LionMan's New Writeups

Electromagnetic Interference (thing)

2000-10-30T01:03:03Z

EMI is Electro-Magnetic Interference. It refers to the intereference or disruption caused in electronic equipment when a pulse of Electro-Magnetic waves (usually with a spectrum of frequencies) of high intensity are generated. An example of EMI is telecom disruptions from solar flares.

tangent vector (thing)

2000-10-30T00:47:31Z

amsaarel is correct in (his? her?) writeup, however, I felt that it needed to be expanded:
If you have an n+1 dimensional manifold M of paramaters t_1, t_2, ..., t_n, then you have an n dimensional vector space which has all the tangent vectors in it. To find the vector with greatest slope (dM, the complete differential) use the vector differential operator del, defined as:
del:=<@/@t_1,@/@t_2,@/@t_3,...,@/@t_n>
where @/@x is the partial with respect to x operator. del(M) will yield a vector in the vector space, and by dotting del(M) with unit vectors, directional derivatives can be found in those directions. By using a multidimensional cross product between all n vectors found, the normal to the vector space can be found, this an equation for the vector space can be found.
I now feel tempted to write "The proof is left as an exercise to the reader" here since it annoys me so!

e (thing)

2000-10-07T05:14:38Z

The Naperian or natural base to logarithms; Naperian does not refer to Napier having created it, in fact his concept of a logarithm is different than the modern concept, but he is credited as creating logarithms, hence this extremely useful number is identified with him. e is approximately 2.718281828459045 to fifteen digits, and can be expressed in many ways:
it is the limit of the slowly converging function

       /     1  \
 lim  |  1 + -   | ^ n
n->oo  \     n  /

or the more quickly converging series

 oo
---
\     1
 |   ---
/     n!
---
n=0

or as the number satisfying d/du (e^u) = (e^u). Euler gave this number the letter it is associated with; some say it is because e is the first letter of his name, but Euler said that all others were taken up to e. Euler discovered the relationship e^(i*theta) = cos(theta) + i*sin(theta), which is one of the most important formulas in complex analysis, and is responsible for…

Gaussian Distribution (thing)

2000-10-07T04:59:09Z

This is the normal density curve defined by a mean of 0 and standard deviation of 1, also called the standardized normal curve. A formula for generating the density curve is:
P=(e^(-(x^2)/2))/sqrt(2*pi)
To determine the probability of an event in a normally distributed set of data of occuring, integrate this function from -infinity to (x-mu)/sigma where mu is the mean and sigma is the standard deviation.

non-trivial roots (thing)

2000-10-07T04:51:04Z

Roots which arise in a system which are not obvious solutions or caused by a definition or well known nature of part of the system. Ex: Trivial roots occur for the Riemann Zeta Function at -2, -4, -6, ... because of the reciprocal of Gamma in the continuous definition of Zeta; all of the other roots, excuding those which are trivial, are non-trivial.

Roots (thing)

2000-10-07T04:31:34Z

The set of values or ordered n-tuples, which when taken as parameters to some system yield the result of zero.
Ex: A number of the set {-2, -4, -6, ... } when taken as a paramater to the Riemann Zeta Function yield zero. These values happen to be non-trivial roots.