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 presents a brief review of risk studies in Geography since the beginning of the 20th century, from approaches focused on physical-natural components or social aspects, to perspectives that incorporate a systemic approach seeking to understand and explain risk issues at a spatial level. The systemic approach considers principles of interaction between multiple variables and a dynamic organization of processes, as part of a new formulation of the scientific vision of the world. From this perspective, the Complex Systems Theory (CST) is presented as the appropriate conceptual-analytical framework for risk studies in Geography. Finally, the analysis and geographic information integration capabilities of Geographic Information Systems (GIS) based on spatial analysis are explained, which position it as a fundamental conceptual and methodological tool in risk analysis from a systemic approach.

This paper is devoted to the discussion of dynamical properties of anisotropic dark energy cosmological model of the universe in a Bianchi type-V space time in the framework of scale covariant theory of gravitation formulated by Canuto et al.(phys.Rev.Lett.39:429,1977).A  dark energy cosmological model is presented by solving the field equations of this theory by using some physically viable conditions. The dynamics of the model is  studied  by computing the cosmological parameters, dark energy density, equation of state(EoS) parameter, skewness parameters, deceleration parameter and the jerk parameter. This being a scalar field model gives us the quintessence model of the universe which describes a significant dark energy candidate of our accelerating universe. All the physical quantities discussed are in agreement with the recent cosmological observations.

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.