Generalized Kac-Moody Algebras from CHL dyons

We provide evidence for the existence of a family of generalized Kac-Moody(GKM) superalgebras, G_N, whose Weyl-Kac-Borcherds denominator formula gives rise to a genus-two modular form at level N, Delta_{k/2}(Z), for (N,k)=(1,10), (2,6), (3,4), and possibly (5,2). The square of the automorphic form is the modular transform of the generating function of the degeneracy of CHL dyons in asymmetric Z_N-orbifolds of the heterotic string compactified on T^6. The new generalized Kac-Moody superalgebras all arise as different `automorphic corrections' of the same Lie algebra and are closely related to a generalized Kac-Moody superalgebra constructed by Gritsenko and Nikulin. The automorphic forms, Delta_{k/2}(Z), arise as additive lifts of Jacobi forms of (integral) weight k/2 and index 1/2. We note that the orbifolding acts on the imaginary simple roots of the unorbifolded GKM superalgebra, G_1 leaving the real simple roots untouched. We anticipate that these superalgebras will play a role in understanding the `algebra of BPS states' in CHL compactifications.Comment: LaTeX, 35 pages; v2: improved referencing and discussion; typos corrected; v3 [substantial revision] 44 pages, modularity of additive lift proved, product representation of the forms also given; further references adde

BKM Lie superalgebras from counting twisted CHL dyons

Following Sen[arXiv:0911.1563], we study the counting of (`twisted') BPS states that contribute to twisted helicity trace indices in four-dimensional CHL models with N=4 supersymmetry. The generating functions of half-BPS states, twisted as well as untwisted, are given in terms of multiplicative eta products with the Mathieu group, M_{24}, playing an important role. These multiplicative eta products enable us to construct Siegel modular forms that count twisted quarter-BPS states. The square-roots of these Siegel modular forms turn out be precisely a special class of Siegel modular forms, the dd-modular forms, that have been classified by Clery and Gritsenko[arXiv:0812.3962]. We show that each one of these dd-modular forms arise as the Weyl-Kac-Borcherds denominator formula of a rank-three Borcherds-Kac-Moody Lie superalgebra. The walls of the Weyl chamber are in one-to-one correspondence with the walls of marginal stability in the corresponding CHL model for twisted dyons as well as untwisted ones. This leads to a periodic table of BKM Lie superalgebras with properties that are consistent with physical expectations.Comment: LaTeX, 32 pages; (v2) matches published versio

Similarities and differences in curricula of a bachelor’s degree in oceanology at the universities in St Petersburg, Klaipeda, and Kaliningrad

Conducting a multi-aspect comparative analysis of curricula of bachelor’s degree programmes in oceanology offered at universities in St Petersburg, Klaipeda and Kaliningrad, the authors trace similarities between the existing variants of oceanologist training in the context of competence modules, disciplines, the so-called academic practices, and the number of hours and credits stipulated in the existing curricula. A formal comparison of generalised quantitative indicators without analysing the content of curriculum components demonstrated certain similarities in all indicators in terms of workload, the number of disciplines (50, 56 and 45) and academic practices. The clustering of competence modules and disciplines at each university within generalised academic areas - physics and mathematics, philosophy, informatics and computers, geoecology, measurement disciplines, etc. - made a more detailed comparison possible. The results of research demonstrate considerable similarities in the curricula used at the given universities in terms of all variants of comparison. The strongest similarity is observed in the areas of basic and professional disciplines

Reflection groups in hyperbolic spaces and the denominator formula for Lorentzian Kac--Moody Lie algebras

This is a continuation of our "Lecture on Kac--Moody Lie algebras of the arithmetic type" \cite{25}. We consider hyperbolic (i.e. signature $(n,1)$) integral symmetric bilinear form $S:M\times M \to {\Bbb Z}$ (i.e. hyperbolic lattice), reflection group $W\subset W(S)$, fundamental polyhedron \Cal M of $W$ and an acceptable (corresponding to twisting coefficients) set P({\Cal M})\subset M of vectors orthogonal to faces of \Cal M (simple roots). One can construct the corresponding Lorentzian Kac--Moody Lie algebra {\goth g}={\goth g}^{\prime\prime}(A(S,W,P({\Cal M}))) which is graded by $M$. We show that \goth g has good behavior of imaginary roots, its denominator formula is defined in a natural domain and has good automorphic properties if and only if \goth g has so called {\it restricted arithmetic type}. We show that every finitely generated (i.e. P({\Cal M}) is finite) algebra {\goth g}^{\prime\prime}(A(S,W_1,P({\Cal M}_1))) may be embedded to {\goth g}^{\prime\prime}(A(S,W,P({\Cal M}))) of the restricted arithmetic type. Thus, Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type is a natural class to study. Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type have the best automorphic properties for the denominator function if they have {\it a lattice Weyl vector $\rho$}. Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type with generalized lattice Weyl vector $\rho$ are called {\it elliptic}Comment: Some corrections in Sects. 2.1, 2.2 were done. They don't reflect on results and ideas. 31 pages, no figures. AMSTe

Regional geographic information systems of health and environmental monitoring

The article describes a new scientific and methodological approach to designing geographic information systems of health and environmental monitoring for urban areas. Geographic information systems (GIS) are analytical tools of the regional health and environmental monitoring; they are used for an integrated assessment of the environmental status of a large industrial centre or a part of it. The authors analyse the environmental situation in Voronezh, a major industrial city, located in the Central Black Earth Region with a population of more than 1 million people. The proposed research methodology is based on modern approaches to the assessment of health risks caused by adverse environmental conditions. The research work was implemented using a GIS and multicriteria probabilistic and statistical evaluation to identify cause-and-effect links, a combination of action and reaction, in the dichotomy "environmental factors - public health". The analysis of the obtained statistical data confirmed an increase in childhood diseases in some areas of the city. Environmentally induced diseases include congenital malformations, tumors, endocrine and urogenital pathologies. The main factors having an adverse impact on health are emissions of carcinogens into the atmosphere and the negative impact of transport on the environment. The authors identify and characterize environmentally vulnerable parts of the city and developed principles of creating an automated system of health monitoring and control of environmental risks. The article offers a number of measures aimed at the reduction of environmental risks, better protection of public health and a more efficient environmental monitoring

Homogenization of the equations of filtration of a viscous fluid in two porous media

A homogenized model of filtration of a viscous fluid in two domains with common boundary is deduced on the basis of the method of two-scale convergence. The domains represent an elastic medium with perforated pores. The fluid, filling the pores, is the same in both domains, and the properties of the solid skeleton are distinc

Problems and prospects of sugar beet cultivation in Kazakhstan (Changed title according to reviewers' comments)

Received: May 21st, 2023 ; Accepted: August 5th, 2023 ; Published: October 24th, 2023Purpose - to ensure the food security of Kazakhstan, domestic sugar industry should aim at a significant reduction in import dependence and transition to self-sufficiency. The share of domestic sugar from sugar beet in Kazakhstan is 7%. Design/methodology/approach - review indicating the main problems in the sugar beet production in Kazakhstan for the purpose of reimagining the domestic sugar beet industry to reduce dependence on sugar import. We analyzed the dynamics of sugar beet cultivation in Kazakhstan over the past 20 years and detected a sharp reduction in the sugar beet production. Findings - we have identified 10 problems in sugar beet production in Kazakhstan and determined the necessary targeted solutions. We consider the main direction to be the development of scientific methodology for sugar beet production (breeding of new highly productive disease-resistant cultivars, improvement of sugar beet protection system, efficient crop rotation). The most notable problems included in this paper are small-scale marketability of sugar beet farms, infectious diseases of sugar beet, water supply shortages, use of outdated agricultural technologies, high cost of imported sugar beet seeds. Originality/value - The present paper includes a full analysis of current problems in sugar beet production in Kazakhstan

Derivation of an averaged model of isothermal acoustics in a heterogeneous medium in the case of two different poroelastic domains

We consider some mathematical model of isothermal acoustics in a composite medium consisting of two different porous soils (poroelastic domains) separated by a common boundary. Each of the domains has its own characteristics of the solid skeleton; the liquid filling the pores is the same for both domain