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.

Telecommunications markets have a giant impact on countries’ economies. An example of this is the great potential offered by the internet service, which allows growth in various aspects such as productivity, education, health, and connectivity. A few companies dominate telecommunications markets, so there is a high market concentrations risk. In that sense, the state has to generate strong regulation in the sector. Models for measuring competition in telecommunications markets allow the state to monitor the concentration performance in these markets. The prediction of competition in the telecommunications market based on artificial intelligence techniques would allow the state to anticipate the necessary controls to regulate the market and avoid monopolies and oligopolies. This work’s added value and the main objective is to measure the current concentration level in the Colombian telecommunications market, this allows for competitive analysis in order to propose effective strategies and methodologies to improve competition in the future of Colombian telecommunications services operators. The main result obtained in the research is the existence of concentration in the Colombian telecommunications market.

An experiment was carried out to investigate the effect of different organic nutrient solutions and day of harvest on growth parameters, biomass and chemical composition of hydroponically grown sorghum red fodder. The experiment was a 3 × 2 factorial design comprising of 3 nutrient solutions (cattle, poultry and rabbit) and 2 harvesting regimes (8th and 10th day). Cattle, poultry and rabbit dungs were collected fresh and processed into nutrient solutions. Sorghum red seeds were treated, planted on trays, and irrigated twice per day with organic nutrient solution according to the treatments. Growth parameters which were investigated included fodder mat thickness, seedling height, leaf length and width, number of leaves, fresh and dry matter yield; and proximate composition. The results showed that sorghum red fodder irrigated with cattle manure nutrient solution (NS) harvested at 10 days was higher in all, except one (fodder mat thickness) of the growth parameters considered. The crude protein (CP) was highest and similar (P > 0.05) for Poultry NS harvested at 8 and 10 days, and Cattle NS at 10 days (13.13%, 12.67%, and 12.69% respectively). The ash content also favored Cattle NS at 10 days. Cattle NS at 10 days harvest was significantly (P < 0.05) the highest (7.00%), but comparable (P > 0.05) with Rabbit NS at 10 days for NDF. Fresh and DM yields were highest for Cattle harvested at 10 and 8 days respectively. The study recommends Cattle NS as hydroponic organic NS for sorghum red as it enhances fresh and dry matter yields, and nutritive values.

Forest transition is a trend change process from decreasing to increasing forest area in a country or region. Since the 1990s, ecological and environmental problems such as climate change and loss of biodiversity have received constant attention. The research theory and method of forest transformation has gradually become the frontier and hot topic pursued by international academic circle. With forest transformation as the theme, on the basis of introducing the origin of forest transformation research, along the development vein and internal logic of forest transformation research, this paper reviews the research progress of forest transition theory from the perspectives of Kuznets curve of forest environment and forest transition path, and summarizes the major issues in forest transformation research. The main direction of future research is proposed, including the impact of economic globalization on forest transition, the refinement of research units and the analysis of forest quality transition.

Quartz sand was used as bed material in a small fluidized bed reactor with 1 kg/h feed. Corn straw powder with particle size of 20–40 mesh, 40–60 mesh, 60–80 mesh and 80–120 mesh was used as raw material for rapid pyrolysis at reaction temperatures of 400 °C, 450 °C, 500 °C and 550 °C. The bio-oil obtained after liquefaction of pyrolysis gas was analyzed. The variation trend of bio-oil composition in pyrolysis of corn straw powder with different reaction temperatures and raw material sizes was compared. The results show that: (1) the content of 3-hydroxyl-2-phenyl-2-acrylic acid in bio-oil increases with the decrease of raw material particle size, but it is less at 450 °C; (2) with the increase of reaction temperature, the content of hydroxyacetaldehyde in bio-oil increases at first and then decreases: the content of hydroxyacetaldehyde in bio-oil is the highest at 500 °C when the particle size is 20–40 mesh, and the highest at 450 °C with the other three particle sizes. Compared with other particle sizes, raw material with the particle size of 60–80 mesh is not conducive to the formation of aldehyde compounds; (3) the reaction temperature of 500 °C and the particle size of 60–80 mesh of raw materials are more conducive to the formation of phenolic compounds in bio-oil; (4) the ester compounds with particle size of 20–40 mesh in bio-oil is 20% higher than that of other particle sizes; (5) the reaction temperature and the particle size of raw materials had no significant effect on the formation of ketones, alcohols and alkane compounds in bio-oils.