This paper presents a numerical method for solving a nonlinear age-structured population model based on a set of piecewise constant orthogonal functions. The block-pulse functions (BPFs) method is applied to determine the numerical solution of a non-classic type of partial differential equation with an integral boundary condition. BPFs duo to the simple structure can efficiently approximate the solution of systems with local or non-local boundary conditions. Numerical results reveal the accuracy of the proposed method even for the long term simulations.

Research on community resilience has been ongoing for decades. Several studies have been carried out on resilience in different groups and contexts. However, few address the relationship between community resilience and depopulated rural areas. This study aims to dig deeper into this, considering the concrete impact of population decline in Spain. We carried out a systematic review of the most relevant contributions. A search protocol was developed and used to consult ten databases. Different combinations of terms such as ‘community resilience’, ‘rural’, and ‘depopulation’, or related terms, were used. 22 scientific texts were analysed. We obtained a set of publications that demonstrate the heterogeneity of research methods, approaches and analytical processes applied to the study of this relationship. A mostly qualitative approach was observed, either as the main technique or complementary to documentary reviews. The results underscore the complex nature of rural depopulation and related constructs. It emphasizes the specific importance of community resilience in these territories in terms of social capital, endogenous resources, sustainability, economic dynamism, local responsibility and effective governance. The findings identify a scarce mention to social intervention professions, which should have a more important role due to their core values. In the studies reviewed, it appears as an emerging and scientifically relevant area to explore, both for investigation and intervention purposes. The strength of a multidisciplinary approach to addressing the phenomena appears in the discussion as a main potential line of research.

The smallest administrative unit of the sixth national census-township (town) is selected as the basic unit, the population spatial distribution characteristics at the township (town) level in karst mountainous areas of northwest Guangxi are analyzed by using Lorenz curve and spatial correlation analysis method, and the influence intensity of natural factors on regional population spatial distribution is detected by using geographic detector method. The results show that: 1. the spatial distribution of population at the township (town) level has the characteristics of imbalance, showing generally significant positive correlation and certain aggregation; 2. There are significant differences in the impact of the spatial distribution of various natural factors on the population distribution. For the towns without karst distribution in the northwest and central south of the study area, the population density increases with the increase of factors conducive to human residence, but the average population density is only 79 people/km². In the towns with karst distribution in the East and south, the spatial distribution of population density and natural factors is not a simple increase or decrease relationship, but fluctuates with the change of karst distribution area. 3. The factor detection results of the geographic detector show that the altitude has the greatest impact on the spatial distribution of population. The interactive detection results show that the impact intensity of any two natural factors after superposition and interaction presents nonlinear enhancement and two factor enhancement. It can be seen that the karst mountain area in northwest Guangxi is similar to other areas. Altitude is one of the main factors affecting the spatial distribution of population, but the river network density and unique geological landform of karst mountain area have a strong catalytic effect on the spatial distribution of population. The superposition and interaction with other factors can further strengthen the impact on population distribution.

In November 2018, the sample plot survey method was used to analyze the population characteristics of Lithocarpus polystachyus in the natural secondary forest with different disturbance intensity in Jianning, Fujian Province, and compile its population static life table. The results showed that the number of individuals in the population was small, but it was clustered. With the increase of interference intensity, the first and second age seedlings and young trees decreased. The population types affected by human disturbance are all lacking level V trees, and the population type belongs to primary population (N₁); The undisturbed population lacks level I and II seedlings and young trees, but there are level V trees, and the population type belongs to medium decline population (S₂). In general, all populations of L. polystachyus are unstable and belong to the transitional type. In the static life table, the mortality of level I and II seedlings and young trees is high, the survival rate has a small peak in level III and IV, and then the survival rate decreases rapidly, and the average life expectation of level II is the highest. It shows that artificial conservation measures and appropriate space re-lease are needed to maintain the stability of the population.

According to official data, modern Russia has the lowest unemployment rate. However, there is still a huge contingent of hidden unemployment, many times higher than the official level. This situation is paradoxically combined with an acute and continuously growing shortage of qualified production personnel. Using a lot of factual material, the author reveals the causes of this phenomenon. The main one is the depopulation of the indigenous population, which is being replaced by people of other ethnic groups with the lowest qualification level. At the same time, due to the destruction (“optimization”) of the education system, the intellectual and qualification level of the indigenous population is continuously decreasing. The other is the various types and waves of growing emigration of “brains” and “golden hands.” As a result, for more than thirty years, the contingent of old engineering and technical personnel has exhausted itself, while new ones have not been trained in the required volume and quality. A huge personnel “hole” has formed. The author proposes to close this “hole” on the basis of a radical reorientation of the entire Russian education system, starting with kindergarten, school, etc. It is also necessary to reformat the public consciousness accordingly, especially the mass consciousness of young people.