The stability and positivity of linear positive Markovian jump systems with respect to part of the variables is considered. The methodologies of stability of positive systems with known transition probabilities based on common linear copositive Lyapunov function and stability of linear systems with respect to part of the variables are combined to find sufficient conditions of the stochastic stability and positivity of Markovian jump systems with respect to part of the variables. The results are extended for a class of nonlinear positive Markovian jump systems with respect to part of the variables. An example is given to illustrate the obtained results.
The aim of the study is to discuss the relationship of the crude oil price, speculative activity and fundamental factors. An empirical study was conducted with a VEC model. Two cointegrating vectors were identified. The first vector represents the speculative activity. We argue that the number of short non-commercial positions increases with the crude oil stock and price, decreases with the higher number of long non-commercial positions. A positive trend of crude oil prices may be a signal for traders outside the industry to invest in the oil market, especially as access to information could be limited for them. The second vector represents the crude oil price under the fundamental approach. The results support the hypothesis that the crude oil price is dependent on futures trading. The higher is a number of commercial long positions, the greater is the pressure on crude oil price to increase.
The third record of Cinara tujafilina occurrence in Poland is given. The population dynamics of the species is presented.
Purging the liquid steel with inert gases is a commonly used treatment in secondary metallurgy. The main purposes for which this method is used are: homogenization of liquid steel in the entire volume of the ladle, improvement of mixing conditions, acceleration of the absorption process of alloy additives and refining of liquid steel from non-metallic inclusions. The basic processing parameters of this treatment are: gas flow rate and the level of gas dispersion in liquid steel. The level of gas dispersion depends on the design and location of the porous plug in the ladle. Therefore, these parameters have a significant impact on the phenomena occurring in the contact zone of liquid steel with slag. Their improper selection may cause secondary contamination of the bath with exogenous inclusions from the slag, or air atmosphere due to discontinuity of the slag and exposure of the excessive surface of the liquid steel free surface. The article presents the results of modelling research of the effect of liquid steel purging with inert gases on phenomena occurring in this zone.
The research was carried out using the physical (water) model of steel ladle. As a modelling liquid representing slag, paraffin oil was used, taking into account the conditions of similarity with particular reference to the kinematic viscosity. The results of the conducted research were presented in the form of visualization of phenomena occurring on the surface of the model liquid free surface in the form of photographs. The work is a part of a bigger study concerning modelling of ladle processes.