Many questions of control theory are well studied for systems which satisfy to the relative degree definition. If this definition is fulfilled then there exists linear state-space transform reducing system to a very convenient canonical form where zero dynamics is a part of system’s equations. Algorithms of such reduction are well-known. However, there exist systems which don’t satisfy this definition. Such systems are the subject of investigation in the presented paper. To investigate their properties here we suggest to consider an analogue of the classical relative degree definition – the so-called column-wise relative degree. It turned out that this definition is satisfied in some cases when classical relative degree doesn’t exist. We introduce this notion here, investigate it properties and suggest algorithm for reducing systems to the column-wise relative degree compliant form if possible. It is possible to show that systems with column-wise relative degree also can be reduced to a convenient canonical form by a linear state-space transformation. Some problems arise from the fact that some systems which do not have relative degree can be reduced to a form with it using linear inputs or outputs transform. Here we show that this is an interesting mathematical problem, which can be solved with the help of properties of relative degree, formulated and proved in this paper.

Benzoxazine resin, a new type of phenolic resin, has many advantages, such as a strong molecular design, no small molecular release in the curing process, excellent thermal stability and mechanical properties, and a high residual carbon ratio. Thus, it is important for electronic communication industry matrix material. To meet the needs of high-frequency and high-speed communication technology for low-dielectric polymer resin, the low-dielectric modification of benzoxazine resin is of great significance to the high frequency and high-speed propagation of the signal, which attracts a wide range of materials researchers’ attention. In this paper, we review a series of studies on the low dielectric modification of benzoxazine resin in recent years, including the synthesis of new monomers, inorganic - organic hybridization, copolymerization with other resins, and low molecular weight benzoxazine resin research trends.

Bagasse fiber from sugarcane waste is used with epoxy resin to make natural composites. The raw fibers are treated chemically to improve compatibility and adherence with the epoxy polymer. It’s anticipated that epoxy resin matrix composites reinforced with bagasse particles would work as a trustworthy replacement for conventional materials utilized in the building and automobile sectors. The amount and distribution of reinforcing particles inside the matrix are two factors that impact the composite’s strength. Furthermore, the precise proportion of reinforcing elements—roughly 20–30 weight percent—into the matrix plays a critical role in providing a noticeable boost in improving the properties of the composites. This research investigates the impact of reinforcing alkali-treated bagasse and untreated bagasse powder into an epoxy matrix on aspects of mechanical and morphological characteristics. The hand layup technique is used to create alkali-treated bagasse and untreated bagasse powder-reinforced epoxy composites. Composites are designed with six levels of reinforcement weight percentages (5%, 10%, 15%, 20%, 25%, and 30%). Microstructural analysis was performed using SEM and optical microscopes to assess the cohesion and dispersion of the reinforcing particles throughout the hybrid composites’ matrix phase. With reinforcement loading up to 20 wt%, the tensile strength, impact strength, and toughness of epoxy-alkali-treated bagasse and untreated bagasse powder-reinforced composites increased. In contrast, treated bagasse epoxy composites were superior to untreated epoxy composites in terms of efficacy. The results indicate that 20 wt% alkali bagasse powder provides better mechanical properties than other combinations.

In order to understand the finishing effect of Waterborne Acrylic Paint under different painting methods and amount, bamboo-laminated lumber for furniture was coated with waterborne acrylic paint, then the effects of different painting methods and amount on the drying rate, smoothness, hardness, adhesion and wear resistance of the paint film were investigated. Further, the mechanism of film formation was described by thermal property analysis using thermogravimetry and differential scanning calorimeter. The results show that different painting methods have little effect on film properties, the drying time of primer and topcoat are not affected by them, which is 8/8.5 min for primer surface/solid and 6.5/7 min for topcoats. The film surface hardness and adhesion can reach B and 0 grade, the best wear resistance of the film is 51.24 mg·100 r⁻¹ when using one-layer primer one-layer topcoat. Different coating amount has great influence on film properties, the drying speed of the film increases with the increase of the painting amount. The film properties reach the best when the painting amount is 80 g/m², while too little painting amount leads to the decrease of hardness, and too much leads to the wear resistance weaken. Thermal analysis of the primer and topcoat show that water decomposition occurs at 100 ℃ and thermal decomposition of organic components occur at 350 ℃. Topcoats have better thermal stability than primers higher than that of topcoat, the topcoat displayed better thermal stability than the primer.

In order to replace conventional materials in the existing composite world, there has been a focus on adopting coir fibres, which are lightweight, adaptable, efficient, and have great mechanical qualities. This study describes the creation of environmentally responsible bio-composites with good mechanical characteristics that employ coir powder as a reinforcement, which has good interfacial integrity with an epoxy matrix. And these epoxy-coir composites supplemented with coir particles are predicted to function as a reliable substitute for traditional materials used in industrial applications. Here, untreated and alkali-treated coir fibres powder were employed as reinforcement, with epoxy resin serving as a matrix. An experimental investigation has been carried out to study the effect of coir powder reinforcement at different weight percentages (5 wt%, 10 wt%, 15 wt%, 20 wt%, 25 wt%, and 30 wt%). The morphological study, followed by a scanning electron microscope (SEM) and an optical microscope (OM), demonstrated that the powder and matrix had the strongest adhesion at 20 wt% coir powder-reinforced composite, with no voids, bubbles, or cracks. Based on the entire investigation, the polymer composite with 20 wt% reinforcement exhibited better mechanical qualities than the other combinations.

The obtaining of new data on the transformation of parent materials into soil and on soil as a set of essential properties is provided on the basis of previously conducted fundamental studies of soils formed on loess-like loams in Belarus (15,000 numerical indicators). The study objects are autochthonous soils of uniform granulometric texture. The basic properties without which soils cannot exist are comprehensively considered. Interpolation of factual materials is given, highlighting the essential properties of soils. Soil formation is analyzed as a natural phenomenon depending on the life activity of biota and the water regime. Models for differentiation of the chemical profile and bioenergy potential of soils are presented. The results of the represented study interpret the available materials taking into account publications on the biology and water regime of soils over the past 50 years into three issues: the difference between soil and soil-like bodies; the soil formation as a natural phenomenon of the mobilization of soil biota from the energy of the sun, the atmosphere, and the destruction of minerals in the parent materials; and the essence of soil as a solid phase and as an ecosystem. The novelty of the article study is determined by the consideration of the priority of microorganisms and water regime in soil formation, chemical-analytical identification of types of water regime, and determination of the water regime as a marker of soil genesis.