A theoretical framework for environmental impact assessment of economic activity is formulated by using methods of mathematical modeling and thematic mapping. Theoretically, environment is considered as a surface of variety (manifold), linking various factors and conditions. Tangential planes to the surface correspond to any natural systems (ecosystems), individual according to their connections with the environment (points of tangency). An example of the display of the environmental variety is provided by landscape-typological maps of a territory. The equation of the plane specifies connections of factor parameters of ecosystems by taking into account their shift relative to environmental coordinates of these reference points. Different types of systemic interpretations of these equations (types of models) are formed with various quantitative criteria for change of in environmental status, such as the measures of responsibility and effectiveness of decisions made. Environmental impact assessment methods generally estimate changes in the state of natural systems rather than the transformation of their environment. Therefore, methods of distinguishing relevant indicators and selecting the characteristic features of their controlled changes are suggested. The antisymmetry of variability and stability is naturally discernible from the factors and conditions of economic activity, which is demonstrated by modeling the impact of economic processes on the environmental status: an assessment was made of the influence of the size of gross regional product on amounts of atmospheric emissions of pollutants as well as of waste water discharges on human health. The findings can be used in developing methods of mathematical modeling of the relationships between the ecological, economic and social blocks of territorial systems in order to solve problems of thematic mapping and seek optimal solutions in the field of environmental management.

中文翻译：

---

经济活动的环境影响评估：建模和绘图问题

运用数学建模和专题制图的方法，制定了经济活动环境影响评价的理论框架。理论上，环境被认为是多样性（流形）的表面，连接着各种因素和条件。表面的切平面对应于任何自然系统（生态系统），根据它们与环境的连接（切点）而不同。一个领土的景观类型图提供了环境多样性显示的一个例子。平面方程通过考虑它们相对于这些参考点的环境坐标的偏移来指定生态系统因素参数的连接。这些方程的不同类型的系统解释（模型类型）形成了环境状态变化的各种定量标准，例如责任和决策有效性的衡量标准。环境影响评估方法通常估计自然系统状态的变化，而不是其环境的转变。因此，提出了区分相关指标并选取其受控变化特征的方法。可变性和稳定性的反对称可以从经济活动的因素和条件中自然地辨别出来，这可以通过对经济过程对环境状态的影响进行建模来证明：评估了区域生产总值规模对大气污染物排放量和废水排放量对人体健康的影响。研究结果可用于开发领土系统生态、经济和社会块之间关系的数学建模方法，以解决专题制图问题并寻求环境管理领域的最佳解决方案。