This paper presents the concept of using algorithms for reducing the dimensions of finite-difference equations of two-dimensional (2D) problems, for second-order partial differential equations. Solutions are predicted as two-variable functions over the rectangular domain, which are periodic with respect to each variable and which repeat outside the domain. Novel finite-difference operators, of both the first and second orders, are developed for such functions. These operators relate the value of derivatives at each point to the values of the function at all points distributed uniformly over the function domain. A specific feature of the novel operators follows from the arrangement of the function values as well as the values of derivatives, which are rectangular matrices instead of vectors. This significantly reduces the dimensions of the finite-difference operators to the numbers of points in each direction of the 2D area. The finite-difference equations are created exemplary elliptic equations. An original iterative algorithm is proposed for reducing the process of solving finite-difference equations to the multiplication of matrices.

In this paper the basic methodology of the coupled response-degradation modelling of stochastic dynamical systems is presented

along with the effective analysis of selected problems. First, the general formulation of the problems of stochastic dynamics coupled with the evolution of deterioration process is given. Then some specific degrading oscillatory systems under random excitation are analyzed with a special attention on the systems with fatigue-induced stiffness degradation. Both, the general discussion and the analysis of selected exemplary problems indicate how the reliability of deteriorating stochastic dynamical systems can be assessed.

The paper discuss a problem of determination of inductances for AC machine windings when saturation of magnetic circuit is not neglected. For such cases, computation of magnetic field distribution in the machine magnetic circuit is a starting point for post processing procedures leading to various values, among others the co-energy in a given area and linkage fluxes of windings. This paper shows how to determine winding inductances in a nonlinear magnetic circuit from these two values and also how to compute directly nonlinear inductances. Problem is not trivial because such inductances are not uniquely determined as for linear case. In the paper a definition of nonlinear inductances is proposed which makes the choice unique.

This paper describes an algorithm for finding steady states in AC machines for the cases of their two-periodic nature. The algorithm enables to specify the steady-state solution identified directly in time domain despite of the fact that two-periodic waveforms are not repeated in any finite time interval. The basis for such an algorithm is a discrete differential operator that specifies the temporary values of the derivative of the twoperiodic function in the selected set of points on the basis of the values of that function in the same set of points. It allows to develop algebraic equations defining the steady state solution reached in a chosen point set for the nonlinear differential equations describing the AC machines when electrical and mechanical equations should be solved together. That set of those values allows determining the steady state solution at any time instant up to infinity. The algorithm described in this paper is competitive with respect to the one known in literature an approach based on the harmonic balance method operated in frequency domain.

Pope Francis often speaks about the new evangelization. He notices areas that need a special care of the Church. One of them is the problem of poverty. The Pope encou-rages all the faithful to engage in the transformation of this situation . It can be called a “throwaway culture” and a sign of real poverty of the whole society when people remain indifferent to the cause of the poor. It is one of the negative consequences of the culture of prosperity. The Pope also calls it a “globalisation of indifference” and calls on all people of the three states in the Church to care for those who are poor and abandoned and to act against poverty. In a particular way Francis addresses his appeal to the consecrated persons, encouraging them to contemplate the poor Jesus, to the consecration of their lives through a faithful fulfilment of their vow of poverty and to the apostolate among the poor and the marginalized . By means of such an attitude of men and women religious they would contribute to their own sanctification, to bearing witness to love to the poor before the world and at least partly they will help those in need among whom they live and serve.

This article presents the use of a multi-criterion Analytic Hierarchy Process (AHP) method to assess

geological and mining condition nuisance in longwall mining operations in selected coal mines in Poland.

For this purpose, a methodology has been developed which was used to calculate the operational nuisance

indicator (WUe) in relation to the cost of mining coal in individual longwalls. Components of the aggregate

operational nuisance indicator include four sub-indicators: the natural hazards indicator (UZN), an

indicator describing the seam parameters (UPZ), an indicator describing the technical parameters (UT)

and an environmental impact indicator (UŚ). In total, the impact of 28 different criteria, which formed

particular components of the nuisance indicators were analysed. In total 471 longwalls in 11 coal mines

were analysed, including 277 longwalls that were mined in the period of 2011 to 2016 and 194 longwalls

scheduled for exploitation in the years 2017 to 2021.

Correlation analysis was used to evaluate the relationships between nuisance and the operating costs

of longwalls. The analysis revealed a strong correlation between the level of nuisance and the operating

costs of the longwalls under study. The design of the longwall schedule should therefore also take into

account the nuisance arising from the geological and mining conditions of the operations. Selective

operations management allows for the optimization of costs for mining in underground mines using the

longwall system. This knowledge can also be used to reduce the total operating costs of mines as a result

of abandoning the mining operations in entire longwalls or portions of longwalls that may be permanently

unprofitable. Currently, underground mines do not employ this optimization method, which even more

emphasizes the need for popularizing this approach.