Pure Definition and 499 Threads

I am approaching an old age of 40, and now pursuing an MSc in Engineering without a thesis nor project. Before that I pursued MScs in Physics and Maths, but never finished writing my theses. I have a sort of perturbed attitude towards both Maths and Physics, I mean something really pure in maths...

Hello, I'm currently a phd candidate in pure maths, doing research in Ergodic Theory (concerning ergodic convergence theorems). When I started studying Ergodic Theory I ran into Statistical Mechanics and I immediately fell in love. I've started studying physics from scratch. As my current...

I've wanted to learn pure math for a while. I bought the book "A Concise Introduction to Pure Mathematics by Martin Liebeck." The first chapter or so misled me into thinking that finishing the rest of the book would be doable. Chapter 1 gets into definitions of sets and related vocabulary and...

Disclaimer: Please read in the following formulas ##E/c^2## instead of ##m##, because W. Rindler used relativistic mass, what might be confusing with today's usage of the term "mass". I am reading the chapter "38. The formal structure of Maxwell's theory" in Wolfgang Rinder's book "Introduction...

TL;DR Summary: education, history I need to devise a module for next academic year which is an introduction to pure mathematics. They need to use this module as a stepping stone module such as number theory, group theory, combinatorics, real analysis. What should I cover to make this an...

Hello everyone, I'm planning to review learned mathematics from high school & start leaning pure math. You can reply to red colored text if you don't want to read full thread. My math level : Graduates as engineer 10 years ago. Got A in Calculus 1 & 2 (Those were single variable calculus), Got...

Suppose a cylinder is launched on a horizontal frictional surface such that it has initial translational velocity v and zero angular velocity .the kinetic friction would be applied between the contact points of the cylinder and the surface, opposite to the direction of the translational motion...

Quantum states are most often described by the wavefunction ,##\Psi##. Variable ,##\Psi(x_1x_2\dots x_n) \Psi^*(x_1x_2\dots x_n)## defines probability density function of the system. Quantum states can also be described by the density matrices (operators). For a pure state, density matrix is...

How will the friction work on a sphere which is purely rolling on a horizontal surface such that both the sphere and surface does not deform. The sphere at any time t will only have one point of contact, which would continuously changing as the sphere rolls. Will The friction be applied to the...

Is simple harmonic motion also a pure translatory motion?"A rigid body moves in pure translation if each particle of the body undergoes the same displacement as every other particle in any given time interval" [Halliday and Resnick, Physics].If not,then how does shm deviate from this definition>

I'm new to the forum and not sure I've chosen the right section. And while not an engineer or physicist, I'm pretty scienc-y. I've been wondering this since I was a kid listening to shortwave radio, and decided in my 60s to try once more to understand. The time broadcasts from NIST stations...

Hey y'all, I'm starting college as a Physics major this fall and I started working through Steve Warner's Pure Mathematics for Beginners in my downtime because I love the math courses I've had, wanted to learn more about proofs and how those things came to be, and most importantly had nothing...

If I have a physical dipole with dipole moment p. Now, this formula for potential (V) is a good approximation when r is much larger than both r1 and r2 in the picture below. It's however said that for a pure dipole for which the separation between charges goes to zero and q goes to infinity, the...

All data I see online about reflectivity of metals is about aluminum in the atmosphere meaning oxidized aluminum, but pure aluminum in vacuum in case of the James Webb telescope would also be extremely reflective but building it on Earth means it's going to get oxidized, similarly there are a...

I’m sure I’m not the first to ask about this but I could use some advice from the internet: I am a sophomore lost in the world and somewhat recently decided I was going to major in physics with my eyes on grad school. I am on track to get a math minor but I am weighing the trade-offs of picking...

To elaborate that summary a bit, suppose ##\mathcal H## is the Hilbert space of the particle, with ##\mathcal{H}_2\subseteq\mathcal{H}## its two-dimensional spin subspace. Now consider any ##|x\rangle\in\mathcal{H}## such that ##|x\rangle\perp\mathcal{H}_2##, i.e., ##\forall ~...

I have a source that says when two particles are entangled, we must describe them using the density operator because it is a mixed state. But I have another source that says that the singlet state of two spins is an entangled state, but that has a wavefunction. So could someone explain what I am...

I have some basic questions about mixed states and entanglement. 1. Do mixed states always imply that the states are entangled and vice versa? 2. Can mixed states ever be separable? 3. Does interference have anything to do with entanglement? In terms of Density Matrices, ρ = |ψ><ψ|: 4...

Suppose we add a weak acid HA into pure water, so that upon addition its initial concentration is c. The following equilibria should establish in the system. $$\text{HA}+\text{H}_2\text{O}\rightleftharpoons\text{H}_3\text{O}^++\text{A}^-$$...

Not from the US. I have a Bachelor of Science in Physics and a Master of Engineering Science. Mid-way through my undergraduate study, I realized that I am more interested in pure math than physics and wanted to apply for a PhD in pure math after my graduation. I had done research and written a...

I am recreationally self studying physics and math with the ultimate goal of understanding theoretical/mathematical framework of classical mechanics, general relativity, and quantum mechanics (in addition to the actual physics). The question I have is how deep in the realm of pure math does one...

There are plenty of physics apps around already but most seem to just be words and pictures. I haven't found many that offer good simulators for proper textbook physics. So I made one. Pure Physicist - Google Play The underlying physics 'engine' uses the as yet incomplete University Physics...

My name is shabani makwaru from Tanzania i am master student in Pure mathematics at University of Dar es salaam Please can help me in advising which area is good in research in pure math

I was often told that If you want to pursue something pure and abstract like theoretical physics and pure maths you have to give up the materialism , say good bye to your dream of living a big house , swimming pool and a yatch. there is no weath in these fields. And people who work in these...

I am currently in my second year of studying a bachelor in physics and applied maths. My aim is to one day do research in physics. I am particularly interested in subjects such as gauge theories, AdS/CFT and gravity. My question is whether it would be more beneficial to switch from studying...

So I'm still doing some soul searching with finding a major. Currently I enjoy physics and math. However, while I'm good at the mathematical side of physics, conceptually I'm pretty frustratingly slow at it. Often I make the mistake of jumping right into the math without considering the actual...

I guess USB powerbank have switching power supply for the 5V output? I need a pure 5V power bank that doesn't use switching power supply but just pure output like the 3.7v lithium battery in cell phone. And why doesn't lithium battery doesn't produce 5 volt dc output?

This is another application of using Taylor recurrences (open access) to solve ODEs to arbitrarily high order (e.g. 10th order in the example invocation). It illustrates use of trigonometric recurrences, rather than the product recurrences in my earlier Lorenz ODE posts. Enjoy! #!/usr/bin/env...

When materials with high permeability are used to shield against low EMF frequencies of the order of 10 Hz, is the effectiveness linearly dependent on thickness and permeability? In other words, pure iron (mu=200,000) can be 10 times thinner than mu-metal (mu=20,000) for the same result with a...

Adapted from this code, which is an implementation of the algorithm described here. Removed dependency on Numpy Use as library code or test Himmelblau's function from copy import copy from sys import stderr, argv def replace_worst(data, new): del data[-1] data.append(new) def...

I want to produce a resource that has a narrative and includes the following topics: Sets, logic and proofs, numbers (irrational, integers, rational, …), binomial theorem, geometric series, inequalities, define things like identity, polynomial, symmetry, sigma and product notation. It is in...

I want to produce a resource that has a narrative and includes the following topics: Sets, logic and proofs, numbers (irrational, integers, rational, …), binomial theorem, geometric series, inequalities, define things like identity, polynomial, symmetry, sigma and product notation. It is in aid...

Greg Bernhardt submitted a new blog post A Pure Hamiltonian Proof of the Maupertuis Principle Continue reading the Original Blog Post.

Homework Statement How many of the following would you NOT expect to be more soluble in acid than in pure water? FeS, CuCN, AlPO4, BaCO3, AgCl Homework Equations None necessary The Attempt at a Solution So we know that anything with OH- or anything that has the conjugate base of a weak acid...

Hi, I'm currently working on showing the relation of quantum fidelity: The quantum “fidelity” between two pure states ρ1 = |ψ1⟩⟨ψ1| and ρ2 = |ψ2⟩⟨ψ2| is given by |⟨ψ1|ψ2⟩|^2. Show that this quantity may be written as Tr(ρ1ρ2). I've been following the wikipedia page on fidelity but can't...

Hi, My question is: If a constant load is applied at the free end of a perfectly elastic cantilever beam, would the beam oscillate about a mean position? Or would it eventually come to rest at the equilibrium position? There are no damping effects. Thank you.

Hello, I have a little problem. I try to find out why the second equation in the picture is correct. How can I get it? Down on the paper is what I did. Where did the (1+V2/V1) disappear from the right side of equation? Thank You for every help.

Features: No external dependencies. Arbitrary order simulation (accuracy limited by float precision). No finite difference errors. Can be extended to arbitrary precision with gmpy2 and two more lines. Enjoy! Parameters: order step size number of steps initial conditions (x, y, z) parameters...

Hello, I am a second year PhD student in pure mathematics, and I'm going through a bit of a dilemma. Up to this point I felt that I wanted to work in Mathematical Logic. To be honest, I think working in any field of math would be fun, but logic had extra cool topics like computability theory...

I'm willing to make postgraduate studies in astronomy or astrophysics so which major is more suitable for me applied or pure phyics?

Homework Statement Is the following matrix a state operator ? and if it is a state operator is it a pure state ? and if it is so then find the state vectors for the pure state. If you don't see image here is the matrix which is 2X2 in MATLAB code: [9/25 12/25; 12/25 16/25] Homework...

i wonder if the motor oil a pure substance or mixture substance i know water are pure substance and i think motor oil same water

I know the mechanism of a circuit containing just a capacitor connected to battery in resistance less wire. The particles are just tending towards making same emf on capacitor. But, I am not able to think clearly for the case of inductor. As, we connect battery and as resistance is 0.So,current...

Myself satyabhaskar. I completed my bachelor's degree with 93% and I got 3rd rank in AUCET with the specialization of physics.Now I have a small confusion about which subject i want to choose in msc physics.My main aim is to get a govt job if it is not possible then after i will enter into...

I am trying to evaluate pure Mode-II SIF using Abaqus for edge normal crack in the plate. The solution i am getting using Abaqus is not matching with the theoretical SIF. The boundary condition i have used is shown in fig attached. suggest me proper boundary condition to evaluate the SIF.

in case of rolling without slipping of a solid sphere having uniform mass density the condition is Vcm (velocity of center of mass ) = Rω or [a][/cm] = Rα ,which comes from the fact that if an object that rolls without slipping the geometric center of the body travels 1 circumference along...

i was desigining a simple ( simple as in no MPPT) PV-pump standalone system, and we decided on using an AC-pump, so while i was searching for inverters i noticed the remarkable difference in price ranges, so i started to read about the difference between the two, so far the disadvantages of the...

Homework Statement This question concerns the resistance wire Nichrome. ''Nichrome is an alloy of nickel (80%) and chromium (20%). The density of Nichrome is 8.56 g cm^-3. Diameter/mm ------------------------->1.219 -- 0.914---0.711----0.560------0.457-------0.315 Current carrying...

Homework Statement [/B] A uniform solid disk of radius R is set into rotation with an angular speed ωi about an axis through its center. While still rotating at this speed, the disk is placed into contact with a horizontal surface and immediately released as shown in figure below (a) What is...