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Bashkir State Univerity The Chair of Mathematical Modeling 450074, Ufa, Zaki Validi str. 32

THE INFORMATIVENESS OF THE KINETICS EXPERIMENT IN INVERSE PROBLEMS OF CHEMICAL. Bashkir State Univerity The Chair of Mathematical Modeling 450074, Ufa, Zaki Validi str. 32 Phone: 7-347-2299635, 7-9174448611 email: s.spivak@bashnet.ru. SEMYEN I . SPIVAK.

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Bashkir State Univerity The Chair of Mathematical Modeling 450074, Ufa, Zaki Validi str. 32

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  1. THE INFORMATIVENESS OF THE KINETICS EXPERIMENT IN INVERSE PROBLEMS OF CHEMICAL Bashkir State Univerity The Chair of Mathematical Modeling 450074, Ufa, Zaki Validi str. 32 Phone: 7-347-2299635, 7-9174448611 email: s.spivak@bashnet.ru SEMYEN I. SPIVAK Institute of Petrochemistry and Catalysis Russia Academy of Science The Laboratory of Mathematical Chemistry 450075, Ufa, October Avenue 141

  2. COMPLEX CHEMICAL REACTIONS MECHANISMTHE SET OF ELEMENTARY STAGES k+ k- - number of stages in the reaction mechanism, -the characters involved in the reactions of substances; - total number of substances; and stoichiometric coefficients of the initial reactants and reaction products, respectively; and - rate constants of stages in the forward and reverse directions respectively. Numbers and characterize the reaction order

  3. – concentrations of substances REACTION RATE The Low of Mass Action:

  4. THE SYSTEMS OF DIFFERENTIAL EQUATIONS OF CHEMICAL KINETICS – transposeГ. The general formula for the element of the stoichiometric matrix Г The chemical composition of substances reflect the molecular matrix A. Element number of atoms of q-th element contained in the molecule of the j-th agent. ГА = 0 The most important condition - the existence of linear integrals (linear relations between the concentrations)/ The number of independence integrals are the number of different types of chemical elements that make up the system.

  5. PROBLEM ABSENSE OF MEASUREMENTS PART OF SUBSTANCES X – vector of the measured substances, precursors and reaction products; У – vector of unmeasured substances, intermediates (radicals, catalysts and their complexes, substances on the surface of the catalyst, enzymes, etc.). Consequence of the lack of experimental data– ambiguity of the solution  the inverse problemidentification of the reaction mechanism.

  6. INVERSE PROBLEMS OF CHEMICAL KINETICS Identify which when substituted in the system of differential equations of chemical kinetics, reproduce the experimentally measured X Informativity of the experiment -the number of independent parametric functions of the constants that allow unambiguous estimation based on the available information. What kind of individual constants, or their non-linear parametric combinations? STRUCTURE OF THE EXPERIMENT 1. Nonstationary 2. Quasistationary Bodenshtein – Semenov Quasistationary Principle Choriuti – Temkin stationary reactions theory 3. Equilibrium Zeldovich function

  7. UNIQUENESS CRITERION(Calman and oth.) The number of independent columns equals the number of unknown constants s. The investigation noninformayivity of measurements The problem of non-uniqueness of solutions of principle. The main problem -informativity analysis of the measurements. Establishment of appropriate methods and algorithms mathematical software.

  8. Consequence of Jacobi matrix degeneration dimension is existence The system of independence nonlinear parametric functions is existence - the independence parameters of model The equations system for independence parameters The system of linear partial differential equations of first degree with variable coefficients

  9. QUASISTIONARY The main theorem There is the dimension of the matrix Instead of the Jacobian matrix is sufficient to consider the matrix U,structure is completely determined by the type of right-hand sides of the original system of equations, therefore, the reaction mechanism We prove the solvability of analytic systems of differential equations to determine theindependent parametric functions.A constructive procedure to determine them.Implemented as a system of analytical calculations

  10. NONSTAIONARY Non-uniqueness of solutions There is a transformation invariant with respect to X. Transformations allowed by the original system, form a group of transformations. The number of generators of the group -number of independent parameters of the model. The explicit form of generators -  expressions for the independent parameters. For quasi-stationary approximationproved to be equivalent to the approach based on an analysis of the matrix U.

  11. EXCEPTION UNMEASURED CONCENTRATIONS Direct exclusion of Y by moving to systems of differential equationshigh dimension of X. Derivation of explicit expressionsfor the independent model parameters. The system ofdesign algorithms for exceptionsbased on the methods of computer algebra.The software is developed.

  12. CRITERIA FOR A CALCULATION OF MEASUREMENTS N – number of measurements Normal distribution of measurement error – the sum of squared deviations (the minimal squares method) Laplace distribution of measurement error - sum of absolute deviations The uniform law of distribution of measurement error - the module maximum deviation (Chebyshev method for alignment) "Everyone believes in the normal distribution in its own way a mathematician thinks he should be out of the experiment, the experimenter believes that it is strictly proved mathematic”. Puankare.

  13. The basic idea -Correlation the measurement errorwith an error in the determination of parameters of mathematical models. The main result -The absence of the hypothesis that the distribution of measurement error.Calculate the domain within which each point describes a measurement within the margin of error of measurementThere is no minimizing the criterion of conformity error measurements. Leonid V. Kantorovich. On new approaches to problems processing observations. // Siberian mathematical journal, 1962, v.3, №5, p. 701-709.

  14. UNCERTAINTY INTERVALS FOR THE PARAMETERS Calculation - experiment: - vector of the maximum permissible error of measurement We determine under the conditions of compliance We decide 2s problems of mathematical programming. For some s No information provided by a constant. The problem -Planning of measurements in order to reduce the uncertainty. The possibility of using solutions dual tasks.

  15. CONCLUSION The methods and algorithms for calculating the domains of uncertainty of kinetic parameters in constructing mathematical models of complex chemical reactions developed and implemented. SCHEME OF STUDY Analytical analysis of information content. The ideology of the Gauss relation of the parameters kinetic models of complex chemical reactionswith the characteristics of the measurements. Kantorovich method.

  16. Thank You for Your Attention!

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