EXAMPLES OF QUANTUM IT IN NEW TECHNOLOGIES OF COMPUTATION

The paper includes definitions of elements of quantum IT referred to classical technologies of computation. It explains the principles of transformation of calculating algorithms to the domain of quantum computations using the optimisation and matrix calculus. Exemplary applications of classical algorithms are presented with possibilities of their realisation in domain of quantum IT. Autor presents some possibilities for using quantum algorithms in new computation technologies concerning quantum cryptography and data analyses with complex computations.

Quantum inspiration to build a neural model based on the Day-Ahead Market of the Polish Power Exchange

The article is an attempt of the methodological approach to the proposed quantum-inspired method of neural modeling of prices quoted on the Day-Ahead Market operating at TGE S.A. In the proposed quantum-inspired neural model it was assumed, inter alia, that it is composed of 12 parallel Perceptron ANNs with one hidden layer. Moreover, it was assumed that weights and biases as processing elements are described by density matrices, and the values flowing through the Artificial Neural Network of Signals are represented by qubits. Calculations checking the correctness of the adopted method and model were carried out with the use of linear algebra and vector-matrix calculus in MATLAB and Simulink environments. The obtained research results were compared to the results obtained from the neural model with the use of a comparative model.

The Multi-Criteria Method for the Evaluation of Combat Capabilities of Anti-aircraft Missile Systems Under the NAREW Programme

The selection of weapon systems involves a number of activities to choose the best system in relation to the predefined operational requirements and other vital criteria. In the case of surface to air missile systems competing for the NAREW program, attempts are being made to obtain an asset that will be capable of engaging a spectrum of air threats, under specified conditions, with a predefined high degree of probability. In order to make the right choice, it is necessary to analyze information on performance and combat capabilities. Thus, the aim of this article is to develop a preliminary method of evaluating the capabilities of surface to air missile systems offered under the NAREW program. The theoretical foundation of the empirical study was provided by the method of literature content analysis. Using the methods of comparison and generalization, the author obtained data on the combat capabilities of surface to air missile systems expressed through their tactical and technical parameters. Among the empirical methods, the author applied the algorithm of a multi-criteria analysis and an assessment of the capabilities of surface to air missile systems based on the use of matrix calculus. The diagnostic survey, conducted by means of the questionnaire technique, made it possible to prioritize the adopted evaluation criteria and, consequently, to conduct proper research. The formulation of the final conclusions and establishing the links between the theoretical and empirical part of the study was achieved by means of a synthesis. The results obtained in such a manner may constitute a valuable information database, showing the directions that should be considered when selecting a short-range surface to air missile (SAM) system for Poland. The evaluations and suggestions included in this study can be used for prospective solutions and research conducted in a similar area.

Applying graph-matrix models in the strategic analysis of production capacity of iron and steel enterprises

Subject. The article addresses the development of a methodology for seeking reserves to increase production capacity through the enhanced balance of production system and bringing the latter to practical use at iron and steel enterprises. Objectives. The purpose is to design a methodology to search for reserves to enhance production capacity of industrial enterprises at the strategic level, using the graph-matrix models of integrated steel works. Methods. The study draws on methods of analysis and synthesis, principles of consistency and complexity, the graph theory, and matrix calculus. Results. The paper offers a method for assessing and analyzing reserves to increase production capacity through enhancing the balance of the production system. Conclusions. If used, the presented approach will help improve the quality of strategic management of production facilities in the iron and steel industry, and, as a result, the profitability and competitiveness of ironworks.

General Bivariate Appell Polynomials via Matrix Calculus and Related Interpolation Hints

An approach to general bivariate Appell polynomials based on matrix calculus is proposed. Known and new basic results are given, such as recurrence relations, determinant forms, differential equations and other properties. Some applications to linear functional and linear interpolation are sketched. New and known examples of bivariate Appell polynomial sequences are given.

Derivations of matrix semirings

It is well known that if [Formula: see text] is a derivation in semiring [Formula: see text], then in the semiring [Formula: see text] of [Formula: see text] matrices over [Formula: see text], the map [Formula: see text] such that [Formula: see text] for any matrix [Formula: see text] is a derivation. These derivations are used in matrix calculus, differential equations, statistics, physics and engineering and are called hereditary derivations. On the other hand (in sense of [Basic Algebra II (W. H. Freeman & Company, 1989)]) [Formula: see text]-derivation in matrix semiring [Formula: see text] is a [Formula: see text]-linear map [Formula: see text] such that [Formula: see text], where [Formula: see text]. We prove that if [Formula: see text] is a commutative additively idempotent semiring any [Formula: see text]-derivation is a hereditary derivation. Moreover, for an arbitrary derivation [Formula: see text] the derivation [Formula: see text] in [Formula: see text] is of a special type, called inner derivation (in additively, idempotent semiring). In the last section of the paper for a noncommutative semiring [Formula: see text] a concept of left (right) Ore elements in [Formula: see text] is introduced. Then we extend the center [Formula: see text] to the semiring LO[Formula: see text] of left Ore elements or to the semiring RO[Formula: see text] of right Ore elements in [Formula: see text]. We construct left (right) derivations in these semirings and generalize the result from the commutative case.