Application Definition and 998 Threads

Application of Schwarz Lemma--Complex Analysis Let f be holomorphic in D = {z: |z| < 1} and suppose that |f(z)| ≤ M for all z in D. If f(z_{k}) = 0 for 1 ≤ k ≤ n, show that |f(z)| ≤ M \prod |z - z_{k}|/|1 - \bar{z_{k}}z| for k = 1 to n and |z| < 1. I am just very confused about...

My current project is as follows: Designing a system that will be mounted to a truck that will be traveling down the equivalent of a dirt road. Part of the system is an ingredient bin that is rigidly mounted to load cells. The loads cells are a cantileaverd beam type. The primary...

Dear All I have a question about the validity of Maxwell Boltzmann velocity distribution in the case of nanoscale systems. When you consider a nanoscale system such as flow of water molecules (less than 100 molecules) through a carbon nanotube or graphene sheet, is it possible to expect a...

Homework Statement Two charges of masses m and 2m, charges 2q and q respectively are placed in a uniform electric field and are allowed to move at exactly the same time. Find the ratio of their kinetic energies. Homework Equations Field = qE Force =(Kq1q2)/r^2 Kinetic energy=1/2mv^2...

So I'm taking my complex variables class and learning about these cool powerful theorems like the Cauchy Goursat theorem. I know this all has huge application in physics however I just don't know what they are. Currently I'm only taking freshmen E@M so I know I won't be using it there. But next...

Hello, I consider starting a master in theoretical physics in a little more than a year. Currently I'm halfway doing a bachelor in both (applied) physics and mathematics and so far it is going pretty good. I looked around a bit on the internet and came across the Cambridge website and read as...

Homework Statement *see attachment* Homework Equations The Attempt at a Solution Alright, so we just began messing with functions in our class and I'm kinda struggling to grasp this assignment. I believe it should begin like this: shape = menu('Choose a shape','1...

Homework Statement A company mines low-grade nickel ore. If the company mines x tons of ore, it can sell the ore for the price p = 225 - 0.25x dollers per ton. How much revenue will the company make by selling an additional 1 ton of ore on top of what is being produced to maximize revenue...

Consider a wire of length l. At time t=0, one end of the wire is at temperature T_0, while the rest of the wire is at temperature T_1, T_1<T_0 (for example, one end of the wire is kept in contact with an external hot body, at temperature T_0). After how much time the temperature near the second...

Real Work Application of "Newthon-Raphson" method. Homework Statement Hi, an undergrad engineering (presentation) question: As a presentation, I am (plus a group mate) tasked to present a real world application of the Newthon-Raphson method (of finding a root). Now I know that we can also...

Homework Statement Compute the integral: ∫ x2/(x4-4x2+5) Homework Equations Uses Residue theorem. The Attempt at a Solution So I found the zeroes of x4-4x2+5 to be 2+i and 2-i, and therefore the one that is of relevance is 2+i since it is in the upper half-plane. Then I used...

hi, I'm simulating a system of molecules (water) and in order to pass through a barrier they have to overcome an energy barrier of 4kT. What is the probability of a water molecule passing the barrier or perhaps what is the average energy of a water molecule in my system? I know it's 1/2 *kT...

HI, I am having some trouble understanding the effects of an impulse on rolling motion, particularly without slipping. For eg, if we take a sphere of radius R and mass M, then what is the point h above the centre C at which when an impulse is imparted, will cause pure rolling motion...

Application of Newtons laws (Friction related) check my solutions please :) Dont forget to check the diagram, as it will probably help you see the problem correctly, don't worry, no need to download diagram attachment to view it. Homework Statement A child pushes a block of wood with a...

Homework Statement Hello everybody, Can you help me solve this: Coal-burning power plants convert the sulfur in the coal to sulfur dioxide (SO2), a regulated air pollutant. The maximum allowable SO2 emission for new power plants (i.e., the maximum allowed ratio of the mass of SO2 emitted...

what is application of Quantum mechanics i need 10 applications at least of Quantum mechanics and I'm beginner at Quantum world i need some books names and i find the math of it very hard need help please? note that I'm need easy MAtrial not complex

what is application of Quantum mechanics i need 10 applications at least of Quantum mechanics and I'm beginner at Quantum world i need some books names and i find the math of it very hard need help please? ψ

Calculating magnitude and direction of an magnetic force on an electron Homework Statement Okay so the question says that the magnetic force (Vector)FM on a particle which is in a magnetic field is found by (Vector)FM = Vector I x Vector B. Vector I = charge multiplied by the velocity of...

Due to unforeseen circumstances (burnout, depression), I recently had to withdraw from all of my courses (5 courses) and this brings my total number of W's up to 11. Am I doomed? Even if I went back to school and continue to excel, would my graduate school application ever be given serious...

1. Homework Statement The figure shows 1.0*10^-6 m diameter dust particles in a vacuum chamber. The dust particles are released from rest above a 1.0*10^-6 m diameter hole, fall through the hole (there's just barely room for the particles to go through), and land on a detector at distance d...

Hi there, I'm trying use the Epanechnikov density kernel to smooth out data that I have collected, but I'm not sure exactly how to use it. I've recorded speed data from a car every second for a journey and I'm trying to smooth the data as it contains some noise. I have document that...

Solve $\begin{aligned} & {{u}_{tt}}={{u}_{xx}},\text{ }x>0,\text{ }t>0 \\ & u(0,t)=0,\text{ }t>0 \\ & u(x,0)=x{{e}^{-{{x}^{2}}}},\text{ }0<x<\infty \\ & {{u}_{t}}(x,0)=0. \end{aligned} $ The condition $u(0,t)$ is new to me, since I usually apply the method when only having $u(x,0)$...

Homework Statement Okay so I'm supposed to find the least squares solution of a set of equations, which I can do, but it adds that I must use QR decomposition. I don't really know how to apply QR decomposition to this problem. Problem: Find the least squares solution of x_1 + x_2 = 4...

Hey all. I sure hope somebody can assist with this! I am a hobby beer brewer and am writing my own heat control algorithms. Part of the process involves heating water to a desired temperature setpoint. I'm using an electric water heater element (5500W) inside the water vessel (~5-10 gal)...

Homework Statement Given: f is an entire function, Re f(z) ≤ n for all z. Show f is constant. Homework Equations The Attempt at a Solution So I thought I'd use Liouville's Theorem which states that, if f(z) is entire and there is a constant m such that |f(z)| ≤ m for all z...

Hello. I am trying to learn how to apply my knowledge of torque to a real life problem but I'm not quite sure how. I have attached a picture describing what I am trying to do. I would be very appreciative if anyone would take the time to take a look at what I have done and see if my view of...

Hi. In my homework I've encountered a discrete probability distribution of this form: f(k,\lambda)=N \frac{\lambda^k}{k!} k is the variable, and \lambda is a parameter. I'm curious what is this distribution - what's its name and where can it be applied. I will be grateful for, for...

Hi there, I am currently a secondary school student in the south east of England, and I wish to become a Physicist or Astro-Physicist somewhere along the line in my wonderous future... *hint of sarcasm for wonderous* Anyway, I think for my Physics exams at GCSE level I would acquire a B, and...

I have spent many hours today trying to determine at what distances certain substances will condense in protoplanetary disks around stars or temperatures different to that of our sun. I have come to the conclusion that the Inverse-Square Law is key to determining this. However, I am unsure as...

Homework Statement http://www.scribd.com/doc/82645310 In Figure 3-31, the lines AB and CD are the center lines of two conduits 1 ft. and 2 ft. in diameter respectively. Determine the maximum value of z so that the two may pass without interference. Conduit CD must pass under AB...

Homework Statement http://www.scribd.com/doc/82645310 In Figure 3-31, the lines AB and CD are the center lines of two conduits 1 ft. and 2 ft. in diameter respectively. Determine the maximum value of z so that the two may pass without interference. Conduit CD must pass under AB. Homework...

I was given an assignment in my Fluid Mechanics Module with the title: Application of the Navier-Stokes Equations in Tribology Applications Yet the lecture has given no starting point and we haven't yet done anything to do with Navier-Stokes Can anyone help me on where to start?

Why are derivatives of inverse functions important? My students are giving me questions like: When would using the theorem be useful? Can't you just find the inverse function and take its derivative? I'm sure many of you know the type of question: "Who cares?" My answers are that the theorem...

Hey all, I've been wondering about a few questions that seem to turn up a lot in math competitions—namely, what are the last 2 nonzero digits of some number x!. I've seen it a lot, and I'm wondering how one would go about solving that? I believe that one can use some modulus techniques to...

f is analytic on an open set U, z_0\in U, and f'(z_0)\neq 0. Show that \frac{2\pi i}{f'(z_0)}=\int_C\frac{1}{f(z)-f(z_0)}dz where $C$ is some circle center at $z_0$. S0 ,f(z)-f(z_0) = a_1(z-z_0)+a_2(z-z_0)^2+\cdots with a_1=f'(z_0)\neq 0. But why can f(z)-f(z_0) be expanded this way?

Hello, I am a sophomore physics and mathematics double major, and I plan to attend graduate school for physics with a concentration in biophysics, or just biophysics. However, this is subject to change, as I find a lot of areas of physics interesting. I was recently accepted to two REU...

Do Wien's displacement law hold true even for bodies with emissivity not equal to 1, that is, non-black bodies?

I apologize for the rather vague title. It's space-limited and I'm not sure how to concisely state what I want to know. Basically, I understand that the solutions to quadratic equations (and if I remember correctly cubic equations) often had surveying problems land surveying. However, quartic...

A "simple" application of dirac delta "shift theorem"...help Homework Statement show that for a, b, c, d positive: δ(a/b-c/d) = bdδ(ad-bc) Homework Equations ∫f(x)δ(x-a)dx = f(a) The Attempt at a Solution Ok so I start with ∫δ(a/b-c/d)f(x)dx But I am not sure how to apply the shift...

Homework Statement My teacher put us into groups and we each selected a wall of the rectangular room. He attached some sort of machine to the wall that spins in a circle with a laser on it, creating a laser point revolving around the walls. Our task is to create a function for the...

I'm just wondering if anyone has any advice on writing personal statements. Is there anything I should absolutely say or anything I should absolutely not say? What should the focus be? Should it go something like: why I like math, what kind of math I like, any relevant experiences with math I...

Suppose I have a non-linear load in my home (A half wave rectifier supplied DC load, say). Since it will consume current from the source only during +ve cycle of the Voltage, the current will be half-wave too. The current isn't sinusoidal. We can mathematically say that Distored Current =...

Homework Statement I need to show that the first equation becomes the last. First sub in for r1 and r2 and then use the binomial theorem to expand to first order in d. Then use the assumption that d<<r1 and r2. To show it reduces to the last eqn **In the first eqn it is NOT r3 is should be r2...

From Acoustics, Resonance, Energy, Power, Intensity and The Doppler Effect Homework Statement An old-fashioned hearing trumpet has the shape of a flared funnel, with a diameter of 8 cm at its wide end and a diameter of 0.7 cm at its narrow end. Suppose that all of the sound energy that...

Homework Statement A generated AC voltage has a value given by V = 4cos2θ. You will need to use the identity cos^2⁡θ = 1/2(1+cos2θ) Homework Equations a) Find the mean value of the voltage over a full cycle (0 ≤ θ ≤ 2π) using integral calculus b) Find the r.m.s. value of the...

Hi, I've had something that's been bothering me for a while and I've been researching it, but I just want to clear something up. I understand that the exclusion principle dictates that fermionic particles with half-integer spin have an anti-symmetrical wavefunction under exchange, and...

Hi all, I want to resonantly charge a capacitor, i.e. using a coil and diode combination instead of a resistor, in a very short period, which means a high current at high frequency. The problem is the coil. I read that at high frequency AC you get to deal with the skin effect, and also the...

Homework Statement I need to take notes in Physics class. I have an iPad and was wondering what apps would be good for the equations/drawing/note taking. I have a bluetooth keyboard to go with it, and am familiar with LaTex. 2. The attempt at a solution I have used Tex Touch but...

I'm completing my transfer application to Towson University. The "essay prompt" is the following: I'd like to highlight the fact that I spent about six years teaching English in China. I learned a lot about the culture, I can speak (and read a bit) of Mandarin, I studied kung fu... Lots of...

Homework Statement a jar containing an iron block was floating on water in a bigger container. the block was taken out and put into water. as a result, the level of water in the container will (a)rise (b)fall (c)remains the same (d)rise or fall depending on the mass of block The Attempt...