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.

Based on the collective forest with common use rights, the social-ecological system analysis framework and autonomous governance theory proposed by Elinor Ostrom are introduced in the forest eco-economic system to analyze the interaction logic among the first-level subsystems and the secondary variables of the forest eco-economic system and the variables related to the autonomous governance of the system to explore the synergistic mechanisms affecting the forest eco-economic system. The results show that: in the case of information asymmetry, collective actions of governmental and non-governmental organizations will aggravate the dilemma of forest eco-economic synergistic development; actors extract forest resource units from the forest resource system to achieve economic benefits; and renewable resources of forest ecosystems can be sustained in the long term when the average extraction rate of humans from forest ecosystems does not exceed the average replenishment rate.

Green manufacturing is increasingly becoming popular, especially in lubricant manufacturing, as more environmentally friendly substitutes for mineral base oil and synthetic additives are being found among plant extracts and progress in methodologies for extraction and synthesis is being made. It has been observed that some of the important performance characteristics need enhancement, of which nanoparticle addition has been noted as one of the effective solutions. However, the concentration of the addictive that would optimised the performance characteristics of interest remains a contending area of research. The research was out to find how the concentration of green synthesized aluminum oxide nanoparticles in nano lubricants formed from selected vegetable oils influences friction and wear. A bottom-up green synthesis approach was adopted to synthesize aluminum oxide (Al₂O₃) from aluminum nitrate (Al(NO₃)₃) precursor in the presence of a plant-based reducing agent—Ipomoea pes-caprae. The synthesized Al₂O₃ nanoparticles were characterized using TEM and XRD and found to be mostly of spherical shape of sizes 44.73 nm. Al₂O₃ nanoparticles at different concentrations—0.1 wt%, 0.3 wt%, 0.5 wt%, 0.7 wt%, and 1.0 wt%—were used as additives to castor, jatropha, and palm kernel oils to formulate nano lubricants and tested alternately on a ball-on-aluminum (SAE 332) and low-carbon steel Disc Tribometer. All the vegetable-based oil nano lubricants showed a significant decrease in the coefficient of friction (CoF) and wear rate with Ball-on-(aluminum SAE 332) disc tribometer up to 0.5wt% of the nanoparticle: the best performances (e_COF = 92.29; e_WR = 79.53) came from Al₂O₃-castor oil nano lubricant and Al₂O₃-palm kernel oil; afterwards, they started to increase. However, the performance indices displayed irregular behaviour for both COF and Wear Rate (WR) when tested on a ball-on-low-carbon steel Disc Tribometer.

Knowledge of the state of fragmentation and transformation of a forested landscape is crucial for proper planning and biodiversity conservation. Chile is one of the world’s biodiversity hotspots; within it is the Nahuelbuta mountain range, which is considered an area of high biodiversity value and intense anthropic pressure. Despite this, there is no precise information on the degree of transformation of its landscape and its conservation status. The objective of this work was to evaluate the state of the landscape and the spatio-temporal changes of the native forests in this mountain range. Using Landsat images from 1986 and 2011, thematic maps of land use were generated. A 33% loss of native forest in 25 years was observed, mainly associated to the substitution by forest plantations. Changes in the spatial patterns of land cover and land use reveal a profound transformation of the landscape and advanced fragmentation of forests. We discuss how these patterns of change threaten the persistence of several endemic species at high risk of extinction. If these anthropogenic processes continue, these species could face an increased risk of extinction.

Potassium dihydrogen phosphate, KH2PO4 (KDP) crystal is an excellent electro-optical nonlinear optical crystal with large electro-optical nonlinear coefficient, high laser damage threshold, and laser frequency doubling effect, electro-optical effect , Piezoelectric effects and other special features, widely used in inertial confinement fusion engineering (ICF) and electro-optical switching devices. Therefore, its growth mechanism, growth process and performance have been systematically studied. In the process of KDP crystal growth, it is found that the stability of the growth solution is an important factor affecting the quality of crystal growth. Therefore, in recent years, more and more research on the stability of the solution, such as the study of ph, doping, supersaturation, overheating time on the stability of the solution. Among them, the research on the doping is mostly reported, and the research on this aspect is mainly focused on two aspects. On the one hand, it is the study of the stability of the solution under doping, and the other is the effect of doping on the optical quality of the crystal. In fact, the stability of the growth solution and the quality of crystal growth is directly related to the quality, but the existing research to isolate the two researches. Therefore, the experiment will be carried out in the case of double-doped KDP solution stability, KDP crystal growth and crystal optical quality and other experiments, and in-depth analysis of the impact of solution stability and crystal optical quality of the reasons, while the solution stability and The relationship between the optical quality of the crystal is briefly analyzed.