Soil moisture is one of the essential variables of the water cycle, and plays a vital role in agriculture, water management, and land (drought) and vegetation cover change as well as climate change studies. The spatial distribution of soil moisture with high-resolution images in Mongolia has long been one of the essential issues in the remote sensing and agricultural community. In this research, we focused on the distribution of soil moisture and compared the monthly precipitation/temperature and crop yield from 2010 to 2020. In the present study, Soil Moisture Active Passive (SMAP) and Moderate Resolution Imaging Spectroradiometer (MODIS) data were used, including the MOD13A2 Normalized Difference Vegetation Index (NDVI), MOD11A2 Land Surface Temperature (LST), and precipitation/temperature monthly data from the Climate Research Unit (CRU) from 2010 to 2020 over Mongolia. Multiple linear regression methods have previously been used for soil moisture estimation, and in this study, the Autoregressive Integrated Moving Arima (ARIMA) model was used for soil moisture forecasting. The results show that the correlation was statistically significant between SM-MOD and soil moisture content (SMC) from the meteorological stations at different depths (p < 0.0001 at 0–20 cm and p < 0.005 at 0–50 cm). The correlation between SM-MOD and temperature, as represented by the correlation coefficient (r), was 0.80 and considered statistically significant (p < 0.0001). However, when SM-MOD was compared with the crop yield for each year (2010–2019), the correlation coefficient (r) was 0.84. The ARIMA (12, 1, 12) model was selected for the soil moisture time series analysis when predicting soil moisture from 2020 to 2025. The forecasting results are shown for the 95 percent confidence interval. The soil moisture estimation approach and model in our study can serve as a valuable tool for confident and convenient observations of agricultural drought for decision-makers and farmers in Mongolia.

Agriculture is one of the most critical sectors of the Mongolian economy. In Mongolia, land degradation is increasing in the cropland region, especially in a cultivated area. The country has challenges to identify new croplands with sufficient capacity for cultivation, especially for local decision-makers. GIS applications tremendously help science in making land assessments. This study was carried out in Bornuur soum, Mongolia. The goal of this study to estimate that best suitable area for supporting crop production in Bornuur soum, using a GIS-based multi-criteria analysis (MCA) and remote sensing. GIS-based multi-criteria analysis (MCA) has been widely used in land suitability analyses in many countries. In this research, the GIS-based spatial MCA among the Analytical Hierarchy Process (AHP) method has employed. The approach was enhanced for each criterion which as soil, topography and vegetation. The opinions of agronomist experts and a literature review helped in identifying criteria (soil data, topography, water and vegetation data) that are necessary to determine areas suitable for crops. The detailed cropland suitability maps indicate that 46.12 % is highly suitable for cropland, 34.68 % is moderate suitable, 13.64 % is marginal suitable and 5.56 % is not suitable. The MCA and AHP tools play an essential role in the multi-criteria analysis. Therefore, the results of these methods allow us to estimate an appropriate area for cultivation in Bornuur soum, Tuv province. The crop suitability method implies significant decisions on different levels and the result will be used for cropland management plan to make a decision. It is an integral role in agricultural management and land evaluation. Future research should further develop this method by including socio-economic (potential citizens for agriculture, current crop growth, water resource, etc.) and environmental variables (rainfall, vegetation types, permafrost distribution, etc.) to obtain specific results. However, it could be also be applied for a single crop type (mainly barley, wheat and potato) in Mongolia.

Sangaku problem is one of Japanese Temple Geometry problems which was studied in Hidetoshi Fukugawa[1]. One of the Sangaku problem is packing 6 equal circles in rectangle of 1:1.934798 size. We examine the problem from a view point of optimization theory and algorithm. We show that Sangaku optimization problem belongs to a class of nonconvex optimization and propose a penalty method for solving the problem numerically. In numerical expirements, we consider equal and unequal 6 circles. Computational results obtained on Python Jupyter Notebook are provided. Сангаку бодлогыг оптимизацийн аргаар бодох нь Хураангуй: Сангаку бодлого нь Японы эртний геометрийн бодлого юм. Энэхүү судалгаандаа бид Хидетоши Фукугава эрдэмтний судалсан 1:1.934798 хэмжээтэй тэгш өнцөгтөд 6 ижил тойрог багтаах сангаку бодлогыг авч үзэв. Энэ бодлогыг хучилтын бодлогын хүрээнд оптимизацийн аргаар бодсон ба энэ нь гүдгэр бус максимумчлалын бодлого болно.Бодлогыг өргөтгөж, ижил бус 6 тойргын хувьд бодож торгуулийн функцийн аргаар нэмж тооцооллыг хийв. Python Jupyter Notebook программ дээр тооцооллыг хийж үр дүнг гаргасан болно. Түлхүүр үгс: Сангаку бодлого, хучилтын бодлого, тойрог, оптимизацийн арга

Classical cost–volume–profit (CVP) analysis usually provides point-wise break-even or target-profit calculations under fixed-price assumptions. This paper developed a nonconvex feasible–profit framework for multi-producer CVP analysis in an oligopolistic market where the common price is endogenously determined by the joint production vector. The framework was applied to a three-country copper export market consisting of Mongolia, Chile, and Peru, which are interpreted as aggregate producers, using annual data for 2013–2025. Export volumes, China's copper import demand, and London Metal Exchange copper prices were obtained from Bloomberg, while cost parameters were calibrated benchmark values. For the three reduced-form price environments, the price coefficient was estimated by least squares, feasible–profit membership was tested, and a penalty method was used to compute local stationary points. The results showed that feasible–profit membership depends strongly on the assumed price mechanism. Under the linear aggregate-output and pairwise interaction specifications, the observed export vector is infeasible only in the early years and becomes feasible later, while under the inverse aggregate-output specification, the observed vector remains feasible throughout the sample but the computed stationary points are infeasible in 2024–2025. The findings suggest that multi–producer CVP analysis should account for endogenous price formation and export competition, and the proposed framework provides an interpretable tool for examining nonconvex feasible–profit regions.