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.

This paper provides a comparative perspective on infrastructure provision in developing Asia's three largest countries: China, India, and Indonesia. It discusses their achievements and shortfalls in providing network infrastructure (energy, transport, water, and telecommunications) over the past two decades. It documents how three quite distinct development paths—and very different levels of national saving and investment—were manifested in different trajectories of infrastructure provision. The paper then describes the institutional, economic, and policy factors that enabled or hindered progress in providing infrastructure. Here, contrasting levels of centralization of planning played a key role, as did countries’ differing abilities to mobilize infrastructure-related revenue streams such as user charges and land value capture. The paper then assesses future challenges for the three countries in providing infrastructure in a more integrated and sustainable way, and links these challenges with the global development agenda to which the three countries have committed. The concluding recommendations hope to provide a platform for further policy and research dialogue.

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.

The use of saline water in agriculture is a viable alternative, considering the increased demand for fresh water. The objective of this study was to evaluate the growth and phytomass production of sugar beet under irrigation with water of different saline concentrations in a field experiment on the campus of the Federal University of Alagoas in Arapiraca. The treatments were five levels of electrical conductivity (1.0, 2.0, 3.0, 4.0 and 5.0 dS m^-1). The design was in randomized blocks, with four repetitions. The maximum yield of sugar beet at 27 days after the application of saline treatments was obtained with a salinity of 3.0 dS m^-1, for the variables plant height (PA), stem diameter (CD), root length (RC), aboveground dry phytomass (FSPA) and total dry phytomass (FST). At 42 days after the application of saline treatments, the variables aboveground fresh phytomass (FFPA), root fresh phytomass (FFR), total fresh phytomass (FFT), aboveground dry phytomass (FSPA) and total dry phytomass (FST) increased with increasing water salinity. Rain may have influenced the results obtained for the evaluations, performed at 42 days after the application of the saline treatments.

Humic substances are used in agriculture as promoters of plant growth, especially of the root system. The objective of the work was to evaluate the effect of the application of different doses of fulvic acid on the growth and productivity of American lettuce, Raider Plus cultivar. The experimental design used was entirely randomized, with five treatments of fulvic acid 0, 1, 2, 4, 8 mL·L^-1 and four repetitions, applied at the time of transplanting. Two experiments were conducted simultaneously: one in the greenhouse, where fresh and dry mass of the aboveground and root parts, length and volume of the roots were evaluated; and the other in the field, where, at the end of the cycle, fresh and dry mass of the aboveground parts, number of leaves, stem length and average head circumference were evaluated. The application of different doses of fulvic acid promoted the growth of lettuce plants, especially the root system. The emission of roots, with predominance, of those of smaller diameter, was found in the higher concentrations of fulvic acid. The number of leaves and the average circumference of the head expressed responses in the concentrations of fulvic acid.