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. K

    Picard-Vessiot Extension over a Differential Field?

    Given a differential field F and a linear algebraic group G over the constant field C of F, find a Picard-Vessiot extension of E of F with G(E/F)=G: This isn't homework, just something I saw in a book that I was curious about. The author says that this can be shown but doesn't illustrate how...
  2. W

    B-L extension of the Standard Model

    i need what we mean by B-L extension of the Standard Model ?
  3. L

    How to prove the field extension is algebraically closed

    Suppose that E is a field extension of F, and every polynomial f(x) in F[x] has a root in E. Then E is algebraically closed, i.e. every polynomial f(x) in E[x] has a root in E. I've been told that this result is really difficult to prove, but it seems really intuitive so I find that...
  4. G

    Approximation of string extension length

    Homework Statement A string of length a is stretched to a height of y when it is attached to the origin so making a triangle with length L=\sqrt{a^{2}+\frac{y^{2}}{a^{2}}} and therefore a length extension ΔL= \sqrt{a^{2}+\frac{y^{2}}{a^{2}}}-a which simplifies to...
  5. T

    Extension on a simple probability question

    An experiment consists of tossing a pair of dice: 1) Determine the number of sample points in the sample space 2) Find the probability that the sum of the numbers appearing on the dice is equal to 7 Issue: Ok so I know how to do this problem, but my question comes with respect to the...
  6. T

    Arrangements of Springs and Extension

    Homework Statement http://www.xtremepapers.com/CIE/International%20A%20And%20AS%20Level/9702%20-%20Physics/9702_s05_qp_1.pdf (not sure how to post the picture directly..) Number 20 Homework Equations F=kx 1/(n springs) weight is supported if parallel n if in series The Attempt at a Solution...
  7. L

    What is the latest on the Group Extension Problem?

    Let K be a finite group and H be a finite simple group. (A simple group is a group with no normal subgroups other than {1} and itself, sort of like a prime number.) Then the group extension problem asks us to find all the extensions of K by H: that is, to find every finite group G such that...
  8. W

    How Do You Calculate the Dimension of F(u,v) Over F(u)?

    Hello, I have a quick question about extension fields. We know that if E is an extension field of F and if we have got an irreducible polynomial p(x) in F[x] with a root u in E, then we can construct F(u) which is the smallest subfield of E containing F and u. This by defining a homomorphism...
  9. S

    Transfinite Theory as an Extension of the Natural Numbers

    Greetings, comrades! In a previous thread, a user articulated a common argument: His analogy mapping knights to horses makes intuitive sense, but how can we apply this idea to two infinite sets of knights and horses? How can we treat finite and transfinite sets equal in that sense and...
  10. T

    Plotting Length of Spring vs Load: Find Unloaded Length & Extension

    Homework Statement The following results were obtained when a spring was stretched: Load/N: 1.0 3.0 4.5 6.0 7.5 Length of spring/cm:12.0 15.5 19.0 22.0 25.0 A) use the results to plot a graph of length of spring against load. b) use the graph to find the: i)...
  11. S

    MHB Degrees of a Field Extension: How to Find Basis and Degree of a Field Extension

    Hi, I've been asked to find $[ \mathbb{Q}(\sqrt{2}, i ): \mathbb{Q} ]$, and to write down a basis. Now I know that $[ \mathbb{Q}(\sqrt{2}, i ): \mathbb{Q} ] = 4$, and that a basis could be $ \left \{ 1, i, \sqrt{2}, i\sqrt{2}\right \} $ it is whether the way I am explaining how I arrived here...
  12. S

    Quick help finishing off a proof: extension of p-adic fields

    Homework Statement Let L_1/K,\,L_2/K be extensions of p-adic fields, at least one of which is Galois, with ramification indices e_1,\,e_2 . Suppose that (e_1,\,e_2) = 1 . Show that L_1 L_2/K has ramification index e_1 e_2. Homework Equations I have most of the proof done: I'm trying to show...
  13. T

    Prove that an element is algebraic over a field extension

    Homework Statement Let F|K be a field extension. If v e F is algebraic over K(u) for some u e F and v is transcendental over K, then u is algebraic over K(v).Homework Equations v transcendental over K implies K(v) iso to K(x). Know also that there exists f e K(u)[x] with f(v) = 0.The Attempt at...
  14. T

    When is an element of a finitely generated field extension algebraic?

    Hungerford says that But if we take K = ℝ and K(x_{1}) = ℝ(i) = ℂ, we have that i is not in ℝ yet is algebraic over ℝ. Guess I'm missing something here. Is it that this need not be true for simple extensions if the primitive element is algebraic over the field?
  15. H

    Smooth Extension of Locally Defined Function on Manifold

    how to extend a locally defined function to a smooth function on the whole manifold ,by using a bump function?
  16. A

    Two block-spring system - finding max extension in the spring

    Homework Statement 2 blocks, mass 'M1' & 'M2' are connected by an ideal spring of force constant 'k' and placed on a frictionless surface. Force 'F' is applied on the 'M2' block. We have to find the maximum extension in the spring. 2. The attempt at a solution (1) The conservation of energy...
  17. S

    Does charges remain in an extension cord when unplugged?

    I am referring to this: A brainwave hit me and I wondered the following: If the moment when i unplug or switch it off (In my country they have a switch for added safety reason), the live wire happens to be at the peak of the AC curve, will my extension cord effectively become similar to a...
  18. B

    Electric Field extension through

    1. The problem statement 1)Do electric fields extend through a vacuum? 2)Do electric fields extend through the interior of a insulator? 3)Do electric fields extend through the interior of a conductor? I am just starting to understand electric fields but I am still very unsure, and am not...
  19. T

    Bungee Jumping-Tension+Air resistance with regards to max extension

    Homework Statement Bungee Jumping l=natural length of rope x=extension of rope y=total distance fallen m=mass,a=acceleration,v=velocity,g=acceleration due to gravity k=air resistance co-efficient Given data: The rope is stretched to twice its natural length by a mass of 75kg hanging at rest...
  20. R

    Why Does a Heavy Spring Extend Differently Under Its Own Weight?

    A spring of mass M is suspended from the ceiling of a room. Find the extension in the spring due to its own weight if it has a spring constant of value k . I am getting answer as \frac{Mg}{2k} , but the answer given in back of the book is \frac{Mg}{3k}. What I did was : Let the natural...
  21. L

    Stretching a rubberband mulitple times, increases extension length

    My group did an experiment on rubber bands. The rubber bands were stretched multiple times from 50, 100 and 150 times and then a weight was attached to the rubber band to record its extension. On average the rubber band's extension increased by 10 cm after each increment of 50 stretches. I...
  22. N

    Is this correct? Field extension of the rationals

    By F[X] I mean the polynomials with coefficients in field F. By F(X) I mean the rational polynomials. I have a feeling that \boxed{ \mathbb Q( \sqrt 2 ) \cong \frac{\mathbb Q[X]}{(X^2-2)}} . (if not readable: the RHS is with [X]) Is this true? If so, how can I prove it? I suppose it would...
  23. N

    Same symbol, different meanings? Subgroup index & field extension

    Hello, Say we have field (F,+,.) and field extension (E,+,.), then the degree of the field extension (i.e. the dimension of the vector field E across the field F) is given the symbol [E:F] . But we can also see F and E as the groups (F,+) and (E,+), and then the same symbol denotes the...
  24. K

    Extension of Rational Roots Test to UFDs

    Homework Statement Show that p(x) = x^2 - \sqrt2 is irreducible in \mathbb Z[\sqrt 2] . The Attempt at a Solution I think I have this, but I just want to make sure my reasoning is correct. I'm sure there are other ways. Firstly, it is sufficient to show that p(x) is irreducible in the...
  25. F

    Homotopy extension property for CW pairs (Hatcher)

    I do not understand the proof of Proposition 0.16 in Allen Hatcher's book Algebraic Topology. If someone has the book, could you please clarify the part of the proof when he says "If we perform the deformation retraction of X^n\times I onto X^n\times\{0\}\cup (X^{n-1}\cup A^n)\times I during...
  26. E

    Extension of Finite Fields: Proving the Number of Elements in F(\alpha)

    Homework Statement Let E be an extension of a finite field F, where F has q elements. Let \alpha \epsilon E be algebraic over F of degree n. Prove F \left( \alpha \right) has q^{n} elements. Homework Equations An element \alpha of an extension field E of a field F is algebraic over F if f...
  27. M

    Proving Gauss's Lemma Extension in Polynomial Factoring

    Ok, the book I'm reading states Gauss's lemma as such: If f(x) is a monic polynomial with integral coefficients that factors into two monic polynomials with coefficients that are rational, f(x) = g(x)h(x), then g(x), h(x) \in \mathbb{Z}[x]. Now one of the exercises says to prove that: If...
  28. K

    Exploring Degree Odd Polynomials and Extension Fields of K

    1.Let F be an extension field of K and let u be in F. Show that K(a^2)contained in K(a) and [K(u):K(a^2)]=1 or 2. 2.Let F be an extension field of K and let a be in F be algebraic over K with minimal polynomial m(x). Show that if degm(x) is odd then K(u)=K(a^2). 1. I was thinking of...
  29. PainterGuy

    C/C++ C++ header files with and without h extension

    c++ header files with and without "h" extension hi fine people,:wink: i have seen some people use header files with ".h" extension and some without it. what is reason? i think there are some header files where you are required to use ".h" such as "#include <windows.h>. you can not use...
  30. K

    Minimal Polynomial, Algebraic Extension

    1.Let F=K(u) where u is transcedental over the field K. If E is a field such that K contained in E contained in F, then Show that u is algebraic over E. Let a be any element of E that is not in K. Then a = f(u)/g(u) for some polynomials f(x), g(x) inK[x] 2.Let K contained in E...
  31. J

    What is the Purpose of rundll32.exe and rundll.exe Commands on Windows?

    I've been seeing this certain file extension lately on my computer, but I do not know what programs to run them. What are file extension dll?
  32. C

    Extension in Spring Homework: Find x

    Homework Statement The Attempt at a Solution first using the initial extension i found out that k = 200. velocity of block = √(2gh) = √(2*10*.45) = 3 then using conservation of momentum ... 120 * 3 = 320 * V V = 1.125 this kinetic energy converts into potential energy of...
  33. B

    Exerting torque on an extension spring to overcome friction in a helical tube

    Does anyone know of an equation that models the build up of potential energy in an extension spring induced by twisting it when its motion is otherwise constrained in the transverse direction?
  34. W

    Talkita is a Google Chrome extension

    I'm surprised no one has posted a thread on this as yet. Talkita is a Google Chrome extension that allows you to talk to people who are on the same website as you. Check it out! https://chrome.google.com/webstore/detail/gffkbdneeepeccpbpoaciomdibieaiii This way, I can chat with whoever is...
  35. T

    Greatest Common Divisor in a strange extension ring.

    Homework Statement I need to show that two elements in \textbf{Z}[\sqrt{-5}] have gcd = 1. The elements are 3 and 2+\sqrt{-5} Homework Equations The Attempt at a Solution My way of thinking was if I can show that both elements are irreducible, then they are both prime and hence...
  36. T

    Showing elements in an extension field Z[sqrt(-5)] have gcd = 1

    Homework Statement Show that the elements 3 and 2+\sqrt{-5} in \textbf{Z}[\sqrt{-5}] have a greatest common divisor of 1, but the ideal I = (3, 2+\sqrt{-5}) is not the total. Conclude that I is not principle. Homework Equations The Attempt at a Solution I have got as far as...
  37. R

    Extension of Variation of Parameters to First Order Non-Linear ODE?

    The equation of motion of a rocket with mass depletion during ascent and subject to drag forces can be written as M(t) dV/dt = A - M(t)g - BV^2 (Eq. 1) with initial condition V(t=0) = 0 (V is velocity and t is time) Let us assume a linear mass depletion according to...
  38. A

    Galois theory. field extension, constructible/algebraic numbers

    Homework Statement Let K be the subfield of all constructible numbers in C Let A be the subfield of all algebraic numbers in C Is the field extension A:K finite? The Attempt at a Solution I don't know where to start! I have read and understood proofs that all constructible numbers...
  39. E

    Relative Extension of Collagen Fiber: %0.8

    [b]1. Collagen fiber is stressed with 12 N force. The cross-sectional area of the fiber is 3 mm2, its coefficient of elasticity is 500 MPa. Give the percentage of relative extension. I think i have found the correct equation but i can't seem to find the rigth answer which is suposed to be...
  40. r-soy

    How Do You Evaluate the Extension Value Under a 6N Load Using F = kx?

    evaluate the value of extension ( x) which elongate under the action of load (w) of 6 N ? [Use your results obtained from rest 1 ] please help me How i can solve this question because I don't understand it clearly
  41. V

    Elitzur–Vaidman Bomb-Tester Extension for Boolean Variable Return

    Hey everyone, I'm new to the forums so sorry if I'm making a post that's obviously ridiculous but my level of understanding only takes me so far, hence the need to post here. I just finished my bachelor of science degree in Biochemistry this summer but only have an A-level qualification in...
  42. W

    Extend Isometry from Semi-normed to Normed Space

    Hello all, May someone help me on this question: Suppose the map F is an isometry which maps a dense set H of a semi-normed space \mathcal{H} to a normed space \mathcal{G} , now the theorem said we can extend this isometry in a unique manner to a linear isometry of the semi-normed...
  43. C

    Extension of the Triangle Inequality

    Pretty much knows the triangle inequality. \left| a + b \right| \le \left| a \right| + \left| b \right| I was reading a source which asserted the following extension of the triangle inequality: \left| a + b \right|^p \le 2^p \left(\left| a \right|^p + \left| b \right|^p\right) This is...
  44. B

    Continuous Extension to a Point (Factoring Question)

    Homework Statement Define f(6) in a way that extends to be continuous at s=6. Homework Equations None. Only limits are required. The Attempt at a Solution In order to figure out which point needs to be added to the function, I have to find the limit of this function as s->6. This will...
  45. Y

    How to Calculate Norms of Field Extensions in Galois Theory

    Hello everyone, I need some help with finding norms of the field extension. I feel pretty comfortable when representing norms as determinants of linear operators but I seem to be stuck with representing norms as product of isomorphims. I have read Lang's GTM Algebra, but I really would...
  46. radou

    Extension of a continuous function

    Homework Statement Let f : A --> Y be a continuous function, where A is a subset of X and Y is Haussdorf. Show that, if f can be extended to a continuous function g : Cl(A) --> Y, then g is uniquely determined by f. The Attempt at a Solution I think I can solve this on my own, but I...
  47. B

    Solve Lebesgue-Stieljes Measure of F(x) w/ Caratheodory Extension Thm

    Homework Statement Let (R, \mathcal{B}, \mu_F) be a measure space, where \mathcal{B} is the Borel \sigma-filed and \mu_F is the Lebesgue-Stieljes measure generated from F(x) = \sum^\infty_{n=1}2^{-n}I(x \ge n^{-1}) + (e^{-1} - e^{-x})I(x \ge 1) Use the uniqueness of measure extension in...
  48. R

    Here's an extension of a list posted earlier. If anybody can think of

    Here's an extension of a list posted earlier. If anybody can think of any additions to the list, please post :D! Perspectives of the world: ------------------------------- Optimist – The glass is half-full. Pessimist – The glass is half-empty. Existentialist – The glass is. Fatalist – The...
  49. E

    Is E an Algebraic Closure of Q a Normal Extension?

    normal extension - an algebraic field extension L/K is said to be normal if L is the splitting field of a family of polynomials in K[X]. (wikipedia) I have a question about the 'family of polynomials' it says the family should be arbitarary large? if E be an algebraic closure of Q(rational...
  50. P

    Calculating the Extension of a Spring with and without a Hanging Mass

    hey all, this is my first post, sorry for not introducing myself formally, but i am on a tight schedule, getting ready for my retakes. my question is; a 5kg monkey, initially at rest, starts climbing up the weightless rope at 0.2g. the top end of the spring is connected to a spring with...
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