Peeing Alot Of Blood And Lower Stomach Pressure

"FEKETE POINTS" the bridges of Königsberg

"English scientists solve one of the great mathematical challenges: The estimate of" Fekete points " have applications in physics and medicine."

A team of researchers from the Polytechnic University of Catalonia (UPC) has resolved one of the "enigmas" convoluted mathematical, which for a century refused to scientists around the world. Problem is so-called Fekete points, which poses how to distribute a finite number of points - particles - on a sphere to obtain a stable configuration. The less is the potential energy of the set of points, the lower the chaos of the portfolio and therefore more stable configuration.

The challenge in the absence of validation of the scientific community at an upcoming conference, has been solved by Enrique Bendito, Andrés Encinas, Angeles Carmona and José M. Gesture, with the help of supercomputer Finisterrae, placing in the Supercomputing Center of Galicia (Santiago de Compostela) and considered the largest shared memory of Europe. The computer work required in February some 350,000 hours of calculation, rather than with a home computer would have taken forty years of work.

Fekete points were ranked at number 7 on the list of outstanding issues mathematician Stephen Smale, grouping the 18 most important problems and difficulty today.

UPC Mathematicians have solved the positioning of tens of thousands of points in 50 million combinations, as previous researchers had not exceeded two thousand points. The solution to the problem have applications in the formation of molecules, crystal structures, protein design, gas dynamics ...

To view the full study, see pdf, here.

Who Makes Acoustic Solutions Tv

Königsberg was a popular and wealthy city of East Prussia, today his name is Pertec Kaliningrad and Russia, is located on the shores of the Baltic Sea and about 50 km from the border with Poland.

In this city two rivers meet, forming an island at the confluence. Seven bridges joined (and no, because the city was partially destroyed during World War II) the different parts of the city, as shown on the map at the time. In the eighteenth century became popular as a riddle / hobby whether it was possible to cross the seven bridges of the city, passing only once each.

Königsberg in Euler time

Kaliningrad, currently

This city is also known for being the birthplace of philosopher Immanuel Kant (1724 - 1804), but in the History of Mathematics is famous for the provision of the bridges that gave rise to this game, just at the time of Kant, which attracted the attention of the most famous mathematicians of the time.

This problem, of course, can be solved by an exhaustive study of all possible itineriarios. But in mathematics we are interested in generalizing the problem and find a simple and valid for all possible maps of cities, and even more general objects.

In 1736, the great Swiss mathematician who lived in St. Petersburg, Leonhard Euler published his "Solutio ad geometriam problematis pertinentis situs" , an article that solved the problem in the general case. This work is regarded as the birth of graph theory, used today in countless applications, and also one of the first appearances of a "new geometry" in the others only the structural properties of an object and not measurements. That is referred to the words "geometry situs" in the title Euler, words that are translated today as topology.

The first observation is that the problem can be reformulated as follows. Since The following "graph" with four vertices and seven edges, can cross it without whole spend twice for the same edge?. In the graph, the four corners represent the four parts into which the rivers divide the city, and edges represent the seven bridges. Put another way, which is more familiar to the amateurs of pastimes: Is it possible to make the drawing of the graph without lifting the pencil from the paper and not passing twice on the same edge? (You can spend twice for the same vertex).


Euler's answer is extremely simple. Suppose indeed it is possible to do the drawing without lifting the pencil from the paper. In making the drawing, we go through each intermediate vertex by an edge enter and come out the other. In particular, the number of edges that meet at each vertex of the graph, except perhaps the initial and final vertices of the drawing, must be even. If we call "valence" of each vertex the number of edges that flow into it, the above means that the problem has a solution is necessary that the graph has at most two vertices of valence par. In the case of the Königsberg graph all four vertices have odd valence, so the problem has no solution . QED

100by100 Multiplication Chart

THE INVENTOR OF CHESS AND FAMOUS

Further to the previous post in which he spoke of progressions, today we focus on the geometric progression, which follow an exponential growth, so that the terms of the inordinately trigger progression (for high) and vanishes quickly in the event (low).

influenza virus

A clear example of exponential growth is the spread of viruses such as influenza, leading to a large extent number of people on the face of the planet, in a few weeks, as well as other natural events ...

But today I will tell you the famous legend of the inventor of chess, reads history, the Persian king dead boring at times, suddenly became fascinated by the game of chess which he / herself a witty and clever inventor. It was so grateful that the king offered the East mathematical whatever he wanted.

The inventor replied

- I'll settle for 1 grain of wheat for the first board box, 2 for second, 4 for third, 8 for fourth and so on until the box 64 of the board.

(ie the sum of the 64 first terms of a ratio PG 2 and whose first term is 1)

King scoffed thinking it was the minutiae asking and asking his vizier to prepare the award requested, did the math and realized it was impossible to enforce the order, as the sum of the grains of the 64 cells was nothing less than the amount of:

18,446 616 grains

.744.073.709.551

(In every kilogram of wheat fit approximately 28 220 grains, so that the result would be about 653 676 260 585 tonnes, that would occupy a cube-shaped deposit of just over 11'5 kilometers on a side.
To produce such a quantity of wheat would need to be cultivating the earth (including oceans), for eight years)

A second part of the story, which is next due to the embarrassment of King of having to accept that there was enough grain to pay, check with other intelligent and witty man of his court for him to pull out of trouble.

And this he proposed that:

- the inventor to see how generous you are, offer not only the sum of the 64 first terms, but the infinite sum.

To which the king said:

- You're crazy!. If I have to pay as I do to extend the sum to infinity would be infinite grains ...

ingenious But the assistant said

- Take me to the inventor and trust me, everything will be alright!

Once assembled, the proposed to assistant ingenious inventor, that the king was so pleased and happy with the game of chess and was so generous, not only offered to give the sum of 64 squares, but the infinite sum. To which, the inventor shrug accepted. And the king's aide went on to explain: Let's call

S = 1 + 2 + 4 + 8 + 16 + ... (An infinite sum)

now multiply by 2, so we have 2S,

2S = 2 + 4 + 8 + 16 + 32 + ...

Then we 2S - 1S,

2S = 2 + 4 + 8 + 16 + 32 + ...

-1S = - 1 - 2 - 4 - 8 to 16 - ... ______________________

S = -1

So we see that 2 and -2 are canceled, and 4 and -4, and equal to infinity ... so that in the end, S = -1. Not only does he no longer had to pay the inventor, but above this it was a pimple. Amazing! (So \u200b\u200bis it about playing with the infinite, such cases are called paradoxes of the infinite )