Bharat Rakshak

Vayutuvan

Some of you - esp. AmberG - might get a kick out of this.

Kiran Kedlaya was a contestant on Jeopardy today and won. So he will be on tomorrow as well.

Vayutuvan

I came across the following quote in one of the discussion lists I subscribe to. Thought this might be of interest to Bade saar and Kasturi garu and others. "I consider it quite possible that physics cannot be based on the field concept, i. e., on continuous structures. In that case _nothing_ r...

Vayutuvan

what "bitter end"? when Duryodhana himself is dying, the idiot goes out to destroy the "poudha" of the Pandavas. when he goes out to kill the baby in the womb, Kauravas already lost for all intents and puposes, and yet he tries to create more destruction by trying to completely ...

Vayutuvan

I will hunt for the verses from MBH and paste them here shortly (by end of next week). about Ashwatthama, well he is the "Paki" character. Atri Ji Is he really? During the Sri Krishna Rayabara he sides with Krishna (and thus Pandava side), but he has to remain loyal to his master and patr...

Vayutuvan

I'd like to raise my knowledge of applied math in general. i.e. learn techniques of problem solving primarily for engineering problems. I know the field of math is vast but what book can you recommend that starts at a basic level (and i emphasize basic) yet leaves me with a reasonably good knowledg...

Vayutuvan

Duck fox problem answer in the form of a puzzle :) - Assuming no fish in the pond, either both die of hunger or both die of Fatigue ^^^Can you expand on that? One can safely assume that by "escape" here, one means: the duck in a finite time escapes by flying away. (one can even put reason...

Vayutuvan

Duck fox problem answer in the form of a puzzle

-
Assuming no fish in the pond, either both die of
hunger or both die of Fatigue

Vayutuvan

nukavarapu wrote:...
-- Yellow people who wants to take pieces out of the country

That is a little beyond the pale

Vayutuvan

A very happy I-day to all. Hope all you in India enjoyed the prabhat bheri and jhenda vandanam.

Vayutuvan

Is it true that they are really discontent? The bakis I interact with are all ga-ga over bakistan, ... If they are sooo discontent then why they do not do what their ummah brothers are doing in syria or egypt? disha ji There is difference between Syria and Paistan - Syria has far higher literacy le...

Vayutuvan

1. We also had had a small part in putting ourselves in "Soviet Camp". What was our part? SwamyG ji This is all OT in this thread (and moreover it is ancient history, so last post) Our voting pattern in the UN was either vote against US or abstain when it would have helped US. Of course, ...

Vayutuvan

Was #1 by choice? How do you actively work towards break up of bakistan? Help the bad taliban to become the good taliban or help the good taliban to become the bad taliban? You are right. While it was involuntary to a large extent, may be we could have done something. I don't know what. "activ...

Vayutuvan

...1. What Pakistan did was to bend over backwards to accommodate the cold war concerns of the US, helping to place India in the "soviet camp". Pakistan also played on China's fears of India to ingratiate themselves with China. ... ... India is faced with two choices 1. Don't make war wit...

Vayutuvan

JE Menon wrote:Meanwhile, note that the author of the article is a cousin of HR Khar ... minor league back-scratching going on

asinus asinum fricat - A jackass rubs another jackass

Vayutuvan

Nandu wrote:...Paki side have always been in the vein of "let us try to win at the negotiating table what we couldn't in the battlefield", ...

IIRC, this was said by the Russians during the Tashkent talks when LBS was the PM.

Vayutuvan

^^^ tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a) * tan(b)) This looks a heck of a lot like your formula, where x[n] = tan(a) and x[n+1] = tan(b) and x[n+2] = tan(a + b). Now the rest of it is pretty easy to figure out :) Nice computer assited pattern recognition. This is how computers can help - si...

Vayutuvan

^
OK. Tried some simple iterations to see if telescoping kind of trick can be applied. Hmm... could it be zero?

Vayutuvan

In my opinion, It does not matter much what you use, "side" or "edge", both are vague, unless you define what you mean by "volume", "box" etc.. in k-dimension..Also meaning of "different" (as in - is 1 x 3 box different than 3 x 1 box..In three dim ...

Vayutuvan

Given a number n and k, how many different k-dimensional boxes of volume n with integral sides can be got? Assume that the sides of the boxes are parallel to the coordinate axes. Hello, Can you define the problem clearly please. What is a k-dimensional box ? What is meant by integral side ? What is...

Vayutuvan

As promised, here is a problem whose solution can be represented as a computer program (i.e. algorithm) very easily.

Given a number n and k, how many different k-dimensional boxes of volume n with integral sides can be got? Assume that the sides of the boxes are parallel to the coordinate axes.

Vayutuvan

brihaspati wrote:Well how about thinking of a small "square" on the "surface"

Bji

Nice

Vayutuvan

Younger days would have read up all the books and tried to understand it. Unfortunately miles to go before I sleep. Cool, My intention was not to be dense but since it comes up quite often just wanted to define it completely and unambiguously. The problem is that once one goes to more than one vari...

Vayutuvan

Thanks for the explanation. So Jacobin for first derivative and then Hessian for second derivative? When the function is scalar valued, then the Jacobian is called the gradient and is a vector, but yes, Jacobian is a generalization of the first derivative to vector-valued functions of several varia...

Vayutuvan

AmberG, What is this Hessian operator? Where is it used and what are its advantages? Ramana garu If I may, it is the second derivative analogue for a scalar valued function of several variables and is a matrix whose entries are defined to be Let $H$ be the Hessian matrix for a function $f(x_1,x_2,....

Vayutuvan

I really liked Interactions by Sheldon Glashow (Nobel Laureate along with Salam and Weinberg). Planning to re-read. What do the Physics gurus here think?

Vayutuvan

Unless someone comes up proving P=NP, in which case we can hope to have non-deterministic polynomial algorithms have polynomial solutions. That would be one of the greatest break through (almost equivalent to solving Riemann hypothesis), but yet COD will still be an issue. Even the simplest n-body ...

Vayutuvan

No use blaming the dimensions. That problem arises because physicists are driven to explain as much by as little as possible. The incorporation of higher number of dimensions is simply to bring together the current three-interaction (some will say two) model into a single GUT. They want one single ...

Vayutuvan

The potential is exactly 1/r, not 1/r^1.1 or 1/r^0.9 -- why? Similarly, the electrostatic potential is also 1/r. Is that a coincidence? To me, there is something deep which science has not yet fully grasped. Guru Prabhu ji Interesting question I had been ruminating on for sometime. On what basis ar...

Vayutuvan

Would they have dared to do this to any islamic country?? Another way of looking at it is that it is a vote of confidence of the Indian pluralism. Wasn't a law passed in India decriminalizing LGBT recently? This is could be a recognition of that fact. If he is good for India, what matter his esxual...

Vayutuvan

Any way, as you know this is known as Erdos-Moser conjuncture.. http://mathworld.wolfram.com/Erdos-MoserEquation.html The limit for lower value of n has been raised to about 10^1000000000 now.(see below) ... BTW there is a talk in December in Amsterdam which you may find interesting... http://event...

Vayutuvan

Few comments.. Can you post the "interesting theorem from Leo Moser's book? P.S... In number theory, sigma (small sigma) is generally used to represent sum of all the factors of a number. Eg (sigma(6)=1+2+3+6=12) , in that case for any prime number (and prime numbers only) sigma(n)=n+1. Inform...

Vayutuvan

an observation - brahmagpta's series, if i may coin the term, is similar to fibonocci's series. defining both recursively, we get fibonocci: $f_1 = 1; f_2 = 1; f_i = f_{i-1} + f_{i-2}$ brahmagupta: $f_1 = 1; f_2 = 2; f_i = 2 f_{i-1} + f_{i-2}$ both are second order linear recurrence relation with co...

Vayutuvan

Folks - Diophantine equations (see wiki, if not familiar with the term)could be interesting and could be very hard. Amber ji and others Hilbert's 10th problem which asks for an "algorithm" (he did not use that particular word as that concept came much later due to Turing, Church and Emile...

Vayutuvan

Are you sure? How about (1+2+...49) which is 1225 = 35^2... (or looking at it as 49*(50/2) = 49*25) Or even (1+2+3....1681) which is 1189^2 :) I only got as far as follows: Suppose $\Sigma_{i=1}^{n} i = m^2$ The following condition has to be satisfied (m^2 mod 4 = 1) && (n mod 4 = 1 || n+1 ...

Vayutuvan

SaiK wrote:Amber ji, any good text books on discrete math that you recommend.

If I may, Elements of Discrete Mathematics by C.L. Liu (ISBN 0-07--038133-X) is an introductory classic.

Bharat Rakshak

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