ADVANCED MODELING AND COMPUTER TECHNOLOGIES FOR FLUVIAL WATER QUALITY RESEARCH AND CONTROL -- ADVANCED MODELING AND COMPUTER TECHNOLOGIES FOR FLUVIAL WATER QUALITY RESEARCH AND CONTROL -- Library of Congress Cataloging-in-Publication Data -- CONTENTS -- INTRODUCTION -- Chapter 1 DETERMINISTIC MATHEMATICAL MODELS OF POLLUTANTS TRANSFER IN RIVERS -- 1.1. MATHEMATICAL MODELING OF POLLUTANTS TRANSFER IN RIVERS -- 1.2. MATHEMATICAL MODELS OF TRANSFER AND TURBULENT DIFFUSION -- 1.3. SOME ANALYTICAL METHODS USING AT SOLVING MULTIDIMENSIONAL PROBLEMS -- 1.4. DESCRIPTION OF RIVER BANKS BY SPLINES -- 1.4.1. The Contour of the River -- 1.4.2. Using Spline-Interpolation for Giving a Curve -- 1.4.3. Trigonometrical Spline-Interpolation -- 1.4.4. Spline-Interpolation by Integrals of Fractional-Rational Functions -- 1.4.5. Final Remarks -- 1.5. ABOUT APPROXIMATION OF RIVER CURRENT SPEED -- Chapter 2 CALCULATION SCHEMATA OF MATHEMATICAL MODELS -- 2.1. NUMERICAL METHODS OF SOLVING DIFFUSION EQUATIONS -- 2.1.1. Boundary Problem -- 2.1.2. Diffusion Equation -- 2.2. FINITE-DIFFERENCE AND ANALYTICAL METHODS OF SOLUTION OF ONE-DIMENSIONAL IN SPACE MODELS OF POLLUTANTS TRANSFER -- 2.3. ALGORITHMIC PRESENTATION OF THE FINITE-DIFFERENCE METHOD -- 2.4. ALGORITHMS FOR SOLVING TWO-DIMENSIONAL MATHEMATICAL MODELS -- 2.5. ALGORITHMS FOR REALIZATION OF THREE-DIMENSIONAL DIFFUSION MODELS -- 2.6. OPTIMIZATION PROBLEMS OF THE ALGORITHMS CONNECTED WITH DIFFERENCE SCHEMES -- 2.6.1. Optimization, Used in Boundary Problem -- 2.6.2. Optimization, Used at Solving Diffusion Equation -- 2.6.3. Estimation of Unknown Function Derivatives -- 2.6.4. Examples of Using of the Offered Optimization -- 2.7. THE EFFECT OF SMOOTHNESS OF THE INHOMOGENEOUS PART OF THE DIFFUSION EQUATION ON THE ACCURACY OF THE RESULTS.

Chapter 3 STOCHASTIC MATHEMATICAL MODELS DESCRIBING POLLUTION OF THE RIVERS -- 3.1. STATISTICAL MODELS OF POLLUTANTS TRANSPORT IN THE RIVERS -- 3.1.1. Statistical Models of Propagation of Pollutants in the Rivers -- 3.2. METHODS OF IDENTIFICATION OF NON-LINEAR REGRETIONS BY MODIFIED LEAST SQUARES CRITERION -- 3.3. RESTORATION OF POLYNOMIAL REGRESSION ON THE BASIS OF ACTIVE EXPERIMENT -- 3.4. INTERPOLATION OF NONLINEAR FUNCTIONS OF CERTAIN CLASS -- 3.4.1. One-parametrical Families of Functions of Polynomials -- 3.4.2. Nonlinear Functions of the Certain Class of Limited Quantity of Parameters -- 1. Function eba cx -- 2. Function ebxa )( cx0 -- 3. Function -- 4. Function -- 5. Function ebea Let be -- 6. Function ebeah -- 7. Function sin()cos((xBxAe sxy -- 8. Function ))sin()cos((BxAeh -- 3.4.3. Solution of Transcendental Equations of Special Types -- 1. Equation containing sum two exponents. -- 2. Equation containing sum of several exponents. -- 3.5. CONSTRUCTION OF CONFIDENCE INTERVALS FOR MATHEMATICAL EXPECTATIONS OF RANDOM VARIABLES -- 3.6. IMITATIVE MODELING OF FORMATION OF THE QUALITY OF SEWAGES -- 3.7. SIMULATION OF REAL MULTIDIMENSIONAL STATIONARY GAUSS-MARKOV SERIES WITH GIVEN DEPTH OF CONNECTIVITY -- Chapter 4 METHODS OF MAKING DECISIONS IN MONITORING OF RIVER POLLUTION -- 4.1. GENERALIZATION OF BAYESIAN RULE OF MANY HYPOTHESES TESTING -- 4.2. GENERAL SOLUTIONS OF UNCONDITIONAL AND CONDITIONAL BAYESIAN TASKS -- 4.2.1. Restrictions on Conditional Probabilities of Omitting True Parameters -- 4.2.2. Restrictions on Averaged Probability of Omitted True Parameters -- 4.2.3. Restrictions on Conditional Probabilities of Omitting Each True Parameter -- 4.2.4. Restrictions on Unconditional Probabilities of Omitting Each True Parameter.

4.3. ALGORITHMS OF SOLVING UNCONDITIONAL BAYESIAN PROBLEMS OF MANY SIMPLE HYPOTHESES TESTING -- 4.3.1. Step Loss Function j -- 4.3.2. Non-Step Loss Function -- 4.4. ALGORITHMS OF SOLVING CONDITIONAL BAYESIAN PROBLEM OF MANY SIMPLE HYPOTHESES TESTING -- 4.5. SOLUTION OF UNCONDITIONAL BAYESIAN PROBLEM AT NUMBER OF HYPOTHESES EQUAL TO TWO -- 4.6. Solution of Conditional Bayesian Problem at Number of Hypotheses Equal to Two -- 4.7. QUASI-OPTIMAL METHOD OF MANY-HYPOTHESES TESTING -- 4.8. RATIO OF VALUES OF THE RISK-FUNCTIONS IN PUT PROBLEMS AND THEIR NUMERICAL RESEARCHES -- 4.9. CONCLUSIVE REMARKS -- Chapter 5 MATHEMATICAL BASES FOR SOLVING PROBLEM OF IDENTIFICATION OF THE SOURCES OF EXCESSIVE RIVER POLLUTION -- 5.1. ESSENCE OF IDENTIFICATION PROBLEM -- 5.2. FORMALIZATION OF THE PROBLEM -- 5.3. GENERALIZED BLOCK-DIAGRAM FOR SOLVING IDENTIFICATION PROBLEM -- 5.4. ALGORITHM OF HYPOTHESES FORMATION -- 5.5. CALCULATION OF A PRIOR PROBABILITIES -- 5.6. DECORRELATION OF THE MEASURED VALUES VECTOR -- 5.7. ALGORITHMS OF CLUSTER-ANALYSIS FOR IDENTIFICATION OF EMERGENCY RELEASE SOURCES -- Chapter 6 SOFTWARE OF MATHEMATICAL MODELS OF POLLUTANTS TRANSPORT IN RIVERS -- 6.1. ASSIGNMENT AND POSSIBILITY OF THE PACKAGE -- 6.2. INPUT AND EDITING OF THE INITIAL DATA -- 6.3. MANAGEMENT OF WORK OF THE SOFTWARE -- 6.3.1. Description of the Files used in the Software -- 6.3.2. Working Language -- 6.3.3. Help Service and Notes -- 6.3.4. Parameters of the Package -- 6.3.5. Data Input and Editing -- 6.4. REALIZATION OF COMPUTATION AND REPRESENTATION OF THE RESULTS -- Chapter 7 SOFTWARE OF IDENTIFICATION OF THE SOURCES OF EXCESSIVE RIVER POLLUTION -- 7.1. APPOINTMENT OF THE PACKAGE -- 7.2. POSSIBILITY OF THE PACKAGE AND ITS APPLICATION -- Chapter 8 INVESTIGATION OF DEVELOPED ALGORITHMS AND PROGRAMS.

8.1. STUDY OF ALGORITHMS FOR CALCULATION OF POLLUTANT CONCENTRATIONS IN RIVERS BY MEANS OF DIFFUSION EQUATIONS -- Designations -- Bounds -- One-dimensional Model. Function I -- Considered Function -- Function -- Function -- One-dimensional Model. Function II -- Considered Function -- Considered Equation -- Function -- Function -- Two-dimensional model. Function I -- Considered Equation -- Function -- Function -- Two-dimensional Model. Function II -- Considered Equation -- Function -- Function -- Three-Dimensional Model ~ -- 8.2. COMPLEX TESTING OF THE DEVELOPED PACKAGE -- 8.2.1. Sensitivity of the Models of Different Dimensionality to Geometric Sizes of the River Cross-Section -- 8.2.2. Dependence of the Identification Quality on the Noise Level -- 8.3. MODELING OF POLLUTANTS TRANSPORT IN RIVERS -- 8.3.1. The Initial Data for Modeling -- 8.3.1.1. The River Chogha -- 8.3.1.2. The River Khobistskali -- 8.3.2. Calculation Results -- 8.3.2.1. The River Choga -- One- and Two-Dimensional Models -- Basic initial data -- Accuracy of calculations -- Geometry and dynamics of the section -- Water parameters -- Calculation results: at 1 m -- Calculation results: at 2 m. -- 8.3.22. The River Khobistskali -- One- and Two-Dimensional Models -- Basic initial data -- Accuracy of calculations -- Geometry and dynamics of the section -- Water parameters -- Calculation results: at 1 m. -- Calculation results: at 2 m. -- 8.3.3. Results of Modeling and Discussion 7 -- 8.4. RIVER POLLUTION COMPONENTS MEAN ANNUAL VALUES ESTIMATION BY COMPUTER MODELING -- CONCLUSION -- APPENDIX 1. GENERATOR OF RANDOM VARIABLES OBEYING THE GIVEN PROBABILITY DISTRIBUTION LAWS -- APPENDIX 2. GENERATOR OF NORMALLY DISTRIBUTED RANDOM VECTORS [212] -- APPENDIX 3. GENERATOR OF MULTIDIMENSIONAL NORMAL MARKOVIAN SERIES WITH A GIVEN CONNECTIVITY DEPTH [1, 213].

APPENDIX 4. THE RESULTS OF REALIZATION OF DESCRIBED IN SECTION 3.2 GENERAL METHODOLOGY FOR IDENTIFICATION OF NONLINEAR REGRESSIONS FOR CERTAIN CLASS OF FUNCTIONAL DEPENDENCES AND PROPERTIES OF RESTORED DEPENDENCES -- 1. GEOMETRICAL REGRESSION -- 2. EXPONENTIAL REGRESSION -- 3. LOGARITHMIC REGRESSION -- 4. GEOMETRIC- EXPONENTIAL REGRESSION -- 5. EXPONENTIAL REGRESSION WITH THE FREE MEMBER -- 6. GEOMETRICAL REGRESSION WITH THE FREE MEMBER -- 7. INVERSE EXPONENTIAL REGRESSION -- 8. LINEAR - EXPONENTIAL REGRESSION -- 9. LINEAR - EXPONENTIAL DEPENDENCE WITH THE FREE MEMBER -- 10. PRODUCT OF GEOMETRICAL DEPENDENCES -- 11. SUM OF EXPONENTIAL DEPENDENCES -- 12. SUM OF GEOMETRICAL DEPENDENCES -- 13. SUM OF EXPONENTIAL DEPENDENCES WITH THE FREE MEMBER -- 14. SUM OF GEOMETRICAL DEPENDENCES WITH THE FREE MEMBER -- 15. EXPONENTIAL - SINE WAVE REGRESSION -- 16. EXPONENTIAL - SINE WAVE REGRESSION WITH THE FREE MEMBER -- 17. POLYNOMIAL REGRESSION -- 18. GEOMETRICAL - POLYNOMIAL REGRESSION -- 19. EXPONENTIAL - POLYNOMIAL REGRESSION -- 20. LOGARITHMIC - POLYNOMIAL REGRESSION -- 21. PERIODIC REGRESSION -- 22. REGRESSION ANALYSIS -- 23. MULTIPLE LINEAR REGRESSION -- 24. THE BASIC PROPERTIES OF RESTORED DEPENDENCES -- Geometrical Dependence -- Exponential Dependence -- Logarithmic Dependence -- Geometric-exponential Dependence -- Inverse-exponential Dependence -- Geometrical Dependence with the Free Member -- Exponential Dependence with the Free Member -- Linear-Exponential Dependence -- Linear-exponential Dependence with the Free Member -- Product of Geometrical Dependences -- The Sum of Exponential Dependences -- The Sum of Geometrical Dependences -- The Sum of Exponential Dependences with the Free Member -- The Sum of Geometrical Dependences with the Free Member -- Exponential-sine Wave Dependence -- Exponential-sine Wave Dependence with the Free Member.

Polynominal Dependence.