Normal Definition and 1000 Threads

Hello Mathematicians! I'm doing some work on obtaining true measures of ability for students, and am trying to find a simple mathematical example that would show that a student's true ability is obtained by having a few equally weighted tests rather than one big test. The example I'm thinking...

Consider a pulley fixed to the ceiling. A mass-less string is wrapped around it, with each side of the string hanging down either side of the pulley. Since the pulley has friction with the string, tension along the string will vary. Let's say the string is attempting to move clockwise, so the...

SU(2) matrices act isometrically on the Riemann sphere with the chordal metric. At the same time the group of automorphisms of the Riemann sphere is isomorphic to the group SL(2, C) of isometries of H 3(hyperbolic space) i.e. every orientation-preserving isometry of H 3 gives rise to a Möbius...

I need help with the proof of an apparently simple Proposition in Aigli Papantonopoulou's book: Algebra: Pure and Applied. The proposition in question is Proposition 5.2.3 and reads as follows:Can someone please help me and provide an explicit and formal proof of this proposition.Since...

Hi all, I'm struggling with the concept of angular frequency in the context of sinusoidal waves. We describe sinusoidal waves with equations like y(x,t) = Asin(kx-\omega t) , where \omega is the angular frequency, yes? But what does this quantity physically represent? The rate at which...

A 250-N force is directed horizontally as shown to push a 29-kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force, FN, and the coefficient of kinetic friction, µk. So, I know I have to find the vertical and parallel forces Vertical: Fn and 250 sin of...

Homework Statement I need to show that any normal matrix can be expressed as the sum of two commuting self adjoint matrices Homework Equations Normal matrix A: [A,A^\dagger]=0 Self Adjoint matrix: B=B^\dagger The Attempt at a Solution A is a normal matrix. I assume I can write...

Homework Statement Homework Equations An = mv^2 / r The Attempt at a Solution I get the 2D free body diagram, and how the vertical components are resolved, but how is Nc sin θ = mv^2 / r when they both are in the same direction? Also another related problem is this diagram...

Homework Statement In Griffiths, the following boundary condition is given without proof: ∂Aabove/∂n-∂Abelow/∂n=-μ0K for the change in the magnetic vector potential A across a surface with surface current density K, where n is the normal direction to the surface. A later problem asks for a...

A 250-N force is directed horizontally as shown to push a 29-kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force, FN, and the coefficient of kinetic friction, µk. FN µk (a) 330 N 0.31 (b) 310 N 0.33 (c) 250 N 0.27 (d) 290 N...

I'll be going into first year of a physics degree in early September and I was looking at the module list and noticed that the university I will be going to does quantum mechanics in fourth year. I've since looked at other universities in the area and noticed that they all seem to do it in third...

Homework Statement N is a normal subgroup of G if aNa^-1 is a subset of N for all elements a contained in G. Prove that in that case aNa^-1 = N. Homework Equations The Attempt at a Solution Given: N is a normal subgroup of G if aNa^-1 is a subset of N for all elements a contained...

Hey guys, I have a couple of questions about this problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help. Question: For 1a, I used implicit differentiation and isolated dy/dx. This gave me the following answer: dy/dx = (-3x^2 -4y)/(4x+12y) Which I...

today i did a oil change on my outboard engine. i found out the oil is green, its normal? If yes, why the oil will be green color? because i fill the new oil is golden color.

Hi, I am an orthopedic surgeon. Many of our long bones are anatomically curved. When they fracture they sometimes heal in a none perfect/anatomic position. How do one calculate the angle/curve or changed angle/curve of a fractured bone healed or fixed none anatomically Please see my drawn...

Okay, so I guess my first question is if the main utility of the normal distribution ##f(x)## is to provide a probability measure for any subspace of the measurable space ##(\mathbb{R},\mathcal{B})## (where ##\mathcal{B}## is the borel σ-algebra on the real numbers) by defining the measure as...

Homework Statement My source textbook is the community college / junior college (confer: undergraduate-lower division) probability and statistics textbook: An Introduction to Mathematical Statistics and Its Applications, 2nd Edition Authors: Richard J. Larsen, Morris L. Marx 1986...

Homework Statement A canon fires a projectile at a speed of 100 m/s at angle of 20 degrees. (a) what is the radius of curvature of the projectile at its highest altitude? (b) What is the radius of curvature of the path .5 seconds after firing? Homework Equations Velocity vector = s'ur...

Homework Statement Homework Equations F_{c} = \frac{mv^{2}}{r} The Attempt at a Solution I think the normal force would be the magnitude of vector sum of centripetal force and gravitational force. So I did: N = \sqrt{(\frac{mv^{2}}{r})^{2} + (mg)^{2}} However, it isn't one...

when the body rotates with uniform motion then the normal acceleration is V^2/r. but what is the normal acceleration when the motion is in non uniform circular motion let's say when body has uniform tangential acceleration.

Consider a circular pin-in-a-hole problem in two dimensions. Let the plate containing the hole be infinite so that the dimensions of the circular pin are very small compared to the plate. The conditions of plane stress be assumed everywhere. Also, let the pin be loaded with a force applied at...

Hi all, For a marble in uniform circular motion within a smooth cone, what is the relationship between the normal force by the surface of the cone and the weight of the marble? My take is that the normal force forms a reaction pair with one of the resolved forces of weight. I have resolved the...

Homework Statement http://i.imgur.com/rwbXqW8.png Homework Equations The Attempt at a Solution So I started off by analyzing the pulley, and determined that each cable carries 100N of force. After that, I drew the FBD of the beam, where there is a 100N force going downwards on the...

##ax +by +cz +d = 0## is the equation of a plane orthogonal to ##(a,b,c)## but why is there a d in the equation? What does it do to the plane geometrically? http://i.imgur.com/sMiLhHc.jpg?1 I don't see how the d fits into that geometric interpretation.

I am giving three AP late testing tests (Mechanics, Calculus BC, Chemistry) in the next two days. Usually, I would be in panic mode at this point of time. However, I am normal, relaxed, just finishing up stuff for the exam in a casual (but thorough manner). I went through a couple of sample...

I have ##\bar{X}## ~ ##N(\mu , 9/25)## I have ##E[X] = \mu## ##Var[X] = 9/25## ##SD[X] = 3/5 = 0.6## An interval for ##\bar{X}## has been recorded: ##\bar{X} \pm 1.05##. I asked to find ##P(\bar{X} > \mu + 1.05)## I can "normalize" the distribution through: ##Z =...

So, usually I like to give a long description of how/why I am asking such a question, but I think this time, I'll be quick and to the point. Truth is when I first came to this site, I think I started asking questions that were well beyond my current knowledge, so I would like to take the time...

Homework Statement A pilot of mass m flies a jet plane on a "loop-the-loop" course by flying in a vertical circle of radius R at a constant speed v. The force that the cockpit seat exerts on the pilot at the top of the loop is (A) mg. (B) mg\left(\frac{v^{2}}{R+1}\right). (C)...

Homework Statement The problem wants me to order the choice for the directions of a force F of a constant magnitude F(a,b,c,d are unit vectors along which F has to be oriented) exerted on the block placed on an incline at 30° to the horizontal based on the normal force Fn that the incline...

Lets say I have 8 samples (weight) of 4 ingredients in particular food by X brand and another 8 samples by Y brand. I would like to test to see if there is any difference between the two brands in terms of weight of particular ingredients. However, I am not sure what statistic test to run and I...

Homework Statement "Cans of lemon juice are supposed to contain 440 ml of juice. It is found that the actual volume of juice in a can is normally distributed with mean 445 ml and standard deviation 3.6 ml." It is found that 94% of the cans contain between 445−c ml and 445+c ml of juice. (ii)...

The question asks to use Fresnel's equations at normal incidence to find the ratio of the refractive indexes of the two materials. We are told equal energy is transmitted and reflected and that both media are non-magnetic and non-conducting dielectrics. So I know that the ratio of Er/Ei and...

Hi, Given a holomorphic function u(x,y) defined in the half plane ( x\in (-\infty,\infty), y\in (-\infty,0)), with boundary value u(x,0) = f(x) , the solution to this equation (known as the Poisson integral formula) is u(x,y) = \int_{-\infty}^{\infty} \frac{y\ f(t) }{(t-x)^2 +y^2} \...

Homework Statement Two independent series of experiments are performed. The probability of a positive result (independent of each other) in the respective series are given by p and q. Let X and Y be be the amount of experiments before the first negative result occur in the respective series...

Hi, let G be any group . Is there a way of embedding G in some other group H so that G is normal in H, _other_ than by using the embedding: G -->G x G' , for some group G'? I assume this is easier if G is Abelian and is embedded in an Abelian group. Is there a way of doing this in...

I don't really understand boundary conditions and I've been trying to research it for ages now but to no real avail. I understand what boundary conditions are, I think. You need them along with the initial conditions of a wire/string in order to describe the shape of motion of the string. I...

prove that U_{m/n_1} (m) , ... U_{m/n_k} (m) are normal subgroups In the attached image I have proved that U_{m/n_1} (m) , ... U_{m/n_k} (m) are normal subgroups But how do i Prove that U(m) = U_{m/n_1} (m) ... U_{m/n_k} (m)? and that their intersection is identity alone. Help will be...

Our task is to determine if P(-c \le X \le c) has a minimum variance unbiased estimator for a sample from a distribution that is N(\theta,1). The one-sided interval P(X \le c) = \Phi(x - \theta) is unique, so constructing an MVUE is just a matter of applying Rao-Blackwell and Lehmann-Scheffe...

Here is a example 1.3 from analytical dynamics of Haim Baruh. a particle moves on a path on the xy plane defined by the curve y=3*x^2 , where x varies with the relation x= sin(a). find the radius of curvature of the path and unit vectors in the normal and tangential directions when a=pi/6...

Homework Statement The displacement, y(x; t), of a tight string of length, L, satisfies the conditions y(0, t) = \frac{\delta y}{\delta x}(L,t) = 0 The wave velocity in the string is v. a) Explain what is meant by a normal mode. Give the form of the displacement, y(x; t), for the normal...

From my understanding, normal and anomalous dispersion are because the phase velocity is a function of k so it is different for different components of a group so the group will spread out over time. So what's group velocity dispersion? Is it the same affect (dispersion/ spreading out)...

Homework Statement A 1300 kg car is traveling at 25 m/s as it passes the crest of a hill that has a radius of curvature of 120m. Determine the normal force acting on the car at the crest of the hill.Homework Equations The Attempt at a Solution I know that for horizontal surfaces the Normal...

Homework Statement How fast would a electric arc be when it ionizes through normal, unpressured air between say, two electrodes? Not the same as lightning as it is hypothetically from an artificial source. Homework Equations How would one calculate (please include your formula's and which...

Hey! :o I have the following exercise: Write in the normal form the differential equation $$u_{xx}+\frac{2y}{x}u_{xy}+\frac{y^2}{x^2}[(1+y^2)u_{yy}+2yu_y]=0$$ Hint: You can suppose that the one new variable is given by $\xi=x$ I have done the following: $a=1, b=\frac{y}{x}...

Wikipedia is not very clear on this. Is there a known computable normal number? I found this paper: http://www.glyc.dc.uba.ar/santiago/papers/absnor.pdf But I'm not sure if it's been peer reviewed.

Homework Statement A large 16.0 kg roll of paper with radius R=18.0 cm rests against the wall and is held in place by a bracket attached to a rod through the center of the roll. The rod turns without friction in the bracket, and the moment of inertia of the paper and rod about the axis is...

Homework Statement complete problem attached Homework Equations The Attempt at a Solution part I in this question was a bit tricky but i managed to solve it , when i read part II i understood nothing , he usually asks about the tangent not the normal , he asks about the point...

Homework Statement Stuck on two similar problems: "State the normal stress boundary condition at an interface x_3-h(x_1,x_2,t)=0between an invisicid incompressible fluid and a vacuum. You may assume that the interface has a constant tension." The second question in the same but the fluid is...

imagine there is a ball on a table on a spaceship that is not moving there is no gravitational force acting on the ball will there be a normal force

Homework Statement Consider the mass m1 on a simple incline plane. It passes from point A downwards with the velocity v0 and stops at point B (still on the plane). What is the work done by the normal force on mass m during the complete motion? Homework Equations The Attempt at a...