LionMan's New Writeupshttp://everything2.com/?node=New%20Writeups%20Atom%20Feed&foruser=LionMan2000-10-30T01:03:03ZElectromagnetic Interference (thing)http://everything2.com/user/LionMan/writeups/Electromagnetic+InterferenceLionManhttp://everything2.com/user/LionMan2000-10-30T01:03:03Z2000-10-30T01:03:03Z<p>
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.
</p>tangent vector (thing)http://everything2.com/user/LionMan/writeups/tangent+vectorLionManhttp://everything2.com/user/LionMan2000-10-30T00:47:31Z2000-10-30T00:47:31Z<a href="/title/amsaarel">amsaarel</a> is correct in (his? her?) writeup, however, I felt that it needed to be expanded:<br>
If you have an n+1 dimensional <a href="/title/manifold">manifold</a> M of paramaters t_1, t_2, ..., t_n, then you have an n dimensional <a href="/title/vector+space">vector space</a> which has all the tangent vectors in it. To find the vector with greatest slope (dM, the complete differential) use the vector differential operator <a href="/title/del">del</a>, defined as:<br>
del:=<@/@t_1,@/@t_2,@/@t_3,...,@/@t_n><br>
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, <a href="/title/directional+derivative">directional derivative</a>s can be found in those directions. By using a multidimensional cross product between all n vectors found, the <a href="/title/normal">normal</a> to the vector space can be found, this an equation for the vector space can be found.<br>
I now feel tempted to write "<a href="/title/The+proof+is+left+as+an+exercise+to+the+reader">The proof is left as an exercise to the reader</a>" here since it annoys me so!e (thing)http://everything2.com/user/LionMan/writeups/eLionManhttp://everything2.com/user/LionMan2000-10-07T05:14:38Z2000-10-07T05:14:38ZThe <a href="/title/Naperian">Naperian</a> or natural base to logarithms; Naperian does not refer to <a href="/title/John+Napier">Napier</a> having created it, in fact his concept of a <a href="/title/logarithm">logarithm</a> 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:<br>
it is the <a href="/title/limit">limit</a> of the slowly converging function
<pre>
/ 1 \
lim | 1 + - | ^ n
n->oo \ n /
</pre>
or the more quickly converging <a href="/title/series">series</a>
<pre>
oo
---
\ 1
| ---
/ n!
---
n=0
</pre>
or as the number satisfying d/du (e^u) = (e^u). <a href="/title/Leonhard+Euler">Euler</a> 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^(<a href="/title/i">i</a>*<a href="/title/theta">theta</a>) = cos(theta) + i*sin(theta), which is one of the most important formulas in complex analysis, and is responsible for…Gaussian Distribution (thing)http://everything2.com/user/LionMan/writeups/Gaussian+DistributionLionManhttp://everything2.com/user/LionMan2000-10-07T04:59:09Z2000-10-07T04:59:09ZThis is the normal <a href="/title/density+curve">density curve</a> defined by a <a href="/title/mean">mean</a> of 0 and <a href="/title/standard+deviation">standard deviation</a> of 1, also called the standardized normal curve. A formula for generating the density curve is:
<br>
P=(<a href="/title/e">e</a>^(-(x^2)/2))/sqrt(2*<a href="/title/pi">pi</a>)<br>
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)http://everything2.com/user/LionMan/writeups/non-trivial+rootsLionManhttp://everything2.com/user/LionMan2000-10-07T04:51:04Z2000-10-07T04:51:04Z<p><a href="/title/Roots">Roots</a> 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 <a href="/title/Riemann+Zeta+Function">Riemann Zeta Function</a> at -2, -4, -6, ... because of the reciprocal of Gamma in the continuous definition of Zeta; <b>all of the other roots, excuding those which are trivial, are non-trivial.</b></p>Roots (thing)http://everything2.com/user/LionMan/writeups/RootsLionManhttp://everything2.com/user/LionMan2000-10-07T04:31:34Z2000-10-07T04:31:34Z<p>The set of values or ordered n-tuples, which when taken as parameters to some system yield the result of zero.
<br>Ex: A number of the set {-2, -4, -6, ... } when taken as a paramater to the <a href="/title/Riemann+Zeta+Function">Riemann Zeta Function</a> yield zero. These values happen to be <a href="/title/non-trivial+roots">non-trivial roots</a>.</p>