Interesting Definition and 790 Threads

Interesting articles online on academia and the "PhD problem" Hi everyone, I've linked here two articles I've found online that specifically address the issue of whether a PhD really prepares its students to careers outside of academia. One is an article from an environmental researcher...

1. What is the smallest degree of a non-constant polynomial f(x), such that all roots of f(x) are in the set {0,2,3}, and the derivative of f(x) is divisible by 8x^2-24x+7? 2. Let x, y, and z be positive real numbers such that $$xyz=945$$ and $$x(y+1)+y(z+1)+z(x+1)=385$$ What is the...

I say holistic because it concerns entropy, thermodynamics. NB. I do not suggest extensive knowledge of thermodynamics but I am learning. To the question! The universe is expanding and thus can be considered boundless. (I know I have made assumptions but they are based on a lack of...

Hi I'm a first year Physics Undergrad and I never quite got satisfied with the answer to this question: "Why would you be rather hit with a pillow than a rock, if they reach the ground at the same time?" I know the obvious answer is because the pillow is soft. But how would you describe...

OK so before I begin I will ask that you forgive me because I do not have a working knowledge of the mathematics involved here and I am admittedly not even at a novice level of understanding these things. However I have done at least some research and understand how an interference pattern does...

Is there any finite dimensional Lie algebra that is not isomorphic to any of the subalgebras contained in GL(n) ?

Hi, Why is there negative current in an LED at low voltage(set up in forward voltage)? Why is there luminescence of an LED at negative current as described above(when LED is in forward voltage)? How would the I-V curves of LEDs of different colours vary? Why? The questions I've asked all...

"Interesting" math problems Since I have naught to do right now and the weather is not great whatsoever, I'm going through a Math problem book I found covered in dust sitting on the shelf at my folks' - it's from 1960 entitled (if word for word translation) "Mathematical Sharpness" by B...

Here is an interesting article from the Economist regarding evidence of "bandwagon" behaviour in the labour market; the chief message of the article being that missing out on one job application has negative consequences on future opportunities...

Hi guys, it's been a while! Here's an interesting problem. Let $A$ be a ring and $Z$ be the ring of $\mathbb Z.$ Consider the cartesian product $A\times Z.$ Define $A\times Z$ the product $(a,n)\cdot(b,m)=(ma+nb+ab,nm).$ Let $f:A\longmapsto A\times Z$ be defined by $f(a)=(a,0)$ for all $a$ in...

Ok so I came up to a very interesting and both practical youtube video.Now I must say i understand by the description and the video how it basically works , so the question is not as much about the workings of this electrostatic phenomenon as rather, can somebody please draw a equivalent...

Hi guys, I'm just wondering if you guys have something that can be described as your entry-point in learning Physics. It's because I'm planning to do self-study using University Physics books before entering university and the problem is I can be quite bored with some of the routine topics...

This paper makes some interesting points: A Dynamic Dark Information Energy Consistent with Planck Data, http://arxiv.org/abs/1308.2382.

Take a look at this theorem. Is it a way to show this theorem? I would like to show it using the standard way of diagonalizing a matrix. I mean if P = [v1 v2] and D = [lambda1 0 0 lambda D] We have that AP = PD even for complex eigenvectors and eigenvalues. But the P matrix...

Hi, I am looking for an interesting new career after a physics phd. I had obtained my phd in physics about 7 years ago. In the last few years, I've fallen behind in publishing papers due to some unfortunate events in my personal life. Despite my interest in research, I think that maintaining...

Recently, an AT&T commercial has been running on TV where a moderator asks some children about the largest number they could think of. At the end, one kid replies “∞ times ∞”, which of course is simply ∞2. Natually, one can instantly think of a larger number: ∞∞. But then, that got me...

Homework Statement Do the energy of the electric and magnetic field depend on their sources or are they scattred all over the space when the fieldds are different from zero?

Homework Statement Two triangular wedges are placed next to each other on a flat floor. Both triangles have two 45 degree angles where they touch the floor and a 90 degree angle up in the air. The Triangular wedges have a mass of m. A cube of mass M is balanced on the wedges so it's weight is...

Here is an integral that I seen in another forum \int^1_0 \frac{\log(x)\log(x+1)}{1-x} \approx -0.5 That was a value return by W|A . This thread will be dedicated to try to solve the integral . Any ideas will always be welcomed . The integral might require some dilogarithm identities . The...

Prove that \int^1_0 \frac{dx}{\sqrt[3]{x^2-x^3}} = \frac{2\pi }{\sqrt{3}}

Hey guys, I had a question about two functions and many more if you look at it right, that have the same derivative. I took the derivative of x^2 and found its derivative is of course 2x. So I decided to take the derivative and x^2+1 and found the same derivative applies? How can This be...

Hey guys, I was actually researching the life of Edmond Halley and discovered that he discovered the relationship between barometric pressure and the height of the sea level. I'm not quite sure what barometric pressure is( I know it has a lot to do with whether fishermen fish or not) and would...

Hi everyone. Just for fun I thought we could post some of the more interesting ways we know of to evaluate integrals :) For starters, to evaluate \displaystyle \begin{align*} \int{\arctan{(x)}\,dx} \end{align*}, first we consider the integral \displaystyle \begin{align*} \int{\frac{2x}{1 +...

Interesting news on Dark Matter, I had no idea this experiment was being carried out: http://news.yahoo.com/hints-dark-matter-possibly-seen-190603469.html

I thought it would be cool to start a thread with a bunch of interesting logic puzzles, brain teasers, math problems, etc. I'll get the ball rolling: Solution: http://www.mindcipher.com/puzzles/141

It seems as if every single statics problem in the textbooks I've seen has so far amounted to proving for the billionth time that you have the pythagorean theorem memorized. It's absolutely mind numbing. At what point do we get to do fun and interesting stuff, like derive the heat equation or...

Suppose that there are m independent and identically distributed variables Y1, Y2, ... Ym. Yi - are random variables. Let Y denote the maxof Y1, Y2, ... Ym. What's the distribution of Y when m is very big? Thank you for any help, in advance.

I have been going through the following interesting paper on the foundations of Quantum Mechanics: http://arxiv.org/pdf/0911.0695v1.pdf 'We define the state of a system as that mathematical object from which one can determine the probability for any conceivable measurement. Physical theories can...

I'm volunteering at an elementary school for the next couple of weeks to teach the kids cool stuff about science and I think it would be great if I had a "Daily Awesome Universe" fact. I think having a funny/cool facts for the kids to see when they come in would interest them. I have a few, but...

In a recent volume of Science magazine, there was a very interesting article on the genesis of migraine. However I found it very difficult to follow as a non-specialist. Someone would like to comment on it? Spreading Depression Triggers Headache by Activating Neuronal Panx1 Channels...

This video is from 2007 but it stated the goal at that time was a 64 mega-joule weapon? I understand the advantages of extended range but it seems like a huge, awkward, and expensive weapon to deliver a relatively small amount of energy. 64 mega-joules is the equivalent of only 14 kg of TNT...

Homework Statement Is this series convergent or divergent? \sum_{n=2}^{\infty} \frac{1}{(ln(n))^{ln \, ln(n)}} Homework Equations ln(x)<x^a, \, a>0 The Attempt at a Solution I don't see a way to tackle this one other than the comparison test. \sum_{n=2}^{\infty} \frac{1}{(ln(n))^{ln...

Supplementary question to "interesting problem" post If f(2x)=f(f(x)) and f(2x+1)=f(2x)+1 then for what value n such that n is in the set of natural numbers could f(0) equal 2^n. also for what value n does f(0) equal 2^n +2?

Dear all, Could someone help me understand what is happening in this video... Does it have any application in science or industry? Many thanks,

Here's a nice challenge that I made up thinking about compressing data one night... Print out a number that you can read within it: The numbers 1 to 20(easier) or 1 to 99(very hard) Rules: →Can be read forward or backwards and use same numbers eg. 123 you can read...

This is a talk by Nima Arkani Hamed of IAS at Princeton from a few days ago, where he discusses his thoughts on the dark energy problems of cosmology and various popular research programs aimed at addressing it by modifying General relativity at large distances (examples like DGP, Galileons...

One of my friends showed me this problem and I've been thinking about it all day. It's something like if f(2x) is equal to f(f(y)) and that f(2y) + 1 is f(2y +1) and f(0) is 0, what is f(n). It seems very maclaurin esque to me but... anyway... first post and pretty nice problem. Would love help...

Please what this. This video will describe Len'z law from 0:00 till 1:25 You can skip till 1:25 and see the interesting part to understand the following question. * Is the aluminum cylinder pushing the magnet down with a higher or lower or the same speed at the initial speed passing only...

This is one of the most interesting integrals I've ever seen $$\frac{1}{2\pi i }\int^{c+i\infty}_{c-i\infty}t^{-a} (1-t)^{-b-1}\, dt = \frac{1}{b\,\beta(a,b)}$$ Does anybody have any idea how to prove it ?

Largest Structure in Universe Discovered By Mike Wall | SPACE.com Astronomers have discovered the largest known structure in the universe, a clump of active galactic cores that stretches 4 billion light-years from end to end. The structure is a large quasar group (LQG), a collection of...

Homework Statement a)A snowball, initially of mass m0, slides down a slope of incline angle ∅. As it moves, mass of additional snow Δm = αx. Write down the differential equation of translational motion for the snowball, ignoring rotation and friction. b)If the snowball starts from rest...

Linking brains and brawn: exercise and the evolution of human neurobiology. Raichlen DA, Polk JD. Proc Biol Sci. 2013 Jan 7;280(1750):20122250. Here is the abstract: http://www.ncbi.nlm.nih.gov/pubmed/23173208 A short precis: endurance running provided access to a high protein diet...

So I was driving my dads truck to pick up my sister when I noticed a very interesting pattern in the raindrops sliding across the truck windshield. It was not raining, but I am currently in the northeast and we just got done with a snowstorm so they really weren't raindrops but simply melted...

I am about to start a second year university course called dynamics and vector calculus and there is not very much (or any information) on good books to help with the course and I was wondering if anybody out there knew of some helpful/interesting books in theses subjects? The course syllabus...

Recently, I came across this review by Cosma Shalizi, a statistics professor at Carnegie Mellon (and who was trained as a physicist, with a PhD focusing on research in statistical mechanics and complex systems), of a book titled "A Call for Judgment" by Amar Bhide, a law professor at Tufts...

I have got next interesting geometry example :-) I have got regular hexagon ABCDEF, when S (mark for area in Czech... and in the USA, British I don't know :D) 30cm2. In the hexagon is M. You know: ABM(S)=3cm2 and BCM(S)=2cm2. What is S of: CDM, DEM, EFM and FAM? So, about me... I don't...

Hi, I was playing with Riemann zeta function on mathematica. I encountered with a quite interesting result. I iterated Riemann zeta function for zero. (e.g Zeta...[Zeta[Zeta[0]]]...] It converges into a specific number which is -0.295905. Also for any negative values of Zeta function, iteration...

I'm not studying physics or anything, I'm just working on a minor in theoretical astronomy for the fun of it on the side. I have a quick question i just wanted to have a few opinions on. Suppose you take a handeful of marbles and toss them on the floor. Imagine that our universe is one of...

I believe the Nordita Perspectives of Fundamental Cosmology Conference ends today, did anybody go. Anything interesting to report to PF?

Homework Statement In procedure 3, you balance the ruler. If the density of the ruler increases without changing its dimensions, the ruler will... →still be balanced →be unbalanced, but the direction depends on the hanging mass, the mass of the ruler, and distances →tip away from m...