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The paper discusses applying complex numbers to describe dynamics in building of a synthetic vector measure. A complex number describes the course of the line of regression of coeffcients used to calculate a synthetic measure. The result is also a complex number, denoting the course of the line of regression of the measure value [ABSTRACT FROM AUTHOR]

This paper presents an outline of a method of optimising the service life of aircraft guns at the stage of design engineering and retrofitting. The essence of this method is a selection of service lives and quantities of preventively replaced components and the service parts of non-reconditionable components resulting in an overall reduction of gun production and operating costs (including the costs of replacement parts stocks) with an improvement of the service life of the whole gun assembly. The method assumes that the service lives to be selected must meet a criterion of predefined reliability, maximum service availability when installed aboard a combat platform (i.e. an aircraft) and the minimum time to re-use. It is pointed out that in the design engineering of preventive component replacement and the assessment of the gun selection, a criterion of total gun cost reduction shall apply; the total gun cost is construed as the cost of production/purchase and maintenance applicable to the operating mode (with the costs and time to provide replacement parts). The total gun cost should be decisive in the definition of service lives and the number of components in preventive replacement. To analyse and select the service life and the MTBR (Mean Time Between Replacements), examples of reliability and life models of guns were developed in reference to the applicable operating standards and changes in total costs. This was followed by a demonstration of an innovative model of mapping gun (production/purchase and operating) costs with a complex number plane. The method presented herein facilitates analysing and assessing the feasibility for improvement of a gun’s availability in combat field and training operations.

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In this paper, a novel approach for coding nominal data is proposed. For the given nominal data, a rank in a form of complex number is assigned. The proposed method does not lose any information about the attribute and brings other properties previously unknown. The approach based on these knew properties can been used for classification. The analyzed example shows that classification with the use of coded nominal data or both numerical as well as coded nominal data is more effective than the classification, which uses only numerical data.