Uniform Definition and 1000 Threads

Solved, thanks :D

How do I determine whether the following sequences of complex functions converge uniformly? i) z/n ii)1/nz iii)nz^2/(z+3in) where n is natural number

Hello everyone, I'm trying to read an economics paper on competitive auction pricing and I'm still coming up to speed with some of the concepts. As the title says, why is the clearing price of a uniform price auction the S + 1st highest of B buyers values? In this case each Seller has...

Homework Statement Write an equation for one component of the position vector as a function of the radius of the circle and the angle the vector makes with one axis of your coordinate system. Calculate how that angle depends on time and the constant angular speed of the object moving in a...

does it have uniform velocity?

or...?

If we take a 1D uniform lattice I understand that we can derive a difference equation after using Hookes law and Newtons 2nd law as seen in the section labelled (Scalar wave equation in one space dimension, Derivation of the wave equation, From Hooke's law) in the link below...

Homework Statement a train starts from station a with a uniform acceleration of 5.00 x 10^-1 m/s^2 (east) and attains full speed after 50.0s. It travels at full speed for 1.20 x 10^2 s, then is brought to rest at station b by the application of the brakes which produces a constant...

Homework Statement A circular-motion addict of mass 82.0 kg rides a Ferris wheel around in a vertical circle of radius 14.0 m at a constant speed of 7.10 m/s. (a) What is the period of the motion? What is the magnitude of the normal force on the addict from the seat when both go through (b)...

What is "linear acceleration" in uniform circular motion? Yesterday, I took an exam and it was asked a concept that we hadn't studied, at least in the way it was written. The exercise explained that a circular motion was decreasing its velocity, and we had to be able to identify which of the...

Homework Statement a single loop of wire with radius A is rotating in a uniform magnetic field at angular frequency ω. The loop of wire drives a current through a resistor R. Determine the torque as a function of time needed to turn the wire. Homework Equations 1) Emf = ∫Fmag.dl...

Hello!A little problem:With the given series,$$Y(x)= \sum_{n=1}^{\infty}(-1)^n\frac{x^n\ln^nx}{n!} $$ ,why $Y(x)$ is Uniformly converges for all $x\in(0,1]$ ?Ok, I know that $Y(x)$ is u.c by M-test: $$\max{|x\ln{x}|}=\frac{1}{e}$$ And, $$ \sum_{n=0}^{\infty}\frac{(\frac{1}{e})^n}{n!} $$ Is...

Hey guys, I have a bunch price observations. I would like to know whether some subset of my observations is uniformly distributed (or close to being uniformly distributed). How could I go about testing this? Thanks.

A 20-cm radius ball is uniformly charged to 80 nC. (a) What is the ball’s charge density (C/m3)? (b) How much charge is enclosed by spheres at points 5, 10 and 20 cm from the center? (c) What is the electric field strength at points 5, 10 and 20 cm from the center? ATTEMPT: part a: i...

Homework Statement If R1 and R2 are two uniformly distributed random variables on the interval [0,1]. What is the density function Z=R1*R2? Homework Equations I'm not sure actually The Attempt at a Solution I have tried to manipulate with moment generating function (which i...

Homework Statement I have a solid cylinder of uniform charge density whose axis is centered along the z-axis. I am trying to calculate the electric field at a point on the z-axis. What I'm trying to do is to start by first calculating the field of a disk centered on the z-axis at a point on...

Homework Statement A uniform sphere rolls down a 30 degree incline θ from height h. Initially, the solid is at rest. Find the acceleration for the center of the mass of the solid. I am not sure where to start with this problem. I started with the energy formulas, but I am not sure how to find...

A solenoid, of sufficient length to consider external flux to be zero, passes through a uniform magnetic field with significant length on both ends extending beyond the field. Will a torque be exerted upon the solenoid ? Or do the windings effectively mask the internal solenoid field from the...

Homework Statement f(x) is defined within [a,b]. f_n(x)=\frac{\big\lfloor nf(x) \big\rfloor}{n} Check if f_n(x) is uniform convergent. The Attempt at a Solution This one seems to be easy however since I didn't touch calculus for quite a time I'm not confident with my solution. |\frac...

In Baby Rudin, Theorem 7.25 states: If K is compact, f_n \in C(K) for n=1,2,3,... and if {f_n} is pointwise bounded and equicontinuous on K, then (a) {f_n} is uniformly bounded on K The theorem continues with point (b), which I understand. My question is, whether point (a) needs the...

A charge q and a charge 3q are released in a uniform electric field. If the force this field exerts on 3q is F, the force it will exert on q is: i think the answer is F/3. is this right? i used E=F/q.

Homework Statement I have a solution to the following problem. I feel it is somewhat questionable though If fn converges uniformly to f, i.e. fn\rightarrowf as n\rightarrow∞ and gn converges uniformly to g, i.e. gn\rightarrowf as n\rightarrow∞ , Prove that fngn...

Homework Statement If U is uniform on [−1, 1], find the density function of U^2. Homework Equations f(u) = 1/(b-a) The Attempt at a Solution I actually solved the problem already, but I am having trouble defining what the boundaries are for U^2. My work is uploaded in paint...

Homework Statement A crystal contains N atoms which posses spin 1 and magnetic moment \mu. Placed in a uniform magnetic field B the atoms can orient themselves in three directions: parallel, perpendicular, and antiparallel to the field. If the crystal is in thermal equilibrium at temperature...

Say that there is a random variable X ~ U(a,b) where U is the discrete uniform distribution on integers on the interval [a,b]. Sample n such variables with the same (unknown) parameters a and b. Using those samples it's possible to estimate the mean either by taking the sample mean (sum the...

Homework Statement A charge q is released from rest at the origin, in the presence of a uniform electric field and a uniform magnetic field \underline{E} = E_0 \hat{z} and \underline{B} = B_0 \hat{x} in frame S. In another frame S', moving with velocity along the y-axis with respect...

Hi, Can someone please help me solve the following: Find the distribution of xy/z where x, y, z is independent and uniformly distributed from 0 to 1 Thanks for the help

Homework Statement http://www.xtremepapers.com/Edexcel/Advanced%20Level/Mathematics/Subject%20Sorted/S2/S2%202008-06.pdf Question 1(d) Homework Equations The Attempt at a Solution So I know this is a conditional probability question. Now I would have said P(X>8) / P(X=5) because it...

hello friend, this is my first post please go easy on me. the best way i can express my problem is below. I attach a pic to give you a better idea. A is a circular disk with 4.5" diameter, DISK A is driven by C which is connected to a DC motor. B is a pin diameter of 1 mm which is going to...

I had to calculate the distance a car traveled in a given time given its starting speed and acceleration. Would this formula x=Vo.t+ (Vf-Vo)/2.t Where Vf= a.t +Vo Be correct?

I thought the external magnetic field had to vary within an object in order for that object's magnetic moment to line up with the field.

Homework Statement An electron is fired at 4.0x106 m/s horizontally between the parallel plates as shown, (see diagram) starting at the negative plate. The electron deflects downwards and strikes the bottom plate. The magnitude of the electric field between the plates is 4.0 x102 N/C. The...

Does this actually happen in outer space? Do things actually move in uniform motion relative to each other? How would this work for the Earth considering it's rotating? Can the Earth ever be considered an inertial frame because it's always rotating?

thanks!

Homework Statement This isn't really a problem but it is just something I am curious about, I found a theorem stating that you have two metric spaces and f:X --> Y is uniform continuous and (xn) is a cauchy sequence in X then f(xn) is a cauchy sequence in Y. Homework Equations This...

If you were to pick two random numbers on the interval [0,1], what is the probability that the sum of their squares is less than 1? That is, if you let Y_1 ~ U(0,1) and Y_2 ~ U(0,1), find P(Y_1^2 + Y^2_2 \leq 1). There is also a hint: the substitution u = 1 - y_1 may be helpful - look for a beta...

Homework Statement A uniform rod AB has a length l and a weight W0. End A is in contact with a rough wall, but it is not fixed. A massless cord connects end B and is fixed to the wall at point C. The rod AB is now horizontal and the angle formed between the cord and rod is θ as shown in the...

Homework Statement http://www.xtremepapers.com/Edexcel/Advanced%20Level/Mathematics/Subject%20Sorted/S2/Solomon/Solomon%20B.pdf Questions 3c and 3d Homework Equations The Attempt at a Solution ok so for Qc) it must be between 6 and 10 cm from the bottom and 8 and 12 cm from the left d) it...

Homework Statement If X and Y are independent uniformly distributed random variables between 0 and 1, what is the probability that X^2+Y^2 is less than or equal to one. Homework Equations P(Z<1) = P(X^2+Y^2<1) For z between 0 and 1, P(X^2<z) = P(X < √z) = √z The Attempt at a Solution...

Homework Statement Find the center of mass of figure , of uniform density Homework Equations X = m1 x1 + m2 x2 + ... / m1 + m2 ... The Attempt at a Solution i broke the figure in 4 rectangles and got individual center of masses my answers comes out to be (13b/8 , 5b/2)...

Homework Statement See attachment! A plank is 4m long and has a weight of 500 N. It is pivoted frictionlessly about a nail which is driven through the center of the plank. When a 200 N weight is hung as shown in the figure (attached), the plank is horizontal and in equilibrium. Suppose...

Find the moment of inertia of a uniform solid sphere of mass,m and radius,a about an axis through its centre. I have tried to solve it but I get the different answer, I don't know where I have done mistake. Please! check and correct my solution below:- Consider a volume element, dv of the...

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Homework Statement A metal bar with length L, mass m, and resistance R is placed on frictionless metal rails that are inclined at an angle \phi above the horizontal. The rails have negligible resistance. A uniform magnetic field of magnitude is directed downward in the figure B. The bar is...

Homework Statement 'Figure 2 shows a uniform rod of length L= 0.2m and mass m=0.2kg pivoted at one end. The other end is attached to a horizontal spring with spring constant k =3.0 N/m. The spring is neither stretched nor compressed when the rod is perfectly vertical. You can also assume...

Homework Statement I am told that X is a random variable with uniform distribution over [0,1] I need to find the mean and variance of log(X) 2. The attempt at a solution I assume I must find the pdf of log(X) so I did this as follows; Let Y=log(X) Then to find the cumulative...

1. Homework Statement Question This is an experiment on a dilute isotopic mixture of helium gas. A spherical vessel of diameter 1 m is first filled with 4He gas to one atmosphere pressure. Then a small amount of 3He gas is introduced through a valve on one side of the vessel. Make a rough...

Assume we have a particle lying in the xy-plane with an initial velocity in the x-direction. If an external, constant and uniform magnetic field is applied in the z-direction, the particle, assuming it has a positive charge, will begin to do circular clockwise laps. However, it seems to me...

Consider that we have a macroscopic, electrically charged, point object tracing out a circular path in a uniform magnetic field in the usual way due to the Lorentz force. Now we very slowly raise the overall strength of the magnetic field (slow enough that on one orbit, the object sees the same...

Homework Statement A bar of length L supports a mass, m2 at the end. It is fastened by a pivot at one end to a wall which is at an angle θ to the horizontal. The bar is supported by a cord a distance x from the wall. The mass of the uniform bar is m1. I already solved for the...