A note on the Gannon–Lee theorem

We prove a Gannon–Lee theorem for non-globally hyperbolic Lorentzian metrics of regularity $$C^1$$ C 1 , the most general regularity class currently available in the context of the classical singularity theorems. Along the way, we also prove that any maximizing causal curve in a $$C^1$$ C 1 -spacetime is a geodesic and hence of $$C^2$$ C 2 -regularity.

Role of Recovery in Evolving Protection against Systemic Risk: A Mechanical Perspective in Network-Agent Dynamics

We propose a model of evolving protection against systemic risk related to recovery. Using the failure potential in network-agent dynamics, we present a process-based simulation that provides insights into alternative interventions and their mechanical uniqueness. The fundamental operating principle of this model is that computation allows greater emphasis on optimizing the recovery within the general regularity of random network dynamics. The rules and processes that are used here could be regarded as useful techniques in systemic risk measurement relative to numerical failure reduction analyses.

Transformation of cenomorphs of grass-dwarf-shrub layer of forest phytocenoses of Zhytomyr Polissya after surface fires

Transformation of cenomorphs of grass-dwarf-shrub layer of forest phytocenoses of Zhytomyr Polissya after surface fires was analyzed in forest ecological types A2, A3, B2, B3, B4, C2. It was shown that the cenomorph spectrum of grass-dwarf-shrub layer after surface fires essentially transforms. In all investigated forest ecological types after forest fires number of cenomorphs increased.It was made a conclusion that the general regularity after surface fires in this layer was an essential decreasing of part of typical forest species — sylvants and sylvants-pratants in species composition of the layer, and increasing of relative part of pratants, entering of ruderants.

Influence of Climatic Conditions on Western Siberian Forest Fires

Current climate changes in Russia are attended by the increase in frequency of dangerous weather events. This chapter researches long-term variations of the dangerous weather's events on Western Siberia and to reveal general regularity, which can be associated with forest fires. The researches have been carried out for the territories of southeast of Western Siberia. The duration of the fire season increases due to climate change. This is due both to the earlier snowfall and the onset of the phenological spring, and to the increase in the duration of the thunderstorm period. Thunderstorms in Siberia are a much more frequent cause of forest fires (28%) than in other territories. Wildfire frequency is correlated with air temperature and drought anomalies.

Development of Simplified Procedures in Civilistic Process in the Context of Legislative Reforms

The article is devoted to the problems connected with the unification of a number of judicial procedural and non-procedural codes of practice in modern civilistic process of Russia. These problems are reviewed in terms of ontology, taking into account new legislative statutes of 2018-2019. Unification and differentiation of judicial procedures is a twin-track trend of the civilistic process, stemming from globalization of the procedural in the 21st century. At the same time, the general regularity is achieved in different ways depending on the type of process and its national realisation. The judicial procedures, which have a structural specificity in relation to the general, “extended” judicial procedure within the civilistic procedural form, cannot be reduced to simplified procedures and simplification of the process only, but rather these procedures testify to the complication of the civilistic process. This article substantiates the thesis that an increase in the coefficient of applied efficiency of the civilistic process can only be implemented through reaching a balance of private law and public law in judicial procedures. The conclusions regarding the essence of court procedures and the methodology of their application in the procedural law are meaningful as regards lawmaking and law enforcement activities

Analysis of a hybridizable discontinuous Galerkin method for the Maxwell operator

In this paper, we study a hybridizable discontinuous Galerkin (HDG) method for the Maxwell operator. The only global unknowns are defined on the inter-element boundaries, and the numerical solutions are obtained by using discontinuous polynomial approximations. The error analysis is based on a mixed curl-curl formulation for the Maxwell equations. Theoretical results are obtained under a more general regularity requirement. In particular for the low regularity case, special treatment is applied to approximate data on the boundary. The HDG method is shown to be stable and convergence in an optimal order for both high and low regularity cases. Numerical experiments with both smooth and singular analytical solutions are performed to verify the theoretical results.

Numerical approximations of McKean anticipative backward stochastic differential equations arising in initial margin requirements

We introduce a new class of anticipative backward stochastic differential equations with a dependence of McKean type on the law of the solution, that we name MKABSDE. We provide existence and uniqueness results in a general framework with relatively general regularity assumptions on the coefficients. We show how such stochastic equations arise within the modern paradigm of derivative pricing where a central counterparty (CCP) requires the members to deposit variation and initial margins to cover their exposure. In the case when the initial margin is proportional to the Conditional Value-at-Risk (CVaR) of the contract price, we apply our general result to define the price as a solution of a MKABSDE. We provide several linear and non-linear simpler approximations, which we solve using different numerical (deterministic and Monte-Carlo) methods.

The chemical composition of ice and water under ice of Lake Onega (the case of Petrozavodsk Bay)

Data on the content of ions, nutrients and organic substance in snow on the ice as well as in the ice and water under ice in the Petrozavodsk Bay and Central part of Onega Lake (March 2017) as well as in the snow cover on the Petrozavodsk Bay shore (2008–2017) are presented. In areas of the Petrozavodsk Bay experiencing anthropogenic and natural impacts, chloride ions prevail among anions in crystallo-hydrates, while sulphate ions are prevalent at the exit from the Bay and in the central part of the lake (clean water). The water under ice has a bicarbonate-calcium composition. Among the inorganic forms of nitrogen compounds (NH4+, NO2, NO3) ammonium ions prevail in the ice(70%), while in snow and the water under ice the prevalent are nitrate ions and organic nitrogen. The content of nitrogen compounds and mineral and total phosphorus is increased in the upper layer of ice. Note, that chemical composition of ice cover is formed by both, a water under the ice and atmospheric precipitation. To determine intensity of involvement of dissolved substances to the ice in combination with ice-forming water, the coefficient of involvement Kv was used. As is shown by our studies, value of the involvement index Kv is individual for each chemical component, however a certain general regularity is observed. Thus, the not proportional relations between contents of ammonium and phosphate ions in ice and water under ice were noticed. The increased involvement indices of NH4+and РО43−into the ice from the water under ice seem to be due to the high rate of migration of these ions together with detachment of them from organic matter molecules.

THE HISTORY OF FORMATION OF ENTOMOLOGICAL COLLECTIONS IN THE MUSEUMS OF KEMEROVO REGION

Collections of insects in the museums are a part of natural heritage. Their preservation presents complexity, but is relevant for scientific, educational and exposition tasks. The history of entomological researches in the territory of Kemerovo region is described, the problem of discrepancy of data in references on stories of collecting entomological material to the maintenance of museum entomological collections in the region is analyzed.The generalizing research on existence and history of completing of entomological collections in the Region’s museums was never carried out earlier. 6 museums with such materials, the collections of the Department of Zoology and Ecology of Kemerovo State University and a number of private collections were revealed. Also detailed description of large collections of Kemerovo State University (materials of the Museum, the Department of Zoology and Ecology) and the Kemerovo Regional Museum of Local Lore is provided for the first time. The example of particular collections allowed observing the general regularity of merge of private collections with museum funds. Unambiguous leadership of of Kemerovo State University collections in quantity of units of storage and their importance is established. They are actively used and involved in research, educational, exposition and exhibition life of the University and the Region (with active support of private collections).