Two-dimensional Id\`eles with Cycle Module Coefficients

We give a theory of id\`eles with coefficients for smooth surfaces over a field. It is an analogue of Beilinson/Huber's theory of higher ad\`eles, but handling cycle module sheaves instead of quasi-coherent ones. We prove that they give a flasque resolution of the cycle module sheaves in the Zariski topology. As a technical ingredient we show the Gersten property for cycle modules on equicharacteristic complete regular local rings, which might be of independent interest.Comment: major change in exposition, streamlined, removed incorrect claim about product map (many thanks to S. Gorchinskiy for pointing this out to me), bibliography update

Manufacture of Two-layers and Double-sided Iron Castings with Differential Structure and Properties

The paper proposes a new method of production of bilayer and double-sided castings with differentiated structure and properties using the technology of in-mold modification of the initial melt, smelted in a single melting furnace, which ensures formation of hard wear-resistant white iron as the working layer, and formation of ductile shock-resistant cast iron with nodular graphite as the core or the mounting part. Numerous laboratory studies confirm the feasibility of the proposed method and provide conditions ensuring differentiation of structure and properties in local parts or layers of castings. The prospects of the method for manufacturing a wide range of industrial castings are indicated

Implementation of the "hyperdynamics of infrequent events" method for acceleration of thermal switching dynamics of magnetic moments

For acceleration of the calculations of thermal magnetic switching, we report the use of the Voter method, recently proposed in chemical physics (also called "hyperdynamics of the infrequent events"). The method consists of modification of the magnetic potential so that the transition state remains unchanged. We have found that the method correctly describes the mean first passage time even in the case of small damping (precessional case) and for an oblique angle between the anisotropy and the field directions. Due to the costly evaluation of the lowest energy eigenvalue, the actual acceleration depends on its fast computation. In the current implementation, it is limited to intermediate time scale and to small system size

Compression Technologies of Graphic Information

The classification of types of information redundancy in symbolic and graphical forms representation of information is done. The general classification of compression technologies for graphical information is presented as well. The principles of design, tasks and variants for realizations of semantic compression technology of graphical information are suggested

Nonlinear gyrotropic vortex dynamics in ferromagnetic dots

The quasistationary and transient (nanosecond) regimes of nonlinear vortex dynamics in a soft magnetic dot driven by an oscillating external field are studied. We derive a nonlinear dynamical system of equations for the vortex core position and phase, assuming that the main source of nonlinearity comes from the magnetostatic energy. In the stationary regime, we demonstrate the occurrence of a fold-over bifurcation and calculate analytically the resonant nonlinear vortex frequencies as a function of the amplitude and frequency of the applied driving field. In the transient regime, we show that the vortex core dynamics are described by an oscillating trajectory radius. The resulting dynamics contain multiple frequencies with amplitude decaying in time. Finally, we evaluate the ranges of the system parameters leading to a vortex core instability (core polarization reversal)

Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki

These notes survey the main ideas, concepts and objects of the work by Shinichi Mochizuki on interuniversal Teichmüller theory [31], which might also be called arithmetic deformation theory, and its application to diophantine geometry. They provide an external perspective which complements the review texts [32] and [33]. Some important developments which preceded [31] are presented in the first section. Several important aspects of arithmetic deformation theory are discussed in the second section. Its main theorem gives an inequality–bound on the size of volume deformation associated to a certain log-theta-lattice. The application to several fundamental conjectures in number theory follows from a further direct computation of the right hand side of the inequality. The third section considers additional related topics, including practical hints on how to study the theory