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. G

    I Determining the number of independent equations

    Hi everyone, In geometry problems involved with triangles (inside a circle in my case), I can write different equations based on some known measures using pythagoras theorem, similarity , trigonometric and geometric relations. But, if I write all these equations I propably get some dependent...
  2. V

    Is Newton I independent of Newton II?

    If Newton II is defined as ##\sum F = \dot{p}## and ##p = mv##, why do we consider Newton I as a separate law for cases where ##\sum F = 0##? Is Newton I really independent of Newton II?
  3. S

    A Is the Randall-Sundrum model background independent?

    Randall-Sundrum model (https://en.wikipedia.org/wiki/Randall%E2%80%93Sundrum_model) is related to string theory. String theory can be background independent (https://en.wikipedia.org/wiki/Background_independence): "String theory is usually formulated with perturbation theory around a fixed...
  4. S

    A Is Seth Lloyd's cosmological model background independent?

    I have been interested in Seth Lloyd's cosmological model (which proposes that the universe is a some kind of quantum computer or at least similar to it: https://en.wikipedia.org/wiki/Programming_the_Universe, https://arxiv.org/abs/quant-ph/0501135) since long ago. I was wondering if his...
  5. Sathish678

    I Independent functions as solutions

    I found three independent functions as solutions for this equation d/dr(r^2dR/dr) = 6R (cauchy equation) r^2 , r^(-3) , (1/7)r^6. But i read that a second order linear differential eqn has only two independent solutions. Why this happened?
  6. M

    I Time independent perturbation theory in atom excitation

    Hello! In Griffiths chapter on Time independent perturbation theory, he has a problem (9.20) in which he asks us to calculate the first order contribution to the electron Hamiltonian in an atom if one takes into account the magnetic dipole/electric quadrupole excitations, beside the electric...
  7. T

    I Why Are Coordinates Independent in GR? - Exploring the Motivation

    I can see that by the tensor transformation law of the Kronecker delta that ##\frac{\partial x^a}{\partial x^b}=\delta^a_b## And thus coordinates must be independent of each other. But is there a more straightforward and fundamental reason why we don’t consider dependent coordinates? Is it...
  8. TytoAlba95

    MCQ: Law of independent assortment

    Answer: (a) Attempt: In Metaphase I, homologous chromosomes separate. Out of the four options, dig (a) and (d) have correct representation of separating homologous chromosomes. Now, according to the law of independent assortment, during segregation the chromosomes can group in any combination...
  9. karush

    MHB 16.1 Show that e^{2x}, sin(2x) is linearly independent on + infinity -infinity

    16.1 Show that $e^{2x}$, sin(2x) are linearly independent on $(-\infty,+\infty)$ https://www.physicsforums.com/attachments/9064 that was the example but... \begin{align*} w(e^x,\cos x)&=\left|\begin{array}{rr}e^x&\cos{x} \\ e^x&-\cos{x} \\ \end{array}\right|\\ &=??\\ &=?? \end{align*}
  10. karush

    MHB 12.6 linearly dependent or linearly independent?

    Are the vectors $$v_1=x^2+1 ,\quad v_2=x+2 ,\quad v_3=x^2+2x$$ linearly dependent or linearly independent? if $$c_1(x^2+1)+c_2(x+2)+c_3(x^2+2x)=0$$ is the system $$\begin{array}{rrrrr} &c_1 & &c_3 = &0\\ & &c_2 &2c_3= &0\\ &c_1 &2c_2& = &0 \end{array}$$ I presume at this point observation can...
  11. T

    Are vectors independent of reference frames?

    Ok, this is the notation I am going to use in this thread: uppercase means vectors, while "[V]c" means coordinates of vector V in frame c. I'm reading from a book: i have a reference frame "a" and a reference frame "b" rotated with respect to "a", the vector connecting the frames origin is R. We...
  12. A

    A Independent variables in higher derivative Lagrangian

    Consider the following Lagrangian density $$\mathscr{L}=\mathbf{E}\cdot\left(\nabla^{2}\mathbf{E}\right)$$ where $$E_{i}=\partial_{i}\phi\;(i=x,y,z )$$. In th is case the potential and its 3rd derivatives are the independent variables. Acording to Barut's classical theory of fields book, for...
  13. R

    Are (X+Y) and (X-Y) independent?

    I have x(0) = .7 x(1) = .3, y(0)=.7 y(1) = .3 since x,y(0) = .5 =/= x(0)y(0), x(0)y(0) = .49, x and y are dependent now I need to determine whether x and y are independent or not for x+y \begin{array}{|c|c|c|c|} \hline x+y & 0 & 1 & 2 \\ \hline p(x+y) & .49 & .42 & .09 \\ \hline \end{array}...
  14. karush

    MHB 10.1 are linear independent ....

    show that $e^{2x},\quad \sin 2x$ are linear independent on $\left\{-\infty,\infty\right\}$ new concept to me but $\sin 2x$ has an amplitude $e^{2x}$ doesn't
  15. Boltzman Oscillation

    I Are two independent functions constant?

    I was reading Griffith's introduction to QM book and he finds the time independent Schrodinger equation by assuming the wave function to be the product of two independent functions. He eventually gets to this: ih(∂ψ/∂x)/(ψ) = -(h^2/2m)*(∂''φ/∂x^2)/φ + V he says that "the...
  16. WMDhamnekar

    MHB Two normal independent random variables

    Let X and Y be independent normal random variables each having parameters $\mu$ and $\sigma^2$. I want to show that X+Y is independet of X-Y without using Jacobian transformation. Hint given by author:- Find their joint moment generating functions. Answer: Now Joint MGf of...
  17. F

    I Quark flavor and color independent?

    Each quark as a flavor charge and a color charge. Are these two properties totally independent of each other? Thanks.
  18. K

    B Number of independent entries of a matrix

    Is there an easy way to figure out the number of independent parameters a given matrix has? For example, a general, real, n x n matrix has n^2 entries and that's easy to realize cause we have a squared array of real numbers. What if this matrix is orthogonal?
  19. S

    Expected Energy Value of a Time Independent Wave

    Homework Statement For a region where the potential V=0, the wave function is given by ψ(x)=2αsin(3πx/a). Calculate the energy expectation value of this system. Note that α and a are two different constants. Homework Equations ψ(x)=2αsin(3πx/a) E=K+V=K K=p^2/2m ∫ψ*Pψdx=Expected momentum...
  20. hilbert2

    A Linearly independent function sets

    It is well known that the set of exponential functions ##f:\mathbb{R}\rightarrow \mathbb{R}_+ : f(x)=e^{-kx}##, with ##k\in\mathbb{R}## is linearly independent. So is the set of sine functions ##f:\mathbb{R}\rightarrow [-1,1]: f(x) = \sin kx##, with ##k\in\mathbb{R}_+##. What about...
  21. W

    B Time independent perturbation theory

    This isn't explained anywhere so it must be super basic and I'll probably kick myself for not getting it, but on the wiki page for time independent perturbation theory, section 3.1: https://en.wikipedia.org/wiki/Perturbation_theory_(quantum_mechanics) It talks about first order corrections and...
  22. M

    A Using standard deviation values as independent variables

    Hey. I am planning on doing some research, where I predict a change based on different types of risk. The question is simple. Can I use values of standard deviation as independent variables in a linear regression analysis (OLS)? The standard deviation values over time will be calculated in...
  23. M

    Probabibility Independent events

    Homework Statement Why is it that the probability of getting a queen in my second draw given that the first card was a spade, independent events? What if the first card drawn was the queen of spades? Homework Equations P(A and B)=P(A)P(B)
  24. A

    I Simplest independent first-order expression in PA

    What is the simplest known first-order expression known to be independent of Peano Arithmetic but decidable in ZFC for some reasonable notion of simplicity (such as number of quantifiers, nesting depth etc.); the precise definition of simplicity does not matter, I just want to see a concrete...
  25. W

    I Independent events and variables

    Hi all, I have a few questions regarding the issue of independence. Many thanks in advance. ##\textbf{1}## If I find that some events ##A, B, C## obey the following formula $$P(A \cap B \cap C ) = P(A)P(B)P(C)$$ it does not necessarily mean that a) they are mutually independent and b) ##A##...
  26. I

    [Linear Algebra] Maximal linear independent subset

    Homework Statement In the follow cases find a maximal linearly independent subset of set ##A##: (a) ##A = \{(1,0,1,0),(1,1,1,1),(0,1,0,1),(2,0,-1,)\} \in \mathbb{R}^4## (b) ##A = \{x^2, x^2-x+1, 2x-2, 3\} \in \mathbb{k}[x]## The Attempt at a Solution The first part of the exercise is...
  27. Mayur Sinha

    Physics How to do independent research in Physics?

    Hey folks! I have a degree in Electrical,Electronics and Communication Engineering and I work in Computer networking/Cybsersecurity field. Lately, I met one guy and we both decided to do some indepdendent research in electromagnetism as we both have fare amount of love for Physics( I'm in...
  28. K

    B Photon particle independent of wave question

    A photon acts like a wave and a particle. In the double slit experiment the photon seemingly interferes with itself which is troublesome to me. To help better understand this, I would rather think of the photon as a particle and the wave as something that is independent of the photon where the...
  29. amjad-sh

    Thermodynamics of the free and independent electron gas

    Homework Statement (a) Deduce from the thermodynamics identities: ##c_v=(\frac {\partial u}{\partial T})_n=T(\frac{\partial s}{\partial T})_n## and equations: ##f(ε)=\frac {1}{e^{ε-μ/k_BT}+1}## and ##u=\int \frac{1}{4π^3}ε(k)f(ε(k)) \, {d \vec k}##...
  30. J

    A Sum of independent random variables and Normalization

    Hi, Lets say I have N independent, not necessarily identical, random variable. I define a new random variable as $$Y=Σ^{N}_{i=0} X_{i}$$ does Y follow a normalized probability distribution?
  31. C

    I Independent arguments of dilogarithms

    I have a series of dilogarithms with various arguments and I was just wondering if it is possible to tell if they are all independent or if there is a way to reduce them to a smaller minimal set? The dilogs in question are of the form ##\text{Li}_2(X_i)##, where ##X_i## is an argument...
  32. Amlan mihir

    What is the probability? Is it independent?

    Homework Statement The Attempt at a Solution ; [/B] I think it is independent event so , the probability would be 0.5 . correct if me i am wrong please.
  33. F

    Substitution in a differential equation, independent variable

    Homework Statement $$y'=-\frac{1}{10}y+(cos t)y^2$$ when doing substitute for ##z=\frac{1}{y}## I understand this is ##z(t)=\frac{1}{y(t)}## I know t is independent variable and y is dependent variable but I want to know what is z role here, is it change the dependent variable? when...
  34. M

    MHB Complement of independent events are independent

    Hey! :o Let $A,B,C$ be independent events. I want to show that $A^c, B^c, C^c$ are independent. We have the following: \begin{align*}&P(A^c\cap B^c\cap C^c)=1-P(A\cup B\cup C)\\ & =1-\left [P(A)+P(B)+P(C)-P(A\cap B)-P(A\cap C)-P(B\cap C)-P(A\cap B\cap C)\right ] \\ & = 1-\left...
  35. CopyOfA

    A Linear regression with discrete independent variable

    Hey, I have a problem where I have a discrete independent variable (integers spanning 1 through 27) and a continuous dependent variable (50 data points for each independent variable). I am wondering about the best method of regression here. Should I just fit to the mean or median? Is there a way...
  36. J

    Linearly Independent Eigen Vectors

    Solved (sorry i tried again and realized my E-values were wrong) 1. Homework Statement Homework Equations Find Eigen Values and then what? The Attempt at a Solution I got eigen values as 3 and -3. Now how to proceed? I got Eigen Vector as: 1, 1 for eigen value of 3 and eigen vector as 8, 2...
  37. lfdahl

    MHB Cos^2(∠POA)+cos^2(∠POB)+cos^2(∠POC)+cos^2(∠POD) is independent of P.

    A cube is inscribed in the unit sphere $x^2 +y^2 +z^2 = 1$. Let $A,B,C$ and $D$ denote the vertices of one face of the cube. Let $O$ denote the center of the sphere, and $P$ denote a point on the sphere. Show that \[\cos ^2(\angle POA)+\cos ^2(\angle POB)+\cos ^2(\angle POC)+\cos ^2(\angle...
  38. fisher garry

    I Independent versus dependent pdf

    In the green box in the attachment I have calculated the integral of the pdf of 24xy in the same manner as in the theory that leads up to 3.1 in the attachment. But I can't see any difference in that calculation that would explain that if 24xy is dependent why is not also the theory that leads...
  39. J

    Independent Physics Institution/Agency

    Is there an institution or maybe just a small agency out there purely for physics education? I am not talking about high schools or universities. I am referring to classes outside of school. Thanks ahead for any sort of insight!
  40. EastWindBreaks

    Why is Theta 2 Independent in Solving for Theta 3 in a 4-Bar Mechanism?

    Homework Statement Homework EquationsThe Attempt at a Solution it seems like because theta 2 is independent, therefor, you can solve theta 3 by just using one equation from the system of equation? on a previous problem where its a 4 bar mechanism( which it didn't specify that theta 2 is...
  41. V

    Independent and dependent sources examples

    I would like to know if the following examples of independent and dependent sources are right and some further examples. Independent sources: Batteries, DC generators, Alternators, Photovoltaics. Dependent sources: Power electronic components (Diodes, Transistors, Thyristors), inverters, ups, cpu.
  42. B

    Linearly Independent Sets in Abelian Groups

    Homework Statement [/B] ##X## is linearly independent if and only if every nonzero element of the subgroup ##\langle X \rangle## may be written uniquely in the form ##n_1 x_1 + ... n_k x_k## (##n_i \in \Bbb{Z} \setminus \{0\}##, and ##x_1,...,x_k \in X## are distinct). Homework Equations [/B]...
  43. Pushoam

    Avg. of sum of independent variables

    Homework Statement Homework EquationsThe Attempt at a Solution The probability that ##X_1 ## is between ## X_1 ## and ## X_1 + dX_1 ## and ##X_2 ## is between ## X_2 ## and ## X_2 + dX_2 ## and so on till the nth variable is dP(##X_1, X_2, ..., X_n) = p ( X_1) p( x_2) p(X_3)...p(X_n) dX_1...
  44. R

    Are Coin Toss Events A, B, and C Independent?

    Homework Statement Hi, I have this question that I've been pondering for a while, I keep flipflopping on what I think is right. I only need help on the last part on whether the events are independent or not, the rest of the text is backstory to the question. I know for events to be independent...
  45. C

    MHB Are components in a gaussian mixture independent?

    Hello all, I have used Expectation Maximization algorithm to approximate a probability density function (pdf) using a mixture of gaussians. I need to square the pdf corresponding to the mixture of gaussians( it is a weighted sum of normal distributions with non-identical parameters). Rather...
  46. O

    Time independent Schrödinger Eqn in a harmonic potential

    Homework Statement I am currently reading a textbook on solving the Schrödinger equation for the harmonic oscillator using the series method; $$-\frac{\hbar^{2}}{2m}\frac{\mathrm{d}^2 \psi }{\mathrm{d} x^2}+\frac{1}{2}m\omega ^{2}x^2\psi =E\psi $$ It starts by using these two dimensionless...
  47. binbagsss

    GR Lie Derivative of metric vanish <=> metric is independent

    Homework Statement How to show that lie deriviaitve of metric vanish ##(L_v g)_{uv}=0## <=> metric is independent of this coordinate, for example if ##v=\partial_z## then ##g_{uv} ## is independent of ##z## (and vice versa) 2. Relevant equation I am wanting to show this for the levi-civita...
  48. maistral

    A Nonlinear regression in two or more independent variables

    Hi. I wanted to learn more on this topic, but it seems all the available resources in the internet points to using R, SPSS, MINITAB or EXCEL. Is there an established numerical method for such cases? I am aware of the Levenberg-Marquardt, Gauss-Newton and such methods for nonlinear regression on...
  49. G

    I Divergent Sums of Linearly Independent Elements

    Suppose we had an infinite series - z = ∑i = 1 to ∞ ( α1(i)x1 + α2(i)x2 + . . . + αm(i)xm ) - rewritten as the cumulative sequence - z(n) = α1(n)x1 + α2(n)x2 + . . . + αm(n)xm - where the xj are linearly independent and normalized (and serve as a finite basis across the sequence). If all...
  50. W

    Schrodinger time independent equation for steps and barriers

    Ok for starters, I am sorry for the length of the question and jamming multiple questions in here i feel like my doubts are all related and it would be best just to put it all in one place instead of creating 2-4 topics. I'm beginning to feel confused with the amount of ways i see people...
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