Singly generated quasivarieties and residuated structures

A quasivariety K of algebras has the joint embedding property (JEP) iff it is generated by a single algebra A. It is structurally complete iff the free countably generated algebra in K can serve as A. A consequence of this demand, called "passive structural completeness" (PSC), is that the nontrivial members of K all satisfy the same existential positive sentences. We prove that if K is PSC then it still has the JEP, and if it has the JEP and its nontrivial members lack trivial subalgebras, then its relatively simple members all belong to the universal class generated by one of them. Under these conditions, if K is relatively semisimple then it is generated by one K-simple algebra. It is a minimal quasivariety if, moreover, it is PSC but fails to unify some finite set of equations. We also prove that a quasivariety of finite type, with a finite nontrivial member, is PSC iff its nontrivial members have a common retract. The theory is then applied to the variety of De Morgan monoids, where we isolate the sub(quasi)varieties that are PSC and those that have the JEP, while throwing fresh light on those that are structurally complete. The results illuminate the extension lattices of intuitionistic and relevance logics

Evaluation of siltation of rivers with intensive economic development of watersheds

In regions with a high degree of agricultural development with an active development of erosion processes and the critical level of degradation of the river network to which the Middle-Russian Upland belongs, the evaluation of sedimentation for various combinations of natural and economic conditions becomes an immediate proble

Geographic Information System and Geoportal "River basins of the European Russia"

The geoinformation system (GIS) and Geoportal with open access "River basins of the European part of Russia" were introduced. The GIS includes the results of spatial analysis and modeling, in particular, the assessment of anthropogenic impact on river basins; estimates of water flow and precipitation; climatic, geomorphological and landscape zoning of the European part of Russi

METHODOLOGICAL APPROACH TO CONDUCTING CORPORATE TECHNOLOGICAL FORESIGHT AND AN EXAMPLE OF ITS USE FOR A COMPANY IN THE OIL AND GAS SECTOR OF RUSSIA

A methodological approach for conducting a technological foresight at the corporate level has been proposed. A corporate foresight based on general methodological approaches used in world practice should take into account a number of additional factors imposed by the specifics of the industry and organization in order to obtain a list of priority technologies and technological directions relevant to the company’s activities. Methodological approach is based on the concept “Markets-Trends-Technologies”. Global markets research allows us to determine key problems and trends of society evolution in economic, social, political and other arears. The transition to the corporate level is carried out by identifying trends in the company’s industry. The methodology have described in detail the methods of attracting experts to assess the power of mutual influence of trends and technologies. The results of the assessment can be used for subsequent technological mapping in scientific and technical forecasting and strategic planning

Vibrational spectroscopy of GdCr3(BO3)4: Quantitative separation of crystalline phases

This work is devoted to the investigation of GdCr3(BO3)4 crystals by the method of infrared spectroscopy. Incongruently melting borate GdCr3(BO3)4 was obtained as a result of spontaneous crystallization. Crystal structures were identified by the method of infrared spectroscopy. Ab initio calculations in the frame of density functional theory enabled us to separate modes belonging to the R32 and C2/c phases and to estimate the ratio of these phases in GdCr3(BO3)4 crystals. We have found that the content of the rhombohedral R32 (non- centrosymmetric) modification is about 85%. © Published under licence by IOP Publishing Ltd

Spontaneous vacuum decay in low-energy collisions of heavy nuclei beyond the monopole approximation

The problem of spontaneous vacuum decay in low-energy collisions of heavy nuclei is considered beyond the scope of the monopole approximation. The time-dependent Dirac equation is solved in a rotating coordinate system with $z$-axis directed along the internuclear line and the origin placed at the center of mass. The probabilities of electron-positron pair creation and the positron energy spectra are calculated in the approximation neglecting the rotational coupling. The two-center potential is expanded over spherical harmonics and the convergence with respect to the number of terms in this expansion is studied. The results show that taking into account the two-center potential instead of its spherically symmetric part preserves all the signatures of the transition to the supercritical regime that have been found in the framework of the monopole approximation and even enhances some of them.Comment: 7 pages, 4 figures, 1 tabl

Scalable stellar evolution forecasting: Deep learning emulation vs. hierarchical nearest neighbor interpolation

Many astrophysical applications require efficient yet reliable forecasts of stellar evolution tracks. One example is population synthesis, which generates forward predictions of models for comparison with observations. The majority of state-of-the-art population synthesis methods are based on analytic fitting formulae to stellar evolution tracks that are computationally cheap to sample statistically over a continuous parameter range. Running detailed stellar evolution codes, such as MESA, over wide and densely sampled parameter grids is prohibitively expensive computationally, while stellar-age based linear interpolation in-between sparsely sampled grid points leads to intolerably large systematic prediction errors. In this work, we provide two solutions of automated interpolation methods that find satisfactory trade-off points between cost-efficiency and accuracy. We construct a timescale-adapted evolutionary coordinate and use it in a two-step interpolation scheme that traces the evolution of stars from zero age main sequence all the way to the end of core helium burning while covering a mass range from ${0.65}$ to $300 \, \mathrm{M_\odot}$. The feedforward neural network regression model (first solution) that we train to predict stellar surface variables can make millions of predictions, sufficiently accurate over the entire parameter space, within tens of seconds on a 4-core CPU. The hierarchical nearest neighbor interpolation algorithm (second solution) that we hard-code to the same end achieves even higher predictive accuracy, the same algorithm remains applicable to all stellar variables evolved over time, but it is two orders of magnitude slower. Our methodological framework is demonstrated to work on the MIST data set. Finally, we discuss prospective applications and provide guidelines how to generalize our methods to higher dimensional parameter spaces.Comment: Submitted to A&

Weakly-nonlocal Symplectic Structures, Whitham method, and weakly-nonlocal Symplectic Structures of Hydrodynamic Type

We consider the special type of the field-theoretical Symplectic structures called weakly nonlocal. The structures of this type are in particular very common for the integrable systems like KdV or NLS. We introduce here the special class of the weakly nonlocal Symplectic structures which we call the weakly nonlocal Symplectic structures of Hydrodynamic Type. We investigate then the connection of such structures with the Whitham averaging method and propose the procedure of "averaging" of the weakly nonlocal Symplectic structures. The averaging procedure gives the weakly nonlocal Symplectic Structure of Hydrodynamic Type for the corresponding Whitham system. The procedure gives also the "action variables" corresponding to the wave numbers of $m$-phase solutions of initial system which give the additional conservation laws for the Whitham system.Comment: 64 pages, Late