مدل‌سازی در ریاضیات

Modeling in Mathematics deals with the concept of modeling in the field of mathematics. It includes a statistical and spectral model for representing noisy sounds with short-time sinusoids, robust Bayesian regularized estimation based on regression model and robust quadratic regression and its application to energy-growth consumption problem. This book also discusses about intuitionistic fuzzy weighted linear regression model with fuzzy entropy under linear restrictions, a hybrid approach of stepwise regression, logistic regression, support vector machine, and decision tree for forecasting fraudulent financial statements, dynamical analysis in explicit continuous iteration algorithm and its applications, dynamical analysis and chaos control of a discrete sis epidemic model, electricity market stochastic dynamic model and its mean stability analysis and using artificial neural networks to predict direct solar irradiation. Cover Title Page Copyright DECLARATION ABOUT THE EDITOR TABLE OF CONTENTS List of Contributors List of Abbreviations Preface Chapter 1 A Statistical and Spectral Model for Representing Noisy Sounds with Short-Time Sinusoids Abstract Introduction Background Justification of a Spectral And Statistical Model For Noises The CNSS Model Analysis Synthesis Application and Conclusion Conclusion Acknowledgments References Chapter 2 Robust Bayesian Regularized Estimation Based on Regression Model Abstract Introduction T Regression Model and L1 Norm Regularization Bayesian Formulation of Robust T Adaptive Lasso Simulation Studies Land Rent Data Conclusion Remarks Appendices Acknowledgment References Chapter 3 Robust Quadratic Regression and Its Application to Energy-Growth Consumption Problem Abstract Introduction Robust Quadratic Regression Models Robust Energy-Growth Regression Models Numerical Experiments Conclusions and Future Works Acknowledgment References Chapter 4 Intuitionistic Fuzzy Weighted Linear Regression Model with Fuzzy Entropy under Linear Restrictions Abstract Introduction Restricted IFWLR Model With Fuzzy Entropy Estimation of Regression Coefficients Numerical Examples Conclusions References Chapter 5 A New Method of Hypothesis Test for Truncated Spline Nonparametric Regression Influenced by Spatial Heterogeneity and Application Abstract Introduction Truncated Spline Nonparametric Regression Influenced by Heterogeneity Spatial Method Parameter Estimation Under Space H0 and Space Population in The Model Statistics Test For Truncated Spline Nonparametric Regression With Spatial Heterogeneity Distribution of Test Statistic and Critical Area of Hypothesis Empirical Study on Unemployment Rate in Java Indonesia Conclusion Acknowledgments References Chapter 6 A Hybrid Approach of Stepwise Regression, Logistic Regression, Support Vector Machine, and Decision Tree for Forecasting Fraudulent Financial Statements Abstract Introduction Literature Review Empirical Analysis Conclusion and Suggestion References Chapter 7 Dynamical Analysis in Explicit Continuous Iteration Algorithm and its Applications Abstract Introduction Construction of Explicit Continuous Iterative Algorithm Error Analysis Numerical Experiments Conclusion Acknowledgements References Chapter 8 A New Stability Analysis of Uncertain Delay Differential Equations Abstract Introduction Uncertain Delay Differential Equation Almost Sure Stability Stability Theorem Comparison Conclusion Appendix Acknowledgments References Chapter 9 Dynamical Analysis and Chaos Control of a Discrete SIS Epidemic Model Abstract Introduction Analysis of Equilibria Analysis of Bifurcation Numerical Simulation Chaos Control Conclusion Acknowledgements Authors’ Contributions References Chapter 10 Applications of Parameterized Nonlinear Ordinary Differential Equations and Dynamic Systems: An Example of the Taiwan Stock Index Abstract Introduction Literature Review Methodology Empirical Study Conclusions References Chapter 11 Electricity Market Stochastic Dynamic Model and Its Mean Stability Analysis Abstract Introduction The Stochastic Dynamic Modeling of Electricity Market Stochastic Differential Equation Theories Mean Stability of Electricity Market Stochastic Model The Numerical Examples Conclusions Acknowledgment References Chapter 12 Using Artificial Neural Networks to Predict Direct Solar Irradiation Abstract Introduction Literature Review of Estimation of Direct Solar Radiation Test Area and Data Feedforward Neural Network Experimental Procedure Results And Discussions Conclusions References Chapter 13 Modeling of Relative Intensity Noise And Terminal Electrical Noise of Semiconductor Lasers Using Artificial Neural Network Abstract Introduction Artificial Neural Network Modeling Results And Discussions Conclusion References Chapter 14 Quantum-Like Bayesian Networks for Modeling Decision Making Introduction Violations of The Sure Thing Principle Violation of The Sure Thing Principle: Classical Approaches Violation of The Sure Thing Principle: Quantum-Like Approaches Problems With Current Classical and Quantum-Like Approaches A Quantum-Like Bayesian Network For Decision And Cognition Experimental Results Discussion and Conclusion Acknowledgments References Index Back Cover