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

The mean meridional circulation and midlatitude ozone buildup

International audienceThe wintertime ozone buildup over the Northern Hemisphere (NH) midlatitudes and its connection with the mean meridional circulation in the stratosphere are examined statistically on a monthly basis from October to March (1980?2002). The ozone buildup begins locally in October with positive total ozone tendencies over the North Pacific, which spread eastward and westward in November and finally cover all midlatitudes in December. The local onset of the buildup in October is not evident in zonal mean ozone tendency, which is close to zero. From November to March, zonal mean total ozone tendency (50°?60° N) shows a strong correlation (|r|=0.7) with several zonal mean parameters associated to the mean meridional circulation, namely: eddy heat flux, temperature tendency, the vertical residual velocity and the residual streamfunction. At the same time, on the latitude-altitude cross section, correlation patterns between ozone tendency and widely used eddy heat flux are not uniform during winter. The strongest correlations are located equatorward (almost throughout the stratosphere) or poleward (only in the lower stratosphere) of the edge of the polar vortex. Such distribution may depend on the existence of the midlatitude and polar waveguides which defined refraction of upward propagating waves from the troposphere either to the midlatitude stratosphere or to the polar stratosphere. As a consequence of the nonuniform correlation patterns, heat flux averaged over the common region 45°?75° N, 100 hPa is not always an optimum proxy for statistical models describing total ozone variability in midlatitudes. Other parameters approximating the strength of the mean meridional circulation have more uniform and stable correlation patterns with ozone tendency during winter. We show that the NH midlatitude ozone buildup has a stable statistical relationship with the mean meridional circulation in all months from October to March and half of the interannual variability in monthly ozone tendencies can be explained by applying different proxies of the mean meridional circulation

Predicting the effects of climate change on Schistosoma mansoni transmission in eastern Africa

Background: Survival and fitness attributes of free-living and sporocyst schistosome life-stages and their intermediate host snails are sensitive to water temperature. Climate change may alter the geographical distribution of schistosomiasis by affecting the suitability of freshwater bodies for hosting parasite and snail populations. Methods: We have developed an agent-based model of the temperature-sensitive stages of the Schistosoma mansoni and intermediate host snail lifecycles. The model was run using low, moderate and high warming climate projections over eastern Africa. For each climate projection, eight model scenarios were used to determine the sensitivity of predictions to different relationships between air and water temperature, and different snail mortality rates. Maps were produced showing predicted changes in risk as a result of increasing temperatures over the next 20 and 50 years. Results Baseline model output compared to prevalence data indicates suitable temperatures are necessary but not sufficient for both S. mansoni transmission and high infection prevalences. All else being equal, infection risk may increase by up to 20% over most of eastern Africa over the next 20 and 50 years. Increases may be higher in Rwanda, Burundi, south-west Kenya and eastern Zambia, and S. mansoni may become newly endemic in some areas. Results for 20-year projections are robust to changes in simulated intermediate host snail habitat conditions. There is greater uncertainty about the effects of different habitats on changes in risk in 50 years’ time. Conclusions: Temperatures are likely to become suitable for increased S. mansoni transmission over much of eastern Africa. This may reduce the impact of control and elimination programmes. S. mansoni may also spread to new areas outside existing control programmes. We call for increased surveillance in areas defined as potentially suitable for emergent transmission

NEURAL NETWORK MODELING AND OPTIMISING OF THE AGGLOMERATION PROCESS OF SULPHIDE POLYMETALLIC ORES

During the operation of the lead-zinc production while processing of polymetallic ores, problems arose related to the quality of products and the efficient use of equipment – agglomeration furnace and crushing apparatus. Previously, such issues were resolved due to the experiences and based on mathematical modeling of processes. The mathematical model for optimizing unnecessary such operating mode is a difficult program. Performing calculations is required a fairly large investment of time and resources. Therefore, the program of the mathematical model for optimizing the operating mode of the agglomeration furnace and the crushing device for sinter firing was replaced with a neural network by implementing the process of training the network based on the results of calculations on a mathematical model. The results obtained showed that neural network models were more accurate than mathematical models, which made it possible to solve production optimization problems of great complexity. The use of neural networks for modeling technological processes has made it possible to increase the efficiency of product quality control systems and automatic control systems for the roasting of sulfide polymetallic ores

Formation of conserved charge at the de Sitter space

The article considers a new mechanism of charge accumulation in the early Universe in theories with compact extra dimensions. The relaxation processes in the extra space metric that take place during its formation lead to the establishment of symmetrical extra space configuration. As a result, the initial accumulation of the number associated with the symmetry occurs. We demonstrate this mechanism using a simple example of a two-dimensional apple-like extra space metric with $U(1)$-symmetry. The conceptual idea of the mechanism can be used to develop a model for the production of the baryon or lepton number in the early Universe.Comment: 9 pages, 3 figure