Construction Definition and 254 Threads

I am trying (struggling! :() to understand tensor products as developed by Dummit and Foote in Section 10.4 - specifically the early section devoted to the "extension of scalars". I have been reflecting on my attempts to understand the material of Dummit and Foote, pages 359 -362 (see...

given :AB=1 and ,CD=a, EF=b Can you construct a segment with length =$\dfrac {1}{a^3}+\dfrac {1}{b^3}$

Hey! :o Given the following two-point problem: $$-y''(x)+(by)'(x)=f(x), \forall x \in [0,1]$$ $$y(0)=0, y'(1)=my(1)$$ where $ b \in C^1([0,1];R), f \in C([0,1];R)$ and $ m \in R$ a constant. Give a finite element method for the construction of the approximation of the solution $y$ of the...

Hello guys, I have a question about the construction of half silvered mirrors. I read that they are created using aluminum vapor (so some sort of vapor deposition process?). And I read that the thickness of the aluminum coating can affect the reflectance and transmittance properties...

Hi, I have a single 2 watt, 8 ohm speaker from an old radio that i wired directly to a headphone audio jack and tried it in my phone. as you can probably guess, my phones speakers are much louder. How could i make a basic transistor amplifier that could give decent volume from the speaker...

So my friend and I are building a helicopter this summer. I was designing the propeller blades and could not figure out what angle a stood for in the pitch equation a=arctan(P/2pi*r) P=tan(a)2pi*r) Also if anyone has any tips or has done this, any advice would be extremely helpful! Thanks!

From 'Modern Quantum Mechanics, revised edition' by J.J. Sakurai, In page 44 the translation (spacial displacement) operator \mathcal{T}(d \boldsymbol{x'}) is introduced. \mathcal{T}(d \boldsymbol{x'}) \mid \boldsymbol{x'} \rangle = \mid \boldsymbol{x'} + d \boldsymbol{x'} \rangle It is...

Homework Statement Let U, V be random variables on [0,+\infty) with probability density functions f_U(x)=2e^{-2x} and f_V(x)=e^{-x}. 1. Give a coupling of U and V under which \{U\geq V\} with probability 1. 2. Give a maximal coupling of U and V. Homework Equations Cumulative distribution...

WHY in step up transformer, the number of turns are less in primary and copper wire is thick. Whereas in secondary number of turns are more and copper wire is thin. In step-down transformer the situation is reversed. I want the reason for this?

How can we define a constraint saying: if b is larger than zero then y has to equal 1 if b is equal to zero then y has to equal 0 ? It concerns the following problem: b[i][k] = amount of vegetable i growing on patch k y[i][k] = 1 if vegetable i is grown on patch k = 0 otherwise So...

Explain why all the end points of the closed intervals that comprise $C_n$ are in the Cantor set $C_n$. I understand why this is true but I don't know how to explain it.

up/down electron gun construction?? Greetings! I'm working on a project that Requires a roughly equal number of up and down spin electrons to be injected into a (vacuum or ATP) chamber. Is there a common device that does this? If not, would it be possible to build one and how would it work...

Homework Statement Given the nonzero vector a ε ℝ3, a\dot{}x = b ε ℝ, and a × x = c ε ℝ3, can you determine the vector x ε ℝ3? If so, give a geometric construction for x. Homework Equations a\dot{}x = ||a||||x||cos\Theta The Attempt at a Solution I'm not really certain what it is...

Homework Statement Please help me in my attempt: There are 20 laborers to four different construction jobs including 4 workers of ethnic minority. The first job required 6 laborers; the second, third, and fourth utilized 4, 5, and 5 laborers, respectively. What is the probability that...

Q. Exhibit (if such exists) a probability space, denoted by (Ω, A, P[·]), which satisfies the following. For A1 and A2 members of A, if P[A1] = P[A2], then A1 = A2. Answer: A = {Ω, ∅}, P[Ω] = 1 and P[∅] = 0. Is this a valid answer to the above question?

Anyone have any ideas how I can make one? Please discuss below!:biggrin: The only thing I know so far is that to time travel you have to go faster than the speed of light...

I was wondering if anyone could give me guidance on the construction of a cryocooler in a DIY setting. As a tinkerer, builder, and a chemistry major with an interest and dabbling in mechanical / system engineering, I want to try my hand at building a cryocooler for liquefaction of small amounts...

I have an equation that I've been trying to solve. I manipulated it until I had a=f(d) and then did by best to put it into a format the computer recognizes. However when I went back to check the results against the unsimplified version of the equation, they didn't work out as they should have...

So, I'm planning on making a Jacob's Ladder. I've considered the high voltage issues and such, and now I'm doing the actual design process. So, a couple of questions. The overwhelming design that I've seen online has been to simply take a high voltage transformer and couple it to the actual wire...

Hi, I'm wondering if anyone has any sources for off-axis point calculation for multiple current carrying loops that contain a soft iron core. I have been using this resource so far and I can figure out how to include multiple loops. How would I approach these calculations with an iron core...

Homework Statement ∛4 ∛5 ∛3 and ∛a Homework Equations The Attempt at a Solution I have started with the problem but i feel like I'm off track. I'll upload a pic of the work so far.

Hi, I read the following recently in a book on genetics: The modular construction of genomes has allowed the relatively rapid evolution of biological complexity. I could'nt understand what the modular construction of genomes mean. Is it referring to genes which make up a genome?

I can't understand how to recover a Riemann surface from the branch data. In particular, given a group acting on the Riemann sphere with some points removed, how can I construct a Riemann surface?

Homework Statement You are given a battery of 220 V and a radio device that requires 1600 W to run. You are also given four resistors: three 3 Ω resistors and one 20 Ω resistor. What circuit configuration will allow the radio device to run without getting fried? The Attempt at a Solution...

Hi all, I am working a design project for a geotechnical engineering subject and it goes as follows: A 6 storey building requires a 12m deep basement comprising 3 levels of car park with plan dimensions of 50m by 50m and is to be constructed in a medium clay. The water table maximum level...

A friend sent me this link, and I thought others may enjoy it. I can't imagine it's too comfortable though. http://imgur.com/a/VWhr7

Homework Statement let a and b be rational numbers if a>b>0 show that there exists a natural number n, which can be considered rational as well, st nb>a Homework Equations The Attempt at a Solution I was trying using the peano theorem of natural numbers define set of...

Hi all, I am looking for US steel manufacturers/fabricators for fabrication of heavy equipment. Typically 200-2000kgs per weldment. 5-50mm mild steel. 2-10 pieces per order. Machines needed: large bending press. horizontal milling machine. CNC drill. Thanks. Huntoon

I need a list of different types of woods used in construction and their properties. I can't find them on any Construction materials and testing books. I hope somebody would give me a direct link of a useful site. Thanks

Hi, I'd like to do a small design project. When I sleep, I switch on my mosquito repellant for about 8 hours. Sometimes I forget switching it off too. Such long durations are little poisonous and generally not required. What I plan to do is to make a timer with a dial from 0 min to 60 min...

I'm designing a pipe-line and need to choose a specific value for pipe roughness. I'm trying to do dimensional analysis to find the needed pi groups. That's what I did ε (roughness of the pipe) = fcn(V,D, ρ μ) V = Velocity D = Diameter ρ = density μ = viscosity Is...

Hi. I am going to start my MSc in a couple of months majoring in nonlinear quantum optics. I have a good basic in quantum mechanics, but have never looked at quantum optics before. My topic will be to investigate quantum properties of nonlinear optical coupler but i have problem with the...

Hi all, Was reading articles on neutron stars and black holes when I started thinking about magnetic fields. I think it is a fact that magnetic shields on Earth block out the harmful radioactive solar flares that come from the sun. So in the article i was reading it mentioned something about...

Hi, Imagine: a computer program like 2D Lego with only 1 type of block (a small square one) with which you can create constructions. Blocks can be placed on an invisible grid. There is gravity, and boxes can't fly, so you need to build any construction from the ground up. Boxes are always...

Background I am currently doing a project that requires me to construct a probe which dentists use to transmit laser light to a patient's teeth to determine if the teeth is vital or not. Wanna know if it is feasible for me to extract the laser from an optical mouse and use it to construct...

Homework Statement Homework Equations The Attempt at a Solution

Homework Statement Find a simple DFA (i.e. deterministic finite automaton) that accepts all natural numbers n for which n mod 3 = 0. Hint: A natural number is divisible by 3 if its checksum (or sum of digits) is divisible by 3. Homework Equations The Attempt at a Solution...

Hi, Homework Statement V is a non-empty, upper bounded subset of R. Show that a sequence (v_n)_{n \geq 0} in V exists such that: 1)v_0 \leq v_1 \leq ... and 2) the limit of the sequence is sup V. (Hint: use a recursive construction) Homework Equations The Attempt at a Solution...

This proof I think is related to our construction of R in class using equivalences classes of Cauchy sequences: Let a\inR, then there exists a sequence b s.t. {b_n}\inQ for all n\inN and lim {b_n} = x. Here's my attempt: Let [{b_n}]\inR be the equivalence class of all Cauchy sequences...

I remember reading a long time ago that there was a straightforward (but operationally difficult) way of constructing General Relativity from the Linear Field Equations. Essentially you start with the Linear Field Equations solution and then generate a stress energy pseudo-tensor for this...

Hi there I'm having some real trouble answering photonics questions that require the use of Huygens construction. For example if I was asked Compare with the help of Huygen's constructions the propagation of o- and e- components of light through a material with ne and no are 1.55336, and...

Homework Statement The arm of a crane at a construction site is 15.0 m long, and it makes an angle of 15.8 with the horizontal. Assume that the max- imum load the crane can handle is limited by the amount of torque the load produces around the base of the arm. What maximum torque can...

Homework Statement can anyone help me:smile: :i need a construction drawings for : 1-Types of Guide ways and wear compensation methods. 2- Cross Carriage of the center lathe with the tool post. please answer me as quick as you can:rolleyes: Homework Equations The Attempt at a...

We're covering this in my History of Mathematics class. I'm not entirely sure what they're asking.

Homework Statement Construct a recursive definition for the following: The number of ways to stack n red, white, green, and blue poker chips so that there are no two consecutive blue poker chips. The attempt at a solution The number of possible combinations is 4^n minus the number of...

The 405 fwy in Los Angeles will be closed for construction work. For anyone who has to drive in the area, what a nightmare this will be! Last night on the Tonight Show, Jay Leno actually played a video of alternate routes...

I would love to know how we can contruct SO(n) matrices. I know we get them from Clifford algebras somehow. I am especially interested in SO(8). Could anybody help? thank you

Greetings everyone, I'm constructing a ferrofluid display cell using FerroTech EFH1 ferrofluid inside of a round bottom pyrex beaker. The ferrofluid is oil based, so it is not hydrophilic. The liquid that the ferrofluid will be suspended in is Magnesium Citrate (a household laxative... and no...

In Greiner & Muller's 'Quantum Mechanics: Symmetries' (section 3.5) they explain that where a system possesses a symmetry, the corresponding Hamiltonian must be 'built up' from the Casimir operators of the corresponding symmetry group. Does anyone know of a reference where this is gone into...

(This could maybe turn out to be a little longer post, so I'll bold my questions) Hi, I was reading a little about affine geometry, and something bothered me. Namely, in some books, there were some paragraphs that were written like "blabla, let's observe an affine plane for instance, and...