The recession cone and recession function are very important research objects in Convex Analysis. They have extensive applications in the optimization theory. Firstly, we study the properties of the recession cone and recession function. The positive homogeneity and subadditivity of recession function are mainly discussed. And the different methods are considered to prove these properties. Secondly, we discuss the unboundedness of the convex sets and convex functions by using recession cone and recession function.

Proposed herein is an environment-friendly method to realize oil/water separation. Nylon mesh is exposed to atmospheric pressure plasma for surface modification, by which micro/nano structures and oxygen-containing groups are created on nylon fibers. Consequently, the functionalized mesh possesses superhydrophilicity in air and thus superoleophobicity underwater. The water pre-wetted mesh is then used to separate oil/water mixtures with the separation efficiency above 97.5% for various oil/water mixtures. Results also demonstrate that the functionalized nylon mesh has excellent recyclability and durability in terms of oil/water separation. Additionally, polyurethane sponge slice and polyester fabric are also functionalized and employed to separate oil/water mixtures efficiently, demonstrating the wide suitability of this method. This simple, green and highly efficient method overcomes a nontrivial hurdle for environmentally-safe separation of oil/water mixtures, and offers insights into the design of advanced materials for practical oil/water separation.

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.

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).

Biomass production (BIO) and its anomalies were modeled using MODIS satellite images and gridded weather data to test an environmental monitoring system in the biomes Atlantic Forest (AF) and Caatinga (CT) within SEALBA, an agricultural growing region bordered by the states of Sergipe (SE), Alagoas (AL), and Bahia (BA), Northeast Brazil. Spatial and temporal variations on BIO between these biomes were strongly identified, with the annual long-term averages (2007–2023) for AF and CT of 78 ± 22 and 58 ± 17 kg ha−1 d−1, respectively. BIO anomalies were detected through its standardized indexes—STD (BIOSTD), comparing the results for the years from 2020 to 2023 with the long-term rates from 2007 to each of these years. The highest negative BIOSTD values were in 2023, but concentrated in CT, indicating periods with the lowest vegetation growth, regarding the long-term conditions from 2007 to 2023. The largest positive BIOSTD values were for the AF biome in 2022, evidencing the highest vegetative vigor in comparison with the long-term period 2007–2022. The proposed BIO monitoring system is important for environmental policies as they picture suitable periods and places for agricultural and forestry explorations, allowing sustainable managements under climate and land-use changes conditions, with possibilities for replication of the methods in other environmental conditions.

Polyurethane is a multipurpose polymer with valuable mechanical, thermal, and chemical stability, and countless other physical features. Polyurethanes can be processed as foam, elastomer, or fibers. This innovative overview is designed to uncover the present state and opportunities in the field of polyurethanes and their nanocomposite sponges. Special emphasis has been given to fundamentals of polyurethanes and foam materials, related nanocomposite categories, and associated properties and applications. According to literature so far, adding carbon nanoparticles such as graphene and carbon nanotube influenced cell structure, overall microstructure, electrical/thermal conductivity, mechanical/heat stability, of the resulting polyurethane nanocomposite foams. Such progressions enabled high tech applications in the fields such as electromagnetic interference shielding, shape memory, and biomedical materials, underscoring the need of integrating these macromolecular sponges on industrial level environmentally friendly designs. Future research must be intended to resolve key challenges related to manufacturing and applicability of polyurethane nanocomposite foams. In particular, material design optimization, invention of low price processing methods, appropriate choice of nanofiller type/contents, understanding and control of interfacial and structure-property interplay must be determined.