In this paper, the energy losses in big band saw machines are investigated. These losses are caused by the geometric and angular inaccuracies with which the leading wheels are made. Expressions for calculating the kinetic energy of the mechanical system in the ideal and the real cases are obtained. For this purpose, expressions for calculating the velocities of the centers of the masses in two mutually perpendicular planes are obtained. A dependence for calculation of the kinetic energy losses of the mechanical system in final form is received. Optimization procedure is used to determine the values of the parameters at which these losses have minimum values. The proposed study can be used to minimize energy losses in other classes of woodworking machines.

The selection of a contractor is one of the most important among decisions made by the ownerof a construction. The application of the prequalification procedure enables the selection of themost competent tenderers. Various mathematical models are helpful in carrying out prequalificationprocedure. In the paper, some selected mathematical models are briefly characterized and modelbased on the theory of fuzzy sets is offered. The applied model takes into consideration theowner’s various objectives, as well as different evaluation criteria. The results of the sensitivityanalysis of the model are also presented. Part of a computer software applying an earlier presentedprequalification mathematical model is described.

In the first part of this article the author suggests a new etymology for the East Slavic adjective horošiĭ ʻgoodʼ (in Old Russian ʻbeautifulʼ) – from IE *ker(ə)- ʻburn, blazeʼ extended by the determinative -s-: richly attested *kor-s- > Proto Slavonic *xor-x- (> *xoršьjь) with the affective x-, like many other words. As proposed by many scholars, one of the variants of this root is present in Slavonic *krasa ʻbeautyʼ that corresponds to the original meaning of the adjective horošiĭ. The determinative -s- is commonly used for extending the root *ker(ə)-. The second part deals with three proper names in the (Old) Russian mythology and folklore that come, in the author’s opinion, from Iranic languages. The analysis of the early Old Russian written sources (The Ostromir’s Gospel and chronicles) allows to approve that the original form of the theonym Xors was Xorŭsŭ coming from the genitive form of the Iranian word for ‘sun’ in the truncated compound name (most likely, ‘son of the sun’ as a name of the deity of sunrise). The name of the tale bird Mogoveĭ/Magoveĭ corresponds to Avestan (Gath.) magavan-, adj. ‘belonging to the Zoroastrian community’, Old Indic maghá-van(t)- ‘generous; giver (also an epithet of Indra)’, Old Persian magav-, an adjective denoting a Median tribe whose representatives had got the rank of priests, ‘magic, magician’, Pāli maghavā, the name of Sakka. This name corresponds to another fairy bird name recorded on the same territory (in the basin of the Mezen, the region of Archangelsk) ‒ Vostrogot (Vostrogor) that continues Young Avestan a-srāvayaT.gāθā ‘not chanting the Gathas’; i.e., these two mythonyms form an opposition based on the semantic feature ‘initiated ‒ uninitiated (into the Zoroastrian doctrine and ritual)’.