Variable Definition and 1000 Threads

A variable star is a star whose brightness as seen from Earth (its apparent magnitude) fluctuates.
This variation may be caused by a change in emitted light or by something partly blocking the light, so variable stars are classified as either:

Intrinsic variables, whose luminosity actually changes; for example, because the star periodically swells and shrinks.
Extrinsic variables, whose apparent changes in brightness are due to changes in the amount of their light that can reach Earth; for example, because the star has an orbiting companion that sometimes eclipses it.Many, possibly most, stars have at least some variation in luminosity: the energy output of our Sun, for example, varies by about 0.1% over an 11-year solar cycle.

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  1. B

    Current-voltage relation for series association of variable capacitors

    Hello, I have an issue with the problem below. I have a series connection of two variable capacitances C_{1}(t) and C_{2}(t). I want to establish the differential equation between the current i and voltage V on the ports of the series connection. The capacitance of the series connection of...
  2. U

    Fluctuating Refractive Index and Light Perception

    Homework Statement A narrow beam of light passes through a slab obliquely and is then received by an eye. The index of refraction of the material in the slab fluctuates slowly with time. How will it appear to the eye? Homework Equations The Attempt at a Solution Let a point object be kept at...
  3. M

    How Do You Calculate P{S < t < S + R} for Independent Exponential Variables?

    Hi, I have a quick question. Let R and S be two independent exponentially distributed random variables with rates λ and μ. How would I compute P{S < t < S + R}? I am a little bit confused because of the variables on either side of the inequalities. I have tried conditioning on both S and R...
  4. D

    MHB How can I use variable transformation to obtain a solution for this ODE?

    Given the following ODE \[ \left(\frac{du}{dx}\right)^2 = \mu u^2 - \frac{2\alpha}{\sigma + 2}u^{\sigma + 2} - \frac{\gamma}{\sigma + 1}u^{2(\sigma + 1)} \] How do I obtain \[ u(x) = \left(\frac{A}{B + \cosh(Dx)}\right)^{1/\sigma} \] where \(A = \frac{(2 + \sigma)B\mu}{\alpha}\), \(B =...
  5. R

    Strange Change of Variable of Integration

    I've been following a few derivations for quantities in classical mechanics of rotating systems, and one of the integrals is transformed in a way I've never seen before. For angle theta, angular velocity omega and angular acceleration alpha: Intuitively I can see that they've 'just' swapped...
  6. C

    Java Java error with variable initialization

    import java.util.Scanner; import java.io.FileNotFoundException; import java.io.FileReader; import java.io.IOException; import java.io.PrintWriter; public class CountryPopulationReverse{ public static void main(String args[])throws FileNotFoundException { //Variable...
  7. F

    MHB Dividing vs Subtracting to Solve Equations w/1 Variable

    If you have the equation \frac{dx}{dt}=4(x^2+1) I sometimes get confused if i should should subtract 4(x^2+1) from both sides or multiply by it's reciprocal. If I subtract from both sides then I'd have 0 on the right side and that would give a different answer after integration but...
  8. L

    Difference between a variable and a constant?

    I know this is a very elementary question, but I suddenly realized in calculus that I don't really know precisely what the definition of a variable and constant was. I know what people tend to call constants and variables in something like: ax + by = c, where you'd call x and y a variable...
  9. S

    Random Variable and Distribution Function Relationship

    I'm in a probability theory class and I feel like I'm missing something fundamental between random variables and their distribution functions. I was given the following questions: 1)Let θ be uniformly dist. on [0,1]. For each dist. function F, define G(y) = sup{x:F(x)≤y}. Prove G(θ) has the...
  10. M

    What are the equations for conic sections in 4 dimensions?

    Homework Statement The problem is given in the picture attached. However we are given the equation of a 4 dimensional shape with certain choice given to explain the shape in that dimension. Homework Equations Equations of different shape such as: sphere: √(x^2+y^2+z^2) = r...
  11. A

    Variable acceleration and terminal velocity

    Homework Statement A cube is falling from a height of 200 m (initial velocity =0) , it reaches it's terminal velocity . Given that :its mass is 100 kg , cross sectional area 40 cm2 and coefficient of drag 2. Putting only weight and drag in consideration , calculate its terminal velocity and...
  12. W

    MHB Need Explanations For The Red Part (2 variable inequality)

    Prove that for any two numbers x,y we have [(x^2 + y^2)/2] >= x + y - 1 Solution) For any number a we have have a^2 > 0. So, (x-1)^2 + (y-1)^2 >= 0 And if we solve this we get the solution.I don't get the red part.
  13. R

    (Probability/Statistics) Transformation of Bivariate Random Variable

    Homework Statement Let X_1, X_2 have the joint pdf h(x_1, x_2) = 8x_1x_2, 0<x_1<x_2<1 , zero elsewhere. Find the joint pdf of Y_1=X_1/X_2 and Y_2=X_2. Homework Equations p_Y(y_1,y_2)=p_X[w_1(y_1,y_2),w_2(y_1,y_2)] where w_i is the inverse of y_1=u_1(x_1,x_2) The Attempt at a Solution We can...
  14. M

    Partial derivative that contains the independent variable as an deriva

    Homework Statement \frac{\partial f}{\partial t},\frac{\partial f}{\partial x} where f=f(x,t,\frac{dx}{dt}) Homework Equations The Attempt at a Solution I think it's impossible to consider it as a simple partial derivative.
  15. N

    MHB Conditional PDF of this random variable

    the random variable X and Y have a joint PDF given by: $f_{x,y}(x,y) = \frac{1}{10}$, $(x,y)\in[-1,1] * [-2,2] \cup [1,2] * [-1,1]$ a) find the conditional PDF for $f_{y|x}(x,y)$ and $f_{x|y}(xy)$ and b) find E[X|Y], E[X] and Var[X|Y]. Use these to calculate var(X) for part a) I am unsure...
  16. A

    An inequality for a two variable function

    Suppose that ##F(u,v)=a|u+v|^{r+1}+2b|uv|^{\frac{r+1}{2}}##, where ##a>1, b>0## and ##r\geq3.## How we can show that there exists a positive constant c such that ## F(u,v)\geq c\Big( |u|^{r+1}+|v|^{r+1}\Big). ##
  17. S

    MHB Dealing with 5 input variable Kmaps

    Just need someone to check my work. Thank you for your time. First time doing a 5 input Kmap. Determine the following 5 input Karnaugh map for function f(V,W,Z,Y,Z) determine the minimal SOP equation. NOTE: (WX are the variables associated with the top column, and YZ are the variables...
  18. P

    Generating level surface from 2 variable function

    Homework Statement given f(x,y)=9/(x+y) find a level surface. Homework Equations The Attempt at a Solution g(x,y,z)=f(x,y)-z=0? g(x,y,z)=9/(x+y) -z=0? That answer is wrong. Apparently i must have the following: g(x,y,z)=z(x+y)=9 How do I solve problems like these? Another...
  19. PsychonautQQ

    Variable Resistors in a Voltage Divider

    My textbook says that in a voltage divider (voltage source Vin, then a resistor, then another path that leads to Vout, Resistor two, Ground, that it is a bad idea to use variable resistors for BOTH of the resistors (but it is okay if you just do one or the other). Does anybody know why?
  20. G

    Why does the multi variable chain rule need to be proven?

    It seems to me to follow from the definition of a partial derivative. If f(x,y) = fx + fy, then what else can Δf be other than ∂f/∂x*Δx + ∂f/∂y*Δy? Then in the limiting case, the changes in f, x and y becomes differentials instead. All this seems to be given by the definitions themselves, is...
  21. BruceW

    Extrinsic thermodynamic variable confusion

    Hi all, Something has been troubling me. To begin with, I have never been certain about this concept of 'extrinsic' thermodynamic variables. I mean, they don't have to be linear with system size, right? They just need to increase with system size? And also, I have a specific 'example problem'...
  22. M

    Find E[(X-mu)^k] - Normal Random Variable

    Hi, I'm having a bit of a problem with a probability question. The question is Let X be a normal random variable with mean \mu and variance \sigma^{2}. Find E[(X -\mu)^{k}] for all k = 1,2,... I'm not really sure what to do and need some help to confirm how to approach the question...
  23. D

    Valid Variable Names: Rules & Tests

    Hi all, I would like to clarify regarding valid variable names. Well what I fairly understand are the rules regarding names.. What I am unsure about is -- in a test, is there any way to spot a reserved name? For example to make things difficult, trick question, sometimes the question will...
  24. F

    MHB Determining if equation is linear in indicated dependent variable

    I was stuck on a question and went back to look at an example but couldn't understand the example. It has (y-x)dx +4xy dy = 0 is linear in y because it can be written as 4xy'+y=x First of all what are dx and dy doing in the equation? They look to be from the end of an integral. Second, how did...
  25. X

    What is the Minimum Size L for Uniform Density with Less Than 1% Error?

    Homework Statement The linear mass density in a string is given by μ = μ0[1 + cos(x/R)] where R is a constant. If one averages this density over the large size L it becomes uniform: <μ> = μ0, where <…> means averaging. What is the minimum size L (in terms of R) such that the density can be...
  26. J

    Variable MOI: Rotational 2nd Law

    I'm having trouble finding any sources that discuss equations of motion that take into account a changing moment of inertia. Just looking at the scaler case, angular momentum is L = I\omega Then, according to the 2nd law, \tau = \frac{d}{dt}(L) = \dot{I}\omega + I\alpha Is this correct...
  27. B

    Research topics in Variable stars

    Hey, I am an undergraduate physics & astronomy student. I am looking for a good research topic to work on for this semester. I have access to a .5 m telescope in Louisville, Ky (38 deg N), a .5 m telescope, and possibly another with a built in spectroscopy as well as photometry capabilities...
  28. naima

    Can hidden variable theories assign values to observables?

    hi PF I read the no-go Kochen theorem using 18 vectors projection (here). One attribute a value to an observable A: v(A) This function is supposed to be linear and verify v(AB) = v(A) v(B) so v(AB - BA) = v(A)v(B) - v(B)v(A) = 0 (v is a real number function) v must assign v(id) = 1 because v(A...
  29. T

    Variable Frequency Drive vs. Servo Drive

    I'm wondering what the difference is between a VFD and servo drive are. I'm pretty familiar with VFDs but not so much with servo drives. From what I read, would the following assumptions be correct? A variable frequency drive without an encoder module will adjust the frequency and amplitude...
  30. J

    Define the function of density of the random variable Y.

    We selected X point from interval (-1,2). If X=x, we selected point Y from (-1,x^2). Define the function of density of the random variable Y.
  31. Saitama

    Variable mass system - sand falling on flatcar

    Homework Statement A flatcar of mass ##m_0## starts moving to the right due to a constant horizontal force F. Sand spills on the flatcar from a stationary hopper. The velocity of loading is constant and equal to ##\mu## kg/s. Find the time dependence of the velocity and acceleration of flatcar...
  32. C

    Change of variable for 2nd partial differentiation and higher.

    Hello, the question I have arises from the 4th Edition of the book "Advanced Engineering Mathematics" written by K.A. Stroud. For those who owns the book, it is the example #2 starting at page 379. More precisely, the example is separated into two parts but the first one is very straight...
  33. P

    Can we rewrite Schrodinger equation using observable variable?

    We know that in Schrodinger equation, Ψ is called wave function, which is not observable, while Ψ·Ψ* is the probability, which is observable. can we rewirte the Schrodinger equation to a form without Ψ but only Ψ·Ψ*? because I think, in this way can I figure out all conservations in the...
  34. S

    MHB Derivative with respect to which variable?

    We have the following trapezoid: The question is to find the length of the fourth side when the area of trapezoid is maximized. I realize we will not be able to find a numerical value for the fourth side due to the given information (rather, lack thereof). So we are essentially going have...
  35. M

    Inverse function of a two variable function

    Homework Statement I'm wondering how to find the inverse function of some f(x,y)? Homework Equations The Attempt at a Solution
  36. M

    Maximize two variable equation

    Hello, This will probably sound like a HW question, but it's not. There is a certain phone system that I can use to call someone. There is an outgoing charge per call and a per minute charge. The per minute charge is $ 7/18 The outgoing call charge is $299/90 Say I have $50 on the...
  37. L

    Prove convergence in probability for n * Poisson variable to zero

    The problem: Let \mu_{n} = \frac{1}{n} for n \in \mathbb{N}. Let X_{n} \; \mathtt{\sim} \; \textrm{ Poisson}\left( \lambda_{n} \right). Let Y_{n} = n X_{n}. Show that Y_{n} \xrightarrow{P} 0 . Work I've done: I've shown that X_{n} \xrightarrow{P} 0 by showing that \mathbb{P} \left(...
  38. G

    Differential Equation with Function of Shifted Variable

    Hey guys, I have a question for you... how would one go about solving an equation like this... or this... This came across my mind the other day. I was wondering how to solve that equation if the function is of t-1, instead of t. Obviously, if it was f(t), the solution would be Ce^t, but I was...
  39. M

    Variable of an equation is in the denominator

    Homework Statement 1/x - 1/a = 1/b Solve for x Homework Equations The Attempt at a Solution I used to be able to do this in high school, but now I am 43! Normally, I would just cross-multiply and solve for x, to get the x out of the denominator, but you cannot...
  40. O

    How to integral ? How can they ignore that variable?

    Homework Statement I don't understand case 1. In case 2 that is normal integration , isn't? Then why case 1 can simply ignore the r ? I don't think r is constant. Homework Equations The Attempt at a Solution Please guide. Thanks
  41. E

    What's the expected value of this problem (random variable)?

    Homework Statement What's the expected value of this problem (random variable)? X: represent the result of dice number 1 - result of dice number 2 example dice 1 first roll = 2; second roll = 3 dice 2 first roll = 1; second roll = 2 X = 2+3 -(1+2) = 2 what's the expected value...
  42. Jeffack

    Generate a Multivariate Random Variable

    Hi, I'm an economics graduate student doing some work on a nested logit model. I am trying to generate random variables that follow the following CDF: F(x_1, x_2) =\textrm{exp}[ -(e^{-2x_1}+e^{-2x_2}) ^{1/2}] (This is an extreme-value distribution) With a single random variable, I...
  43. I

    Jacobian Determinant/ mult. variable implicit differentiation

    Homework Statement Let F: x^2 + y^2 - z^2 + 2xy - 1 = 0 and G: x^3 + y^3 - 5y - 4 = 0. Calculate dz/dx. Note: This is NOT the partial derivative ∂z/∂x. I do not need help in taking the derivative of many polynomials. What I need help in is setting up a Jacobian determinant to evaluate this...
  44. P

    Who first studied variable speed of light? - Einstein

    Who first studied variable speed of light? --- Einstein Variable speed of light is a hypothesis that states that the speed of light, usually denoted by c, may be a function of space and time. Einstein's first mentioned a variable speed of light in 1907, and he reconsidered the idea more...
  45. C

    Covariance Matrix of a Vector Random Variable w/ Components Related

    Homework Statement Given X=ZU+Y where (i) U,X,Y, and Z are random variables (ii) U~N(0,1) (iii) U is independent of Z and Y (iv) f(z) = \frac{3}{4} z2 if 1 \leq z \leq 2 , f(z)=0 otherwise (v) fY|Z=z(y) = ze-zy (i.e. Y depends conditionally on...
  46. trash

    [Probability] Expected Value of Random Variable

    Homework Statement A man wants to travel to four cities (A,B,C,D) but he has such a bad memory that he can't remember the cities that visited, therefore, if he travel to city A he can choose between (B,C,D) and if he then travel to B he can choose between (A,C,D). Find v, If v it's the...
  47. H

    MHB PGF of a conditional random variable

    I have a queueing system. The probability Generating Function of the number of packets in the queue (queue length) is given by Q_G(z)=\frac{e^{\lambda T(z-1)}(1-z^{-1})(1-\lambda T)}{1-z^{-1}e^{\lambda T(z-1)}}. I need to find the PGF of a conditional quantity. X=(Q_G|Q_G>0) i.e. to say in...
  48. K

    Question on variable definitions in Paschens law? (breakdown voltage)

    Hello all, In the equation V= apd/Ln(pd)+b as described by Paschens law regarding breakdown voltage, I was wondering what the "L" and the "n" stood for. Example of what I'm looking for: p stands for pressure. Thanks.
  49. A

    Magnitude of the tension when there is static (variable) friction

    Hello folks, I'm being tricked by the pesky friction force again. I know that static friction acts just to put everything in equilibrium as long as its magnitude doesn't exceed a certain value. That is ok. But when there are other adjustable force such as TENSION and NORMAL, (which in this...
  50. A

    I do not understand Variable density

    Hey forum I need to ask for a link to a page for Variable density or preferably an explanation from someone who can describe it simply. I am trying to teach myself about the function of Qubits and have run into probability density functions and cannot find a good reference on what exactly...
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