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Advances in algebra and analysis i by v madhu, a manimaran, d easwaramoorthy, d kalpanapriya, m mubashir unnissa

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  • Preface

  • Contents

  • Volume II Contents

  • Part I Algebra

    • IT-2 Fuzzy Automata and IT-2 Fuzzy Languages

      • 1 Introduction

      • 2 IT-2 Fuzzy Sets

      • 3 IT-2 Fuzzy Automata and IT-2 Fuzzy Languages

      • 4 Construction of Deterministic IT-2 Fuzzy Automata for IT-2 Fuzzy Languages

      • 5 Algebraic Aspects of an IT-2 Fuzzy Automaton

      • 6 Conclusion

      • References

    • Level Sets of i_v_Fuzzy β-Subalgebras

      • 1 Introduction

      • 2 Preliminaries

      • 3 Level Sets of i_v_ Fuzzy β-Subalgebras

      • References

    • Interval-Valued Fuzzy Subalgebra and FuzzyINK-Ideal in INK-Algebra

      • 1 Introduction

      • 2 Preliminaries

      • 3 Interval-Valued Fuzzy INK-Ideal in INK-Algebra

      • 4 Homomorphism of INK-Algebra

      • References

    • On Dendrites Generated by Symmetric Polygonal Systems: The Case of Regular Polygons

      • 1 Introduction

        • 1.1 Dendrites

        • 1.2 Self-similar Sets

        • 1.3 Zippers

      • 2 Contractible P-Polygonal Systems

      • 3 Symmetric Polygonal Systems

        • 3.1 The Case of Regular Polygons

        • 3.2 Self-similar Zippers, Whose Attractors Are Dendrites

      • References

    • Efficient Authentication Scheme Based on the Twisted Near-Ring Root Extraction Problem

      • 1 Introduction

      • 2 Preliminaries 5-Muthukumaran

        • 2.1 Cryptography Assumptions in a Near-Ring 5-Muthukumaran

      • 3 Proposed Entity Authentication Schemes

        • 3.1 Proposition

        • 3.2 Proposition

      • 4 Conclusion

      • References

    • Dimensionality Reduction Technique to Solve E-Crime Motives

      • 1 Introduction

      • 2 Preliminaries

      • 3 Principal Component Analysis

      • 4 Dataset Information

      • 5 Interpretation of the Principal Components

      • 6 Summary

      • References

    • Partially Ordered Gamma Near-Rings

      • 1 Introduction

      • 2 Preliminaries

      • 3 T-Fuzzy Ideal of Partially Ordered Γ-Near-Ring

      • 4 Main Results

      • 5 Conclusion

      • References

    • Novel Digital Signature Scheme with Multiple Private Keys on Non-commutative Division Semirings

      • 1 Introduction

        • 1.1 Background of Public Key Environment and Protocols Based on Commutative Rings

        • 1.2 Outline of the Paper

      • 2 Assumptions of Cryptography on Non-commutative Groups

        • 2.1 Two Well-Known Assumptions on Cryptography

        • 2.2 Symmetrical Decomposition and Computational Diffie–Hellman Assumptions over Non-commutative Groups

      • 3 Building Levels for Proposed Digital Signature Scheme

        • 3.1 Integral Coefficient Ring Polynomials

        • 3.2 Semiring

        • 3.3 Division Semiring

        • 3.4 Polynomials on Division Semiring

        • 3.5 Further Assumptions of Cryptography on Non-commutative Division Semirings

      • 4 Proposed Signature Scheme

        • 4.1 Signature Scheme on Non-commutative Division Semiring

      • 5 Confirmation Theorem

        • 5.1 Completeness

        • 5.2 Security Analysis

        • 5.3 Soundness

      • 6 Conclusion

      • References

    • Cozero Divisor Graph of a Commutative Rough Semiring

      • 1 Introduction

      • 2 Preliminaries

        • 2.1 Rough Sets

        • 2.2 Algebraic Structures

      • 3 Ideal and Cozero Divisor Graph of a Commutative Rough Semiring

        • 3.1 Properties

        • 3.2 Cozero Divisor Graph of a Commutative Rough Semiring

        • 3.3 Examples

      • 4 Conclusion

      • References

    • Gorenstein FI-Flat Complexes and (Pre)envelopes

      • 1 Introduction and Preliminaries

      • 2 Gorenstein FI-Flat Complexes

      • 3 Existence of Preenvelopes

      • References

    • Bounds of Extreme Energy of an Intuitionistic Fuzzy Directed Graph

      • 1 Introduction

      • 2 Preliminaries

      • 3 Bounds of Extreme Energy for Complex Roots

      • 4 Numerical Examples

      • 5 Conclusion

      • References

  • Part II Analysis

    • On Ultra Separation Axioms via αω-Open Sets

      • 1 Introduction

      • 2 Preliminaries

      • 3 αω-Kernel and αω-Closure

      • 4 αω-T0 and αω-T1

      • References

    • Common Fixed Point Theorems in 2-Metric Spaces Using Composition of mappings via A-Contractions

      • 1 Introduction

      • 2 Preliminaries

      • 3 Main Result

      • References

    • Coefficient Bounds for a Subclass of m-Fold Symmetric λ-Pseudo Bi-starlike Functions

      • 1 Introduction and Definitions

      • 2 Coefficient Bounds for the Class Lσmλ(ϕ)

      • 3 Fekete–Szegö Inequalities for the Function Class Lσmλ(ϕ)

      • References

    • Laplacian and Effective Resistance Metric in SierpinskiGasket Fractal

      • 1 Introduction

      • 2 Construction of Sierpinski Gasket

      • 3 Laplacian in Sierpinski Gasket

        • 3.1 Laplacian in Finite Graphs 15:8

        • 3.2 Vertex Degree 15:3

        • 3.3 Standard and Normalized Laplacian

      • 4 Effective Resistance Metric and Laplacian in Sierpinski Gasket

      • 5 Conclusion

      • References

    • Some Properties of Certain Class of Uniformly Convex Functions Defined by Bessel Functions

      • 1 Introduction

      • 2 Coefficient Estimates

      • 3 Convex Linear Combinations

      • 4 Integral Means Inequalities

      • References

    • A New Subclass of Uniformly Convex Functions Defined by Linear Operator

      • 1 Introduction

      • 2 Main Results

      • 3 Partial Sums

      • References

    • Coefficient Bounds of Bi-univalent Functions Using Faber Polynomial

      • 1 Introduction

      • 2 Bi-univalent Subclass GΣ(λ,α)

      • 3 Faber Polynomial Expansion for GΣ(λ,α)

      • References

    • Convexity of Polynomials Using Positivity of Trigonometric Sums

      • 1 Preliminaries

      • 2 Main Results

      • References

    • Local Countable Iterated Function Systems

      • 1 Introduction

      • 2 Local Iterated Function Systems

      • 3 Local Countable Iterated Function System

      • 4 Approximation of Local CIFS Attractor by the Family of Local IFS Attractors

      • 5 Conclusion

      • References

    • On Intuitionistic Fuzzy C-Ends

      • 1 Introduction

      • 2 Preliminaries

      • 3 On Intuitionistic Fuzzy C-Ends SC

      • 4 Conclusion

      • References

    • Generalized Absolute Riesz Summability of Orthogonal Series

      • 1 Introduction

      • 2 Preliminaries

      • 3 Main Theorems

      • 4 Conclusion

      • References

    • Holder's Inequalities for Analytic Functions Defined by Ruscheweyh-Type q-Difference Operator

      • 1 Introduction and Definitions

      • 2 Characterization Properties

      • References

    • Fuzzy Cut Set-Based Filter for Fixed-Value Impulse Noise Reduction

      • 1 Introduction

      • 2 Existing Techniques

        • 2.1 Median Filters

        • 2.2 Partial Differential Equation-Based Filters

        • 2.3 Switching Filters

        • 2.4 Fuzzy-Based Filters

      • 3 Proposed Filter

        • 3.1 Algorithm of the Proposed Filter

      • 4 Results and Discussions

      • 5 Conclusion

      • References

    • On (p,q)-Quantum Calculus Involving Quasi-Subordination

      • 1 Introduction

      • 2 Initial Coefficient Bounds for Some Subclasses of Univalent Functions Involving Quasi-Subordination

      • References

  • Part III Operations Research

    • Sensitivity Analysis for Spanning Tree

      • 1 Introduction

      • 2 Travelling Salesman Problem

      • 3 Illustration

      • 4 Conclusion

      • References

    • On Solving Bi-objective Fuzzy Transportation Problem

      • 1 Introduction

      • 2 Bi-objective Fuzzy Transportation Problem

      • 3 Fuzzy Dripping Method

      • 4 Numerical Example

      • 5 Conclusion

      • References

    • Nonlinear Programming Problem for an M-Design Multi-Skill Call Center with Impatience Based on Queueing Model Method

      • 1 Introduction

      • 2 Preliminaries

      • 3 M-Design Multi-Skill (MDMS) Model

        • 3.1 MDMS State Transition

        • 3.2 Calculation of MDMS State Transition Using the Erlang-A Queueing Formula

      • 4 Calculation of the Steady-State Probability

      • 5 Calculation of the Service Level

      • 6 Staffing Problem

      • 7 Numerical Examples

        • 7.1 Remark

      • 8 Conclusion

      • References

    • Optimizing a Production Inventory Model with Exponential Demand Rate, Exponential Deterioration and Shortages

      • 1 Introduction

      • 2 Assumptions and Notations and Assumptions

      • 3 Description of the Proposed Model

      • 4 Numerical Example

      • 5 Conclusion

      • References

    • Analysis of Batch Arrival Bulk Service Queueing System with Breakdown, Different Vacation Policies and Multiphase Repair

      • 1 Introduction

      • 2 Mathematical Model

      • 3 Notation

      • 4 Queue Size Distributions

      • 5 PGF of the Queue Size

      • 6 Performance Measures

        • 6.1 Expected Queue Length

        • 6.2 Expected Busy Period

        • 6.3 Expected Length of Idle Period

      • 7 Numerical Example

      • 8 Conclusion

      • References

    • An Improvement to One's BCM for the Balanced and Unbalanced Transshipment Problems by Using Fuzzy Numbers

      • 1 Introduction

      • 2 Preliminary

      • 3 Formulation of the General Fuzzy Transshipment Problem

      • 4 Ghadle and Pathade One's Best Candidate Method

      • 5 Conclusion

      • References

    • An Articulation Point-Based Approximation Algorithm for Minimum Vertex Cover Problem

      • 1 Introduction

      • 2 Proposed Approach

      • 3 Illustrative Example

      • 4 Comparative Analysis

      • 5 Conclusions

      • References

    • On Bottleneck-Rough Cost Interval Integer Transportation Problems

      • 1 Introduction

      • 2 Preliminaries

      • 3 Bottleneck-Rough Cost Interval Integer Transportation Problems

      • 4 Level Maintain Method

      • 5 Conclusion

      • References

    • Direct Solving Method of Fully Fuzzy Linear Programming Problems with Equality Constraints Having Positive Fuzzy Numbers

      • 1 Introduction

      • 2 Preliminaries

        • 2.1 Mathematical Form of a Linear Programming Problem

        • 2.2 Fuzzy Set

        • 2.3 Fuzzy Number

        • 2.4 Positive Fuzzy Number

        • 2.5 Operations on Fuzzy Number

        • 2.6 Triangular Fuzzy Number

      • 3 Fully Fuzzy Linear Programming Problem Having Positive Fuzzy Numbers

      • 4 Proposed Method of Solving

      • 5 Numeral Example

      • 6 Comparison and Advantages

      • 7 Conclusion

      • References

    • An Optimal Deterministic Two-Warehouse Inventory Model for Deteriorating Items

      • 1 Introduction

      • 2 Assumptions and Notations

      • 3 Mathematical Formulation and Solution of the Model : 0<μ<td<tr<tw<T

      • 4 Numerical Examples

      • 5 Observations

      • 6 Conclusion

      • References

    • Analysis on Time to Recruitment in a Three-Grade Marketing Organization Having Classified Sources of Depletion of Two Types with an Extended Threshold and Shortage in Manpower Forms Geometric Process

      • 1 Introduction

      • 2 Model Description

        • 2.1 Analytical Results

      • 3 Numerical Illustration

      • 4 Conclusions

      • References

    • Neutrosophic Assignment Problem via BnB Algorithm

      • 1 Introduction

      • 2 Preliminaries

      • 3 Assignment Method problem,Ones,Intustinistic,Using,Robust

      • 4 Branch and Bound Technique Solution,Using,Method

        • 4.1 Branching Methodology

      • 5 Numerical Example

      • 6 Conclusion

      • References

  • Part IV Statistics

    • An Approach to Segment the Hippocampus from T2-Weighted MRI of Human Head Scans for the Diagnosis of Alzheimer's Disease Using Fuzzy C-Means Clustering

      • 1 Introduction

      • 2 Proposed Method

        • 2.1 Applying Geometric Mean (GM) Filter for Image Smoothing

        • 2.2 Image Binarization Using Fuzzy C-Means

      • 3 Materials Used

      • 4 Results and Discussions

      • 5 Conclusion

      • References

    • Analysis of M[X]/Gk/1 Retrial Queueing Model and Standby

      • 1 Introduction

        • Practical Application of the Model

      • 2 Model Description

      • 3 Steady-State Distribution

        • Steady-State Equations

      • 4 Performance Measures

      • 5 Numerical Illustration

      • 6 Conclusion

      • References

    • μ-Statistically Convergent Multiple Sequences in Probabilistic Normed Spaces

      • 1 Introduction

      • 2 Preliminaries

      • 3 μ-Statistically Convergent Multiple Sequences in PN-Space

      • 4 μ-Statistical Limit Points for Multiple Sequences in PN-Space

      • References

    • A Retrial Queuing Model with Unreliable Server in K Policy

      • 1 Introduction

      • 2 The Model and Governing Equations

        • 2.1 Model Description

          • 2.1.1 Arrival Process

          • 2.1.2 Retrial Process

          • 2.1.3 Service Process

          • 2.1.4 Breakdown and Repair Process

        • 2.2 Governing Equation

          • 2.2.1 Retrial State

          • 2.2.2 Idle State

          • 2.2.3 Busy State

          • 2.2.4 Repair State

      • 3 The Analysis

        • 3.1 Matrix Geometric Method

        • 3.2 Performance Measures

          • 3.2.1 Server State Probabilities

          • 3.2.2 Queue Length

          • 3.2.3 Throughput

          • 3.2.4 Expected Delay

          • 3.2.5 Waiting Time

      • 4 Numerical Study

      • 5 Conclusion

      • References

    • Two-Level Control Policy of an Unreliable Queueing System with Queue Size-Dependent Vacation and Vacation Disruption

      • 1 Introduction

      • 2 Model Description

        • 2.1 Notations

      • 3 Steady-State Queue Size Distribution

      • 4 Probability-Generating Function (PGF) of the Queue Size

      • 5 Performance Measures

        • 5.1 Expected Length of Busy Period

        • 5.2 Expected Length of Idle Period

        • 5.3 Expected Queue Length

      • 6 Cost Model

      • 7 Numerical Illustrations

        • 7.1 Optimal Value of `a'

      • 8 Conclusion

      • References

    • Analysis of M/G/1 Priority Retrial G-Queue with Bernoulli Working Vacations

      • 1 Introduction

      • 2 Description of the Model

      • 3 Steady-State Analysis

      • 4 Performance Measures

      • 5 Special Cases

      • 6 Conclusion

      • References

    • Time to Recruitment for Organisations having n Types of Policy Decisions with Lag Period for Non-identical Wastages

      • 1 Introduction

      • 2 Model Description and Analysis for Model-I

        • 2.1 Main Result for Model-I

      • 3 Model Description and Analysis for Model-II

        • 3.1 Main Result for Model-II

        • 3.2 Results

          • 3.2.1 Result-1

          • 3.2.2 Result-2

          • 3.2.3 Result-3

      • 4 Numerical Illustrations

      • 5 Conclusion

      • References

    • A Novice's Application of Soft Expert Set: A Case Study on Students' Course Registration

      • 1 Introduction

      • 2 Literature Survey

      • 3 Foundations

      • 4 Soft Expert Set and Decision-Making

      • 5 Conclusion

      • References

    • Dynamics of Stochastic SIRS Model

      • 1 Introduction

      • 2 Existence of a Unique Global Solution

      • 3 Stochastic Stability of Infection-Free and Endemic Equilibrium States

      • 4 Example

      • 5 Conclusion

      • References

    • Steady-State Analysis of Unreliable Preemptive Priority RetrialQueue with Feedback and Two-Phase Service UnderBernoulli Vacation

      • 1 Introduction

      • 2 Model Description

      • 3 Stability Condition

      • 4 Steady-State Analysis of the System

        • 4.1 The Steady-State Equations of the Model

        • 4.2 The Steady-State Solution

        • 4.3 System Performance Measures

        • 4.4 Mean System Size and Orbit Size

      • 5 Conclusion

      • References

    • An Unreliable Optional Stage MX/G/1 Retrial Queue with Immediate Feedbacks and at most J Vacations

      • 1 Introduction

      • 2 System Description

      • 3 Analysis of Steady-State Probability Distributions

      • 4 Performance Measures

      • 5 Special Cases

      • 6 Conclusion

      • References

    • Weibull Estimates in Reliability: An Order Statistics Approach

      • 1 Introduction

      • 2 Graphical Estimation for a Complete Sample

        • 2.1 Parameter Estimation Using Graphical Method and Moment Derivation

      • 3 Conclusion

      • References

    • Intuitionistic Fuzzy ANOVA and Its Application Using Different Techniques

      • 1 Preliminaries

        • 1.1 Definition

        • 1.2 Definition

        • 1.3 Definition

        • 1.4 Definition

        • 1.5 Definition

      • 2 Two-Way Analysis of Variance

      • 3 Intuitionistic Two-Way ANOVA

        • 3.1 Example

      • 4 Conclusion

      • References

    • A Resolution to Stock Prices Prediction by Developing ANN-Based Models Using PCA

      • 1 Introduction

      • 2 Backpropagation-Based Neural Network (BPNN)

      • 3 Radial Basis Function Network (RBFN)

      • 4 Principal Component Analysis (PCA)

      • 5 Experimentation and Result Analysis

        • 5.1 Data Acquisition

        • 5.2 Experimentation

          • 5.2.1 Error Estimation

        • 5.3 Result Analysis

      • 6 Conclusion and Scope

      • References

    • A Novel Method of Solving a Quadratic Programming Problem Under Stochastic Conditions

      • 1 Introduction

      • 2 Review of Literature

      • 3 Methods and Discussion

        • 3.1 Statement of an Optimization Problem

        • 3.2 Abstract in the Stochastic Process

        • 3.3 Stochastic Process Linear Equality

        • 3.4 Stochastic Process in Kuhn–Tucker Conditions of the Moving Average

      • 4 Stochastic Process in Quadratic Programming

      • 5 Conclusion

      • References

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