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Purpose. The purpose of this work is to obtain a statistical mathematical model of cement-ash stone with the response function – the strength of the stone. In particular, the task is to establish the effect on the strength of cement stone additives in the form of ash-removal of thermal power plants (pozzolanic additive). Methodology. A rotatable central composition plan of the experiment was used to obtain a statistical model. The results were processed using the method of computer mathematical modeling using the system STATGRAPHICS Plus for Windows. Originality. It is established that the hypersurface G (X₁, X₂) has an extremum point, which allows to optimize the composition of the cement mixture by factors X₁, X₂. Practical value. The results obtained in this work make it possible to predict the strength characteristics of the stone on the basis of cement-ash composition. Finding. The statistical mathematical model of cement-ash stone on the basis of cement of general construction purpose of the ПЦI-500-Н brand is received. From the obtained pareto-graphs, hypersurfaces and contour curves, the nature and degree of influence of each of the polynomial members on the objective function – the strength of cement stone G (X₁, X₂, X₃) are determined. The factors of model X₁, X₃ have the greatest statistical significance, the factor X₂ is statically the least significant. The simulation results confirm that the water-mixture ratio does not have a significant effect on the strength of cement stone in a given range of formulations. The maximum strength of cement stone G = 13,582 MPa takes place at the optimum point with coordinates: Х₁ = 0,689; Х₂ = −0,295; Х₃ = 1,105.

Purpose. The purpose of this work is to obtain a statistical mathematical model of cement-ash stone with the response function - the strength of the stone. In particular, the task is to establish the effect on the strength of cement stone additives in the form of ash-removal of thermal power plants (pozzolanic additive). Methodology. A rotatable central composition plan of the experiment was used to obtain a statistical model. The results were processed using the method of computer mathematical modeling using the system STATGRAPHICS Plus for Windows. Originality. It is established that the hypersurface G (X1, X2) has an extremum point, which allows to optimize the composition of the cement mixture by factors X1, X2. Practical value. The results obtained in this work make it possible to predict the strength characteristics of the stone on the basis of cement-ash composition. Finding. The statistical mathematical model of cement-ash stone on the basis of cement of general construction purpose of the ПЦI-500-Н brand is received. From the obtained pareto-graphs, hypersurfaces and contour curves, the nature and degree of influence of each of the polynomial members on the objective function - the strength of cement stone G (X1, X2, X3) are determined. The factors of model X1, X3 have the greatest statistical significance, the factor X2 is statically the least significant. The simulation results confirm that the water-mixture ratio does not have a significant effect on the strength of cement stone in a given range of formulations. The maximum strength of cement stone G = 13,582 MPa takes place at the optimum point with coordinates: Х1 = 0,689; Х2 = -0,295; Х3 = 1,105. [ABSTRACT FROM AUTHOR]

Paper presents kinetic models of changes in genetic controlling systems of cells in the states of cell proliferation and differentiation. It was shown that the changes in the genetic control of cells in the state of proliferation and differentiation occur at the maximal rate of reactions constants. It was built on response surfaces for each of the reaction rate constants showing what parameters of the model make the largest contribution to the value of each of them. It was established that the greatest contribution to the rate of reaction constants of changes in the genetic controlling systems of cells in the state of proliferation have histone genes and cyclin-dependent kinases, and a little less – genes-stimulators of proliferation and transcription factors. In cells in diffe­rentiation a state of inhibitors of cyclin-dependent kinases, and equally transcription factors, cell cycle genes, transcription proteins genes, structural genes and hyperpolarization of the cell membrane. As a result, we got data that the value concentration of cyclin-dependent kinases and inhibitors of cyclin-dependent kinases in the cell is the trigger that determines whether a cell proliferates or differentiates. Also, it was set specific numerical value of each of the reactions rate constants which characterize changes in the genetic control of cell in the state of proliferation and differentiation.