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.

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.

  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.  

In this review are developed insights from the current research work to develop the concept of functional materials. This is understood as real modified substrates for varied applications. So, functional and modified substrates focused on nanoarchitectures, microcapsules, and devices for new nanotechnologies highlighting life sciences applications were revised. In this context, different types of concepts to proofs of concepts of new materials are shown to develop desired functions. Thus, it was shown that varied chemicals, emitters, pharmacophores, and controlled nano-chemistry were used for the design of nanoplatforms to further increase the sizes of materials. In this regard, the prototyping of materials was discussed, affording how to afford the challenge in the design and fabrication of new materials. Thus, the concept of optical active materials and the generation of a targeted signal through the substrate were developed. Moreover, advanced concepts were introduced, such as the multimodal energy approach by tuning optical coupling from molecules to the nanoscale within complex matter composites. These approaches were based on the confinement of specific optical matter, considering molecular spectroscopics and nano-optics, from where the new concept nominated as metamaterials was generated. In this manner, fundamental and applied research by the design of hierarchical bottom-up materials, controlling molecules towards nanoplatforms and modified substrates, was proposed. Therefore, varied accurate length scales and dimensions were controlled. Finally, it showed proofs of concepts and applications of implantable, portable, and wearable devices from cutting-edge knowledge to the next generation of devices and miniaturized instrumentation.