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. _N3WTON_

    Probability of Independent Events

    Homework Statement Consider three events A1, A2, and A3, and let pi = P(Ai), for i = 1, 2, 3. a) Express the probability that at least one of these three events occurs in terms of the pi ’s. b) Express the probability that at least two of the events occur. c) Suppose that A1, A2 and A3 are...
  2. gfd43tg

    Time independent schrödinger equation query

    Hello, the TISE can be simplified $$H \psi = E \psi$$ Where ##H## is the Hamiltonian, and ##E## is the eigenvalue, but why don't the ##\psi## terms cancel, leaving ##H = E##? Also, what the heck does the eigenvalue ##E## have to do with the eigenvalue that I have previously encountered in...
  3. K

    Question regarding time independent perturbation theory

    Let's say we've a system which can be described by the Hamiltonian: $$H_0 = \dfrac{p^2}{2m} + V(x)$$ Now suppose we introduce a perturbation given by: $$H_1 = \lambda x^2$$ Our total hamiltonian: $$H = H_0 + H_1 = \dfrac{p^2}{2m} + V(x) + \lambda x^2 $$ Normally, the perturbation doesn't...
  4. Dethrone

    MHB Linearly Independent: Why ${}\left\{X+Y, Y+Z, Z+W, W+X\right\}$ Isn't

    Let ${}\left\{X, Y, Z, W\right\}$ be an independent set in $\Bbb{R}^n$, is the following set independent? ${}\left\{X+Y, Y+Z, Z+W, W+X\right\}$ My textbook says it isn't, but I'm not sure why. Let $\lambda_1, \lambda_2, \lambda_3, \lambda_4$ be scalars, then...
  5. F

    Power for a mean difference of two independent groups

    Homework Statement "The Daily Planet ran a recent story about Kryptonite poisoning in the water supply after a recent event in Metropolis. Their usual field reporter, Clark Kent, called in sick and so Lois Lane reported the stories. Researchers plan to sample 288 individuals from Metropolis...
  6. B

    Time independent perturbation theory

    Homework Statement The following text on the time independent perturbation theory is given in a textbook: \hat{H} = \hat{H}_0 + \alpha \hat{H'} We expand its eigenstates \mid n \rangle in the convenient basis of \mid n \rangle^{(0)} \mid n \rangle = \sum_m c_{nm} \mid m \rangle^{(0)}...
  7. R

    Maximize Success in Independent Study Calculus: Tips from Experienced Students

    Has anyone been through independent study calculus course ( DE through a university out of Utah)? I really miss the aspect of having an instructor but I do enjoy being able to focus on the aspects that I am not great at while passing over things that I've already learned. I would really like to...
  8. D

    Vectors in Tangent Space to a Manifold Independent of Coordinate Chart

    In Nakahara's book, "Geometry, Topology and Physics" he states that it is, by construction, clear from the definition of a vector as a differential operator [itex] X[\itex] acting on some function [itex]f:M\rightarrow\mathbb{R}[\itex] at a point [itex]p\in M[\itex] (where [itex]M[\itex] is an...
  9. A

    What is the independent variable in Boyle's Law?

    I asked my teacher, and I was told that volume is the independent variable, and that pressure is dependent. The textbook I'm using said the same thing. After looking up some graphs of the law, I found that both pressure and volume were used as independent variables. It seems counter-intuitive...
  10. binbagsss

    R computation from 1 independent Riemann tensor component

    We have ##R^{1}_{212}## as the single independent Riemann tensor component, and I'm after ##R##. From symmetry properties and contracting we can attain the other non-zero components. The solution then states that ##R_{11}=R^{1}_{111} + R^{2}_{121}=R^{2}_{121}## . I thought it would have been...
  11. N

    Voltage drop over an independent current source?

    Homework Statement I am supposed to give a thevenin equivalent circuit to the one posted in the picture. Homework Equations V=IR KVL: "voltage drops around a closed loop sums to zero KCL: "current into a node equals current out of a node" The Attempt at a Solution The part I'm confused...
  12. T

    Showing Chi squared is independent with another variable

    So I have X1 and X2 are iid standard normal. Then I have Y=X1^2+ X2^2 and Z=X1/(X1^2+x2^2) I'm supposed to find the distribution of Y and Z and then determine if they are independent. Clearly Y is chi squared with degrees of freedom 2. But I have no idea how to find the distribution of Z...
  13. M

    Show integral is independent of time

    Homework Statement Given that u(x,t) satisfies u_t-6uu_x+u_{xxx}=0 (*) and u, u_x, u_{xx} \to 0 as |x| \to \infty show that I_1 = \int_{-\infty}^{\infty}u^2dx is independent of time ( \frac{\partial I_1}{\partial t}=0 ). Homework Equations - The Attempt at a Solution I...
  14. I

    Distribution Difference of Two Independent Random Variables

    Homework Statement Z = X - Y and I'm trying to find the PDF of Z. Homework Equations Convolution The Attempt at a Solution Started by finding the CDF: Fz(z) = P(Z ≤ z) P(X - Y ≤ z) So I drew a picture So then should Fz(z) be: since, from my graph, it looks as though Y can go from...
  15. B

    Tensor calculus independent study questions?

    I'm a mathematics major and up until now I've taken Calc 1,2,3 (so single + multivariable) a combined course in Elementary Linear Algebra + Differential Equations and PDE's. My school doesn't offer any tensor calculus classes, but I was interested in learning some of it on my own. Do I have...
  16. U

    3-angular momentum : independent of pivot?

    Homework Statement [/B] (i) Prove that dL/dt = 0 (ii) Find the relation between space part and 3-angular momentum vector (iii)Show that 3-angularmomentum vector is independent of pivot Homework EquationsThe Attempt at a Solution [/B] I'm not sure what part (iii) is trying to get at, but I...
  17. grassstrip1

    Linearly Independent Sets and Spans in R4

    Hey everyone I just had a quick thought that was bothering me. For a set to be a basis it must be linearly independent and span the vector space. I've seen cases however of only two vectors forming a basis for R4 I don't see how two vectors could span 4 space or am I missing something. Thanks!
  18. A

    Independent Study: What is next?

    Hello everyone, I am new to these forums, so if this question is in the wrong place, I will relocate it. Long story short, my school has no real physics department anymore, but I have an insatiable appetite for it. I was wondering what the next course in a physics sequence would be after...
  19. V

    Big Bang: A True Singularity That is Coordinate Independent

    Consider a flat Robertson-Walker metric. When we say that there is a singularity at $$t=0$$ Clearly it is a coordinate dependent statement. So it is a "candidate" singularity. In principle there is "another coordinate system" in which the corresponding metric has no singularity as we...
  20. P

    Depdendent, Independent, and Complementary Events

    For two events ##A## and ##B##, where ##A∩B ≠ ∅##, is it possible to deduce from a venn diagram whether or not those two events are dependent? Or is such information unattainable from a mere venn diagram? Also, if we define ##C## as the complement of the union of ##A## and ##B##, why must ##C##...
  21. F

    MHB Different ways to determine if functions are linearly independent

    Is calculating the determinant the Wronskian the only way to show that a set of functions is linearally independent? For example could you build a matrix where the numbers represent the coefficents to the polynomial functions and if it rref's to the identity matrix wouldn't this show it's...
  22. W

    Linearly independent vectors

    http://tinypic.com/r/euht06/8 Hi everyone! It was the question given to us in today's test & I was wondering if anyone can tell me what is the correct answer. The teacher will post the answers by the end of this week but I am feeling anxious to know the answer. Thanks in advance. P.S. Sorry...
  23. J

    Probability - 3 Independent Events

    Homework Statement Three tanks are sent to shoot a certain target. Each tank is to shoot one round. The probabilities of a tank's round hitting the target are 1/2, 2/3 and 3/4 for tanks A, B, and C respectively. Assuming independence of A, B and C hitting, find the probability that: a. rounds...
  24. QuantumCurt

    Determine if the set of functions is linearly independent

    Homework Statement Determine if the given set of functions is linearly independent or linearly dependent.Homework Equations $$S=x~sin~x, ~ x~cos~x$$The Attempt at a Solution My first instinct was to use the Wronskian. $$W[y_1(x), y_2(x)]=\begin{vmatrix} x~sin~x & x~cos~x\\ x~cos~x+sin~x &...
  25. QuantumCurt

    Finding maximum number of functions that can be linearly independent

    Homework Statement Hey everyone. I'm in an introductory differential equations class, and I think this homework problem has got me stumped. The functions y1(x), y2(x), ... , yn(x) are linearly independent on an interval I. c1y1(x)+c2y2(x)+...+cnyn(x)=0 for all x in I, implies that...
  26. ChrisVer

    Poincare Transformations: Parametrization-Independent

    Well if I have a worldline given by x^{\mu}(\tau) And I want to make a Poincare transformation: x^{\mu} (\tau) \rightarrow \Lambda^{\mu}_{\nu} x^{\nu}(\tau) + a^{\mu}. I have one question,why can't a, \Lambda explicitly depend on \tau? that is to have: x^{\mu}(\tau) \rightarrow...
  27. A

    Independent Current Source In Series With Resistor

    Homework Statement Write the KVL Equation for the outer loop Homework EquationsThe Attempt at a Solution The question above is a sample I have made for such a condition. The goal is not to find the value, but only write the correct equation. If an independent current source is connected in...
  28. J

    MHB NP Problems: Weighted Vertex Cover vs Weighted Independent Set

    There is a Theorem that states that if G = (V, E) is a graph, then S is an independent set $\Leftarrow\Rightarrow$ V - S is a vertex cover. Suppose the vertices have positive integer weights. Does it follow from the theorem that: S is an independent set with maximum weight...
  29. S

    CHI square independent test (small expected frequency)

    Homework Statement the expected frequency for the age of (21-30, 31-36, more than or equal to 37) for operation is less than 5 , so combination of these numbers are required for the expected frequency to be more than or equal to 5 . my question is which numbers should i combine? would my ans...
  30. emeriska

    Show that expecting value of energy is independent of time

    Sorry I failed to make Latex work, don't know why... 1. Homework Statement We consider for a given potential. Psi is also normalized... Homework Equations Show that expectation value of energy is independent of time. The Attempt at a Solution Well, I'm use to expecting values, but not of...
  31. evinda

    MHB Help Proving That $T_n \sim t_n$ with Z and Y Independent

    Hello! (Wave) Could you help me at the following exercise? (Thinking) Let $Z \sim N(0,1) $ , $Y \sim \chi_n^2$ and $Z,Y$ independent . Show that the random variable $T_n := \frac{Z}{ \sqrt{\frac{Y}{n}}} \sim t_n$.
  32. N

    Solution of diffusion equation with three independent variable (r,z,t)

    Hi, I want to solve the following diffusion equation: (d/dt) C(r,z,t)=D*∇^2 C(r,z,t) where C is the concentartion and D is the coefficient of diffusivity (constant) with initial condition C(r,z,0)=C0 (constant) and boundary condition dc/dr=0 at r=0; (dc/dz) at z=-L equal to (dc/dz)...
  33. P

    Circuit with 1 independent current source

    Hi I've tried to solve the following circuit using Kirchoff's laws but i get wrong results.I know that because I've got a different solution of the same excercise.I've attached the image.My question is what are the equations of Kirchoff's laws because I try this over 2 hours and I can't figure...
  34. B

    Understanding Cell Volume: Why It's Independent of Choice

    "Volume of a primitive cell is independent of the choice of the cell." Why?
  35. J

    Two independent driven inputs one output

    Hello everyone, I've been trying to figure out how i can have two different inputs that are switchable from one to another that drive a single output. However i don't want the inputs to drive each other, and also want the mechanism to be compact in size and fairly lightweight. So how can i do...
  36. L

    Why do 2nd-order linear ODEs have at most two independent solutions?

    Homework Statement Why does the following ODE ALWAYS have two linearly independent solutions? x''(t) + a(t) x'(t) + b(t) x(t) = f(t) The characteristic polynomial argument is not sufficient?
  37. P

    Only conservative vector fields are path independent?

    does anyone have a proof of this?
  38. C

    Green's function in n-dim, but with one independent variable.

    Suppose we have some partial differential equation for a scalar ##f## $$Df = \rho$$ taking values in ##\mathbb{R}^n##, and further suppose that the differential equation is completely independent of the variable ##y:=x^n## so that the differential operator ##D## only contains derivatives with...
  39. K

    2D Density of States Energy Independent

    It's known that the Density of States in 2D is given by, g_2(E)dE = \frac{a^2m}{\pi\hbar^2}dE The density of states in 1D and 3D are as follows, g_1(E)dE = \left(\frac{a}{\pi}\sqrt{\frac{2m}{\hbar^2}}\right)\frac{1}{\sqrt{E}}dE g_3(E)dE =...
  40. D

    Probability of independent events

    i have drawn the venn diagram for the question... i am not sure it's correct or not. the question states both are independent events. i don't understand the working in part b ... for me , my ans would be p(A) +p(B).. correct me if i am wrong. thanks in advance.
  41. S

    Why the topological term F\til{F} is scale independent?

    why the topological term in gauge theory, ε_{\mu\nu ρσ}F^{\mu \nu} F^{ρσ} ,is scale-independent?
  42. N

    Show that non-zeros rows in REF are linearly independent

    Homework Statement Given 2 1 1 0 0 0 1 1 0 0 0 3(i) Show that the rows of A are linearly independent. (ii) Show that the nonzero rows of any matrix in row echelon form are linearly independent.The Attempt at a Solution i) REF gives 1 0 0 | 0 0 1 0 | 0 0 0 1 | 0 0 0 0 | 0 x1 = x2 = x3 =x4 =...
  43. M

    MHB Proof that the integral is independent from the path from A to B

    Hey! :o I am facing some troubles understanding the proof of the following theorem. Let $\overrightarrow{F}$ be a vector field, $\overrightarrow{F}=M\hat{\imath}+N\hat{\jmath}+P\hat{k}$, where $M,N,P$:continuous at a region $D$ ($M,N,P \in C^0(D)$) . Then a suficient and necesary condition so...
  44. W

    What are the independent terms in the Magnetic Tensor

    I am trying to understand the magnetic gradient tensor which has nine components. There are three magnetic field components, but there are also three baselines. These nine gradients are organised into a 3x3 matrix. I have read that only 5 of these terms are independent. What exactly does this...
  45. J

    Independent variables of the Lagrangian

    Why are y and y' treated as independent variables, while they are not? Another slightly related question: if ' = d/dt then df'/dg' = df/dg because f' = df/dg g', but if we differentiate f' to g' we implicitly assume that df/dg is independent of g', is it?
  46. D

    How can I be energy independent?

    I am thinking about acquiring some battery storage units for single residential house. What is the cheapest and efficient battery for homes and where can I buy it? Would it be bloom energy, fuel cell or solar panel( transparent)? What are some creative solutions? One idea was next to a river...
  47. J

    Two linearly independent vectors in a plane that don't span the plane

    Homework Statement Say we have the plane, x+2y+4z=8 (part of a larger problem) Homework Equations The Attempt at a Solution The vectors (8,0,0) and (0,0,2) both lie in the plane. They are linearly independent. But (0,4,0) lies in the plane and is not a linear combination of the first two...
  48. D

    Are fractional polynomials linearly independent?

    i.e., does the set of functions of the form, \{ x^{\frac{n}{m}}\}_{n=0}^{\infty} for some fixed m produce a linearly independent set? Either way, can you give a brief argument why or why not? Just curious :)
  49. S

    Schrodinger's time independent equation

    [Mentor's note: This thread does not use the standard homework template because it was moved here from one of the non-homework forums.] Hi, Looking for help on what to do next. Question (it's in two parts but part 1 is like two lines): Part 1: http://imgur.com/BwyNwsE [1] Part 2...
  50. W

    What are independent terms in Magnetic Tensor

    I am trying to understand the magnetic gradient tensor which has nine components. There are three magnetic field components, but there are also three baselines. These nine gradients are organised into a 3x3 matrix. I have read that only 5 of these terms are independent. What exactly does this...
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