1539. - Roots

I pseudoprune, descendés of the monkey, like all :-)

it is an entertaining pastime, if a group of physicists puts himself, they have the most difficult part made, because the 'old' physicists are already almost all: Bohr, Heisenberg, Einstein, Sommerfeld... (and the oldest, with more reason: I found round there Ohm, now I have to add the Huygens line in Leibniz, etc)

1540. - Jueguitos

I recommend to them to prove the chat to nongo. In this game there is an element random, that joined a limited board, alters the theory known for the game of the Angel.

On this another game, we can say that it is almost liquidated: four demonstrations say that the angel wins if it is allowed to the angel to give two steps. But if the angel moves of one, as a king in a Chess board, is cooked. Very good summary of the demonstrations and links to the papers, here.

And, to relax the mind, an abstract jigsaw puzzle, sencillito, without images that they distract.

1542. - Omerta

(we go, carajo!! I am returning: newly it was going to put bold faces, and instead of the code html usually, I appealed to the téxico textbf {})

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(mmm... and now I started begin {center}, before realizing..., fault of that is not a question of not postear either!!)

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Exercise: analyze the Quandary of the Prisoner in case (at least) one of them belongs to the mafia (*).

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If the DdelP does not know, two citizens are detained and isolated up to confessing a crime and accusing other. If they do not do it, prisoners go 3 years c/u. If the two do it, prisoners go 10 years c/u. If one does it and other not, that speech goes out freely and other goes 15 years prisoner.

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Omerta comes, it was creating or not, of hombredad, prudently replaced in our language for manliness.

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(*) if it is necessary to clarify it, the Omerta is the categorical prohibition (**) of cooperating with the police authorities, still having been a victim of a crime.

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(**) With arrows and everything!

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Advanced exercise: in a population of N you present yourself, pN they are of the mafia (p between 0 and 1). The police choose a pair at random and they play the DdelP. How does the percentage of gangsters endure after k games? (suppose that they are realized before nobody remains free)

(if someone wants to catch fire, we write something)

1543.-Three theorems on the water and his absence of form

Teor 1: Imagenemos a river, and let's put a hexagonal network in a part of the watercourse, between two coasts. We choose hexagons at random, and place in them a cement column (if two are nearby, they join hermetically).

Only there are two possible results: or a water course remained open, or the columns form a dike. Finally, all Hex game ends with the victory of one of the players.

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Teor 2. In a flat area we place columns some next to other one, hermetically joined the column i with i-1 and i+1 (and only with them), such that the first one and the last one also stick. There stay two separated regions, a nursery, which we can fill with water without it happening to other one.

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Teor 3: In a square pond, we wave the water (gently) and at least a point will not move (or the waters are opened).

Warning: the next paragraphs contain the demonstration. It can be omitted in the first, second, third one... reading. The simbolito √ in front of some numbers 2 refers to 'root'. The html is not math-friendly.

Let's see: if any point displaced at least a distance h, let's cover the surface with a network of triangles of diameter d minor to h (we will say in the end who are h and d).

Let's paint the apexes of red if the coordinate x changed h / √ 2 or more. If not, we paint it of green (the coordinate and it changed h / √ 2 or more).

the way is only an indicative, it might be any other

There will stay a way of red apexes or one of green (I replaced a triangle by a column if it has at least two red apexes: it has a dike, or the water happens). Let's suppose that the way is red, it does not matter. It begins in to *, and the coordinate x increased at least h / √ 2. It comes to b *, where it diminished at least h / √ 2. Then, in some moment, a change of signs took place: in two apexes of the same triangle 2 jumped at least 2 h / √ (that is major to h).

Now, we need a little analysis to say who are h and d:

If T is the transformation that waves the water, and the norm euclídea of T (x, y) - (x, y) it is not annulled, is bigger than one h (since it is continuous).

The images of two points of the square for T will be over a distance minor than h if they were over a distance minor to one d' (since T uniformly continuous).

Then, if d it is minor to d', there are two apexes of the same triangle where the function jumps more than h Ridiculously!

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These three big theorems are equivalent between themselves. It is not difficult to demonstrate any more or less general version once one has the idea.

On them, let's say that the first one identifies it to Jordan. Gauss used it several decades earlier, without demonstrating, considering it to be 'clear'.

Brouwer, intuicionista, was pushing the 'traditional' mathematics back, but his theorem of fixed point demonstrated to be of big utility in the classic mathematics. An application that it did was to generalize that of Jordan to Rn, changing curves into hypersurfaces. It seems that Poincaré knew by intuition it: his idea was that if one was throwing sugar in a cup of coffee and it was stirred, some granite in the surface was not changing place (his theorem ergódico is one of so many people ramifications of this so simple idea).

The Hex was invented by Nash (a few years earlier Piet Hein had invented it). The relation of this game with the theorem of Jordan is clear, it is not difficult to prove the equivalence. With Brouwer it is more difficult, but it goes out: the existence of a balance of Nash is a direct consequence of this theorem (and it cost him a Nobel Prize). For another implication, it is necessary only to check what we did above, an idea of David Gale.

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The idea that connects them is that the water has no form, but it reveals to us the local form that it occupies. Serve as moral, or better that it serves as base for the demonstration of some another theorem.

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(special for the Mathematical, organized Carnival this time for Tito Eliatron)

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1544. - Aumann and the poker

Last year we had a strange meeting with Aumann: approximately twenty teachers of economic and exact, and approximately fifty agents of the mossad around. There was a question that I did not cheer up to rise to him, and I imagine which his answer would have been.

More than fifty years behind, the Israeli police closed a gambling den in Jerusalem, where one was playing the poker for silver, and the defense called it Aumann to testify. To testify on what? That the poker is not a gambling game, but of skill, and therefore, it was not punished by the law. But despite his mathematical defense, the judge condemned the timberos.

Kalai was telling that then Aumann met the judge, and he asked him for his mistake. His answer would have been that in these places the people lose quite, ruining his families.

Kalai argues that the judge is right. Re-formulating his argument, the laws point at an ideal, and the bets games are harmful to this social ideal (also he quotes a variant of the argument, the judge had to discard Aumann, appealing to the Misnah: the players must not bear witness since they do not contribute to the creation of the world!)

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It had in mind the history, and the post who linkeo was reminding to me something that happened to me at the beginning of '90. Vívía with a few friends, we were all students, and we were buying many things in a municipal fair that we had close (on Santa Fe, under the bridge of Pacific Ocean). In one of the positions, a pair of old men was playing the chess, and when it was going was doing some party with them, according to the time that it had, or his clientele.

But one day, there was no any more board: the municipal inspectors appeared one day, and they left to them a cartel that remembered an old ordinance that was prohibiting the gambling games...

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It had never counted this anecdote, I suspect that Aumann would be still laughing at us. It is not a gambling game, with which the strict law is not applied; neither nor were bets of for way, which discards the social ideal after the law.

But I hesitated to ask Aumann if he kept on thinking how he was thinking earlier: that the mistake was unacceptable, because these judges were not obeying the law, but his personal vision of how there had to be the things. I suspect that yes, because this keeps on being his position against the economic salvatajes (in the fund, which there fuck the banks that took risks, they knew that it could happen) which shows a surprising coherence over the course of time.

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1546. - The relativity of the indexes (II)

Let's explain the mini post of the one of the dawn, at this hour it was not to write much more. Let's define the necessary minimal thing so that the formula is understood.

An investigator published different (je) papers that we can call a1, a2..., an.

Each of them is quoted by himself, his friends, and other investigators, with which we count the number of appointments and see that
there are c1 works that they quote a1, c2 that they quote to a2..., cn
they quote an.

That defines an index of very rapid impact to us to evaluate the quality of the investigator:

c = c1 + c2 +... + cn
(many appointments not always guarantee that he is a good investigator, but very few guarantee to us that it is not very good).

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In 2005, Jorge Hirsch (an Argentine physicist who spent to better life in '70 (*)), introduced the h-index: let's suppose that we arrange the works as the number of appointments, of bigger than minor, and we place below the succession of natural numbers of minor to major:
c1>...> cn
1
Now, we have c1> major or equal to 1, and it will be last j such that cj is major or equal to j (since there are two lists of points, the decreasing one and another flood).

That one is h, the h-index, that it is understood easier saying that there is j papers, each one with j or more appointments.

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Hirsch had already said that h it was climbing like the root of the entire appointments. Now, Redner demonstrates (**) the formula of the previous post:

c = 4h2
Redner analyzes the cases where the quotient √c/2h moves away much of 1, and finds common characteristics in every class of scientists. Very pretty.

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The formula walks well with me (the quotient is 0.98) and with Caffarelli (1.02), so we can make sure that it covers both ends of the quality bogey.

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(*) It Emigrated, it is in California.

(**) It Demonstrates to the physical thing: plotea semilog 255 information. I believe that with the mathscinet thousands might be obtained. Equal, I have fondness to R, believe that it was referee of a paper that we start with Matías in this blog.

1547. - The evolution of the mathematical literature

1660 (in Latin):

London, March, 1668

Dear Fulanitus: the previous year I received a Menganeus letter dated in August, 1664, where it receives geometrically the extract of the movement of the fluid bodies. With big pleasure I verify that it obtains the same results to which I had already come approximately twelve years earlier, and I am useful now to communicate them to him.

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1760 (in French):

Note presented in the Academy of Sciences of Paris, pair Monsieur Fou L'Anneaux et Monsieur Mainganau.

In this note we analyze the movement of a fluid in case it remains in absolute rest (and we will demonstrate that it does not move), or that it is in rest as regards a receptacle that contains it but that translada (we will demonstrate that translada with him). As the remaining cases were already analyzed by Euler and the Bernoulli, we put this way a golden brooch to the theory of the hydraulics and the hidrodinamia.

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1860 (in German)

Herr Doktor Proffessors Vulanner und Menkganniten demonstrated the continuity and difereciabilidad of the flow of a particle inside a fluid and analyzed the distinguishing equation that it satisfies. We will re-write here these way results vectorial.

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1960 (in English)

In the works of Fulanov and Menganiev there was analyzed the probability of which a particle inside a fluid was following a family of curves given inside a space of functions so generally that it includes those of Sobolev, Besov, and Orlicz. Here, we are going to restrict ourselves to a grafo of ten nodes, faced, and the set of discreet ways between his nodes when it is chosen at random and with uniform probability the nearby node to which it will go.

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2060 (in???)

We translate here the last article that Ning came to our hands of Fu-Lan Oh and Meng Ah. We omit the previous definitions, and the demonstration of some of the most used mottoes, since they were published in the journal of certain university of a province that we could not identify in the map.