jQuery Page Layout Manager

Rather than use the iframe itself as a layout 'pane', you could also
put the iframe 'inside' a regular pane-div. Since the pane-div has a
width and height set, all you need is:

<iframe width="100%" height="100%" ...>

This will auto-size the iframe to fit within the inner-dimensions of
the pane - ie, inside the padding.

jQuery Page Layout Manager

Demo

Left / Right Panes


South / North Panes

Equivalence Relation

Equivalence Relation: A binary relation R on a set A is an equivalence relation if and only if
(1) R is reflexive
(2) R is symmetric
(3) R is transitive

Example: The equality relation (=) on a set of numbers such as {1, 2, 3}
Example: The congruent modulo m relation on the set of integers

The set of elements of A that are equivalent to each other is called an equivalence class. The equivalence relation partitions the set A into muturally exclusive equivalence classes.


Equivalence Relation & class


applet-magic.com

Euler Circuit and Hamiltonian Circuit

In graph theory, an Eulerian trail is a trail in a graph which visits every edge exactly once. Similarly, an Eulerian circuit is an Eulerian trail which starts and ends on the same vertex. They were first discussed by Leonhard Euler while solving the famous Seven Bridges of Königsberg problem in 1736. Mathematically the problem can be stated like this:



Given the graph on the top, is it possible to construct a path (or a cycle, i.e. a path starting and ending on the same vertex) which visits each edge exactly once?

The term Eulerian graph has two common meanings in graph theory. One meaning is a graph with an Eulerian circuit, and the other is a graph with every vertex of even degree. These definitions coincide for connected graphs.

Hamiltonian Circuit is a circuit that visits each vertex once without touching any vertex more than once. (Postman problem)
Every complete graph (n>2) has a Hamilton circuit.



www.pballew.net - Special Graph Problems

Implementing a Left Join with LINQ

LINQ doesn't define keywords for cross join, left join, or right join.
As part of the LINQ grammar, you get join and group join.

The two common joins are the inner join (or just join in LINQ) and the left join. Suppose you have two collections of data. One you will call the master or left collection, and the other you'll call the detail or right collection. A left join is a join whereby all of the elements from the left collection are returned and only elements from the right collection that have a correlated value in the left sequence. Usually, the correlation is a key or some kind of unique identifier.

Using another analogy, if the left collection is the parent and the right is the child, a left join is all parents but only children with parents.
A right join returns orphans but no childless parents.


developer.com - Implementing a Left Join with LINQ