What is Independent: Definition and 743 Discussions

The Independent is a British online newspaper that was established in 1986 as a national morning printed paper. Nicknamed the Indy, it began as a broadsheet and changed to tabloid format in 2003. The last printed edition was published on Saturday 26 March 2016, leaving only the online edition.It tends to take a pro-market stance on economic issues. The newspaper was controlled by Tony O'Reilly's Irish Independent News & Media from 1997 until it was sold to the Russian oligarch and former KGB Officer Alexander Lebedev in 2010. In 2017, a Saudi Arabian investor bought a 30% stake in it.In June 2015, the newspaper had an average daily circulation of just below 58,000, 85% down from its 1990 peak, while the Sunday edition had a circulation of just over 97,000. The daily edition was named National Newspaper of the Year at the 2004 British Press Awards. The website and mobile app have a combined monthly reach of 22,939,000.

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  1. X

    Prove vector space postulate 1.X = X is independent of others

    Hi everyone, I would like to seek help in proving that the vector space postulate 1.X = X cannot be derived from the other postulates, e.g. X + 0 = X, X + (Y + Z) = (X + Y) + Z. The only hint I am given is to construct the "pseudo-scalar product" c # X = the projection of c.X on a fixed...
  2. ZapperZ

    Experimental interference of independent photons

    Don't miss this paper from the Zeilinger group: R. Kaltenbaek et al, PRL 96, 240502 (2006). In particular, read the first paragraph: Zz.
  3. C

    Linearly Independent Killing Fields in n-D Manifold

    A question on a General Relativity exam that I have asks how many linearly independent Killing fields there can be in an n-dimensional manifold. I'm sure I've seen this question before and I think that the answer is n(n+1)/2, but I can't remember why! Any help?
  4. R

    How many independent components

    How many independent components are there to describe the EM field? The six in the field tensor, the four in 4-vector potential or the two when Coulomb gauge is being used? thanks
  5. U

    Can Vectors be Linearly Independent if Det Not Equal 0?

    I don't know if this is a rule, but can a set of vectors be linearly independent if their determinant is not equal to zero? say 4 vectors are given in R^4, if I took the determinant of the 4 vectors such that det{v1 , v2, v3, v4} is not equal to zero, could i say that these vectors are...
  6. H

    Is Tibet an independent country?

    Just like above, is it?
  7. K

    Making society independent of fossil fuels.

    Original here : http://www.everything-science.com/content/view/155/2/ After reading this , a question sprung into my head : "Where are they going to get that much Hydrogen , to replace all the fossil fuels that are used today ?" Any ideas ?
  8. JasonRox

    More independent you make your own happiness

    I picked number 2. Just so you get a sense of how my comments relate to the poll. I'm curious to know what brings happiness to the members here at PF. I have got into many conversations with people where they think my views are just insane and flat out stupid. I believe happiness is...
  9. U

    How to find a linearly independent vector?

    Find a linearly independent set of vectors that spans the same subspace of R^3 as that spanned by the vectors \left(\begin{array}{c} -2 & -1 & -2 \end{array}\right) , \left(\begin{array}{c} -2 & 3 & -8 \end{array}\right) , \left(\begin{array}{c} 0 & -2 & 3 \end{array}\right)...
  10. W

    Solving a Trig Question: Identifying Independent & Dependent Variables

    Here is a trig question that I've been thinking about. I want to know which one would be the independant and the dependant of the points (r , theta)
  11. S

    Is friction independent from area of contact?

    Now, my textbook says that force of friction is independant from the area of contact. But, when the tyres of my bicycle get deflated i have to exert extra force than otherwise. Why?
  12. marcus

    Can Spinfoam Quantum Gravity Naturally Incorporate Feynman Diagrams?

    This seems to be the goal expressed most clearly at Loops '05. it is a slight redirection or change in emphasis in the common program. Matter should naturally occur in quantum gravity. It's explicit. two leading talks in this regard were by Rovelli and Freidel In the latter's talk, Feynman...
  13. K

    Time Independent Rotational Kinematics equation?

    Time Independent Rotational Kinematics equation? Ok i was trying to figure out the angular acceleration for a problem, but i didn't have the time...so the book said to use the "time independent rotational kinematics equation" but i couldn't find it in the book anywhere or even on the...
  14. dextercioby

    Find # of Independent Components of Riemann Curvature in D Dimensions

    How do i find the number of independent components of the Riemann curvature tensor in D space-time dimensions. One is given that the Riemann tensor is an (2,2) irreducible rep of GL(4, \mathbb{R}) and obeys Bianchi I R_{[\mu\nu|\rho]\lambda}=0 Been trying this problem for 3 days and...
  15. G

    Complex Scalar Field in Terms of Two Independent Real Fields

    I am working with a complex scalar field written in terms of two independent real scalar fields and trying to derive the commutator relations. So, \phi = \frac{1}{\sqrt{2}} \left(\phi_1 + i \phi_2) where \phi_1 and \phi_2 are real. When deriving...
  16. Reshma

    Lagrangian of a system is independent of time

    The Lagrangian of a system is given by: L = T - V, T = kinetic energy of the system, V = potential energy of the system. L is a function of the generalised coordinates for a system of N particles given by: L = L(q_1, q_2, ...,q_{3N},\dot{q_1}, \dot{q_2},...,\dot{q_{3N}}, t) Suppose L is...
  17. E

    News Not so independent investigation?

    Heard on the news that G.W.Bush was going to let a committee investigate why the help to New Orleans was so ineffective, and what could have been done better. This sounds like a perfectly good idea. However they also claimed that he would lead this committee by himself! :bugeye: Is this true?
  18. W

    Independent random variables

    Hi I'm wondering if someone can help me out on this question as to how to go about doing it: X_1, X_2... X_7 are independent random variables represnting a random sample of size 7 from the normal N(10, 7) distribution. Find to 3 dp probablitity that the sample total exceeds 88. I tried to...
  19. L

    Speed of Light: Independent to Observer?

    :confused: I am sooo intrigued. The speed of light is independent to the speed of the observer. Why? I don't understand and is it the speed of light only that is independent to the speed of the observer? What makes it so special?
  20. H

    Branch Points and Independent Current

    What is the relationship between the number of branch points and the number of independent current in a circuit?
  21. P

    Probability of Repeated Events

    Hello my question is not academic based just personal. I wanted to know if an event as a probability of P of occurring per day and it occurs everyday for a week. Then, for the week the probability is P? i.e. The probability of picking the correct number in a dice roll is 1/6. Then at...
  22. T

    Good Texts for Independent Study

    Hello. I was wondeirng if anyone knew any good textbooks on Differential Geometry for independent study, at an undergraduate level. Thanks a bunch! -Tim
  23. P

    Linear independent or dependent

    Given y1=3t, y2=|t|, determine whether the given pair of functions is linearly independent or linearly dependent. I can't do the Wronskian on this one since y2 is not differentiable at 0, is there any other way to do this?
  24. P

    Independent or dependent

    prove if {v1,v3}, {v2,v3}, and {v1,v3} are all linearly independent, then{v1,v2,v3} is not linearly independent. I'm having trouble showing that is true other than showing a counter example when it doesn't work, namely when v1=1,v2=0, and v3=1. TIA.
  25. C

    Question about Independent Random Variables and iid

    I have a question about independent random variable: Let say we flip a fair coin, the set of outcome is S={H,T}, P(H)=1/2, P(T)=1/2. Define random variable X:S->R by X(H)=1, X(T)=-1. From what I read in books, I can define X1 and X2 as independent identically distributed (iid) random variables...
  26. L

    How to Find a Maximal Subset of X in V=C[0,1]?

    Let V=C[0,1] be the vector space for all-real valued continuous functions on [0,1]. If X={1,cosx,cos2x, cos3x, cos^2x, cos^3x}. How do I find a maximal subset of X?
  27. D

    Proving Independent Functions: Wronskian for n=2

    Hello out there. I'm working on a proof by induction of the Wronskian and need a little boost to get going. So, here goes: If y_1,...,y_n \in C^n[a,b], then their Wronskian is...
  28. M

    How do I determine linear independence of vectors in 3-dimensional space?

    Hi I'm presented with a set of vectors in \mathbb{R}^{3} v_1 = (a_1,a_2,a_3) v_2 = (b_1,b_2,b_3) and v_3 = (c_1,c_2,c_3) I'm suppose to determain if these vectors are linear independent. My question is: The most simple way of proving the above is that written the vectors as a...
  29. S

    Prove whether or not the following are linearly independent

    f1(x)= (sqrtx) + 5, f2(x)= (sqrtx) + 5x f3(x)= x-1 i don't know how to start
  30. E

    Independent Study: What Goes Into It?

    What goes into an independent study? I need to take one this summer to take a math course that isn't offered then, but I'm not really certain what it involves. Do I study on my own and show up periodically to take exams? Or do I receive one on one instruction from a professor for a few hours a week?
  31. E

    Is a Subset of a Linearly Dependent Set Linearly Dependent?

    I HAVE searched the threads before posting this but I didn't find the same question. Anyway, the question is T-F: A subset of linearly dependent set is linearly dependent. I think it is F, because for non-zero linearly dep. set a proof can be constructed so that some...
  32. A

    News What do you think should Kosovo be an independent country, or not?

    Basing it on history?
  33. T

    Independent study on Logarithms

    I'm in grade 11 and I have to do an independent study on Logarithms. I need a problem or puzzle that I will solve after learning logarithms. I was wondering if someone had an example of a really good use of logarithms (i.e. something made a lot easy by the use of logarithms).
  34. T

    Time-step independent friction model

    Help with Friction Greetings , all fellow scientists! I've been struggling with time-step independent physics for a programming project. The problem is that it doesn't seem to be time-step independent after all. Here's some of it in a pseudo-code form. It seems to be the friction part...
  35. P

    What is an Independent Variable?

    What is an independent variable. Is that what you have to solve for? Like for example in the problem; y^2 = x - y.. If x is the independent variable, is that what I have to solve for, or does it mean something completely unrelated?
  36. J

    What does it mean by background independent and background dependent?

    What does it mean by background independent and background dependent?
  37. J

    Exploring Background Independent Physics

    What is background independent physics?
  38. P

    Prove any three vectors of R^3 are linear independent

    I was just wondering if I can make this statement, if I was to prove any three vectors of R^3 are linear independent, can I also say those three vectors span R^3? Philip
  39. marcus

    Background Independent Quantum Gravity-new survey paper

    Background Independent Quantum Gravity---new survey paper http://arxiv.org/gr-qc/0404018 this just out Background Independent Quantum Gravity: A Status Report Abhay Ashtekar, Jerzy Lewandowski 125 pages, 5 figures "The goal of this article is to present an introduction to loop quantum...
  40. marcus

    Online copy? Background Independent Quantum Gravity: a Status Report

    several recent papers have cited Ashtekar and Lewandowski "Background Independent quantum gravity: a status report" as in preparation or as a 2003 preprint not up on arxiv Does anyone know of a draft version online? I was reminded of their status report paper when I saw it as the...
  41. MathematicalPhysicist

    Background independent string theory

    can there be such an ST with BI?
  42. R

    Advice on Advanced Calculus Textbooks for Independent Study

    Hello I want to buy a somewhat advanced calculus textbook to independently study from. The text doesn't need to be too pure and rigorous, but it should be more so than an engineering math text would be because I want to eventually get into theoretical physics, and I don't want to find out...
  43. P

    Ow is velocity independent of mass

    How is velocity independent of mass, specifically when talking about the Conservation of Mechanical Energy. Thanks for your time.
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