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This paper continues formalization in the Mizar system [2, 1] of basic notions of the composition-nominative approach to program semantics [14] which was started in [8, 12, 10]. The composition-nominative approach studies mathematical models of computer programs and data on various levels of abstraction and generality and provides tools for reasoning about their properties. In particular, data in computer systems are modeled as nominative data [15]. Besides formalization of semantics of programs, certain elements of the composition-nominative approach were applied to abstract systems in a mathematical systems theory [4, 6, 7, 5, 3]. In the paper we give a formal definition of the notions of a binominative function over given sets of names and values (i.e. a partial function which maps simple-named complex-valued nominative data to such data) and a nominative predicate (a partial predicate on simple-named complex-valued nominative data). The sets of such binominative functions and nominative predicates form the carrier of the generalized Glushkov algorithmic algebra for simple-named complex-valued nominative data [15]. This algebra can be used to formalize algorithms which operate on various data structures (such as multidimensional arrays, lists, etc.) and reason about their properties. In particular, we formalize the operations of this algebra which require a specification of a data domain and which include the existential quantifier, the assignment composition, the composition of superposition into a predicate, the composition of superposition into a binominative function, the name checking predicate. The details on formalization of nominative data and the operations of the algorithmic algebra over them are described in [11, 13, 9]. [ABSTRACT FROM AUTHOR]

This paper continues formalization in Mizar [2, 1] of basic notions of the composition-nominative approach to program semantics [13] which was started in [8, 11]. The composition-nominative approach studies mathematical models of computer programs and data on various levels of abstraction and generality and provides tools for reasoning about their properties. Besides formalization of semantics of programs, certain elements of the composition-nominative approach were applied to abstract systems in a mathematical systems theory [4, 6, 7, 5, 3]. In the paper we introduce a definition of the notion of a binominative function over a set D understood as a partial function which maps elements of D to D. The sets of binominative functions and nominative predicates [11] over given sets form the carrier of the generalized Glushkov algorithmic algebra [14]. This algebra can be used to formalize algorithms which operate on various data structures (such as multidimensional arrays, lists, etc.) and reason about their properties. We formalize the operations of this algebra (also called compositions) which are valid over uninterpretated data and which include among others the sequential composition, the prediction composition, the branching composition, the monotone Floyd-Hoare composition, and the cycle composition. The details on formalization of nominative data and the operations of the algorithmic algebra over them are described in [10, 12, 9]. [ABSTRACT FROM AUTHOR]

This paper presents an original method for checking influence of lubricating oil improvers on performance of crankshaft seals of combustion piston engine. Crankshaft seals were tested with the use of a modified friction node of T-02 four- ball apparatus in laboratory conditions. The tests were conducted according to a worked-out algorithm. Their results confirmed usefulness of the method for determining „harmful" performance of sealing systems, which makes it possible to assess operational usability of lubricating oil improvers. On the basis of an analysis of the results a scientific hypothesis saying that lubricating oil quality affects correctness of performance of crankshaft seals of combustion piston engine, was formulated. The hypothesis was verified by means of induction inference and statistical method with taking into account Fisher statistics. [ABSTRACT FROM AUTHOR]

A possibility of utilising the GPS system for navigation and transport are fundamentally dependent on the accuracy in positioning. Two fundamental factors decisive for its value are the values of the User Range Error (URE) and Dilution of Precision (DOP), strictly related to the number of satellites forming the constellation. The nominal constellation of GPS satellites consists of 24 units which gives a possibility of identification of coordinates all over the globe. In the last few years, however, the nominal number of satellites in the constellation was much higher, and the URE value has been constantly increasing. The authors of the paper try to estimate the impact of the changing number of GPS satellites on accuracy of position coordinates with a variable URE value. Mathematical model for estimating geometrical indicators' value, utilising data derived from the almanac files has been presented. Following a drawn-up algorithm and calculations made with Mathcad software, the authors carried out a comparative analysis of mean daily values of DOP indicators for a variable number of satellites included in the GPS constellation in the years 2001-2013. Then, the authors have established representative values of Two Distance Root Mean Square Error (2drms) 2D and 3D, and calculated a percentage increase of accuracy in the period under discussion. [ABSTRACT FROM AUTHOR]

The paper introduces methods of dynamic games for automation of ship control in the collision situation, the game control processes in marine navigation and the fundamental mathematical model of the game ship control. First, state equations, control and state constraints and then control goal function in the form of payments: the integral payment and the final one, have been defined. Multi-stage positional, and multi-step matrix, non-cooperative and cooperative, game and optimum control algorithms for a collision situation, have been presented. Te considerations have been illustrated with an exemplary computer simulation of algorithms to determine a safe own ship's trajectory in the process of passing the ships encountered in Kattegat Strait. [ABSTRACT FROM AUTHOR]