Can anybody please help me locate Annapurna's paper which has the result: sigma(N) < N*sqrt(N) for N > 2?
613652
They might be in the paper "Inequalities for $&#92;sigma (n)$ and $&#92;varphi (n)$".  It was published in Mathematics Magazine volume 45 in 1972.  The Journal was also called Delta previously, so it might have been under this name at the time of publication.
115539
Check out wikipedia.org for info on sigma notation.
961641
http://hamilton.bell.ac.uk/hncexam/Samplepaper.doc ;-)
1143752
http://cis.jhu.edu/~bruno/s06-311/\n\nhttp://www.eng.wayne.edu/page.php?id=1434\n\nhttp://web.njit.edu/~dhar/math333/fin333_sp02A.pdf#search='sample%20Probability%20and%20Statistics%20exam'
383816
!!, !!!!!!!! are "multifactorials". They are described in the first attached article.\n\nBriefly,\nn!! = 1 for n=0 or 1,\nn!! = n * (n-2)!! for n>=2.\n\nn!!...! (k "!" signes) = 1, for n<k\nn!!...! (k "!" signes) = n * (n-k)!!...! (k "!" signes)\n\n(2n)!! = n! * 2^n\n(kn)!!...! (k "!" signes) = n! * k^n\n\nSo, we have\n1) 6! = 1*2*3*4*5*6 = 720\n2) 6!! = 2*4*6 = 48\n3) 0! = 1\n4) 5!! = 1*3*5 = 15\n(5!!)!! = 15!! = 1*3*5*7*9*11*13*15 = 2027025\n\nOther factorials are too huge to compute precisely, but we can evaluate them using Stirling formula (second article)\nln n! ~= n*(ln n) - n + (ln(2*pi*n))/2 + 1/(12*n)\n\n5) 5! = 120\n(5!)! = 120! =~ e^(120*ln(120) - 120 + (ln(2*pi*120))/2 + 1/(12*120)) =~ e^457,81 =~ 6.69*10^198\n6) 1234!!!!!!!! = 1234 * 1233 * 1232!!!!!!!! =\n= 1521522 * (154*8)!!!!!!!! =\n= 1521522 * 154! * 8^154 = e^972.43 =~ 2.1*10^422\n\nThus, 6!! - 6! + (5!)! - 1234!!!!!!!! - 0! + (5!!)!! =\n=~ 48 - 720 + 6.69*10^198 - 2.1*10^422 - 1 + 2027025 =~ -2.1*10^422\n\nAnswer: about -2.1*10^422
207423
Not the answer, but a suggestion.\n\nThis is a college level questionm, so I'm assuming that you are in college. Go to the math department library and find other texts on complex analysis. Look at the chapters that cover the same material. Look at the examples the authors have worked out. You may be surprised to find this problem or one enough like it to give you a clue on how to proceed.\n\nThis is not that tough a problem. N years ago, (where 0 < N  < 50) I could have given you an answer, but since then, the analysis sections of my brain have shrunken.
1151044
http://www.allaboutcircuits.com/vol_6/chpt_7/5.html\nhttp://hyperphysics.phy-astr.gsu.edu/Hbase/electronic/nandlatch.html
1057306
Here's a copy of the actual paper. Good luck understanding it:\n\nhttp://math.stanford.edu/~lekheng/flt/wiles.pdf
1163094
Just google it and you would get the full details..here is the source..\nhttp://mathworld.wolfram.com/Hardy-RamanujanNumber.html\n\nI suggest you should at least try in google before asking anything. You could get it straight away.
319998
http://www.math.iitb.ac.in/resources/manuals/algorithms.html click d link to know. It may be helpful to u.
108492
Assuming you are talking about standard deviation...\n\nSigma is the square root of variance.  If you need to add sigma's together, they are added by taking the square room of the sum of squares.
1002263
hope this helps\n\nhttp://www.thea.nesinc.com/ptmath.htm
379578
I think you are talking about that book:\n\nOldrich Vasicek, "A test for normality based on sample entropy," Journal of the Royal Statistical Society, Series B, vol. 38, no. 1, pp. 54--59, 1976.\n\nI couldn't find a copy of this article, but it is easy to find a lot of other articles that are refer to it.\nHope, one of them will help you.\n\nAlso I strongly recommend to use a Citeseer scientific article database (2nd attached link). It usually contains a lot of information.
652164
This theorem has an amazing number of proofs but this theorem(like many other mathematical concepts) as you said was known way before pythogorean times but only to INDIANS who didnt share it on the global scale!!
348293
There are two seminar papers by Magnus Hestenes that should give you a good start:\n\n"A  Ternary Algebra with Applications to Matrices and Linear Transformation"\n\n"On a Ternary Algebra"
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http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP?Res=150\n\nhttp://www.math.sfu.ca/~cbm/aands/subj.htm\n\nhttp://clusterfie.epn.edu.ec/ibernal/html/CURSOS/AbrilAgosto06/Metodos/Libros/Fundamentals%20Of%20Numerical%20Computing%20-%201997%20-Wiley%20%20(By%20Laxxuss).pdf
589334
http://aleph0.clarku.edu/~djoyce/mathhist/mathhist.html