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The purpose of this paper is to find effective methods of loop analysis of multi‐branch and multi‐node non‐linear circuits using a singular formulation.

The classical loop analysis and the loop analysis using a singular formulation have been compared. The non‐linear systems of equations have been considered and iterative procedures of solving non‐linear equations have been applied. Special attention has been paid to the Newton‐Raphson method combined with successive over relaxation and incomplete Cholesky conjugate gradient methods. The convergence of the methods has been discussed.

It has been shown that in the case of the loop analysis of non‐linear circuits it is not necessary to form fundamental loops. The system of loop equations with a singular coefficient matrix can be successfully solved iteratively. Using a singular formulation one of the infinitely many solutions can be found quicker than the only one resulting from a classical method with a non‐singular coefficient matrix. Therefore, in the case of the analysis of multi‐branch and multi‐node non‐linear circuits using iterative methods, it is beneficial to introduce superfluous loops. This results in more economical computation and faster convergence.

The presented methods of solving multi‐branch and multi‐node non‐linear circuits using a singular formulation are universal and may be successfully applied both in circuit analysis and the FE analysis using edge elements for non‐linear problems with a large number of unknowns.

The article proposes a new method of strategic analysis. The method was called the grey portfolio analysis method. The presented method is complementary to the popular BCG matrix. The use of the grey portfolio analysis method enables to make a dynamic portfolio analysis for data with a high level of uncertainty.

First, the article presents current problems related to the application of portfolio methods in strategic management, in particular with reference to the BCG matrix. Second, the basics of grey numbers, operations with them and the way of acting in the grey portfolio analysis method are presented. Finally, the developed method is presented in a case study concerning an IT enterprise, whose portfolio includes cloud computing services.

In the article, a new method of a strategic analysis based on the BCG matrix was presented. It combines grey methodologies of decision making with a grey prognostic model in the context of a strategic analysis. Due to this fact, a dynamic approach to the issues of portfolio methods is possible.

The article fits the current need related to the development of new expert systems supporting strategic management in enterprises.

An introduced method is new and innovative in the area of portfolio methods. Its originality results from the fact that it eliminates a static nature of the BCG matrix through the use of grey prognostic models. What is more, when grey numbers are used, a problem of uncertainty of information, which appears, is solved at a methodological level.

The airline industry has been significantly hit by the occurrence of the new coronavirus SARS-CoV-2, facing one of its worst crises in history. In this context, the present paper analyses one of the well-known boarding methods used in practice by the airlines before and during the coronavirus outbreak, namely back-to-front and suggests which variations of this method to use when three passenger boarding groups are considered and a jet bridge connects the airport terminal with the airplane.

Based on the importance accorded by the airlines to operational performance, health risks, and passengers' comfort, the variations in three passenger groups back-to-front boarding are divided into three clusters using the grey clustering approach offered by the grey systems theory.

Having the clusters based on the selected metrics and considering the social distance among the passengers, airlines can better understand how the variations in back-to-front perform in the new conditions imposed by the novel coronavirus and choose the boarding approach that better fits its policy and goals.

The paper combines the advantages offered by grey clustering and agent-based modelling for offering to determine which are the best configurations that offer a reduced boarding time, while accounting for reduced passengers' health risk, measured through three indicators: aisle risk, seat risk and type-3 seat interferences and for an increased comfort for the passengers manifested through a continuous walking flow while boarding.