What is Extension: Definition and 293 Discussions

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. M

    MHB The extension is Galois iff E is a splitting field of a separable polynomial of F[x]

    Hey! :o Let $E/F$ be a finite extension. I want to show that this extension is Galois if and only if $E$ is a splitting field of a separable polynomial of $F[x]$. I have done the folllowing: $\Rightarrow$ : We suppose that $E/F$ is Galois. So, we have that the extension is normal and...
  2. M

    MHB The extension is Galois iff H_i is a normal subgroup of H_{i-1}

    Hey! :o Let $E/F$ be a finite Galois extension and let the chain of extensions $F = K_0 \leq K_1 \leq \dots \leq K_n = E$. Let $G = Gal(E/F)$ and, for $i = 0, 1, \dots , n$, let $H_i$ be the subgroup of $G$, that corresponds to $K_i$ through the Galois mapping. I want to show that, for any...
  3. PsychonautQQ

    Prove an extension is not normal

    Homework Statement let b be a square root of 1+i, show that Q(b):Q is not a normal extension. Also, what is the Galois group of the extension? Homework EquationsThe Attempt at a Solution so b = +/- (1+i)^(1/2), and it's minimal polynomial is x^4+4 which has roots -(2)^1/2 and 2^(1/2) that are...
  4. PsychonautQQ

    Identifying type of field extension

    Homework Statement Let [ S] = {2^(1/n) | for all n in the natural numbers}, is Q[ S] algebraic? finite? simple? separable? Homework EquationsThe Attempt at a Solution I believe it is algebraic because every element of [ S] will be a root of x^n-2, and every element of Q is obviously algebraic...
  5. K

    I Evaluation of SMASH - most minimal extension of SM

    does this paper Standard Model-Axion-Seesaw-Higgs Portal Inflation. Five problems of particle physics and cosmology solved in one stroke Guillermo Ballesteros, Javier Redondo, Andreas Ringwald, Carlos Tamarit (Submitted on 5 Oct 2016) We present a minimal extension of the Standard Model (SM)...
  6. M

    MHB How to Prove Galois Extension Statements in a Normal and Separable Field?

    Hey! :o Let $E/F$ be a Galois extension. I want to show the following: $F\leq K\leq E \Rightarrow \mathcal{F}(\mathcal{G}(E/K))\geq K$ $H\leq \mathcal{G}(E/F)\Rightarrow \mathcal{G}(E/\mathcal{F}(H))\geq H$ Since $E/F$ is a Galois extension, we have that the extension is normal and...
  7. Metals

    B A statistical definition of Young's Modulus?

    Young's Modulus is usually defined as the intrinsic property of a material indicating it's stiffness, or it's ability to resist deformation. Though, it is measured in Pa, meaning it should have some statistical description. Spring constant, for example, can be define as the stiffness of an item...
  8. M

    MHB Extension of degree 2 is normal

    Hey! :o I want to show that each extension of degree $2$ is normal. I have done the following: Let $K/F$ the field extension with $[F:K]=2$. Let $a\in K\setminus F$. Then we have that $F\leq F(a)\leq K$. We have that $[K:F]=2\Rightarrow [K:F(a)][F(a):F]=2$. There are the following...
  9. PsychonautQQ

    Proving an extension is simple

    Homework Statement Let c be a primitive 3rd root of unity in the complex numbers and b be the real root of x^4-2=0. If a = c*b, show that Q(b,c) = Q(a)Homework EquationsThe Attempt at a Solution So [Q(a):Q(c)]=3 and [Q(a):Q(b)]=4, and c and b contain no 'overlapping material', so [Q(a):Q)=12...
  10. M

    MHB Eisenstein polynomial and field extension

    Hey! :o Let $f = x^4−2x^2−1 \in \mathbb{Q}[x]$. We have that $f(x+1)=(x+1)^4-2(x+1)^2-1=x^4+4x^3+6x^2+4x+1-2(x^2+2x+1)-1=x^4+4x^3+4x^2-2$ We have that $p=2$ divides all the coefficients $4,4,-2$ and $p^2=4$ does not divide the constant term $-2$. So, the polynomial $f(x+1)$ is Eisenstein...
  11. caffeinemachine

    MHB Finite Extension Simple iff Purely Inseparable Closure Simple

    Question. Is it true that a finite extension $K:F$ is simple iff the purely inseprable closure is simple over $F$? I think have an argument to support the above. First we show the following: Lemma. Let $K:F$ be a finite extension and $S$ and $I$ be the separable and purely inseparable...
  12. I

    How do I calculate the extension and strain at peak load?

    Homework Statement If a question gives us a max load with different extensions, how do I calculate the strain? For example: 1900KN=x mm 1900KN=x mm 2000KN=x mm 2000KN=x mm 2000KN=x mm 1900KN=x mm 1900KN=x mm Homework Equations strain= ΔL / L The Attempt at a Solution What I think is...
  13. Q

    Electricity Laws for 5km Extension Cord Use

    So, complete hypothetical on laws governing power transmission over a distance: Lets say I have a generator as a source of power - and attached to that is FIVE KILOMETERS worth of extension cords. :) In this situation, what laws of electricity do I need to look out for? Voltage drop over...
  14. C

    3 Extension power cords connected one after another

    Hi, I have a friend with whom I got into an argument of what happens when you multiple power cord extension connected. So here is the problem: - There are 3 extension power cords, each power cord has 3 plugs. - First extension power cord is connected to the wall outlet - Second one is...
  15. PsychonautQQ

    Finding roots in an extension field

    Homework Statement Let q be a root of p(x) = x^3 + x^2 + 1 in an extention field of Z2 (integers modulus 2). Show that Z2(q) is a splitting field of p(x by finding the other roots of p(x) hint: this question can be greatly simplified by using the frobenius automorphism to find these zero's...
  16. terryds

    Extension of spring pulled at both ends

    Homework Statement A spring with spring constant 50 N/m is pulled with 10 N force at both ends of the spring. So, the extension of spring length is.. A. 0.0 m B. 0.1 m C. 0.2 m D. 0.3 m E. 0.4 m Homework Equations F = k Δx The Attempt at a Solution F = 10 N <--- 0000000000000000000000...
  17. Math Amateur

    MHB Extension of Scalars: Dummit & Foote's Section 10.4 Q&A

    I am reading Dummit and Foote's book: Abstract Algebra ... ... and am currently focused on Section 10.4 Tensor Products of Modules ... ... I have a basic question regarding the extension of the scalars ... Dummit and Foote's exposition regarding extension of the scalars reads as...
  18. Math Amateur

    I Extension of scalars .... D&F, Section 10.4: Tensor Products

    I am reading Dummit and Foote's book: Abstract Algebra ... ... and am currently focused on Section 10.4 Tensor Products of Modules ... ... I have a basic question regarding the extension of the scalars ... Dummit and Foote's (D&Fs) exposition regarding extension of the scalars reads as...
  19. G

    Divergence and transversal extension integral definitions

    Hi. I am reading a paper about gaussian beams and the author says that gaussian beams have simultaneously minimal divergence and minimal transversal extension. In order to prove it, the author states that \mathrm{divergenece} \propto \int_{-\infty}^{+\infty} \frac{d\,k_{x}}{2\pi}...
  20. L

    Backwards extension torque wrench formula + cheat sheet review

    Hello! I took a quality certification test yesterday and there was a question on there about torque wrench formulas. I didn't have anything about that in my notes, so I took some time this morning to create a cheat sheet based on what I could find on the web. 1) In some of the forums, they...
  21. P

    Finding Spring Constant from Mass and Extension

    Homework Statement A block of mass 1 kg is attached to a spring. The spring extends by 10 cm. Find spring constant.Homework EquationsThe Attempt at a Solution Potential energy of spring = kx2/2 work done by block = PE Hence mg*x=kx2/2 ∴1*9.8*0.1=k*0.1*0.1/2 ∴k=196N/m But solution says mg = kx...
  22. M

    Polynomial splits over simple extension implies splitting field?

    This is a question that came about while I attempting to prove that a simple extension was a splitting field via mutual containment. This isn't actually the problem, however, it seems like the argument I'm using shouldn't be exclusive to my problem. Here is my attempt at convincing myself that...
  23. K

    MHB What is the Simplest Form of a Field Extension of the Reals?

    I am happy with my solutions of questions 1-4 below, but need some help on question 5. 5. The squares in the reals are simply the positive reals and the non-squares are the negative reals so the quotient of two no squares is the quotient of two negative reals that is a positive real of in...
  24. B

    Maximum extension of a spring on an inclined plane

    Homework Statement A block of mass ##M = 1 kg## is placed of a fixed rough incline of inclination ##\theta=sin^{-1} \frac{7}{10}## and coefficient of friction ##\mu=\frac{1}{\sqrt{51}}##. It is connected to a spring of spring constant 100 N/m. Initially the spring is in natural state with...
  25. O

    The meaning of 'Extension' in History of Physics

    I was reading the Wikipedia page on Dynamism in order to get an idea of the motivation and thinking behind Liebniz's physics. In it there is this paragraph: In the opening paragraph of Specimen dynamicum (1692), Leibniz begins by clarifying his intention to supersede the Cartesian account of...
  26. Mayzu

    Maximum extension of a bungee cord

    Homework Statement (a) An 81 kg student is launched from a bridge by his best friends, some 50 metres above the river surface. Fortunately, he is attached to a 30 m bungee cord with a spring constant of 270 N/m. i) What is the equilibrium length of the bungee cord, including the force of...
  27. freutel

    What is the speed when a disk has reached maximum extension?

    Homework Statement Two identical disks with mass m and radius r are connected via a massless wire of length L which is winded up around both disks. Disk B is connected to the ceiling and is free to rotate around its axis. Disk A is besides disk B and will fall due to the gravitational force...
  28. caffeinemachine

    MHB Understanding Extension of Scalars in a Vector Space

    $\newcommand{\R}{\mathbf R}\newcommand{\C}{\mathbf C}$ Low-Tech Complexification: Let $V$ be a finite dimensional vector space over $\R$. We can forcefully make $W:=V\times V$ into a complex vector space by defining addition component-wise and product $\C\times W\to W$ as $$ (a+ib)(u...
  29. Satvik Pandey

    Maximum extension in spring connecting two masses.

    Homework Statement In the figure shown below all surfaces are friction-less. Find the maximum extension in the spring(in meters) , if the blocks are initially at rest and the spring is initially in its natural length. Details and Assumptions: F=30N k=700N/m m=5kgHomework EquationsThe Attempt...
  30. P

    UC Berkeley Extension program for IC design or semicon tech

    Hello everyone, I graduated with a BSEE in 2008 and tried a PhD program in EE (semicon device specialization) for a while but it didn't work out. I struggled with an illness that forced me to drop out. I have been working in industry (NOT The semicon industry) since leaving the PhD program...
  31. binbagsss

    Schwarzschild Extension Coordinate Transformation Algebra

    So I have the metric as ##ds^{2}=-(1-\frac{2m}{r})dt^{2}+(1-\frac{2m}{r})^{-1}dr^{2}+r^{2}d\Omega^{2}##* I have transformed to coordinate system ##u,r,\phi, \theta ##, where ##u=t-r*##(2), where ##r*=r+2m In(\frac{r}{2m}-1)## and to the coordinate system ##v,r,\phi, \theta ##, where...
  32. binbagsss

    Extension of Schwarzschild Light Cones: White Hole/Black Hole

    The coordinates ##u## and ##v## are defined as ##u=t+r*##, ##v=t-r*##, where ##r*=r+2M In(\frac{r}{2M}-1)##. In ##u,r,\theta,\phi ## coordinates the radially null geodesics are given by: ##\frac{du}{dr}=0 ## for infalling, ##\frac{du}{dr}=2(1-\frac{2M}{r})^{-1} ## for outgoing. In the...
  33. M

    Extension of measure on sigma-algebra

    Suppose ##\mu:\mathcal{F}\rightarrow[0,\infty)## be a countable additive measure on a ##\sigma##-algebra ##\mathcal{F}## over a set ##\Omega##. Take any ##E\subseteq \Omega##. Let ##\mathcal{F}_{E}:=\sigma(\mathcal{F}\cup\{E\})##. Then, PROVE there is a countable additive measure...
  34. George Zucas

    0.2% Offset vs. 0.5% Extension Under Load Yield Strength

    Hello everyone, I have designed a part that should be able to withstand a shear stress of 43 MPa ( give or take). The part will be made of Nickel Aluminum Bronze (CuAl10Ni5Fe4). When I check yield strength values for this material (I'll multiply it by 0.6 to estimate its shear strength), they...
  35. A

    SHM Question: What is the maximum extension of the spring?

    Homework Statement A 50g block is attached to a vertical spring whose stiffness constant is 9N/m. The block is released at the position where the spring is unextended. What is the maximum extension of the spring? How long does it take the block to reach the lowest point? Homework Equations...
  36. H

    Does buoyancy affect the extension of a real spring?

    In Hooke's law, F=-kx. Assume that a mass is hung from the end of an ideal massless spring, the spring stretches a distance of x. However, in real life the spring has mass and it is submerged in a "fluid" of air. Compared to an ideal spring, would the real spring have a slightly different...
  37. A

    Finding Strain Without Extension: A Guide

    Homework Statement hi guys i have a sheet of i have the W,L and T a force and also the elastic modules etc now my issue is i need to find the strain i have the stress etc but the is no extension figure given i have the usual strain equation e=x/l can anyone point me in the right direction in...
  38. PsychonautQQ

    Basic transcendental field extension question

    My textbook says: If u is transcnedetal over F, it is routine to verify that: F(u) = {f(u)g(u)^(-1) | f,g in F[x]; g /= 0} However, me being the scrubbiest of all scrubs does not understand what they did here. First of all, I don't understand why they needed to invert the g(u) function. It...
  39. M

    Calculating the maximum load that can be carried & extension

    Ive been given a question which I'm stuck on and cannot answer. I've only been able to calculate the maximum allowable working stress and other then that I am stuck on how to answer the following question: A specimen of the same material that was used in the above test (mild steel), had a cross...
  40. B

    Fourier series and even extension of function

    I'm trying to solve this exercise but I have some problems, because I haven't seen an exercise of this type before. "f(x)= \pi -x in [0, \pi] Let's consider the even extension of f(x) in [-\pi, \pi] and write the Fourier Series using this set ( \frac{1}{\sqrt{2 \pi}}, \frac{1}{\sqrt {\pi}}...
  41. praveenpandiyan

    How to Calculate Extension of a Rod with Varying Young's Modulus?

    Homework Statement see attachement Homework Equations dl= PL/AE The Attempt at a Solution as you see here my youngs modulus E varies linearly. i doubt that adding up E1 &E2 wld give solution.. any help?
  42. S

    Fortran [Fortran] How to open .hdf5 file extension

    Hello, i am relatively new linux user so please be as thoroughly descriptive as you can. i am starting a project and i have a file "file.hdf5" which contains velocity data i need to process in my fortran program. What do i have to do in order to use the data inside this file? i normally use...
  43. M

    MHB Field extensions and degree of odd prime numbers

    Hey! :o Let $p$ be an odd prime number. We set $a=Re \left (e^{\frac{2\pi i}{p}}\right )$. Show that: 1) $$\mathbb{Q}(a)\leq \mathbb{Q}(e^{\frac{2\pi i}{p}}) \text{ and } \left [\mathbb{Q} \left (e^{\frac{2\pi i}{p}} \right ):\mathbb{Q}(a)\right ]=2$$ 2)...
  44. V

    Need help with files with "mlp" extension

    Good Evening! I have a few files with "mlp" extension, which are pH vs Time graphs from a lab data logger. The original software is unavailable to me, but in the Internet I can`t find anything to open it. Please, help!
  45. D

    Finding the extension of a spring

    Homework Statement A weight of ##50## N is suspended from a spring of stiffness ##4000## N/m and is subjected to a harmonic force of amplitude ##60## N and frequency ##6## Hz. Homework EquationsThe Attempt at a Solution Since ##W = mg = 50##, we have that the suspended mass, ##m = 5.10204##...
  46. D

    MHB Extension of Spring from Mass of 50N

    A weight of \(50\) N is suspended from a spring of stiffness \(4000\) N/m and is subjected to a harmonic force of amplitude \(60\) N and frequency \(6\) Hz. Since \(W = mg = 50\), we have that the mass, \(m = 5.10204\), and we know that \(f = \frac{\omega}{2\pi} = 6\) so \(\omega = 12\pi\)...
  47. Hunter Brandon

    Flat & Sticky Extension Cord: No More Mess, No Trips!

    I have an idea about an extension cord that is flat and sticky like tape. This will cause less mess around the TV and will prevent anyone from tripping over any cords
  48. H

    QBism - Is it an extension of "The Monty Hall Problem"?

    I just watched a video discussion on the modern interpretations of the wave function. In it I was introduced to QBism, i.e. Quantum Bayesianism. To me sounded a lot like the famous Monty Hall problem. Is QBism's probability similar to that?
  49. P

    Calculate persistence length from force extension data of a single DNA

    Hello! From a data set of F-x measurements of a single dsDNA molecule I want to calculate the persistence length P . So I plotted \frac {1} {\sqrt{(F)}} vs. x and fitted these data points (linear). According to an interpolation formula the extension x of a worm like chain with contour...
  50. Ackbach

    MHB VimFx Firefox Extension: Speed Up Browsing with Vim Keybindings

    I just discovered VimFx extension for Firefox: it installs some Vim-like keybindings for Firefox. Unfortunately, you don't get Vim keybindings for text boxes such as the one I'm in now. But you do get some very nice keyboard-only shortcuts for browsing that make sense to a Vim user. If you're...
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