Suchergebnisse

AbstractThe role of mathematical models in engineering design is no longer that of simply automating techniques which were previously carried out manually. Throughout industry models are now becoming accepted as one of the main decision support systems to managers. This is certainly the case in engineering design for managing the environment. We are rapidly moving into the age of expert systems and hydro‐informatics, where the primary aim of most models is decision support. In this paper the role of the models in modern practice is reviewed and illustrated by case histories.

Theoretical basis for presenting research results in agricultural science is mathematical statistics and probability theory using empirical forms of generalization of experimental data. To improve the methods of planning field experiment and processing its data using digital technologies, we proposed to use mathematical modeling based on physical principle of balance of cause-and-effect interactions in a closed physical system as a priority option. When analyzing impact of environmental factors on crop yields, the initial provisions, the mathematical modeling of the crop yield is based, on are not associated with characteristics of crops and natural conditions, therefore, the model options are universal in application and are valid for any agricultural crop, regardless of the region of cultivation. To ensure statistically correct digital information, based on the established forms of mathematical model, the field experiment layout aimed at establishing the dependence of the crop yield on yield-forming factors should include at least 4 options for nutritional levels (NPK) with a research duration of at least 4 years. To check the accuracy of the developed crop yield model, the data of independent field experiments of Professor N.N. Semenenko with barley and winter triticale has been used. It has been determined that, in Belarus, yield-forming factors, as a result of their impact on the grain yield, are arranged in the following decreasing sequence: total dose of applied NPK º the amount of precipitation during the active phases of growing season → air temperature for the same period. Calculations have shown that decrease in the number of yield-forming factors taken into account in the mathematical model from three (food, moisture and heat) to two (food and moisture) reduces the accuracy of calculating the grain crop yield insignificantly.

An integrated set of mathematical models has been developed for use in the identification and quantitative measurement of logistics problems, and the prediction of probable results of proposed changes or corrective actions. The models can be used individually or in various combinations. Used together, they provide the logistics planner with a means for making a complete analysis of requirements for logistics and operations during any phase of a weapon system program.

This paper presents a new common mathematical model which is able to describe fatigue characteristics in the whole necessary range by one equation only:log N = A(R) + B(R) ∙ log Sawhere A(R) = AR2 + BR + C and B(R) = DR2 + AR + F.This model was verified by five sets of fatigue data taken from the literature and by our own three additional original fatigue sets. The fatigue data usually described the region of N 104 to 3 x 106 and stress ratio of R = -2 to 0.5. In all these cases the proposed model described fatigue results with small scatter. Studying this model, following knowledge was obtained:– the parameter "stress ratio R" was a good physical characteristic– the proposed model provided a good description of the eight collections of fatigue test results by one equation only– the scatter of the results through the whole scope is only a little greater than that round the individual S/N curve– using this model while testing may reduce the number of test samples and shorten the test time– as the proposed model represents a common form of the S/N curve, it may be used for processing uniform objective fatigue life results, which may enable mutual comparison of fatigue characteristics.