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Posts Tagged ‘LaTeX’

Palindromic numbers

June 2nd, 2010 No comments

I was reading an article about palindromes the other day, and came across a formel definition of palindromic numbers.

Although palindromic numbers are most often considered in the decimal system, the concept of palindromicity can be applied to the natural numbers in any numeral system.

For the few who does not know it already, here it is – and it gave me an excuse to write a little more \LaTeX :)

Consider a number n>0 in base b\le 2, where it is written in standard notation with k+1 digits a_i as:

\displaystyle n = \sum_{i=0}^k a_i b^i

with, as usual, 0\le a_i < b for all i and a_k \ne 0. Then n is palindromic if and only if a_i = a_{k-i} for all i. Zero is written 0 in any base and is also palindromic by definition.

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Scientific writing

December 6th, 2009 No comments

I was cleaning out some old CDs the other day, when I happen to stumble over a copy of my master thesis. My thesis was about the mathematical properties of artificial neural networks and I would never have been able to do it without \LaTeX. Try to typeset something like

f_j(x,\theta) = F\displaystyle{\left(\sum_{h=0}^lG(\bar x'\gamma_j)\beta_{jh}\right)},\ h=1,\ldots,l.

in Word. Or how about this

Definition 2.2
For any (Borel) measurable function G(\cdot) mapping R to R and n\in N let \sum^n(G) be the class of functions

\displaystyle{\left\{f:\mathbb R^n\rightarrow \mathbb R | f(x)=\sum_{j=1}^l\beta_j G(A_j(x)),\ x\in\mathbb R^n,\ \beta_j\in\mathbb R, A_j\in\mathbf A ^n,\ l\in\mathbb N\right\}}

The WordPress plugin I have found for typesetting \LaTeX does not do a very good job, so please bear with the above.

I have recently installed MacTeX on my iMac. I have no idea of what I should use if for right now, but it feels good and maybe I should try to finish some of the stuff I’m writing on and try to get it published, even though it will be hard not being in the university community any more.

Let’s just take another few equations for the fun of it :)

\displaystyle{\int_{\mathbb R^n}\int_{\mathbb R} a^\alpha D^{|\alpha} G(a'x - \theta)\frac{|b|^n \hat f(ba)e^{2\pi ib\theta}}{\hat G(b)}\mbox{d}a\ \mbox{d}\theta}
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