<?xml version="1.0" encoding="UTF-8"?>

<record version="8" id="7542">
 <title>data stream</title>
 <name>DataStream</name>
 <created>2005-12-27 07:46:37</created>
 <modified>2007-06-23 14:48:47</modified>
 <type>Definition</type>
 <creator id="7107" name="michal"/>
 <author id="7107" name="michal"/>
 <classification>
	<category scheme="msc" code="11B83"/>
 </classification>
 <defines>
	<concept>Stream of Tuples</concept>
 </defines>
 <synonyms>
	<synonym concept="data stream" alias="time series"/>
	<synonym concept="data stream" alias="sequence of tuples"/>
	<synonym concept="data stream" alias="stream"/>
 </synonyms>
 <related>
	<object name="BeattySequence"/>
	<object name="FraenkelsPartitionTheorem"/>
	<object name="WideraInterlaceAndDeinterlace"/>
 </related>
 <keywords>
	<term>sequence</term>
 </keywords>
 <preamble>% this is the default PlanetMath preamble.  as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.

% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}

% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}

% there are many more packages, add them here as you need them

% define commands here</preamble>
 <content>A {\it data stream} is an ordered pair $\left( s,\Delta \right) $

where:

 1. $s$ is a sequence of tuples,

 2. $\Delta $ is the sequence of time intervals (i.e. rational or real numbers) and each $\Delta _{n} &gt; 0$
</content>
</record>
