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The use of low-temperature heat of industrial and natural origin for heating the soil in greenhouses allows practitioners to get very early vegetable and berry crops. The paper suggests a mathematical model of greenhouse heat exchange with a system of soil surface heating for substantiating the system structure and its efficiency in different conditions. The solution of the mathematical model was performed using the method of least squares in COMSOL Multiphysics software. The comparison of the results of experimental studies with the results of mathematical modelling revealed that the proposed mathematical model with a high degree of reliability allows predicting the thermal regime in greenhouses with surface soil heating using cover sleeves.

The aim of the present study was to substantiate theoretically and to test in practice scheme of multi-environment trials at the final stage of spring barley breeding process and to distinguish the genotypes which combine superior yield performance and stability. In the first year of competitive testing (2015) nine promising spring barley breeding lines have been selected under condition of the Central part of Forest-Steppe of Ukraine (latitude 49°64′, longitude 31°08′, altitude 153 m). In 2016 and 2017, the genotypes were additionally tested in two other different agro-climatic zones of Ukraine: Polissia (latitude 50°93′, longitude 31°69′, altitude 126 m) and Northern Steppe (latitude 48°56′, longitude 32°32′, altitude 171 m). In addition to the standard variety Vzirets, the breeding lines were compared with ten widespread spring barley varieties in agricultural production. Significant total yield variability of the genotypes and cross-over genotype by environment interaction has been revealed. It confirmed the validity of proposed combination of spatial (zones) and temporal (years) gradients for more efficient evaluation of the genotype by environment interaction and differentiation of genotypes in terms of yield performance and stability. As a practical result, using additive main effects and multiplicative interaction (AMMI) and genotype main effects plus genotype by environment interaction (GGE) models, four spring barley breeding lines with combination of superior yield performance and high stability have been identified.