Confusing Definition and 407 Threads

Hi there, I know that primitive cell is not unique and there are more than one way to define the primitive vectors but my question is when we said "primitive vectors" do we have to construct the Bravais lattice with choosing a proper basis first? My reasoning is suppose the crystal consist of...

I don't understand how you're supposed to prove this: Let A=uvT (vT = v transpose) where u is in R^M and v is in R^N. Prove 2-norm of A = 2 norm of v * 2 norm of u. I'm not sure if I'm supposed to look at v and u as vectors or what. If they are just vectors, this does not make any sense...

This conceptual question really got me thinking but I'm not sure how I would explain it: Your friend has been studying physics. She tells you that because of Newton's Third Law, she exerts a force on the Earth opposite to the force that it exerts on her. this worries her a lot because she...

we have just started to learn a new chapter in my physics class about de broglies hypothesis. In my textbook it shows a diagram of a line of electrons being fired at a constant speed, hitting a sheet of thin metal foil and then diffracting. The explanation in my book says ' A narrow beam of...

Q) I have a first order ODE of the form dy/dx = F(ax+by+c)/(Ax+By+C) ---> (a,b,c,A,B,C all non zero constants) Under what condition, does there exist a linear substitution that reduces the equation to one in which the variables are separable? (A) Never (B) if aB = bA (C) if bC = cB...

Let R be a ring in which 1_R = 0_R .Show that R has only one element. I'm assuming the idea behind the problem is to prove that the additive identity and multiplicative identity are the same.This can only happen if either 1 or 0 or both are part of the Ring. If R={1},then all the axioms that...

Homework Statement A light source in a flat, single-component universe has a redshift z when observed at a time t_{0} . Show that the observed redshift changes at a rate \frac{dz}{dt_{0}} = H_{0}(1+z) - H_{0}(1+z)^{3(1+w)/2} Homework Equations H_{0} = (\frac{\dot{a}}{a})|_{t = t_{0}} =...

So I learned that if you sit on a chair, you are applying downwards force because of gravity, and the chair is applying an upwards force to stop you from falling down. However I thought that if you remove the chair, you would fall, but when you get off the chair, why doesn't the chair fly into...

So, as anything approaches the speed of light, times slows, and once an object reaches the speed of light, aka a photon, time stops passing for it. I'm fine and dandy with this concept, until I start thinking about light traveling through space from distant galaxies. If you're looking at a...

SUPER CONFUSING linear algebra question :) Homework Statement I have attached a picture of the question with a solution. The Attempt at a Solution Well... First i found the parametric equation of the vector L... Yeah... So even looking at the solution I am confused. I get the...

Suppose you start with a system of N particles identified by position vectors r_1, r_2, \ldots, r_N and masses \mu_1, \mu_2, \ldots, \mu_N. Then (quantum mechanically) the kinetic energy operator for this system is given by (assuming \hbar = 1) T = \sum_{i = 1}^N -\frac{\Delta_i}{2\mu_i}...

Homework Statement I'm having an enormously hard time wrapping my head around the following definition, which is using some concepts that keep showing up in other definitions and theorems. I'll state the definition and then i'll ask about the parts that i don't understand: We say that...

Hi everyone I don't know if I can find someone here to help me understand this issue, but I'll try the jensen inequality can be found here http://en.wikipedia.org/wiki/Jensen%27s_inequality I have the following discrete random variable X with the following pmf: x 0...

I confronted "something" in math which is way too confusing to me ! Hello forums , I am currently in class 10th , and 15 years... I was doing Khan Academy Pre-calculus yesterday and I confronted something too weird ... not weird though but way too confusing... :cry: Here is the link ...

Hi there, I am reading some materials on statistical mechanics and for the section on momentum distribution, there mention for some non-interacting system, the momenta distribution are satisfying the Maxwell-Boltzmann distribution, which is summarized in...

This is a pretty basic counting problem, but it is confusing me to no end. I know the answer (from the back of the book), but I just don't understand the answer. Homework Statement Find the probability of getting exactly 4 numbers correct in a lottery where 6 numbers are chosen from 49...

Can someone please help me understand what this means?: "And therefore if weight 'p' is to weight 'A' in a ratio compounded of the reciprocal ratio of the least distances of the chords PN, AM, from the center of the wheel, and of the direct ratio of pH to pN, the weights will have the same...

Homework Statement 1. A truck is pulling a car on a horizontal highway using a horizontal rope. The car is in neutral gear, so we can assume that there is no appreciable friction between its tires and the highway. As the truck is accelerating to highway speeds, draw a free-body diagram of...

thermal condution? little confusing can u please help to remove my doubt. According to law of thermal conduction dQ/dt=-kAdθ/x. variable have their usual meaning. first of all i want to know what is meaning of dQ/dt in this law?? If we see it in a cylindrical object with it's curved part...

Hello everyone, Aspirin(acetylsalicylic acid) is a weak acid. So in the acidic PH of stomach it must be more in nonionised form. In the alkaline PH of intestine it must be more in ionised form. Now my note says something is more absorbed if it is in non ionised form, this makes sense because...

Homework Statement A 240gram toy car is driven by an electric motor that has a constant power output. The car can climb a 24° incline at 16m/s and can travel on a horizontal table at 39m/s. The frictional force retarding the motion is kv, where k is a constant and v is its speed. How steep...

This question about the twin paradox(twins A,B). I hope everyone knows the statement. I have read explanations for this but they differ. Some authors say twin(say B) who takes the trip accelerates so he can't be an inertial frame of reference. Some say it has nothing to do with acceleration and...

Okay, so I have an expression for V(R) in atomic units (bohrs, hartrees, etc), where V is an energy. I'm assuming this means that if I plug in a value for R (in bohrs), I get back an energy (in hartrees). But if I take the SECOND derivative of V with respect to R, and I want to convert that to...

The work done by the frictional force on a surface in drawing a circle of radius r on the surface by a pencil of negligible mass with a normal pressing force N(co-efficient of friction μ) is ? my textbook says it is zero but i don't understand it why.

Hi! I'm a beginner for a subject "topology". While studying it, I found a confusing concept. It makes me crazy.. I try to explain about it to you. For a set X, I've learned that a metric space is defined as a pair (X,d) where d is a distance function. I've also learned that for a set...

Energy and Work Concept. Confusing. Help please :) 1. Homework Statement A train composed of flat cars, travels with s constant speed V along a straight track. A crate of mass m is attached to a rope and is slowly lowered from a bridge when the train passes under it. At the instant that...

The canonical example of a function that is not Riemann integrable is the function f: [0,1] to R, such that f(x)=1 if x is rational and f(x)=0 if x is irrational ( i know some texts put this the other way around, but bear with me because i can reference at least one text that does not). Hence...

Hello, I am in my first year in college and my major is COMPUTER ENGINEERING. However I just learned that computer engineering is supposed to be about hardware stuff, and I love programming and coding, so that means the software stuff. My dream job would be to work at Apple, Microsoft or Google...

Hello guys, I'm reading and trying to understand this and going no where. From what I gather in Type 3 hypersensitivity, there is too much antigen and small immune complexes are made, which are not phagocytosed and deposit in tissue causing tissue damage. Then what has Arthus reaction and...

Why a test charge is always positive. WHy can't we assume the test charge to be negative? Just that if we assume it to be negative test charge, will the electric field turns to be negative? Additional Details reply: does it mean that if we put a negative charge as a test charge near a...

Hi, At one point in Chapter 1 of Sakurai he is deriving the momentum operator in the position basis - I just don't see how he makes some of the mathematical leaps (at least leaps for me) between the following expressions \int dx' |x' + \Delta x'> < x' | \alpha > = \int dx' | x' > < x' -...

Homework Statement int[x/((L/2)+d-x)^2] * the integral of x over [(L over 2 + d - x) all squared]* Homework Equations Integral chart The Attempt at a Solution I have done this so many ways with so many different answers. Could somebody who is without a doubt sure of the...

Homework Statement I'm new to matrix mechanics in quantum mechanics and I admit that linear algebra is the weakest part of my maths toolkit but I have an operator to convert to matrix form. I'm about 85% sure I've done it right, however I can't solve for the eigenvectors. I'm sure I'm...

Hi, The first law of thermodynamic is sometimes written as \DeltaU = \DeltaQ-P \DeltaV and sometimes as \DeltaU = Q+W, and sometimes \DeltaU = Q - W. I am confused about all these. I also know that W is positive when the system in question does work to its surrounding and negative...

Homework Statement Optical tweezers have been used to control and manipulate atoms. For simplicity, we model a very small quantum tweezer as a structure having quan- tum levels with energies E n = n, where n = 0, 1, 2...N, and N  1. A) Assume that the atoms are distinguishable and...

Homework Statement Find k such that the area between the function and the x-axis, bounded by x = 1 and x = k, is equal to 100 square units. Homework Equations y = 4e^(x/5) The Attempt at a Solution 1. Wrote the problem as the definite integral from 1 to k of 4e^(x/5)dx = 100...

The Monty Hall problem is so confusing...can anyone explain it to me? :confused: For those of you who don't know what it is: You are invited to a game show in which there are three doors. "A car is behind one of the doors, and the other two doors have monkeys behind them. When you choose a...

Homework Statement Freight transport on Titan is mostly by ship, with three types of ship called pangs, quizzers and roodles in common use. All three ships have the same shape and design but differ in size. The cargo capacity depends on the hold volume, while the number of crew required is...

I have been posting on here pretty frequently; please forgive me. I have an exam coming up in functional analysis in a little over a week, and my professor is (conveniently) out of town. We proved in our class notes that if T:X\to X is a compact operator defined on a Banach space X, \lambda...

The definition I have found in a couple of places is the following: We have \lambda \in \rho(T) for a bounded linear operator T on a Banach space X iff (T-\lambda) is bijective with a bounded inverse. (This seems to be equivalent to just saying that (T-\lambda) is both injective and surjective...

1. Jake rides a lift to the top of a maountain at a speed of 5 miles per hour. He then skis straight back down the slope to the bottom of the ski lift at an average speed five times faster than he went up the mountain. If the whole trip took 30 minutes, how long is the ski slope? a. 1 mile...

Homework Statement Let two particles of collide in a perfectly elastic collision. Particle 1 has a mass of 2m, while particle 2 has a mass of m. Particle 1 has initial velocity v, directed to the right, while particle 2 is at rest. What are the final velocities, v1 and v2, of particle 1 and...

Homework Statement 1. limh->0 (sqrt(a+h)-sqrt(a))/h 2. limx->1 (1-sqrt(x))/(1-x) Homework Equations --------------------------------------------- The Attempt at a Solution I tried conjugate, etc., but couldn't solve it without L'H's Rule.

Homework Statement I'm trying to work through revisit some basic physics and am working through some electrostatics examples (in Griffith for example). I'm currently working through the 'classic' problem for the http://en.wikipedia.org/wiki/Method_of_image_charges" i.e. a pont charge a...

I have yet to see or understand the benefit of knowing the cosine and sine sum and difference of two angles identity... can someone please explain why you would want to break up one angle into two angles... then solve from there... does not make sense to me... just use a calculator.

Homework Statement Find the curl of the vector field \mathbf{F} = <xyz,0,-x^2 y> The Attempt at a Solution I am mostly just having problems with computing the determinant. I could just go with crossing the first row and first column. But i noticed that the intermediate step...

Hello friends, I have this question which stumps me because i have no idea what its actually asking for :S - it reads: calculate the value of the first derivative of f(x) = x^(2) -3x - 1/x at x = 2. In which interval does it lie? (a) -x <= x < 0 (b) 0 <= x < 4 (c)...

Hello. There is no agreement on the meaning of terms electrochemical potential and chemical potential (see for example http://web.mit.edu/6.730/www/ST04/Lectures/Lecture26.pdf"). While proper definitions would call chemical potential to \mu\equiv\left(\frac{\partial U}{\partial...

Homework Statement http://img842.imageshack.us/img842/1404/unledro.png Now what I don't understand is this part [PLAIN][PLAIN]http://img821.imageshack.us/img821/7479/unledoq.png Is he trying to say that \frac{1}{2n^3} = R_n? Is that how he deduced that \frac{1}{2n^3} < 0.0005?

Homework Statement Determine the solution to the initial value differential equation: y'=0.0016 y (1800 − y), y(0)=66 Homework Equations Getting x's on one side and y's on the other and integrating. Then solve for c The Attempt at a Solution I'm in calc 2 and this is the first time we...