APPROXIMATING MATHEMATICAL MODEL DEVELOPMENT ACCORDING TO POINT EXPERIMENTAL DATA THROUGH “CUT-GLUE” METHOD

A solution to the problem on describing experimentally obtained dependences is considered. The autho r’s method is based upon getting some local approximations of fragments of these relations, and their additive reduction to a single analytical expression. This effect is determined using special “allocating” functions limitin g the domain of non zero definition for each of the approximation functions. The method is called “cut - glue” according to the applied principles. The closest analogue of the proposed method is spline approximation. However, the “cut - glue” method is much more adaptable, as it is bonded to neither the number of spline - approximable points, nor the function order approximating the areas. The order of the polynomial approximant, or another approximating function, as well as its structure for each site, can be arbitrary. Another advantageous difference of “cut - glue” approximation consists in a single a nalytic notation of the whole piecewise function instead of defining a vector spline - function through a cu mbersome system of equations. This effect has been achieved using an analytical function approximatin g and par ametrically arbitrarily approaching the Heaviside step function. The analytical and numerical studies of the properties and the effects of applying the proposed method are resulted. The obtained results are illustrated w ith the specific technical sample applications of the method to practical pr oblems, tabular and graphical data

SPEEDING ALGORITHM FOR MINIMAX OPTIMIZATION OF ALLOCATION PROBLEM SOLUTIONS IN HOMOGENEOUS SYSTEMS

The optimization algorithm for solving homogeneous allocation problems of the scheduling theory is described and proved. It is a modification of Romanovsky’s algorithm known in this problem domain. Romanovsky’s algorithm is a classical version of the branch-and-bound method with one-way traversing a decision tree. A systematic study of this algorithm that allows revealing reasons for its operate time increment when traversing some decision tree branches is carried out. It allows proposing modification free of the revealed shortcoming. It is called a combinatorial-modified Romanovsky's algorithm. The essence of this modification is as follows. In the process of solving the allocation problem, those rules, stages, and steps that lead to the sorting on executors the sets of tasks deliberately duplicating the previous effects are selectively skipped. The essence of the new algorithm is illustrated by an example. The statistically presented studies are resulted. They demonstrate the algorithm capabilities on the high dimensional allocation problems. (Such problems cannot be solved by the classical algorithm due to the limited timing budgets.) The results of processing these solutions have shown that the new modification does not solve the problem of NP-complete allocation tasks, but it provides a resource-time gain associated with the significant reduction in the exponential model index of the average solution time

TESTING DESIGN METHODOLOGY BASED ON TWO-LEVEL MULTIFACTOR EXPERIMENT PLANNING AND DATA PROCESSING

The decomposition of knowledge into an array of “micro-knowledge” permitting a single-valued binary test score is studied. In this case, the test task is formulated as a set of micro-knowledge responses jointly revealing the knowledge level of the specific subsection. It allows presenting the development of a set of responses to a test question as the objective of investigating the multifactor dependence. Thus, the development process of a set of responses can be considered from the perspective of planning a multifactor two-level experiment. This approach allows a good formalization of the test construction, and its result estimation which becomes available to the teachers who do not specialize in the test task development. The method is illustrated by an example of the test construction, and application to assess the knowledge level on the automatic control theory. The data statistics has shown the respondents’ knowledge level, as well as the degree of a tester’s belief to the response awareness

RESEARCH ON BUOYANT FORCE DEPENDENCE OF SPECIALIZED AEROSTAT ON ITS MOTION VIRABLES

The international scientific-research MAAT (Multibody Advanced Airship for Transport) project supported by the European Union on the Seventh framework program solves the global problem on the ecologically safe transportation. One of its sections has the aim to research the aerodynamics of the specialized high-altitude balloons — so-called shuttles. They are designed for supporting communications between the earth-based airports and the aerostats which are permanently cruising in the stratosphere — cruisers. One of the aerodynamic research tasks needed to develop an appropriate mathematical model is solved. The problem on the mathematical description of the buoyant force changes under the shuttle plunging in its both undisturbed and disturbed position is set and solved. For that, a simulation experiment based on the so-called “electronic airflow” through the computer modeling is conducted. The computing results of the buoying drag force under varying conditions are processes through the regression analysis techniques. The obtained expression permits to identify the mathematical model of the shuttle motion dynamics presented through Euler's equations. The results are illustrated by the table and graphical data