed opinions I have so as to guide me on the path of truth. I have been patiently been trying to think certain riddles through, but the wise...
  28. B

    A balloon and a springfind extension

    Homework Statement A light spring of constant k = 85.0 N/m rests vertically on a table (as shown in part a) of the figure below). A 2.25 g balloon is filled with helium (density = 0.180 kg/m3) to a volume of 5.95 m3 and is then connected to the spring, causing it to stretch as shown in part...
  29. Y

    Finding Extension of Rod with FcosQ and FsinQ Applied

    Hi all, I have a rod which is part of a greater structure and I resolved the forces along the rod. This rod is under tension with a force FcosQ on the left end (force direction towards left) and FsinQ on the other end (force direction towards the right). I need to find the extension of the rod...
  30. M

    Irreducible polynomial in extension field

    Homework Statement Let p\in\mathbb{Q}[x] be an irreducible polynomial. Suppose K is an extension field of \mathbb{Q} that contains a root \alpha of p such that p(\alpha^2)=0. Prove that p splits in K[x]. The Attempt at a Solution I was thinking contradiction, but if p does not split in...
  31. R

    Spring Compression from 8.0kg Mass Sliding 7.00m Down 51deg Incline

    block of mass 8.0 kg slides from rest down a frictionless 51degree incline and is stopped by a strong spring with The block slides 7.00 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest, how far has the spring been compressed...
  32. A

    How Do You Apply Hahn-Banach Theorem to Extend Functions and Preserve Norms?

    Homework Statement I am to illustrate a particular theorem by considering a functional f on R^2 defined by f(x)=\alpha_1 \xi_1 + \alpha_2 \xi_2, x=(\xi_1,\xi_2), its linear extensions \bar{f} to R^3 and the corresponding norms. I'm having a couple problems with this problem. For one, I...
  33. J

    Is u Algebraic Over K if u^2 is Algebraic Over F?

    I'm currently trying to prove that (for a field extension K of the field F) if u\in K and u^2 is algebraic over F then u is algebraic over K. I thought of trying to prove it as contrapositive but that got me nowhere--it seems so simple but I don't know what to use for this. Any help with this...
  34. S

    Proving a Sequence of Extension Fields for $\sqrt{1+\sqrt{2}+\sqrt{3}+\sqrt{5}}$

    Homework Statement Find a sequence of extension fields (i.e. tower) Q= F_{0}\subseteq...\subseteqF_{n}. where \sqrt{1+\sqrt{2}+\sqrt{3}+\sqrt{5}} \in F_{n} Prove that all the steps are non-trivial. except the last one. btw Q is the set of rational number. and 0 and n on F were...
  35. W

    Compactification and Extension of maps.

    Hi: a couple of questions on (Alexandroff) 1-pt. compactification: Thanks to everyone for the help, and for putting up with my ASCII posting until I learn Latex (in the summer, hopefully.) I wonder if anyone still does any pointset topology. I see many people's eyes glace when I...
  36. W

    Finding Fourier extension and if it converges

    Homework Statement Let f(x) = sin(x)/x for |x| <= pi with the obvious definition at x = 0 Extend it periodically. Will the Fourier series converge at x=0?Homework Equations Fourier coefficients: ao = 1/\pi \int_{-\pi}^{\pi} (sin(x)/x) an = 1/\pi \int_{-\pi}^{\pi} (sin(x)/x) * cos(nx) bn =...
  37. M

    Can [F: F ∩ E] Differ from 2 in Quadratic Field Extensions?

    if K/E is a quadratic extension and field F is contained in K such that FE=K and [K:F] is finite, how do I give a non-example to show [F: F intersects E] might not be 2? Thanks a lot!
  38. N

    Energy in a spring system and static extension

    The spring constant of a helical spring is 28Nm^-1. A 0.40 kg mass is suspended from the spring and set into simple harmonic motion of amplitude 60mm. Calculate (i) the static extension produced by the 0.40 kg mass, (ii) the maximum potential energy stored in the spring during the first...
  39. L

    Extension of a basis (exchange theorem)

    hi. ok if I'm using the exchange theorem for extension to a basis. i have the standard basis of 4 dimensional real space is {e1,e2,e3,e4}. and v1=e1+e2 then i can say that the coefficient at e1 is 1 which is non zero therefore i can exchange and get {v1,e2,e3,e4} as a basis. however if v2 =...
  40. M

    Galois extension, lattice of subfields

    K=\mathbb{Q}(\sqrt{2+\sqrt{2}}) is a Galois extension of \mathbb{Q} [I showed this]. Determine \text{Gal}(K/\mathbb{Q}) and describe the lattice of subfields \mathbb{Q} \subset F \subset K. I found that \text{Gal}(K/\mathbb{Q})=\mathbb{Z}_4. I do not know how to draw the lattice of subfields...
  41. W

    Max extension of spring/ magnitude of its acceleration

    Homework Statement An ideal spring has a spring constant k = 30 N/m. The spring is suspended vertically. A 1.1 kg body is attached to the unstretched spring and released. It then performs oscillations. (a) What is the magnitude of the acceleration of the body when the extension of the...
  42. F

    Is Every Algebraic Element of a Field Extension Contained in the Base Field?

    My notes say: If K is an extension of F then A={a in K | a is algebraic} is a subfield of K contained in F. But the elements in A need not be in F, right? Shouldn't it be: If K is an extension of F then A={a in K | a is algebraic} is a subfield of K contained in K. But I don't see the...
  43. F

    In algebra I'm having trouble with this definition: simple extension

    In algebra I'm having trouble with this definition: The extensions K of F is a simple extension of F if F = F(a) for some a in K. What I understand so far: F is a set. But the notation F(a) has me lost-- what is it? Is is the values you get when you plug a into any polynomial over th field F...
  44. C

    Solving an AS Physics Problem: Steel & Brass Extension

    hello, i am currently going over past exam questions to further my knowledge in as physics when i came across this old question which i don't quite understand, a length of steel and a length of brass are joined together. This combination is suspended from a fixed support and a force of 80n is...
  45. E

    Is the Function g Continuous on [a,b]?

    Suppose we have a function f from R to R that is continuous on (a,b]. Define g by g(x) = f(x) if x <> a and g(a) = lim f(x) as x approaches a. Is it true that g is continuous on [a,b]? I would think it is, but I'm having a hard time proving it. I'm trying to use sequences to do this: Suppose...
  46. W

    Extension of Lebesgue Convergence Theorem

    Homework Statement This comes courtesy of Royden, problem 4.14. a.Show that under the hypothesis of theorem 17 we have \int |fn-f| \rightarrow 0 b.Let <fn> be a sequence of integrable functions such that fn \rightarrow f a.e. with f integrable. Then \int |fn-f| \rightarrow 0 if and only...
  47. P

    Proving Cyclic Extension of Finite Galois Group L/F

    Homework Statement Let K be a field, and let K' be an algebraic closure of K. Let sigma be an automorphism of K' over K, and let F be the fix field of sigma. Let L/F be any finite extension of F. Homework Equations Show that L/F is a finite Galois extension whose Galois group...
  48. K

    Does Mass of Cart Affect Spring Extension?

    Homework Statement I'm writing a paper on one of my lab experiments and I'm not sure my physics concept is right? The question asks if the mass of a cart affects the extension of the spring. A spring is attached to a cart which is attached to sting through a pulley and connected to a hanging...
  49. E

    How to Apply Leibnitz Rule When Integration Limits Depend on a Variable?

    Does anybody know, how to find the derivative of the F with respect to a? As far as I know the Leibnitz rule is only applicable, when the integration limits do not depend a. But what happens, when one of the limits is a function of a? F(a,x)=\int ^{c+h(a)}_{c} f[g(a,x)] dx Thank you so much!
  50. marcus

    MDM (a minimal extension of standard model) and PAMELA

    A proposed MDM goes beyond the standard model in a minimal way, so as to produce a candidate for dark matter. Here is story from Nature News: http://www.nature.com/news/2008/080902/full/455007a.html Here is a key excerpt: ==quote== ...It now seems that some physicists have taken...
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