THE MAIN DIRECTIONS OF RUSSIA'S TRANSITION TO THE DIGITAL ECONOMY

The article emphasizes the importance of Russia's transition to a digital economy to ensure the techno-logical independence of Russia, as well as to accelerate the development of all spheres of the economy. Risks and problems of digitalization are considered, and in addition, the main directions that were formulated in the federal projects of the national program "Digital Economy".

Logical independence, its algebraic generalization and applications

We present a short history of the notion of logical independence, its counterpart and gen-eralization in universal algebra, and their applications in different areas.

Comparison of some solution concepts for linear first-order hyperbolic differential equations with non-smooth coefficients

We discuss solution concepts for linear hyperbolic equations with coefficients of regularity below Lipschitz continuity. Thereby our focus is on theories which are based either on a generalization of the method of characteristics or on refined techniques concerning energy estimates. We provide a series of examples both as simple illustrations of the notions and conditions involved but also to show logical independence among the concepts.

PLANCK FLUCTUATIONS, MEASUREMENT UNCERTAINTIES AND THE HOLOGRAPHIC PRINCIPLE

Starting from a critical analysis of recently reported surprisingly large uncertainties in length and position measurements deduced within the framework of quantum gravity, we embark on an investigation both of the correlation structure of Planck scale fluctuations and the role the holographic hypothesis is possibly playing in this context. While we prove the logical independence of the fluctuation results and the holographic hypothesis (in contrast to some recent statements in that direction) we show that by combining these two topics one can draw quite strong and interesting conclusions about the details of the fluctuation structure and the microscopic dynamics on the Planck scale. We further argue that these findings point to a possibly new and generalized form of quantum statistical mechanics of strongly (anti)correlated systems of degrees of freedom in this fundamental regime.