The work is devoted to the numerical solution of the initial boundary value problem for the heat equation with a fractional Riesz derivative. Explicit and implicit difference schemes are constructed that approximate the boundary value problem for the heat equation with a fractional Riesz derivative with respect to the coordinate. In the case of an explicit difference scheme, a condition is obtained for the time step at which the difference scheme converges. For an implicit difference scheme, a theorem on unconditional convergence is proved. An example of a numerical calculation using an implicit difference scheme is given. It has been established that when passing to a fractional derivative, the process of heat propagation slows down.

Projects implemented under life cycle contracts have become increasingly common in recent years to ensure the quality of construction and maintenance of energy infrastructure facilities. A key parameter for energy facility construction projects implemented under life cycle contracts is their duration and deadlines. Therefore, the systematic identification, monitoring, and comprehensive assessment of risks affecting the timing of work on the design and construction is an urgent practical task. The purpose of this work is to study the strength of the influence of various risks on the duration of a project implemented on the terms of a life cycle contract. The use of the expert assessment method allows for identifying the most likely risks for the design and construction phases, as well as determining the ranges of deviations from the baseline indicator. Using the obtained expert evaluations, a model reflecting the range and the most probable duration of the design and construction works under the influence of risk events was built by the Monte-Carlo statistical method. The results obtained allow monitoring and promptly detecting deviations in the actual duration of work from the basic deadlines set in the life cycle contract. This will give an opportunity to accurately respond to emerging risks and build a mutually beneficial relationship between the parties to life cycle contracts.

Aiming at the problem of road network multi-scale matching, a multi-scale road matching method under the constraint of road mesh of small-scale data has been proposed. First, two road meshes with different scale data are constructed; Secondly, under the constraint of the small-scale road mesh, the composite mesh composed of several road meshes in the large-scale road is extracted, and the mesh matching with the small-scale road mesh is completed; Then, many-to-many matching of road meshes with different scales is realized; finally, the matching relationship between composite mesh and small-scale road mesh is transformed into the matching between multi-scale road mesh boundary roads and internal roads, and the matching of the whole road network is completed. The experimental results show that this method can better realize the matching of multi-scale road network.

Vegetable production is an important sector of economy for farmers in Nepal. The analysis was carried out to explore the trends in vegetable production sector in Nepal along with the recent trend of some major vegetables in terms of area, production and yield. The time series data from 1977/78 to 2016/17 (40 years) of vegetables production and 5 years data (2011/12 - 2015/16) of major vegetables were collected from reliable source and analysis was done through Microsoft Excel. The results show that between 1977/78 and 2016/17 the area under vegetables cultivation has jumped by 222.8% while production is increased by 728.21% and productivity is increased by 156.6% during this course. The result also reveals that during the period of 5 years (2011/12 - 2015/16), solanaceous and cruciferous vegetables has an increasing trend in area, production and yield except for the area under cultivation for eggplant (declined by 5.2%) and for radish (declined by 6.0%) respectively while cucurbitaceous vegetables has increasing trend in area and production but an declining trend in yield except for the yield of cucumber (increased by 15.8%). However, the trend of other major vegetables is seen highly fluctuating over the years. 

In Emerging economies, MNCs (Multinational corporations) encounter several issues while devising Strategies to penetrate foreign markets, examining these SMEs’ performance in present times and assessing their internationalisation process is crucial. The purpose of this research is to investigate how international entrepreneurial orientation affects SMEs’ international performance during internationalization, as well as how organizational culture in the Kingdom influences the international performance of these MNCs. To attain this objective (n = 206) MNCs in the Kingdom have adopted internationalisation strategies. Questionnaires were administered as part of a survey approach for this study. To forecast and estimate relationships, partial least squares structural equation modelling (PLS-SEM) was employed. This study indicates that improving internationalization performance, mainly through active participation in foreign markets, is one of the SMEs’ strategies during the internationalization process. The empirical findings demonstrate that international entrepreneurial orientation influences the internationalisation performance of SMEs largely influenced by organisational culture. Previous research shows that the success of SMEs’ internationalization, however, is not directly impacted by their international entrepreneurial orientation. This study supports the significance of organisational culture during internationalisation. This study offers insightful information that motivates policymakers and owner-managers in developing nations, especially in KSA, to build organizational cultures and dynamic capacities that meet the demands of globalization in today’s business scenario.