‘Demazure roots of a convex cone or a fan of cones form a remarkable combinatorial structure that originated in the work of the French mathematician Michel Demazure in 1970. Demazure’s work marked the beginning of a new branch of mathematics—toric geometry!’ explains Ivan Arzhantsev. ‘Each root defines a one-parameter subgroup! making it possible to describe the symmetry group of a complete toric manifold. Despite the rapid development of toric geometry! the root construction was forgotten for some time and was rediscovered in the 2010 dissertation of Chilean mathematician Alvaro Liendo.
Over the past Digital watermarking 15 years
involvement of our research group! this construction has been significantly advanced and applied to numerous problems in modern algebra and algebraic geometry. While indonesia phone number library preparing the application! we analysed all existing work and developed a three-year plan to advance our understanding of the structure of symmetry groups of algebraic varieties.
The Russian Science Foundation’s support for the project indicates that it has received high scores from experts! which is extremely important to us. It also means that over submit the new site to search engines the next three years! we must publish 12 articles in top-tier journals—an excellent incentive for further development. We have the maximum allowed team of ten members! all of whom are enthusiastic early-career mathematicians! so we are confident we will succeed. We have also committed to preparing an overview of Demazure roots! and we will fulfil this promise as well.’
The project titled ‘Methods for Embedding
Digital Watermarks in Multimedia Data Using Soft Computing and Noise-Resistant Coding’ focuses on developing new solutions for protecting multimedia data! such as digital be numbers images and videos! according to Evsyutin. ‘The solutions to be developed in the course of the project aim to combat the illegal distribution! forgery! and misattribution of authorship of images and videos!’ explains the head of the project. ‘Given the widespread use of images and videos! these tasks in the field of cybersecurity are highly relevant! particularly in areas such as digital art! advertising! and the media.