Interesting Definition and 790 Threads

I have taken general chem 1&2 and orgo chem 1&2, but I honestly don't know how the chemistry I know relates or is used in anything. I can write page long synthesis and mechanisms, but I don't really know what I'm making, if it's safe, or if it's impossible. I only have one chemistry class left...

The question is from http://www.xtremepapers.com/CIE/International%20A%20And%20AS%20Level/9709%20-%20Mathematics/9709_w10_qp_13.pdf question no. 7 (i). I think it should be more than easy for a functions fanatic( or someone who does math regularly for that matter) to get the right answer, but...

Homework Statement In the given integral, both A and B are constants. Homework Equations ∫{[A+(1/x²-Bx)]^1/2}dx The Attempt at a Solution Well, I have solved the problem by expanding the root and considering the first two terms only, but it gives a very crude approximation of...

I recently came across an interesting video. What do you think it might be? http://www.youtube.com/watch?v=Ypqfq0SYrAQ&feature=player_embedded

A diffraction grating has 150 "lines" per mm etched upon it. When light of wavelength 275 nm is normally incident upon the grating, how many bright spots appear on a screen a short distance away?:smile:

suppose there are two people it is of course, possible that one of them could lift up another person by one hand (or two) if he is powerful enough. I just wonder if it is possible for someone to lift up himself by his own hand(s) in the world suppose he is strong and powerful enough. It's...

I've recently been confronted with the limit as n goes to 0 of sin(\pi*n/4)*\Gamma(x) , and have no idea on how to confront the problem, as I have little familiarity with the gamma function. Is there any relatively easy ways to prove this, or at least ways that use methods not difficult to...

Traceless protein labeling http://www.nature.com/nchembio/journal/v5/n5/abs/nchembio.157.html http://www.nature.com/nchembio/journal/v5/n5/full/nchembio0509-275.html If this procedure really does work as they say, what a really, really slick idea this group has come up with. Not only...

Ok so I am a professional freestyle skier who jumps off of cliffs into powder (light fluffy snow). I found a big cliff that I may go jump off and I know that it is physically possible to land and ski away from, but I also have an interest in physics, (with 0 knowledge), and I have been trying to...

Hey guys, I stumbled on an interesting and unexpected identity when looking for a simpler summation technique for inverse kinementics. Basically, I was trying to find a simpler way of summing IK vectors for some particular armature (like a tentacle or multi-branch armature on a robot). This...

Homework Statement Evaluate the intergrals: a) integral of 3^(-4*z^2) dz from 0 to infinity b) integral of dx/(sqrt(-ln(x))) from 0 to 1 c) integral of x^m * e^(-a*x^n) dx from 0 to infinity Homework Equations gamma(n) = integral of e^(-w) * w^(n-1) dw from 0 to infinity The...

I'm looking for a list of the most interesting pages on physics, on the internet. By "most interesting", I mean pages which are rigorous, well done graphically, and no discussions boards/forums and NO crackpots ! It could be simulations applets, papers, Wikipedia articles, etc. I prefer things...

Homework Statement Let (a_n)_{n\in\mathbb{N}} be a real sequence such that a_0\in(0,1) and a_{n+1}=a_n-a_n^2 Does \lim_{n\rightarrow\infty}na_n exist? If yes, calculate it. Homework Equations The Attempt at a Solution I have a solution but I'd like to see other solutions..

Prove that $\displaystyle\sum_{n=1}^\infty\frac1{n H_n}=\infty$ where $H_n$ is the n-term of the harmonic sum.

class. I did a lecture last semester on financial mathematics and stochastic processes. Know of any cool topics that I could lecture on?

I was making a PCB drilling machine at home with my brother, and came across this mathematical? problem. I needed to fix the drill machine. But I needed to determine where should it be fixed so that I could drill largest possible PCB boards. In other words, find the value of x so that you...

This whole unit thing of mols is somewhat tricky and interesting. if one mol of Na is 23g, then wouldn't 100.3g of NaCl be one Mol as well. I am under the impression from my lecture notes in class that the grams of a substance is the same a s a mol. I was asked a school of thought question by...

Homework Statement Suppose an elastic ball is set into projectile motion on an inclined plane, which makes an angle of 30 degrees to the horizontal. It is projected with an initial velocity of 5 m/s, making an angle of 20 degrees to the slope of the plane. Suppose the plane is very long, and no...

So, its a long post and I feel I've been pushing this thing further and further without considering it properly. Here's the background: I am doing a 5 year B. Tech. + M. Tech. Integrated course in Biotechnology and Bioprocess Engineering. There's one major issue though. My curriculum doesn't...

Today while working I found that an M6 x 1.0 Thread bold will easily screw into a hole tapped 1/4"-28. At first when I found this, I thought one of my boxes of bolts was labeled wrong, but I tried another set and it work. Has anyone else come across this similarity before? -CR

Hello and thanks for your consideration, I'd like some insight into the function f(\phi) = \frac {1 - \phi}{\phi - 1} Does this apply to any known modeling situations? Is it recognized as belonging to a more general class of functions that may have interesting or unique characteristics? Or...

Hi, I would like to know if anyone has good ideas for problems involving calculus of variations, other than the classic textbook questions (brachistochrone, Fermat, catenary, etc..) that I could create as a classical mechanics class project? Thank you

People have found ways to extend the definition of some operations that are ostensibly discrete (such as differentiation - e.g. 1st, 2nd, 3rd derivatives) to operations that are defined for fractions ( e.g. fractional derivatives). Is there an interesting way to extend the operation of...

Hello, Has anyone read any good or interesting Cosmology books lately? Thanks

I'm in the point of my life where I am about to be applying for universities. I'm completely unsure of what I want to do with my life, and I'm in a worrying frenzy. Now, the ever-so-controversial question: What is the most interesting, unique and fascinating major? I know it depends for...

Recently, my friend tested me on a puzzle. The puzzle goes like this, if there is 8 balls (1 of them which weighs either lesser or heavier), how are you going to find out which is the different ball using a two sided weight scale with 3 tries? This is a pretty easy puzzle which everyone would...

Can anyone tell me what this is? My son created it as an entertaining exercise -- he says it transposes positive integers. Is he right? \left(n\right)=\sum_{k=0}^{[log_b\left(n\right)]}\left(b^k\left(\left\lfloor \frac{n}{b^{\left\lceil log_b\left(n\right)\right\rceil}-k-1}\right\rfloor \%b...

Homework Statement You have been tasked with the design of a new far-field, high resolution imaging system to be placed on the Hubble Space Telescope. This system will be used for taking deep space astronomical images with an exposure adjustable between 10 minutes and 24 hours based on the...

For my research I am trying to solve a particular integral. I know that I have to transform it properly to use the residue theorem, but I am having difficulty attaining this form. Here is the integral: \int^{\infty}_{-\infty}\frac{e^{ix}dx}{\sqrt{a - x^2 + ib}} where a and b are real...

The properties arise from infinitely nested functions such as: x=\sqrt[n]{x^{n-1}\sqrt[n]{x^{n-1}\sqrt[n]{x^{n-1}\sqrt[n]{x^{n-1}...}}}} You can solve it algebraically to verify that x is equal to the nested function (all of the following functions can be solved in a similar manner)...

Hey, I'm starting a career of knowledge in the subject of physics. I'm so interested in it because to me physics is the language of the universe and to know anything at all is to start in physics. I am just curious of what part of the subject made you so interested in physics.

Just bored and looking for some new (<2 years ago) articles people find interesting. If anyone knows of any diseases that may be caused by neurological disorders which isn't proven yet, for example diabetes, they'd be a good start. Cheers

I have almost no idea how to start! I'm just doing this problem for fun(or was at one time): Find all a such that the equation x^2+axy+y^2=1 has infinitely many solutions in integers for x and y. I know that the solution of this problem would follow from a complete understanding of integer...

I saw a shadow of a catenary (or close enough) on a cylinder and wondered about the shape. Specifically, it was a powerline strung between 2 utility poles, and the sun angle would have been around 45 degrees or so, and the cylindrical grain bin was between and north (I am in northern...

I'm a senior in HS. Took AP Physics B last year had a 93 avg and got a 5 on the AP. Taking Ap Physics C this year. Started reading "The Fabric of the Cosmos" by Brian Greene and learning about astronomy over the summer. I really like this kind of stuff but the actual class, Physics B and C...

Looking for an interesting Mathematical problem "family" And what do I mean by that. All right, I think this was the most fitting category, I hope I'm not too off-topic. So I want to write a puzzle game, but, as everyone who loses his time playing puzzle flash games (like me), knows that you...

Perhaps it is known to you, it was something new to me. After Andy confirmed that reasonable circle of confusion for my camera should be about 0.02mm, I did some calculations - and I was surprised by the result. Say you have an object that you want to take a picture of (be it flower, book...

Interesting Telescoping Series -- Calc 2 My problem with this series arose when I attempted a partial fractions decompisition of the following, (k-1)/(2^(2k+1). I attempted to factor the denominator with 2(2^k) which is right, but where do I go from there? It does not help much to multiply...

Let A and B be two coprime integers. Find X = zero mod A such that Y = 2*X +1 = 0 mod B. Then 8*(Y +2*N*A*B)*(X + N*A*B) + 1 is a square for all integer N. If A = 5,B = 7, X = 10, Z = 21 then the sequence of square roots of the Squares for N = -3 to 3 is -379, -249, -99, 41, 181, and 321. Of...

Hi everybody, I'm a long-time reader and new poster. At the moment I am looking for some interesting Calculus of variations problems to present to 2nd year maths students. Naturally, I am already looking at the historical problems, The Brachistochrone, and I also have an applications of...

A natural integer N can be written as x mod p, for instance: N... 1 2 3 4 5 6 7 8 9 10 11 12 p=2 1 2 1 2 1 2 1 2 1 2 1 2 p=3 1 2 3 1 2 3 1 2 3 1 2 3 p=5 1 2 3 4 5 1 2 3 4 5 1 2 p=7 1 2 3 4 5 6 7 1 2 3 4 5 Etc. The puzzle is quite difficult to state in this format but I'll have a go: You...

3^3 = [3^3 - 3^2] +[3^2 - 3^1] + [3^1 - 3^0] + 3^0 Practical Demonstration: 27 = [27-9] + [9-3] + [3-1] + 1 27 = 18 +6+2+1 27 = 27 Is this property discussed in theory of games?

Hello, recently, I have found so called Batman graph and equation, which basically plots Batman sign. I have even found Python code that plots this implicit equation. Code can be found here: . And the equation is given here: [url]http://i.imgur.com/CNy9J.jpg If you look closelx...

Find the sum of : [2^{}0/3] + [2^{}1/3] + [2^{}2/3] + [2^{}3/3] + [2^{}4/3] + ... + [2^{}2008/3] where [] is the greatest integer function symbol... if the question is not clear here is the question.. Find the sum of : [(2^0)/3] + [(2^1)/3] + [(2^2)/3] + [(2^3)/3] + ... [(2^2008)/3]

I watched a video explaining a card trick today, there were no tricks, it was all based on math. Here's the set up: 52 cards in the deck. person A takes some of them, then person B takes some as well. The dealer counts the remaining cards in his hand, say he has 18. Then he says...

Homework Statement Find all x in |5x-2| = 6x-12 The Attempt at a Solution http://www.wolframalpha.com/input/?i=Plot[|5x-2|+%3D+6x-12%2C{x%2C-1.5%2C1.5}] Notice how only x = 10 is a solution? So my question is, why isn't x = -14/11 a solution? I mean sure they don't...

Mechanical energy against gravity? (Interesting energy problem) Why doesn't the above picture work? (I think it has to do with relativity, not 100% sure)

Given N= 1.2.3 + 2.3.4 + ... + n(n+1)(n+2), prove that 4N + 1 is a square (n is a positive integer)

Homework Statement http://www2.seminolestate.edu/lvosbury/images/VibSpringAnNS.gif Find the governing differential equation and position functions for a 32 pound object attached to the end of a spring with a spring constant of 1 and a forcing function that yields a constant velocity in the...

Homework Statement n2<=2n n is a natural number For what values of n is the statement true and prove by induction. Homework Equations The Attempt at a Solution I tried 1 and it worked, I tried 2 and it worked, just for fun I tried 3 and it didn't work, so I assumed the...