Recent Advances In Mathematical And Computational Science

The Present Book Demonstrates The Recent Advances In Mathematics And Computational Science, Consists Of Twelve Research Contributions By The Various Authors. In The Chapter I, Importance Of Mathematics Is Demonstrated For The Society Development. The Chapter Presents The Contribution Of Mathematics For The Human Interests. The Chapter II Presents The Stability And Bifurcation Of A Predator-Prey Model With Allee-Effect 2 In Prey Species. Numerical Simulations Are Performed For Getting The Analytical Accurate Results. In The Chapter III, Modified Cubic B-Spline Differential Quadrature Method Is Presented To Solve Fisher's Reaction-Diffusion Equation. The Presented Method Is Very Easy, Economical, Powerful And Efficient Method For Finding The Numerical Results. Chapter IV Presents The Effect Of Temperature Modulation On Chaotic Convection In A Viscoelastic Fluid Saturated Porous Medium. The Phase Portrait And Time Domain Diagrams Of The Lorenz System For Suitable Parametric Values Have Been Used To Analyse The System. In Chapter V, Author Presented Methods To Optimize The Losses Due To Cyber Crime Through The Optimization Techniques. For This Purpose Various Cases Studies Have Been Performed And Computed Results Are Reported In The Form Of Tables And Graphs. In Chapter VI, Different Latest Test Case Generation Techniques Have Been Described. Some Latest Research On Test Case Generations Has Been Summarized. Test Case Generation From Different Design Model Is Also Investigated By Authors. Chapter VII Deals With Proposal Of Unified Modeling Language (UML) Model For Real Case Study Of Electrical Bill Deposit System (EBDS). By The Use Of UML, Class And State Diagrams Are Designed For Static And Dynamic Representation Of Any Complex Research Problem. When The Data Size Of An Electrical Organization Becomes Very Large Then Mining Techniques Are Used For The Searching The Hidden Record Stored In Large Database. In Chapter VIII, Authors Presented The Applications Of The Energy Optimization Techniques For Wired Networks. The Optimization Is Done To Minimize The Electric Energy With Routing Algorithms By Reducing The Number Of Active Mode, Sleep Mode, Idle Mode And Busy Mode In The Communication Processes. The Major Performance Factors Like Latency, Packet Throughput And Packet Messaging Complexity For Energy Optimization Are Described In Detail. Chapter IX, Presents Homotopy Perturbation Method For Fractional Moving Boundary Problem In A Finite Domain With Temperature Dependent Thermal Diffusivity. The Whole Analysis Is Presented In A Non Dimensional Form. The Location Of Moving Interface And Temperature Distribution During Melting Process Is Studied In Detail. The Effect Of Stefan Number, Variability Coefficient Of Thermal Diffusivity, And Order Of Time Fractional Derivative Has Been Discussed In Detail. It Has Been Observed That The Process Of Melting Is Faster When Order Of Time Fractional Derivative Is Smaller. Chapter X Demonstrates The Big Data Analysis, Its Advantages, Security And Privacy Concerns That Need To Be Addressed To Make Big Data Processing And Computing Infrastructure More Secure. In Chapter XI, Authors Investigate Thermal Instability In An Electrically Conducting Nanofluid Layer Under Magnetic Field Modulation. The System Is Confined Between Two Horizontal Surfaces. Time Periodic Magnetic Field Is Associated In Vertical Direction With Convective Boundary Conditions. The Revised Boundary Conditions Are In Practical Because In Case Of Nanofluid The Temperature At Boundaries Can Be Adjusted But Not The Concentration. Truncated Fourier Series Method Has Been Adopted To Perform Weak Nonlinear Stability Analysis. Effect On The Nusselt Number Due To Magnetic Field Modulation Has Been Obtained, And The Results Have Been Depicted Graphically And Discussed In Detail. In The Last Chapter XII, The Shortcoming Of Proposed Methods For Comparing Generalized Triangular Trapezoidal Fuzzy Numbers (TTFN) Is Pointed Out. In This Chapter, The Proposed Ranking Method Is Used For Solving Unbalanced Transportation Problem, In Which The Total Availability/Production Is Less Than The Total Demand. A Generalized TTFN Is A Combination Of A Normal Triangular And Nonnormal Trapezoidal Shaped Fuzzy Numbers. An Unbalanced Fuzzy Transportation Problem Converted Into A Balanced One By Existing And Newly Proposed Minima Rowcolumn Method (MRCM). A Comparison Is Also Set Between The Optimal Fuzzy And Crisp Solutions By Using Vogel's Approximation Method (VAM) And Improved Zero Suffix Method (IZSM). The Results Presented In The Book Shall Be Very Helpful To Carry Out Further Research In The Advanced Fields Of Mathematics And Computational Science.