about the previous topic for perfect distance forests, two references that might be helpful for anyone interested,

References:

[1] B.Calhoun, J. Polhill, Perfect distance forests, Australian Journal of Combinatorics, vol. 42(2008), p. 211-222.(NOT AVAILABLE ONLINE)

[2] W.Calhoun, K. Ferland, L. Lister and J. Polhill, Minimal distinct distance trees, J.Combin. Math. Combin. Computing vol. 61(2007) p. 33-57.(AVAILABLE HERE)

so leech trees of order 6 or smaller are known. For order 9,11 or 16 there no Leech trees either leaving 18 the smallest open case. Szekely has conjectured that no additional Leech trees exist but this is still open. Another generalization can be studied in a different domain, .

Let be a tree of vertices and let . We say that is a modular Leech tree if there exists an edge weighting function such that each of the paths within has a distinct weight from with the sums taken modulo . We call such an edge weighting function a  -Leech labeling. Since the pathweights are all distinct, the function induces a bijection between the paths of and the elements of the group . We use to refer to this bijection as well.

Note that a perfect distance tree as defined previously of order is also a modular Leech tree over in which none of the path sums, before applying the mod operation, have a weight greater than . Thus Leech’s original five examples provide us with five modular Leech trees. For more read here.

 

is it cold at 0.95 mach?

be greedy darling !!!

A greedy algorithm is an algorithm that follows the problem solving heuristic of making the locally optimal choice at each stage with the hope of finding a global optimum. In many problems, a greedy strategy does not in general produce an optimal solution.

Features

Greedy algorithms are simple and straightforward. They are shortsighted in their approach in the sense that they take decisions on the basis of information at hand without worrying about the effect these decisions may have in the future. They are easy to invent, easy to implement and most of the time quite efficient. Many problems cannot be solved correctly by greedy approach.

The greedy algorithm consists of four functions.

1)  A function that checks whether chosen set of items provide a solution.
2)  A function that checks the feasibility of a set.
3)  The selection function tells which of the candidates is the most promising.
4)  An objective function, which does not appear explicitly, gives the value of a solution.

Well the question is whether to implement a greedy algorithm in our lives or not. What we lose and what we win. Since the decisions we make is for our benefit and nothing more it is ok to try things in a not secure environments and loose out convenience. We only live once and we have to make mistakes to win things and experiences… so I guess it ok to be wild, or should I say greedy !!!

I hope Katherine would read that !!!

ANSI C yeaaah

there are times that it is really an enjoyment to study something difficult to learn understand and finally code. For me nowdays is DATA STRUCTURES in C.

WHAT IS A STRUCTURE?

A structure is a collection of one or more variables, possibly of different types, grouped
together under a single name for convenient handling. (Structures are called “records” in
some languages, notably Pascal.) Structures help to organize complicated data, particularly in
large programs, because they permit a group of related variables to be treated as a unit instead
of as separate entities.

CATEGORIES of Abstract Data Types

Simple/Double/Circularily/Preordered Linked Lists, Binary trees, AVL trees, Stacks, Queues…

An example:

For a binary tree(or a linked list) we know the information in every node of the tree, the address left node and the address of the right node with the following piece of code:

struct Treenode
{
int data;
struct Treenode *left;
struct Treenode *right;
};

typedef struct Treenode *TreePtr;

If we want to add or delete a node we may use already existing functions. The same method is used to visit all nodes of the tree in a particular way. In many cases you have to use recursive functions.

Even with its flaws, its depicted functionalities, the Object Oriented Programming disability, we must thank Dennis Ritchie 🙂

Many years, almost a decade since I first read THE CHICKEN FROM MINSK. The famous book with problems and puzzles from the rich Russian literature concerning Math, Physics, Mechanics and their applications in simple description  but brightly inspired from this beautiful thing called science ….

well about the book if you are a more of ‘math’ type I would not recommend it. I initially hated and found it that these problems were  not my style, but life is a bitch and proved me that I was wrong. You should definitely should try it and will learn many things (especially for engineers) . Well even if you try good old style problems from All Russian Math Olympiads on a piece of paper or even you are trying to solve Navier-Stokes with numerical analysis with multiple processors, the trip is the same and it is yours, the best trip by your self …

so there are times in our lives we should say: fuck money, honours and degrees I want just science …

Cubic with multiple roots

graphs fun

It’s been a long since I posted something. I just started reading the marvellous book about graphs: Graph Theory by Bin Xiong,Zhongyi Zheng. There are some really good problems with solutions too and the basic theory. Graph problems are about stating the problem, fixing vertex connectivity, coloring edges/vertices and pretty much using the imagination to identify the constraints of the given conditions. The book’s chapters are: Definition of Graphs, Degree of vertex, Trees, Turin’s theorem, Euler-Hamilton graphs, Planar graphs and Ramsey applications. A nice problem with coloring:

PROBLEM: Nine mathematicians meet at an international conference and discover that among any three of them, at least two speak a common language. If each of the mathematicians speak at most three languages, prove that there are at least three of the mathematicians who can speak the same language.

For a quick view you will find it at google books. For a solution of the problem look here

Mathematical beauty activates same brain region as great Music and Art

This is not new. Mathematics is a joyous occupation of mind and a major source of fun and entertainment. This is true now in a more scientific way seen  which is illustrated here ( for details also see here)

   According to this article, the study’s results point to the theory that beautiful formulas of  Mathematics has nothing be jealous of a beautiful painting. This research  published in the journal: Frontiers in Human Neuroscience. Researchers used functional magnetic resonance imaging (fMRI) to image the brain activity of 15 mathematicians when they viewed mathematical formulas that they had previously rated as beautiful, neutral or ugly.

~What we do in life echos in eternity

http://jacquelinemhadel.files.wordpress.com/2013/10/ipadechoes-002.jpg

error of energy is higher when you look at a shock wave closer and closer … and even closer (like the abyss of human soul)…