Soulskill, Slashdot, Kazakh Professor Claims Solution of Another Millennium Prize Problem, here. Did time as a first year grad student in the Navier Stokes mines, coding and debugging (mostly debugging) numerical PDE solver schemes for Wavy Vortex flow on an IBM mainframe. Can’t parse the paper in Russian though. I hope Tao can read Russian, otherwise confirmation could take a while.
An anonymous reader writes “Kazakh news site BNews.kz reports that Mukhtarbay Otelbaev, Director of the Eurasian Mathematical Institute of the Eurasian National University, is claiming to have found the solution to another Millennium Prize Problems. His paper, which is called ‘Existence of a strong solution of the Navier-Stokes equations’ and is freely available online (PDF in Russian), may present a solution to the fundamental partial differentials equations that describe the flow of incompressible fluids for which, until now, only a subset of specific solutions have been found.
Otelbaev M., EXISTENCE OF A STRONG SOLUTION OF THE NAVIER-STOKES EQUATION, here. 100+ pages and last page is in English. Confirmation complexity compared to ABC Conjecture should be a layup, unless of course the result depends on InterUniversal Teichmuller Theory. How do you say “InterUniversal Teichmuller Theory” in Russian? Here is an earlier publication M. Otelbaev et. al. 2006, in English – Existence Conditions for a Global Strong Solution to One Class of Nonlinear Evolution Equations in a Hilbert Space, here.
otelbaev.com, Activities, here. Work summary.
His main works are grouped around the following fields:
I. Spectral theory of differential operators.
M. Otelbaev developed new methods for studying the spectral properties of differential operators, which are the result of a consistent and skilled implementation of the general idea of the localization of the problems under consideration. In particular, he invented a construction of averaging coefficients well describing those features of their behaviour which influence the spectral properties of a differential operator. This construction known under the name made it possible to answer many of the hitherto open questions of the spectral theory of the Schrödinger operator and its generalizations.
The function and its different variants have a number of remarkable properties, which allowed to apply this function to a wide range of problems. Here we note some problems for the first time solved by M. Otelbaev by using the function on the basis of sophisticated analysis of the properties of differential operators.
1) A criterion for belonging of the resolvent of the Schrödinger type operator with a non-negative potential to the class was found (previously only a criterion for belonging to was known) and two-sided estimates for the eigenvalues of this operator were obtained with the minimal assumptions of the smoothness of the coefficients.
2) The general localization principle was proved for the problems of selfadjointness and of the maximal dissipativity (simultaneously with the American mathematician P. Chernov) which provided significant progress in this area.
3) Examples were given showing the classical Carleman-Titchmarsh formula for the distribution function of the eigenvalues of the Sturm-Liouville operator is not always correct even in the class of monotonic potentials and a new formula was found valid for all monotonic potentials .
4) The following result of M. Otelbaev is principally important: for there is no universal asymptotic formula.
5) From the time of Carleman, who found the asymptotics for and, by using it, the asymptotics of the eigenvalues themselves, all mathematicians started with finding the asymptotics for and as a result they could not get rid of the so-called Tauberian conditions. M. Otelbaev was the first who, when looking for the asymptotics of the eigenvalues, omitted the interim step of finding the asymptotics for , which allowed getting rid of all non-essential conditions for the problem including Tauberian conditions.
6) The two-sided asymptotics for for the Dirac operator was for the first time found when and are not equivalent.
The results of M. Otelbaev on the spectral theory were included as separate chapters in the monographs of B.M .Levitan and I.S. Sargsyan “ Sturm-Liouville and Dirac operators» (Moscow: Nauka, 1985), and of A.G. Kostyuchenko and I.S. Sargsyan «Distribution of eigenvalues» (Moscow: Nauka, 1979), which became classical
Tyler Durden, Zerohedge, How Twitter Algos Determine Who Is Market-Moving And Who Isn’t, here.
Now that even Bridgewater has joined the Twitter craze and is using user-generated content for real-time economic modelling, and who knows what else, the scramble to determine who has the most market-moving, and actionable, Twitter stream is on. Because with HFT algos having camped out at all the usual newswire sources: Bloomberg, Reuters, Dow Jones, etc. the scramble to find a “content edge” for market moving information has never been higher. However, that opens up a far trickier question: whose information on the fastest growing social network, one which many say may surpass Bloomberg in terms of news propagation and functionality, is credible and by implication: whose is not? Indeed, that is the $64K question. Luckily, there is an algo for that.