Some more GRE words.

16. Conspicuous - completely obvious.
17. Preclude - prevent from happening.
18. Germane - relevant.
19. Glut - excessive supply.
20. frivolous - not serious in attitude/content/behavior
21. audacious - willing to be bold in social situations.
22. Chortle - to chuckle in a muffled, breathy way.
23. Gall - trait of being rude.
24. Vociferous - conspicuously and offensively loud.
25. mawkish - overly sentimental to the point that it is disgusting.
26. aesthete - someone who appreciates beauty of art and nature.
27. concede - to accept defeat, surrender.
28. Torpor - inactivity resulting from lethargy.
29. Prescience - Power to foresee the future.
30. superfluous - add no value, serving no useful purpose.

Some GRE words

1. Demur - to object or show reluctance.
2. veracious -  truthful.
3. Disinterested - unbiased / neutral.
4. Tirade - long angry speech of criticism or accusation.
5. Galvanize - to excite/inspire.
6. Acrimony - bitterness and ill will.
7. Enervate - to sap energy from.
8. Profligate - spending resources recklessly or wastefully.
9. ingenuous - to be naive and innocent
10. censure - to express strong disapproval.
11. auspicious - favourable.
12. Platitude - obvious remark.
13. trite - lacking originality or freshness.
14. Gainsay - deny / contradict / oppose.
15 - Apathetic - Lack of interest.

Excerpts from "An Essay concerning Human Understanding" by John Locke.

Will be continually updated as i proceed through the book -

1. For the understanding, like the eye, judging of objects only by its own sight, cannot but be pleased with what it discovers, having less regret for what has escaped it, because it is unknown.

ISR addresses for 8051 microcontroller

SPI in AT89C5131 - configuration tables

Some definitions used in graphs

A walk  : Sequence of vertices and edges v_i and e_i such that for 1 <= i <= k, the edge e_i has endpoints v_(i-1) and v_i.

The length of a walk is the number of edges in it.

A trail  is a walk with no repeated edges.

A path is a walk with no repeated vertex.

fact - path be a trail, but path may or may not be a trial.

The distance d(u,v) between vertices u and v equals the shortest length of a u,v path.

A circuit is a closed trail.

A cycle is a closed path.

A graph is connected if any two of its vertices are joined by a path.

 A tree is an undirected graph in which any two vertices are connected by exactly one simple path.

Laplacian matrix of a graph

The incidence matrix of an oriented graph -
Orientation of a graph X is the assignment of direction to each edge.
An arc of a graph is an ordered pair of adjacent vertices.
Formal definition -
       An orientation of X can be defined as a function sigma from the arcs of X to {-1,1} such that, if (u,v) is an arc, then sigma(u,v) = -sigma(v,u).

Let D be the incidence matrix of the graph X.
The laplacian of X is the matrix Q(X) = D*D'
Laplacian does not depend on the orientation.

Q is symmetric => its eigen values are real.
Its positive semidefinite => evas are all non-negative.

TREES - The number of spanning trees is determined by the laplacian.
[Spanning tree - The spanning tree of a connected undirected graph G is a tree that includes all the vertices and some or all of the edges of G.]

Let e = uv be an edge of X.
The graph obtained by deleting the edge e is denoted by X \ e. Its edge set is denoted by E(X) \ e.
Vertex set remains the same.
contracting the edge e => X / e.