The LQR (linear quadratic regulator) control problem subject to singular system constitutes a optimization problem in which one must be find an optimal control that satisfy the singular system and simultaneously to optimize the quadratic objective functional. In this paper we establish a sufficient condition to obtain the optimal control of discounted LQR optimization problem subject to disturbanced singular system where the disturbance is time varying. The considered problem is solved by transforming the discounted LQR control problem subject to disturbanced singular system into the normal LQR control problem. Some available results in literatures of the normal LQR control problem be used to find the sufficient conditions for the existence of the optimal control for discounted LQR control problem subject to disturbanced singular system. The final result of this paper is in the form a method to find the optimal control of discounted LQR optimization problem subject to disturbanced singular system. The result shows that the disturbance is vanish with the passage of time.

The effect of the air-entraining agent on properties of mortar mixtures as well as on the compressive strength of hardened mortars was the objective of this study. Such mortars contain a certain amount of evenly spread closed air-voids pores with dimensions of 0.02-0.05 mm. On the one hand, the presence of a large volume of such air bubbles results in the reduction of mechanical properties of mortar. On the other hand, the use of this technological approach improves rheological properties of mortar mixture. The effect of the air entrainment on the flow, density, volume of entrained air of mortar mixture and compressive strength of hardened mortar was established. Obtained results show substantial increasing in the mortar flow at cement to sand ratio 1:2 by 1.8 times. The further decrease of C:S ratio results in a slight increase of the flow and even negligible its decrease at C:S = 1:4 compared to the reference mortar. The increase of the volume of entrained air results in the decrease of the density and compressive strength of mortar, but improve the resistance to freezing/thawing cycles. The results of this study can be a guide for mortar mix design to choose the most appropriate mix proportion to produce economically efficient mortars.

For a very long period of time, Polish waste management was based mainly on landfilling at landfills, which had a negative impact on the surrounding environment. The EU requirements for the Member States have led to a revolution in Polish legislation on waste management and local governments have become responsible for creating local waste management systems that will affect the achievement of EU targets. One of the solutions undertaken by several municipalities is the construction and operation of a municipal waste thermal treatment installation, which not only reduced the amount of waste deposited, but also supported the local power industry by generating electricity and heat. The emission standards for installations producing energy from waste, as in the case of conventional power plants and combined heat and power plants, are very strict, therefore, the continuous monitoring of emitted pollutants is carried out, and waste gas treatment systems are developed based on the best available techniques (BAT). The article presents emission standards applicable to waste incineration plants, including duties in the field of the environment, as well as issues related to the installation as a source of energy. In addition, the currently functioning waste incineration plants in Poland have been briefly characterized, and development plans in this area in the country have been described.

The condition number of the Generalized Inertia Matrix (GIM) of a serial chain can be used to measure its ill-conditioning. However, computation of the condition number is computationally very expensive. Therefore, this paper investigates alternative means to estimate the condition number, in particular, for a very long serial-chain. For this, the diagonal elements of the GIM are examined. It is found that the ratio of the largest and smallest diagonal elements of the GIM, when scaled using an initial estimate of the condition number, closely resembles the condition number. This significantly simplifies the process of detecting ill-conditioning of the GIM, which may help to decide on stability of the system at hand.