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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.

Intro -- Contents -- List of Figures -- Chapter 1 -- Introduction -- Chapter 2 -- Savings and Investment -- 2.1. Preface -- 2.2. Model of Economic Growth -- 2.2.1. Introduction -- 2.2.2. Model of Economy at the Undisturbed State -- 2.2.3. Model of One-Time Investment -- 2.2.4. Model of Constant-Rate Investment -- 2.2.5. Model of Constant-Accelerated Investment -- 2.2.6. Model of Exponential Investment -- 2.2.7. Conclusion -- 2.3. Growth Factors for Few Types of Investments -- 2.3.1. Introduction -- 2.3.2. Economic Growth Induced by Investments -- 2.3.2.1. Growth for Constant-Rate Investments -- 2.3.2.2. Growth for Constant-Accelerated Investments -- 2.3.3. Maximal Growth Rates Induced by Investments -- 2.3.3.1. Maximum Growth for Constant-Rate Investments -- 2.3.3.2. Maximum Growth for Constant-Accelerated Investments -- 2.3.4. Conclusion -- Chapter 3 -- Economic Trends -- 3.1. Preface -- 3.2. Model of Credit Expansion -- 3.2.1. Introduction -- 3.2.2. Model of Economy at the Undisturbed State -- 3.2.3. Model of Constant-Rate Credit Expansion -- 3.2.4. Economic Implications -- 3.2.5. Conclusion -- 3.3. Economic Growth and Debt -- 3.3.1. Introduction -- 3.3.2. Model of Economy at the Undisturbed State -- 3.3.3. Model of Constant-Rate Debt and Constant- Rate Investment -- 3.3.4. Model of Constant-Rate Debt and Constant-Acceleration Investment -- 3.3.5. Economic Implications -- 3.3.6. Conclusion -- 3.4. Model of Economic Trend -- 3.4.1. Introduction -- 3.4.2. Outline of the Mathematical Apparatus -- 3.4.3. Changes of the Trend Line -- 3.4.4. Graphical Presentation and Implications -- 3.4.5. Conclusion -- Chapter 4 -- Models of the Crises -- 4.1. Preface -- 4.2. Model of the Financial Crisis -- 4.2.1. Introduction -- 4.2.2. Model of Interactions between Real Market and Financial Market -- 4.2.2.1. Real Product Market -- 4.2.2.2. Financial Market

A convective drying model is proposed which may be used to describe the drying behavior of leather. Using this model, the calculated transient leather temperature agrees well with experimental values. Variations in temperature and moisture content distribution are solved using the finite-difference method. The effects of operation parameters, such as temperature and humidity in the dryer, initial moisture content of the leather, and heat and mass transfer coefficients are examined using the model.

This paper presents a dynamic model of smoking with optimal control. The mathematical model is divided into 5 sub-classes, namely, non-smokers, occasional smokers, active smokers, individuals who have temporarily stopped smoking, and individuals who have stopped smoking permanently. Four optimal controls, i.e., anti-smoking education campaign, anti-smoking gum, anti-nicotine drug, and government prohibition of smoking in public spaces are considered in the model. The existence of the controls is also presented. The Pontryagin maximum principle (PMP) was used to solve the optimal control problem. The fourth-order Runge-Kutta was employed to gain the numerical solutions.

"This book is written for readers who are either practicing engineers in industry or engineering-degree students taking a course in manufacturing technology. The book is divided into three parts which includes problems and solutions in basic manufacturing processes, problems and solutions in non-traditional and computer aided manufacturing, and problems and solutions in quality assurance and economics of manufacturing"--