Pure Definition and 482 Threads

Hi, this is probably a straightforward question over something simple but it's confusing me. I don't get what the difference is between a mixed state, a superposition and a pure state. I'm looking through my notes about density operators and it's talking about a qubit system where |0> =...

Which wavelength of light will look blue without any bias toward cyan or violet? I know it's somewhere around 460nm but I don't know exactly where it is. And if you happen to know the same for green (not in any way cyanish or yellowish), please let me know.

Hi everyone. I want to get into an okay PhD program for pure math (analysis or algebra). I don't care if it is a lowly university, just so it is accredited. What are my chances of getting into such a program with funding? To how many universities should I apply? My background is as follows...

Looking for ideas that allow me to create Methane ( CH4 ) from gaseous hydrogen. This requires bonding one carbon atom to four hydrogen atoms, which should be simple enough, but there needs to be a minimum explosive danger. I know there are appliances to go the other way, but don't have the...

I can't figure out why this happens with pure substances. My book is a piece of junk, perhaps someone could recommend a better book. But why does water, for example, sublime below triple-point pressures? If I'm below triple point pressure and I add energy to solid water, there should be a...

Example of a "pure existence metaproof" http://en.wikipedia.org/wiki/Existence_theorem A pure existence theorem is a theorem which states the existence of something, but the proof of the theorem does not indicate a construction of the thing in question. As the article mentions, this is...

Hi all, I have loved science since primary school and want to pursue it as a career, but as I also love building things I was thinking engineering. The good salary also pushes me towards engineering. So I thought I had decided on chemical engineering, but I was afraid that the course would...

I know that the selection rule is : \DeltaJ = +/- 1 but our prof said that according to some quantum mechanical calculations the odd values of J are not allowed. So, the allowed transitions are : J 0 <-> 1 ; 2 <-> 3 ; 4 <-> 5... as...

Homework Statement Find the values of Σ(a^2), Σ(1/a), Σ(a^2)(B^2) and ΣaB(a + B) for: x^4 - x^3 + 2x + 3 = 0 Homework Equations Σa = 1, ΣaB = 0, ΣaBC = -2, aBCD = 3 The Attempt at a Solution I found the Σ(a^2) and Σ(1/a) successfully correct bt could neither find Σ(a^2)(B^2)...

Hi, I am in need of some expert advice please. I am enrolling for my honours degree in mathematics next year. I am trying to mix it up in order to have a strong foundation in pure mathematics with specialisation in applied mathematics. My interests are financial mathematics, probability...

Hi, I am a physics undergraduate student, and was wondering why so many people would prefer to become an Electrical Engineer or Mechanical Engineer as opposed to a Theoretical Physicist or a Mathematician or a Biologist? What attracts you to the applied science fields so much (APART FROM...

How many hydrogen atoms are there in a 5 sample of pure hydrogen?

This question is from an example taken from Zurek 1991 (Decoherence and the Transition from Quantum to Classical). Start with a spin state of an electron, \Psi= a|+> + b|-> Question 1: Why is this considered a pure state? I figured it would not be called "pure" since it is a superposition...

The only requirement is that the pure random numbers generated have to be purely random to its creator, not for some other inferior species. (To keep Evo happy, a super being is someone who is omniscient and omnipotent.)

I'm currently a graduate student doing theoretical physics at a tier 1 school. I'm trying to decide between these two. 1) stay in pure physics PROS: - since I've already taken field theory, I can start doing research quickly - will probably learn some useful simulation skills (I'm...

Hello, Am trying to make dc/ac inverter with pure sine wave output, while am searching i found an IC which is SG3524 which can generate a pwm signal. Is it a good choice for pure sine wave output, and what is the difference between the pwm signal generated by micro controller and the pwm...

Hi everyone. I have recently completed a 4 year mathematics pure mathematics degree from Australia. I am now very interested in studying in an engineering field. I am most drawn to the idea of biomedical or aerospace engineering. However I am having a difficult time trying to figure out a...

Hello, I need to get around 100g of pure Na but this metal is not available, or I don't know where to find it. My idee is to take NaOH and using electrolyze process to get the Na. Basically I what to put put NaOH in a jar filled with water and then to start the electrolyze. What do you...

Homework Statement How would you use chromatography to determine whether an unknown pure liquid is 1-pentene, cis-2-pentene, or trans-2-pentene? Homework Equations The Attempt at a Solution I looked up the boiling points of the three and see that 1-pentene is lower, but the cis...

what is shear? from looking at books etc i understood that the shear of a direction was the change of angle. but then pure shear doesn't have a change in angle between the axes, its just stretched in one direction and contracted in the other. so why is this called pure shear? I am rather...

I am unsure there is any thread similar to this. Today in morning I was making a thread but I can not find it. Anyway, When I enrolled to CSE I was crazy about it but gradually I found myself in love of Math and I also found I am actually not good in CSE but in Math. I read in the best uni of my...

My book saya that in a pure circuit , the phase difference between the voltage and current must be pi/2 , otherwise it is not pure . Why it is so ? What is a pure circuit by the way ?

Is light "pure" energy? I've been working out how much energy 60KG of material is equivalent to. However it strikes me as a possibility that I should not be using E=MC^2 because what I actually want to calculate is 60KG equivalent in light. Is there a factor I need to incorporate? I am...

Hi All, I'm currently teaching Intermediate Algebra and have taught the class how to solve algebraic problems where a denominator such as (x-2) exists. In other words, the term is not defined at x=2. Now say that the alleged solution to the problem is x=2. In that case, the correct...

Hi. I'm entering university this year and planning to do a double degree. My chief aim would be theoretical physics. I'm facing the dilemma that my university's math department offers Mathematics and Applied Mathematics. Since I hope that my second degree would compliment and strengthen my...

For a while now I have been looking for a series of texts that I can read in order to learn some of the basics of abstract/pure mathematics. I am currently taking Calculus II with Stewart's book as my text, and this summer I plan on going through Spivak's Calculus. I have finished my...

Hello, What careers outside of academia can one hope to find with a bachelor's degree (Honours with GPA>3.5) or even a graduate degree in pure math? Let's assume I've taken Cal 1-2-3, Linear Algebra, Diff. Eqns, Metric spaces and topology, complex analysis, real analysis, discrete mathematics...

"Pure" planets? What is the likelihood of a planet being almost entirely one element? Is it possible to have a planet that is purely water?

Homework Statement I apologize for having to upload an attachment but I couldn't describe this circuit. Basically, there is set of capacitors and the question is asking for the charge on one of them, when a 72 volt source is attached. All capacitances are 8.9 microFarads. Homework...

Hi, I keep confusing myself between decoherence and the transition from pure to mixed, both of which, as far as I know, come about due to the interaction of a system with the environment. I like to think about things in terms of the density matrix to get it solid in my head. Can someone...

Is this the right subforum? This is my friend's question but he is not very fluent in English. He has a bachelor degree in biology and now he is working towards a PhD in science (biology-oriented) and technology education in a Southeast Asian university. However, it seems that his true...

Mixed light and "pure" light? We all know from our young days that mixing paints give you different colors, like yellow and blue gets green. What i wondered about is what kind of light will it be? If you shine blue and yellow light on something, you will see green. There is also not much...

Hi all, if you have very pure oxygen (+99%) in your pipeline. HOW does the velocity of the oxygen causes fire in the pipeline? Thanks!

Hi Is graph theory a more pure or applied subject? I thought it was pure but now I am confusing myself because it has so many applications. Thanks

Homeopathic remedies "can be easily distinguished from the pure solvent"...

Homework Statement I am attempting to collect bubbles that are being produced under the water surface. The bubbles are natural gas, lighter than air I can collect the by bubbles by directing them into a funnel and up a hose and into an airtight collection vessel. I want to know what pressure...

Hello, I'm finishing up my personal statement for grad school, and wondering how much the things I'm worried about we also be cause for concern for the admission's committees? Briefly, my background is this: I switched to mathematics late, and did very few of the 1st/2nd year courses. My...

I would like to design a Pure Sine wave inverter for DC to AC rectification. I want to drive motors with this applicaiton. (At most 120VAC .5HP) I don't want to specify too much, because the main point here is design basics. With the right information, I should be able to design accordingly. I...

I have read quite a bit on here and elsewhere, but am still coming to terms with pure, mixed, entangled and product states. I know a state is either mixed or pure, but then is engtaglement a sub-class of being mixed? Or a sub-class of being pure? Or is entangled another name for pure? Or...

Books for self-study in "pure areas" of mathematics Hi, I am starting an applied mathematics course this year at university. Unfortunately I don't have the option to study "pure" areas of mathematics, but I would like to learn more about them to become a more complete mathematician at the end...

Pure maths is obviously abstract compared to the applied areas but which areas of pure maths are considered not as abstract or relatively less abstract?

Homework Statement a license plate has 3mos then 3letters then 3nos(numbers) if there are no constraints how many license plates are possible Homework Equations 9x9x9x9x9x9x9(..maybe) The Attempt at a Solution The same as the one above, I am very confused.

I am working on a Project that involves determination of Quality of Steam. In that I have few queries, so please help if possible: 1. Is there any mathematical relationship between Resistivity of water and temperature? because i am not able to find one, but since i am working on this...

has luck been a factor in your exam? How does it compare in pure math exams to applied math exams? I personally feel that in applied math I'm able to do w/e i have practiced, luck isn't that important. But in pure math i need a luck factor as well, along with a good practice. I feel like have...

The only kind of electrolysis I've learned about is electrolysis of salts dissolved in water. In that case there's current flowing through between the two electrodes but what do you call the process where you submerge 2 electrodes of the same metal in pure water in order to produce a solution of...

"Pure" Mathematics vs. Applied Math vs. Discrete Math I'm approaching the point where I'm going to have to decide which four-year university I'm going to finish my Bachelor's degree at. I'm pretty much restricted to colleges in Georgia, and I am primarily looking at Georgia State and Georgia...

I am just wondering if pure carbon and graphite have the same resistivity? Resistivity for pure carbon = 3.5 x 10^-3Ωm:frown:

Hi all! I'm applying to several universities in the US. Among them is the University of Utah, I'm applying for a PhD in pure mathematics. Do you know what's the reputation of this university? I was told it is good, but I'd prefer to read comments from Americans or from anyone who studied...

How useful would a year-long course in advanced differential equations be for a pure math major who wants to go to grad school? I can't decide whether or not it would be worth my time to take this course. Thanks in advance for your advice.

Homework Statement Prove that 10^n + 1 cannot be expressed in the form a*a*c, where n,a,c are positive integers. Homework Equations By considering the reminder of 10^n + 1 when it is devided by 3, I arrived at the conclusion that: a*a = 3z +1; c = 3v + 2 for some positive integers...