One functional class is described in terms of one-sided modulus of continuity and the modulus of positive (negative) variation on which there
is a uniform convergence of the truncated cardinal Whittaker functions.

Based on the characteristics of liquid lens sparse aperture imaging, a radiative multiplet array structure is proposed; a simplified model of sparse aperture imaging is given, and the analytical expression of the modulation transfer function is derived from the optical pupil function of the multiplet array structure; the specific distribution form of this multiplet array structure is given, and the structure parameters are approximated by the dimensionless method; the two types of radiative multiplet array structures are discussed, and the filling factor, redundancy, modulation transfer function and other characteristic parameters are calculated. The physical phenomena exhibited by the parametric scan are discussed, and the structural features and imaging characteristics of these two arrays are compared. The results show that the type-II structure with larger actual equivalent aperture and actual cutoff frequency and lower redundancy is selected when the average modulation transfer function and the IF characteristics of the modulation transfer function of the two structures are close to each other; the type-II structure has certain advantages in imaging; the conclusion is suitable for arbitrary enclosing circle size because the liquid lens-based multiplet array structure adopts dimensionless approximation parameters; compared with the composite toroidal structure, the radiative multiplet mirror structure has a larger actual cut-off frequency and actual equivalent aperture when the filling factor is the same.

This study investigates the impact of extreme rainfall events on soil erosion in the downstream Parnaíba River Basin, located in the Brazilian Cerrado. The analysis focused on rainfall erosivity (R factor) and soil erodibility (K factor) as key indicators. The average erosivity in the region was 9051 MJ mm h⁻¹ha⁻¹year⁻¹, with a variation between 7943 and 10,081 MJ mm h⁻¹ha⁻¹year⁻¹, suggesting a high erosive potential, mainly in the rainiest months, from December to April. The soils of the studied area, mainly Ultisols and Chernosols, present high to very high erodibility, with K factor values ranging from 0.025 to 0.050 t h MJ⁻¹ mm⁻¹. Furthermore, fieldwork revealed areas, near highways, with apparently fragile soils, as well as rills and gullies, identified through photographs taken during fieldwork. These locations, due to the combination of high erosivity and susceptible soils, were considered prone to the occurrence of erosion processes, representing an additional risk to local infrastructure. The spatialization of R and K factors, along with field observations, showed that much of the area is at high risk of erosion and landslides, particularly in regions with greater topographic variability and proximity to water bodies. These results provide a basis for the development of mitigation strategies, being important for the effective prevention of landslides.

This paper proposes to apply a microfluidic chip combining DSC, DTA, and PCR-like functions for studying synthesis and selection of precursors of the genetic code carriers at hydrothermal conditions including those in natural high frequency fields (such as magnetosphere emission, atmospherics, auroras and lightings).

Small watershed ecological compensation is an important economic means to solve the contradiction between protecting the ecological environment and developing the economy. Taking the Changtian small watershed in the Xixiu District of Anshun City as an example, this paper uses the ecological service function value method to roughly calculate the ecological service function value of the small watershed ecosystem: the ecological service function value of the Changtian small watershed is 913.586 million yuan, and the total amount of ecological compensation is 11.6245 million yuan, of which the farmland system compensation is 1.3194 million yuan, the forest system compensation is 7.5336 million yuan, and the water system compensation is 256,000 yuan, The compensation for the fruit forest system is 2,515,500 yuan. Based on the value of ecosystem service function, the compensated and non-compensated ecosystem service functions are distinguished, and the equivalent factors that different ecosystems can provide compensated ecosystem functions are expressed, so that the determination of ecological compensation amount is scientific and more accurate, and then provides a basis for the determination of ecological compensation standard of the small watershed.

In the past, Sabah has often been reported as Malaysia’s poorest state, with the recorded highest incidence of absolute poverty among all the other states. The consumption patterns of households in Sabah have been significantly impacted by such circumstances. This further draws light on the adverse impact on the broader economy, as low levels of spending may restrict demand for products and services, stifling economic growth. The understanding of households’ consumption functions based on the Permanent Income Hypothesis (PIH) will advance knowledge in identifying the key factors that influence the households’ spending decisions. Pointing out the scant number of past studies done within this very context, and focusing on the Sabah state in particular, further motivated this study, this paper aims to develop a conceptual framework that can estimate and examine the households’ consumption functions in Sabah. As such, the methodology of drawing upon narrative reviews from research in the past will be used in this paper to develop the conceptual framework. The result of this study built upon the framework developed will help in identifying the factors that explain the households’ consumption patterns, in particular, whether the function estimated will be consistent with the Permanent Income Hypothesis (PIH). It is hoped that the conceptual framework built will aid in providing valuable empirical insight for policymakers in designing effective policies that can uplift households that are living in poverty.