Math Forum / Mathematics / General Topics / September 2004

Given a 1xn matrix A and nx1 matrix B, what is
d(AB)^2/dA ?
Can anyone give me some cue?
Thank you a lot.

2 CIRCLES 1 RADIUS 2CM FIT INSIDE A RECTANGLE 5CM X 6CM
BOTH CIRCLES TOUCH EACH SIDE OF THE RECTANGLE AND ALSO EACH OTHER WHAT IS THE RADIUS OF THE 2ND CIRCLE

How does one show, definitively, that n/2^n -> 0 as n -> infinity?  I
can't figure out the trick.  Can one use a natural logarithm?  I would
think not, but I'm not sure.  As well, if one were to use a delta
epsilon proof on this, how would you do it?

What do you call a matrix which is its own inverse? I know that if a
matrix is the inverse of its Hermitian transpose it is orthogonal. But
what if it is just the inverse of itself. An example is the type-IV
DCT which when applied twice to a block of data returns the original

If f(x)=ax^3 + bx^2 + cx + d  has real coefficients and f(x)>= 0 on [0,1],
then prove the inequality
       ==============================
       I[x*f(x)] =< 0.84499 * I[f(x)]

I came across a problems about sequences that seem to be stumping me.
The 1st states suppose that the sequence {a_n} is defined recursively by
a_(n+2) = [a_(n+1) + a_n]/2, for all n in naturals with a_1 and a_2 any two
real numbers.

Consider
x^2 + (2s_1 + 3s_2)x + s_1 s_2 6 = (x + 2s_1))(x + 3s_2)
where s_1 s_2 = 1, and 2s_1 + 3s_2 is an integer.
Note that s_1 and s_2 cannot be algebraic integers if they are

Consider the graph below.  The vertices in each level force the colors
of the vertices in the level above. Eventally vertex X0 is forced to
be the fifth color.  However, the last level cannot be forced.
Now if G is infinite, there will always be another level.  

Wednesday July 16th 2003 197/168 16950
11 12 13 14 15 16 17   <-Dawn's positions
G  A  B  R  I  E  L
7  1  2 18  9  5 12 = 54 <-value

Gentlemen,
This is Dr. Andrew Beckwith. I am spaking to you after having had
people from another forum tell me that James Harris's patriotism has
been questioned.

If you open any visual basic editor of word
or excel etc. and run the following program
it will generate a large file 20M that
contains alot of regularity. Is this chaos

P.S. This program is used to optimize strategies for the computer game
Dark Age of Camelot.
I'm struggling with the following problem. Below I'll discuss what
I've done so far, but I'm not happy with my results. Any help

I have to define a function by parts whose domain is [0, 30] and its range is [0,15]. The intervals are [0, 5], (5,25] and (25,40].
I know that over [0, 5] the function is constant but over the intervals (5,20] and (20,30] the function is deacreasing and satisfies
                ...

Suppose k is a positive integer and mu is a real number in [0,1].  Then
consider the complex number
c=(  (exp(i*theta))2/(exp(i*theta)*(1+mu)-mu)  )^(1/k)
(i is the complex unit (sqrt(-1))).

If * is a binary operation (x, y) |--> x * y, then
what is the correct name for the operation @ where
(x, y) |--> x @ y = y * x ?
The only reference I have for this is R. Godement,