ریاضیات چندمتغیره

The book "Multivariable Mathematics" is a collection of contemporaneous articles combines several topics of multivariate mathematics, from extensions of uni-variate methodologies to practical applications in several research areas of multivariate calculus, statistical analysis, time series, polynomial geometry and differential topology. It navigates through several applications in numerous scientific domains such as physics, economics, data science, network science, and more. Cover Title Page Copyright DECLARATION ABOUT THE EDITOR TABLE OF CONTENTS List of Contributors List of Abbreviations Preface Chapter 1 Multivariate Spectral Gradient Algorithm for Nonsmooth Convex Optimization Problems Abstract Introduction Algorithm Global Convergence Numerical Results Conclusions Acknowledgments References Chapter 2 U-Statistic for Multivariate Stable Distributions Abstract Introduction New Estimators Simulation Study Conclusion References Chapter 3 A Kind of System of Multivariate Variational Inequalities and the Existence Theorem of Solutions Abstract Introduction Preliminaries Main Results Conclusion Acknowledgements Authors’ Contributions References Chapter 4 An Axiomatic Integral and a Multivariate Mean Value Theorem Abstract Introduction And Motivation Axioms And Their Consequences Mean Value Theorem For Continuous Multivariate Mappings Some Particular Cases And Open Problems Competing Interests Acknowledgements References Chapter 5 Multivariate Longitudinal Analysis with Bivariate Correlation Test Abstract Introduction Materials And Methods Results And Discussion Conclusion Acknowledgments References Chapter 6 Generalized Inferences about the Mean Vector of Several Multivariate Gaussian Processes Abstract Introduction Continuous Time Generalized Tests And Confidence Regions Estimation Method The Behrens-Fisher Problem Inferences About The Vector Means Of Several Independent Gaussian Processes References Chapter 7 A New Test Of Multivariate Nonlinear Causality Abstract Introduction The Multivariate Nonlinear Causality Test Extended From Hj Test A New Multivariate Nonlinear Causality Test Numerical Study Conclusion And Remarks Appendix Acknowledgments References Chapter 8 Multivariate Time Series Similarity Searching Abstract Introduction Related Work The Proposed Method Experimental Evaluation Conclusion And Future Work Acknowledgments References Chapter 9 A Method for Comparing Multivariate Time Series with Different Dimensions Abstract Introduction Model Results Acknowledgments Author Contributions References Chapter 10 Network Structure of Multivariate Time Series Abstract Introduction Results Discussion Methods References Chapter 11 Networks: On the Relation of bi- and Multivariate Measures Abstract Introduction Theory On Data-Based Network Inference Theoretical Results Simulation Setup And Results Conclusion References Chapter 12 Cubic Trigonometric Nonuniform Spline Curves and Surfaces Abstract Introduction Basis Functions The Property Of The Basis Functions Spline Curves Spline Surfaces Conclusion Acknowledgment References Chapter 13 Fitting Quadrics with a Bayesian Prior Abstract Introduction Related Work Bayesian Quadrics Choice Of Prior Parametrisation Eigendecomposition Results Simulated Data Conclusions References Chapter 14 Multivariate Rational Response Surface Approximation of Nodal Displacements of Truss Structures Abstract Introduction Polynomial-Basis Response Surface Approximation For Nodal Displacement of Truss Structures Determination of Nodal Displacements of Truss Structures Conjecture About The Determinant Expression of Stiffness Matrix And Elements Of Adjoint Matrix Multivariate Rational Response Surface Approximation of Truss Nodal Displacements Verification of Multivariate Rational Rs Model For Truss Displacement Approximation Conclusions References Chapter 15 Visual Data Mining Based on Differential Topology: A Survey Abstract Introduction Overview Analyzing Samples Of A Function R2. R Or R3. R Analyzing Samples Of A Function Rn. R Analyzing Samples Of A Function Rn. Rm Conclusion References Chapter 16 The Method of Finding Solutions of Partial Dynamic Equations on Time Scales Abstract Introduction Basic Concepts On Time Scales The Exact Solution Of Linear Initial Value Problems on Time Scales Approximation Solutions of Nonlinear Q-Partial Dynamic Equations Numerical Results Conclusion And Future Direction Appendix: Basic Ideas Of The Variational Iteration Method References Index Back Cover Presents a collection of contemporary articles combines several topics of multivariate mathematics, from extensions of uni-variate methodologies to practical applications in several research areas of multivariate calculus, statistical analysis, time series, polynomial geometry and differential topology.