Proof claimed for deep connection between primes The usually quiet world of mathematics is abuzz with a claim that one of the most important problems in number theory has been solved. Mathematician Shinichi Mochizuki of Kyoto University in Japan has released a 500-page proof of the abc conjecture, which proposes a relationship between whole numbers — a 'Diophantine' problem. The abc conjecture, proposed independently by David Masser and Joseph Oesterle in 1985, might not be as familiar to the wider world as Fermat’s Last Theorem, but in some ways it is more significant. Like Fermat’s theorem, the abc conjecture refers to equations of the form a+b=c. The 'square-free' part of a number n, sqp(n), is the largest square-free number that can be formed by multiplying the factors of n that are prime numbers. If you’ve got that, then you should get the abc conjecture. It turns out that this conjecture encapsulates many other Diophantine problems, including Fermat’s Last Theorem (which states that an+bn=cn has no integer solutions if n>2).
Biographie de Georg Cantor Il fallait probablement être un peu fou pour pouvoir imaginer que tous les ensembles infinis n'ont pas le même nombre d'éléments, pour définir des entiers infinis, les ordonner, et même les additionner. Georg Cantor était ce fou-là, et ses idées révolutionnaires n'ont pas manqué de détracteurs. Georg Cantor est né le 3 mars 1845 à St Petersbourg. Son père est commerçant prospère, sa mère est issue d'une famille de musiciens; tous les deux sont très cultivés, et donnent à leur fils une éducation sérieuse, religieuse, et bercée par les arts. En 1846, la famille s'installe en Allemagne, où elle espère trouver un climat plus favorable à la santé du père. Georg Cantor se révèle être un étudiant brillant, notamment dans les mâtières manuelles. Les premières recherches post-doctorales de Cantor sont consacrées à la décomposition des fonctions en sommes de séries trigonométriques (les célèbres séries de Fourier) et particulièrement à l'unicité de cette décomposition.
Polymathematics Georg Cantor Georg Ferdinand Ludwig Philipp Cantor Georg Cantor est un mathématicien allemand, né le 3 mars 1845 à Saint-Pétersbourg (Empire russe) et mort le 6 janvier 1918 à Halle (Empire allemand). Il est connu pour être le créateur de la théorie des ensembles. Il établit l'importance de la bijection entre les ensembles, définit les ensembles infinis et les ensembles bien ordonnés. Il prouva également que les nombres réels sont « plus nombreux » que les entiers naturels. Cantor a été confronté à la résistance de la part des mathématiciens de son époque, en particulier Kronecker. Poincaré, bien qu'il connût et appréciât les travaux de Cantor, avait de profondes réserves sur son maniement de l'infini en tant que totalité achevée[n 1]. Biographie[modifier | modifier le code] Enfance et études[modifier | modifier le code] Georg Cantor fut élevé dans la foi luthérienne, qu'il conserva toute sa vie. En 1863, à la mort de son père, Cantor préféra poursuivre ses études à l'université de Berlin. J.P.
Mathgen paper accepted! | That's Mathematics! I’m pleased to announce that Mathgen has had its first randomly-generated paper accepted by a reputable journal! On August 3, 2012, a certain Professor Marcie Rathke of the University of Southern North Dakota at Hoople submitted a very interesting article to Advances in Pure Mathematics, one of the many fine journals put out by Scientific Research Publishing. (Your inbox and/or spam trap very likely contains useful information about their publications at this very moment!) This mathematical tour de force was entitled “Independent, Negative, Canonically Turing Arrows of Equations and Problems in Applied Formal PDE”, and I quote here its intriguing abstract: Let \rho = A. The full text was kindly provided by the author and is available as PDF. After a remarkable turnaround time of only 10 days, on August 13, 2012, the editors were pleased to inform Professor Rathke that her submission had been accepted for publication. has been accepted. Bummer.
Social Science Research Network (SSRN) Home Page Les rhinos sauvés par les maths? « Sachant que le nombre de rhinocéros en liberté en Afrique du Sud avoisine les 20 000, que l’augmentation du braconnage suit une courbe exponentielle et que le prix de la corne atteint au marché noir 50 000 euros le kilo, vous répondrez à la question suivante : l'élevage intensif de rhinocéros dans des fermes et l'ouverture officielle d'un marché de la corne permettraient-ils: 1) de faire suffisamment chuter les prix pour décourager le braconnage, 2) de générer assez d'argent pour protéger et gérer les représentants de l’espèce en liberté dans les parcs nationaux? Vous tiendrez compte, dans vos projections du coût des mesures de protection et de lutte contre le braconnage ». Un MISG est un atelier de plusieurs jours, durant lequel chercheurs universitaires et étudiants travaillent en collaboration avec des représentants de l'industrie sur des problèmes de recherche appliquée à la réalité locale. L’exercice, pour le moment, n’en reste pas moins théorique. Catherine Vincent
Julia set A Julia set Three-dimensional slices through the (four-dimensional) Julia set of a function on the quaternions. The Julia set of a function f is commonly denoted J(f), and the Fatou set is denoted F(f).[1] These sets are named after the French mathematicians Gaston Julia[2] and Pierre Fatou[3] whose work began the study of complex dynamics during the early 20th century. Formal definition[edit] Let f(z) be a complex rational function from the plane into itself, that is, , where p(z) and q(z) are complex polynomials. the union of the Fi's is dense in the plane andf(z) behaves in a regular and equal way on each of the sets Fi. The last statement means that the termini of the sequences of iterations generated by the points of Fi are either precisely the same set, which is then a finite cycle, or they are finite cycles of circular or annular shaped sets that are lying concentrically. These sets Fi are the Fatou domains of f(z), and their union is the Fatou set F(f) of f(z). Examples[edit] For ). .
Unicity distance Consider an attack on the ciphertext string "WNAIW" encrypted using a Vigenère cipher with a five letter key. Conceivably, this string could be deciphered into any other string — RIVER and WATER are both possibilities for certain keys. This is a general rule of cryptanalysis: with no additional information it is impossible to decode this message. Of course, even in this case, only a certain number of five letter keys will result in English words. Trying all possible keys we will not only get RIVER and WATER, but SXOOS and KHDOP as well. Relation with key size and possible plaintexts[edit] In general, given any particular assumptions about the size of the key and the number of possible messages, there is an average ciphertext length where there is only one key (on average) that will generate a readable message. A tremendous number of possible messages, N, can be generated using even this limited set of characters: N = 26L, where L is the length of the message. Practical application[edit]
Catalog Page for PIA16075 This composite image, with magnified insets, depicts the first laser test by the Chemistry and Camera, or ChemCam, instrument aboard NASA's Curiosity Mars rover. The composite incorporates a Navigation Camera image taken prior to the test, with insets taken by the camera in ChemCam. The circular insert highlights the rock before the laser test. The square inset is further magnified and processed to show the difference between images taken before and after the laser interrogation of the rock. The test took place on Aug. 19, 2012. In the composite, the fist-sized rock, called "Coronation," is highlighted. The widest context view in this composite comes from Curiosity's Navigation Camera. Curiosity's Chemistry and Camera instrument (ChemCam) inaugurated use of its laser when it used the beam to investigate Coronation during Curiosity's 13th day after landing. ChemCam hit Coronation with 30 pulses of its laser during a 10-second period. ChemCam was developed, built and tested by the U.S.
Statistique multivariée Un article de Wikipédia, l'encyclopédie libre. En statistique, les analyses multivariées ont pour caractéristique de s'intéresser à la distribution conjointe de plusieurs variables. Les analyses bivariées sont des cas particuliers à deux variables. Les analyses multivariées sont très diverses selon l'objectif recherché, la nature des variables et la mise en œuvre formelle. Principales analyses[modifier | modifier le code] Méthodes descriptives[modifier | modifier le code] Méthodes explicatives[modifier | modifier le code] Voir aussi[modifier | modifier le code] Articles connexes[modifier | modifier le code] Portail des probabilités et de la statistique
After almost 20 years, math problem falls Mathematicians and engineers are often concerned with finding the minimum value of a particular mathematical function. That minimum could represent the optimal trade-off between competing criteria — between the surface area, weight and wind resistance of a car’s body design, for instance. In control theory, a minimum might represent a stable state of an electromechanical system, like an airplane in flight or a bipedal robot trying to keep itself balanced. There, the goal of a control algorithm might be to continuously steer the system back toward the minimum. For complex functions, finding global minima can be very hard. Almost 20 years later, researchers in MIT’s Laboratory for Information and Decision Systems have finally answered that question. Downhill from here On the first paper, Parrilo and Ahmadi were joined by John N. "If you take any textbook of optimization that we use to teach undergrads, it will typically start, 'Let the convex optimization be given,'" de Klerk says.
The Unreasonable Effectiveness of Mathematics in the Natural Sciences Reading Materials by R. W. HAMMING Reprinted From: The American Mathematical Monthly Volume 87 Number 2 February 1980 Prologue. Man, so far as we know, has always wondered about himself, the world around him, and what life is all about. Philosophy started when man began to wonder about the world outside of this theological framework. From these early attempts to explain things slowly came philosophy as well as our present science. Our main tool for carrying out the long chains of tight reasoning required by science is mathematics. Mathematicians working in the foundations of mathematics are concerned mainly with the self-consistency and limitations of the system. Once I had organized the main outline, I had then to consider how best to communicate my ideas and opinions to others. In some respects this discussion is highly theoretical. The inspiration for this article came from the similarly entitled article, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" [1.