Forging Connections between Computational Mathematics and Computational Geometry Papers from the 3rd International Conference on Computational Mathematics and Computational Geometry 1st Edition by Ke Chen, Anton Ravindran 3319161396 9783319161396

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ISBN-10 :  3319161396 

ISBN-13 :  9783319161396

Author:  Ke Chen, Anton Ravindran

This volume presents original research contributed to the 3rd Annual International Conference on Computational Mathematics and Computational Geometry (CMCGS 2014), organized and administered by Global Science and Technology Forum (GSTF). Computational Mathematics and Computational Geometry are closely related subjects, but are often studied by separate communities and published in different venues. This volume is unique in its combination of these topics. After the conference, which took place in Singapore, selected contributions chosen for this volume and peer-reviewed. The section on Computational Mathematics contains papers that are concerned with developing new and efficient numerical algorithms for mathematical sciences or scientific computing. They also cover analysis of such algorithms to assess accuracy and reliability. The parts of this project that are related to Computational Geometry aim to develop effective and efficient algorithms for geometrical applications such as representation and computation of surfaces. Other sections in the volume cover Pure Mathematics and Statistics ranging from partial differential equations to matrix analysis, finite difference or finite element methods and function approximation. This volume will appeal to advanced students and researchers in these areas.

Forging Connections between Computational Mathematics and Computational Geometry Papers from the 3rd International Conference on Computational Mathematics and Computational Geometry 1st table of contents: 

Part I Computational Mathematics
An Augmented Lagrangian Approach with Enhanced Local Refinement to Simulating Yield Stress Fluid Flo
Introduction
Mathematical Formulation
The Constitutive Laws for the Liquid and the Gas Regions
Equations of Motion and Boundary Conditions
The Augmented Lagrangian Method
Numerical Implementation of ALM
Yield Surface Detection with an Enhanced Mesh Adaptive Strategy
Numerical Results
Conclusions and Future Investigations
References
On Classical Solution in Finite Time of BGK-Poisson’s Equations
Introduction
Existence of Solution
Class of Functions
Notations
Notations
Uniqueness of the Solution
Conclusion
References
A Note on Lanczos Algorithm for Computing PageRank
Introduction
Arnoldi Method
Lanczos Algorithm for Computing PageRank
Numerical Experiments
Conclusion
References
Superconvergence of Discontinuous Galerkin Method to Nonlinear Differential Equations
Introduction
The Discontinuous Galerkin Method
Error Estimation for Nonlinear Boundary Value Problem
Error Estimation
Computational Results
Conclusion
References
A Least Squares Approach for Exponential Rate of Convergence of Eigenfunctions of Second-Order Ellip
Introduction
Discretization and Prior Estimations
Main Result
Conclusion
References
Multivariable Polynomials for the Construction of Binary Sensing Matrices
Introduction
Sparse Recovery from Linear Measurements
On the Equivalence Between P0 and P1 Problems
Deterministic CS Matrices Through Multivariable Homogeneous Polynomials
On Constructing Circulant RIP Matrices
Generalization from Two Variables to n Variables
Concluding Remarks
References
An Ant Colony Algorithm to Solve the Container Storage Problem
Introduction
Context
Mathematical Modeling
Notations
The Proposed Model
Ant Colony Algorithm
Solution Representation
Construction Method of a Solution
Update the Set of Couples
Probability Calculation
Update Pheromone
Numerical Results
Setting the Parameters
Comparison with CPLEX
Conclusion
References
FEM Post-processing in Identifying Critical Points in an Image
Flow of Ideas
Flow of Ideas: Segmentation
Flow of Ideas: Discrete Hessian Approach
Introduction
Image Segmentation and Segmentation Methods
Watershed/Separatrix Segmentation
Material and Methods
Results on Two-Dimensional Functions and Images
Results on Two-Dimensional Functions
Initial Results on Images
Conclusions and Further Work
References
Global and Local Segmentation of Images by Geometry Preserving Variational Models and Their Algorith
Introduction
Selective Segmentation with Active Contours
Model 1: Dual Level Set Model
Model 2: Coefficient of Variation Model
Model 3: Area Model
Model 4: P-Model
Model 5: Local Information Model
Model 6: Interactive Segmentation Model
Implementation
Results
Model 1: Dual Model
Model 2: CoV Model
Model 3: Area Model
Model 4: P-Model
Model 5: LI Model
Model 6: IS Model
Future Developments
Conclusions
References
Part II Pure Mathematics
Positive and Negative Interval Type-2 Generalized Fuzzy Number as a Linguistic Variable in Interval
Introduction
Preliminaries
Interval Type-2 Fuzzy Sets
Entropy Weight
Generalized Fuzzy Number
An Algorithm
Development of PNIT2GFN
Decision-Making Based on the Interval Type-2Entropy Weight
Numerical Example
Conclusion
References
The Number of Complex Roots of a Univariate Polynomial Within a Rectangle
References
Proof of Fermat’s Last Theorem for n == 3 Using Tschirnhaus Transformation
Introduction
Method
References
Part III Computational Geometry
Geometrical Problems Related to Crystals, Fullerenes, and Nanoparticle Structure
Introduction
How Small a “Small domain” Could Be to Describe a Global Structure
Focus on the Local Structure in Connection to Fullerenes and Related Problems in Computational and D
References
Tomographic Inversion Using NURBS and MCMC
Introduction
NURBS
Tomographic Measurement Model
Bayesian Inversion
Computational Result
Discussion and Conclusion
References
Solving Fuzzy Differential Equation Using Fourth-Order Four-Stage Improved Runge –Kutta Method
Introduction
Preliminaries
Fuzzy Initial Value Problems
Fuzzy Improved Runge–Kutta Method of Order Four with Four Stages
Numerical Example
Conclusion
References
Effect of Bird Strike on Compressor Blade
Introduction
History
Need for Simulation
FAA Regulation on Bird Strike
Methodology
Blade Material
Theory of Bird Strike
Steps in Creating the Bird Model
Bird Surrogates
Bird Shape
Bird Model
Contact Algorithm
Equation of State
Numerical Analysis
Lagrangian Approach
Arbitrary Lagrangian Eulerian Approach
Smooth Particle Hydrodynamic Approach
Results and Discussion
Lagrangian Approach
ALE Approach
Conclusions
References
Part IV Statistics
Asymptotic Density Crossing Points of Self-Normalized Sums and Normal
Introduction
Notation and Preliminaries
ACP Theorem for Generalized Self-Normalized Sums
Concluding Remarks
References
Exponential Ratio-Cum-Exponential Dual to Ratio Estimator in Double Sampling
Introduction
The Proposed Estimator
Efficiency Comparisons
Case II
Efficiency Comparisons
Empirical Study
Conclusions
References
Analysis of Performance of Indices for Indian Mutual Funds
Introduction
Literature Reviews
Data and Methodologies
Net Asset Value
Calculation of Returns
Indices for Calculating Mutual Fund Performance
Initial Observations
Classification of Mutual Funds
Summary of Observations
Bootstrapping of Samples
Confidence Intervals
Advantages and Disadvantages of Bootstrapping
Other Important Variables
Results
Conclusion
References
Counting Regular Expressions in Degenerated Sequences Through Lazy Markov Chain Embedding
Introduction
Pattern Matching, NFA, and Lazy Determinization
Pattern Matching
NFA
Lazy Determinization
Lazy Markov Chain Embedding
Markov Chain Embedding
Our Contribution
Illustration on NGS Data
Conclusions
References
Generalized Variance Estimations of Normal-Poisson Models
Introduction
Normal-Poisson Models
Generalized Variance Estimations
Maximum Likelihood Estimator
Uniformly Minimum Variance Unbiased Estimator
Bayesian Estimator
Simulation Study
Conclusion
References
Vehicle Routing Problem with Uncertain Costs via a Multiple Ant Colony System
Introduction
Problem Definition
Methodology
The Ant Colony System
The RMACS Approach
Experimental Results
Conclusions
References
The Granger Causality Effect between Cardiorespiratory Hemodynamic Signals
Introduction
Definitions of Some Variables Studied
Data and Methodology
Data Analysis
Methodology
The Method and Findings
The Model Specification
Bivariate Granger Causality Test
Multivariate Granger Causality

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