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The results of 8-variable column experiment on a strongly acidic sod-podzolic sandy loam reclaimed by the finely ground dolomite in a wide dose range are presented. The aim of the research was to measure and estimate leaching of magnesium (Mg) and its migration pattern. The dolomite powder at the different doses calculated by hydrolytic acidity (Hy) was applied at 225, 337.5, 450, 675, 900, 1350 and 1800 mg, that corresponded to 0.5, 0.75, 1.0, 1.5, 2.0, 3.0 and 4.0 Hy, respectively. The migratory ability of Mg was studied in 12-times washing column experiment. Each washing was carried out by 400 ml distilled water, simulating the volume of annual precipitation percolating through the soil stratum yearly. The increase in the amount of leaked moisture contributed to the enhancement of the eluvial losses of Mg. The maximum loss of Mg due to migration was established in the filtrates of the first washing. As the dose of dolomite increased, the amount of the soil Mg migrating with the total amount of Mg decreased from 27% to 7.5%. Complete removal of water-soluble Mg from the soil was not achieved in any of the studied treatments. Applied empirical estimations correctly described the process of leaching of Mg during repeated washing of the soil. Based on the data on the amount of leached Mg from soil reclaimed by a wide range of dolomite doses, a clustering of the empirical equations was performed. It was shown that in the 1 st stage of the experiment (from 1 to 4 washings) the rate of Mg leaching increased significantly with an increase in the dose of the dolomite. In the 2 nd stage (4 to 12 washings) such a pattern was not established. Depending on the dolomite dose applied, the losses of Mg increased from 14.05 to 50.6 mg compared to 3.8 mg in the non-limed (control) treatment. The main finding is that finely ground dolomite in an amount exceeding a full dose calculated by 1 Hy applied to sod-podzolic forest soil resulted in unproductive losses of Mg, i.e., with increasing dolomite dose, the losses of Mg increased.

This paper presents an algorithm of hub number p robustness estimation using specific simulations in the single allocation hub location problem. The simulation has to model the service demand trends in each origin node to each destination node. This idea is based on the hub network dependence on service demand forecasting, which is modeled by random values from random distribution with parameters reflecting the demand changes. The algorithm includes the mixed integer programming model which describes the hub location-allocation problem with single allocation (each node is connected exactly to one hub). The model chooses the optimal locations for the fixed number of hubs p from the fixed possible location set in the problem. The perturbed data simulate the changes in the service need and present the perspectives of the network changes, and the algorithm fixes these changes. The number of changes in the network is consolidated into the variety frequencies which describe the variabilities in the set of simulations. The algorithm is implemented on Python 3.5 and model optimization is fulfilled using Gurobi Optimizer 7.0.1 software. The results in the real dataset are illustrated and discussed. Refs 18. Fig. 1. Tables 3.

Санкт-Петербургский государственный университет, Российская Федерация, 199034, Санкт-Петербург, Университетская наб., 7-9 В данной статье предлагается модель, которая является обобщением классической модели Маки-Томпсона и стохастической модели Дэйли-Кендалла. Вводится новый параметр для оценки вероятности распространения слухов. Обобщенная модель формулируется и рассматривается в непрерывном времени. Процесс распространения слухов описывается системой линейных дифференциальных уравнений. Строится общее решение для динамики распространения слухов. Приводятся численные примеры. Библиогр. 13 назв. Ил. 2. Табл. 2. Ключевые слова: информационные сети, дифференциальные уравнения, вероятность, распространение слухов. V. V. Karelin, V. M. Bure, M. V. Svirkin GENERALIZED MODEL OF INFORMATION SPREADING IN CONTINUOUS TIME St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian FederationThe diffusion of information or spreading of rumours is a social phenomenon and plays a significant role in a daily life. Rumours play a very important role in social life and have existed as a social fact since ancient times. The rumour model explains the spread of rumours and serves as a tool for understanding this social phenomenon. Rumours in economics have become more intensively discussed and investigated in recent decades. There are examples of rumour dynamics based on communication and exchange at auctions, in the stock markets and during trading. These backgrounds and motivations give the basis for a mathematical model of the diffusion of information or the spreading of rumours. We give a model that is a generalization of the classical Maki-Thompson model and the stochastic Daley-Kendall model of rumour spreading using the probability approach. A new parameter is suggested for the probability of rumour spreading. The generalized model is formulated and is considered in continuous time. The process of spreading rumours is described by a system of linear differential equations. The general solution for dynamics of spreading of rumours is constructed. Refs 13. Figs 2. Tables 2.

There are many problems associated with the prediction of the spatial distribution of ecological parameters. In this paper as an example the detection of plant nitrogen status with aerial photos is considered. An accurate prediction of plant nutritional needs during the growing period is necessary for the efficient use of fertilizers, low yields and high quality products. A method of this problem solution is based on the analysis of the optical characteristics of the plants on digital images. To improve this method, a module responsible for automatic construction of calibration curves for the quantitative assessment of plant nitrogen status was developed.

The hub location-allocation problem under uncertainty is a real-world task arising in the areas such as public and freight transportation and telecommunication systems. In many applications, the demand is considered as inexact because of the forecasting inaccuracies or human's unpredictability. This study addresses the robust uncapacitated multiple allocation hub location problem with a set of demand scenarios. The problem is formulated as a nonlinear stochastic optimization problem to minimize the hub installation costs, expected transportation costs and expected absolute deviation of transportation costs. To eliminate the nonlinearity, the equivalent linear problem is introduced. The expected absolute deviation is the robustness measure to derive the solution close to each scenario. The robust hub location is assumed to deliver the least costs difference across the scenarios. The number of scenarios increases size and complexity of the task. Therefore, the classical and improved Benders decomposition algorithms are applied to achieve the best computational performance. The numerical experiment on CAB and AP dataset presents the difference of resulting hub networks in stochastic and robust formulations. Furthermore, performance of two Benders decomposition strategies in comparison with Gurobi solver is assessed and discussed.