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. A

    Proving Linear Independence: If v\notin\left\langlev1,...,vk\right\rangle

    Homework Statement If v11,...,vk,v are linear independent, prove that v\notin \left\langlev1,...,vk\right\rangle Homework Equations n/a The Attempt at a Solution i can prove it by contrapositive, but I'm curious how to proof it with "If v11,...,vk,v are linear...
  2. M

    Can dy and dx in dy/dx Be Treated as Independent Variables?

    A quote from the book of T.L. Chow 'Mathematical methods for physicists' The reader may notice that dy/dx has been treated as if it were a ratio of dy and dx, that can be manipulated independently. Mathematicians may be unhappy about this treatment. But, if necessary, we can justify it by...
  3. J

    Are these two sub-sigma-algebras independent?

    Homework Statement Let \Omega=\{HH,HT,TH,TT\} and let F and U be two partitions of \Omega: F=\{G,K\} with G=\{HH,TT\} and K= \Omega\backslash G, while U=\{V,W\} where V=\{HH,TH\} and W= \Omega\backslash V. If 2^\Omega is the \sigma-algebra of \Omega, and A=2^F and B=2^U...
  4. N

    Linearly independent field homomorphisms.

    Should be simple, but can't figure out :) Why is that , for a field K, the linear independence of field homomorphisms g1, ..., gn: K -> K equivalent to the existence of elements a1, ..., an \in K such that the determinant det| gi(aj)| != 0 (...so, just like in a case of linear...
  5. G

    Show integral is independent

    du/dt = d2u/dx2 u(x,t) = (t^a) * (g(e)) where e = x/sqrt(t) and a is a constant Show that integral from -inf to inf [ u(x,t) ] dx = integral from -inf to inf [ (t^a) * g(e) ] dx is independent of t only if a=-0.5 My attempt was to diff both sides by t (sorry not x) giving integral from...
  6. R

    Time independent acceleration equation?

    Hi, Is this differential equation valid for time independent acceleration" a = dV/dt = dV/ (V dx) = ( dV / dx ) * (1/V) ?
  7. D

    Why is the speed of light independent of a frame of reference?

    I understand the Michelson–Morley experiment and its result; but what I don't know yet is the REASON. Example: A torch in free space is moving at a velocity [v] w.r.t me. Considering the material nature of light, shouldn't the speed of photons emitted from the torch be [v+c] w.r.t ME? According...
  8. Q

    Programs Graduating HS senior - independent study, dual major

    thanks everyone I found an answer
  9. H

    C++ Independent Study for Research Position Advice

    Hey, I go to the University of Rochester, and I am currently entering my sophomore year as a physics major. Speaking to one of the physics department's staff members at the school, I was able to set up a research position with one of the professors in the astrophysics department. In order for...
  10. O

    Cubic equations with independent variables

    Hi colleages. can you help me to solve the cubic equation below: 2N(Ep-En)hp^3(x)-3[M(x,t)(Ep-En)-2NEnh]hp^2(x)-6Enh[M(x,t)+Nh]hp(x)+Enh^2[3M(x,t)+2Nh]=0 notice that all variables in the...
  11. DaTario

    About Photon as an independent entity

    Hi All I was re-reading the first pages of the book from Mr Claude Cohen-Tannoudji ,... (Quantum Mechanics) and something called my attention. In commenting the appearence , in 1905, of the photon notion in Albert Einstein's paper on photelectric effect, he (Mr. Claude) says that only in...
  12. T

    Laplace transform of function with independent variables OTHER than time

    Hi all Conventionally we used to seeing the Laplace transform applied to problems that use time as the independent variable, can anybody point me at some examples that do not use time as the independent variable? Thanks Tim
  13. Z

    Definition of linearly independent

    I've looked it up and can't really find a clear answer.. For a system of 3 simultaneous linear equations, is there any difference between 'the equations are linearly independent' and 'the equations have a unique solution'. If so what is it? Thanks!
  14. H

    General Solution to time independent schrodinger equation

    Homework Statement This is really a maths problem I'm having. I need to get the general solution for the infinite square well in the form: u = A cos(kx) + B sin(kx) I found the general solution to be: u = A exp(ikx) + B exp(-ikx) Using Euler's formula: exp(ikx) =...
  15. K

    How can I prove X = (X1, X2, X3) is independent?

    For (Y1, Y2, Y3, Y4) ~ D4(1,2,3,4;5) let Xk = [∑(from i=1 to k) Yi] / [∑(from i=1 to k+1) Yi] where k = 1,2,3 How can I prove X = (X1, X2, X3) is independent? What I did was... (Y1, Y2, Y3, Y4) ~ D4(1,2,3,4;5) = (Z1, Z2, Z3, Z4) / (Z1+Z2+Z3+Z4+Z5) where Z ~ N(0,1), Z IID G(1/2) Now...
  16. S

    How Do Independent Current Sources Work Without a Potential Drop?

    I still can't visualise them. They deliver the same current all the time, however there is no potential drop across them. Is it just a theoretical device that doesn't exit? I am sure current sources do not add new charge into the circuit, but rather move charges around but this requires a...
  17. I

    Independent Trials: Probability of Events A_i

    Say I have an urn containing a set of balls numbered 1 through N. I then make n selections from the urn with replacement. Thus each selection is independent. Let the event: A_{i} i=1,2,3...,N be that the ball numbered i was not chosen in the n selections. Then...
  18. S

    If a 3 x 4 matrix can have independent columns?

    Hi, can anyone explain to me if a 3 x 4 matrix can have independent columns? How about independent rows? Thanks!
  19. H

    Show if its a lin. independent subset

    Homework Statement V = { (x_{1},x_{2},x_{3},x_{4},x_{5}) \in R^{5} : x_{1} -2x_{2} + 3x_{3} - x_{4} + 2x_{5} = 0 } show that S = { (0,1,1,1,0) } is a linearly independent subset of V. The Attempt at a Solution I don't get it.. it's a set with 1 non zero vector, it's going to be...
  20. D

    Expected value of stationary independent increments.

    Homework Statement Let \{ X(t),t \ge 0\} be a random process with stationary independent increments and assume that X(0)=0 . Show that: E[X(t)] = {\mu _1}t Homework Equations The Attempt at a Solution I tried to work backwards by argueing that the mean between time...
  21. G

    Sum of independent uniform distribution conditional on uniform

    Homework Statement Let X and Y be independent and normal, then we know that It must be the case that X+Y and X are jointly normal Therefore we can apply the projection theorem: which states that if A and B are jointly normal then VAR(A|B)=VAR(B)-\rho^2VAR(B) , apply the theorem to A=X+Y, B=Y...
  22. R

    Problem with complex conjugates and the Time Independent Schrodinger equation

    I can understand that if z= a + ib then z*=a - ib, where the definition of the complex conjugate is reversing the sign in front of the imaginary part. I'm now confused about how the complex conjugate works in the TISE. in a stationary state, i\hbar\frac{\partial\Psi}{\partial\\t}= E\Psi...
  23. K

    Vector and matrices are the independent or dependent

    Vector and matrices...are the independent or dependent Homework Statement Determine whether the vectors v1=[1,-1;0,0],v2=[2,-2;1,... and v3=[-5,5;1,0] are independent or dependent. Find the span {v1,v2,v3} and give a description. Explain why W = [4,4;4,4,] is not in the span {v1,v2,v3}...
  24. K

    Are These Vectors Linearly Independent?

    Homework Statement Determine whether the vector v1=(!,2,3),v2(3,2,1) and v3(1,1,1) are independent or dependent. Homework Equations I'm so lost The Attempt at a Solution I'm so lost
  25. B

    Layout for defining prob. for Independent Events.

    Hi, everyone: I was reviewing some intro material, and I ended up confused with the issue of independence with the following problem: We are given two teams, A,B, playing against each other. A wins with probability P(A)=0.6 , B wins with P(B)=0.4 (games are played until...
  26. D

    Meaning of Independent Identically distributed random variables

    I am a little fuzzy on the meaning of Independent Identically distributed random variables. I understand the independent part but still not 100% on the identically distributed part. I understand that identically distributed means they have the same pdf and cdf but does this mean that they have...
  27. T

    Number of independent subcubes of a hypercube

    Number of "independent" subcubes of a hypercube Hello, I am trying to solve this problem: I have an n-dimensional hypercube and m of its vertices. Now I want to compute the maximum number of subcubes of the entire hypercube such that: - each subcube from the set may contain only those m...
  28. S

    Independent events in probabilities

    Homework Statement Let S be the sample space for rolling a single die. Let A={1,2,3,4}, B={2,3,4}, and C={3,4,5}. Which of the pairs (A,B), (A,C), and (B,C) is independent? Homework Equations P(A|B)=P(A) P(A|B)=P(A&B)/P(B) P(A&B)=P(A)*P(B) The Attempt at a Solution P(A)=2/3...
  29. S

    Identifying Independent and Dependent Variables in Circular Motion Experiment

    Homework Statement Hi there, I'm doing a practical investigation to see how the centripetal force required for circular motion varies with the frequency of rotation, and I was just wondering which is the independent variable, and which is the dependent one. The investigation involves...
  30. P

    Linearly independent vectors

    Homework Statement Suppose that A, B, and C are not linearly independent. Then show how the \alpha_{i} can be computed, up to a common factor, from the scalar products of these vectors with each other. Hint: Suppose that there are non-zero values of the \alpha_{i}'s that satisfy...
  31. H

    Linearly Independent Sets and Bases

    Homework Statement So I'm trying to find a basis for the space that is spanned by the given vectors. {(1,0,0,1) (-2,1,-1,1) (6,-1,2,-1) (5,-3,3,-4) (0,3,-1,1)} These are written as column vectors. Homework Equations None really (that I know of) The Attempt at a Solution So I...
  32. L

    Are the columns linear independent?

    Homework Statement Were the columns of A linearly independent? The matrix A is given in row reduced echeleon form 1 2 0 0 0 0 1 0 0 0 0 1 Homework Equations Hint: Consider the solution set to A x = 0 The Attempt at a Solution I think that the...
  33. D

    Linearly Independent Vectors: Exploring Deletion of Vector xk

    Let x1, x2,...,xk be linear independent vectors in a vector space V. If we delete a vector, say xk, from the collection, will we still have a linearly independent collection of vectors? Explain. By deleting a vector from linearly independent span, the other vectors, I believe, will remain...
  34. D

    Linearly Independent Vectors: Deleting a Vector & Its Impact

    Let x1, x2,...,xk be linear independent vectors in a vector space V. If we delete a vector, say xk, from the collection, will we still have a linearly independent collection of vectors? Explain. By deleting a vector from linearly independent span, the other vectors will remain independent...
  35. Z

    Exploring Independent University of Moscow: Seeking Recommendations & Advice

    In short, I think I may want to spend either next semester or all of next year at the Independent University of Moscow, but I've only really decided this recently. I haven't spoken to my university, asked for recommendations yet, or filled out the application form, and all of this must be...
  36. S

    Independent events in statistics

    Homework Statement Two cards are drawn from a standard deck with replacement. A=first card is an ace. B=second card is an ace. Show that A and B are independent Homework Equations P(A and B)=P(A given B)/P(B) P(A given B)=P(A) The Attempt at a Solution P(A)=4/52 P(B) =4/52 P(A...
  37. A

    Electrostatic potential independent of distance?

    Say I have a packet of electrons just sitting there, before they repel each other, what is their potential energy? I have no idea of how to calculate their potential energy since at r = 0 , U = infinity, which is not helpful since my problem requires U to be finite but the only way I know of...
  38. S

    Linearly Independent R^3 -> Linearly Independent R^4

    Standard Matrix for R^3 -> R^4 where if domain is Linearly Independent so is codomain Homework Statement 5. Suppose T : R^3 -> R^4 is a linear transformation with the following property: For any linearly independent vectors v_1, v_2 and v_3 in R^3, the images T(v_1), T(v_2) and T(v_3) are...
  39. J

    Showing that something is a basis of an independent set

    Homework Statement Among all independent vector sets in a vector space U, let M = {v1, v2, ... vp} be an independent set. p is as large as it can get. Show that U is a basis of M. Homework Equations The Attempt at a Solution If U is a basis of M then U is an independent set (we...
  40. R

    What is a mass independent renormalization scheme

    What is it meant by "mass-independent renormalization scheme"? Does it mean that the counter-terms that cancel the infinities do not have dimensions of mass? In this case, any regularization scheme not involving the cutoff method, such as dimensional regularization? Or does it mean that...
  41. D

    Independent variables in termodynamics

    Say I want to parametrize the plane. I can use cartesian (x,y) or polar (r,theta). But I cannot use x and r, because if I draw a circle and a vertical line, there are two points of intersection. I guess x and theta will do, because theta specifies a ray that will intersect any vertical line...
  42. W

    Independent variable that is a distribution?

    Hi, I am attempting a logistic regression analysis with a binary response and explanatory variables measured at the individual level and also some measured within subgroups of the observations (nests). For each nest containing individual observations I know the distribution of income in the...
  43. C

    Why use mann-whitney U test rather than independent sample test?

    why use non parametric mann-whitney U test rather than parametric independent sample test. I have a question regarding this because i just complete two question, as one I am using parametric tests, independent sample test, solve the mean selling price of a home with a conservatory different...
  44. P

    Second order approximation in time independent perturbaton theory

    Is there any physical reason why second order approximation to ground state in time independent perturbation theory is always negative. I know how to prove it mathematicly but I wonder whether one may justify it using only physical arguments.
  45. C

    Schools Independent Research Opportunities for High School Senior?

    I am currently a senior in high school and I am working towards a career which involves the study of physics. I am somewhat aware of independent research opportunities for high school students in other areas of science, but I do not know of any opportunities which I could explore for physics...
  46. P

    RPM independent grid tie induction generator

    Through our research we discover that an AC induction motor can act as a DC amplifier, as long as there is torque making it turns. Applying the process we are able to build RPM independent grid tie induction generator. Tested with variable US grid at consumer configuration. Similar to PMA...
  47. S

    Working with UV-C on independent project

    Hello, I'm using UV-C (Hg low pressure lamp) and I wanted to see if someone could give me some insight. I have a couple of questions: 1) How far does UV-C penetrate through various materials? In my testing, it seems to go straight through plastics. I have UV blocking glasses - but those are...
  48. L

    Multiple independent exponential random variables

    Let X1, X2, ...Xn be independent exponential variables having a common parameter gamma. Determine the distribution of min(X1,X2, ...Xn). The Attempt at a Solution I know how to do it with one X and one parameter but I am at a loss with these multiple ones... Thanks so much!
  49. C

    Finding joint pdf of independent variables.

    Homework Statement Suppose X1 and X2 are two independent gamma random variables, and X1~Gamma(a1, 1) and X2~(a2, 1). a) Find the joint pdf of Y1 = X1 + X2, and Y2 = X1/(X1 + X2). b) Show that Y1 and Y2 are independent. c) Find the marginal distributions of Y1 and Y2. The Attempt...
  50. K

    Temperature Gradients of Independent Radiating Bodies within A Mixture.

    I am interested in describing the heat transfer and temperature gradients within a mixture of independent radiating bodies. States like this occur in many systems and i have been having a bit of trouble modeling this simple scenario. An example of a system is charcoals within a BBQ, and also...
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