Numerical Investigation of the Effects of Velocity and Particle Concentration on Heat Transfer of Vibrational Flow of Non-Newtonian Nanofluid

Volume 8 Issue 1 January - March 2019

Research Paper

Numerical Investigation of the Effects of Velocity and Particle Concentration on Heat Transfer of Vibrational Flow of Non-Newtonian Nanofluid

Santosh K. R. Mishra*, H. Chandra**, Arun Arora***

*_***Bhilai Institute of Technology, Durg, Chhattisgarh, India.

Mishra, S. Kr., Chandra, H., Arora, A. (2019). Numerical investigation of the effects of velocity and particle concentration on heat transfer of Vibrational flow of non-Newtonian nanofluid. i-manager's Journal on Mathematics, 8(1), 35-47https://doi.org/10.26634/jmat.8.1.16239

Abstract

In this paper, the effect of solid particle concentration and flow velocity of nanofluid with and without superimposed vibration at the wall were numerically investigated. For this purpose, non-newtonian nanofluid containing Al2O3 and aqueous CMC solution as a single phase with an average particle size of 25 nm and four particle concentration of 0.0, 0.5, 1.0, and 1.5% were used. Effects of volume concentration on convective heat transfer coefficient were investigated in different Reynolds number for different vibration parameters. The results showed that in a steady flow, with Reynolds number, dispersion of nanoparticles causes the thermal boundary layer to grow rapidly than that of base fluid in axial direction and vibration act as a catalyst; at a given concentration much enhancement results than steady state. The ratio of convective heat transfer coefficient of unsteady state to a steady state flow of nanofluid with an increase of Reynolds number and increases with concentration. Vibration effects reduce in significance as frequency increases, and that they are more sensitive to amplitude to frequency. The largest increase of about 300% was observed under the condition of vibrational flow of nanofluid compared with a steady flow of base fluid.

On β -Change Of Special Finsler (α, β)-Metrics Of Dougls Type

Volume 8 Issue 1 January - March 2019

Research Paper

On β -Change Of Special Finsler (α, β)-Metrics Of Dougls Type

M. Ramesha*, S. K. Narasimhamurthy**

*Department of Mathematics, School of Engineering and Technology, Jain Global Campus, Jakkasandra, Bangalore, Karnataka, India.

** Department of P.G. Studies and Research in Mathematics, Kuvempu University.

Ramesha, M., & Narasimhamurthy, S. K . (2019). On beta-Change of Special Finsler (alpha,beta)-Metrics of Dougls Type. i-manager's Journal on Mathematics, 8(1), 24-34 https://doi.org/10.26634/jmat.8.1.16186

Abstract

Let Fn =(M, L) be an n-dimensional Finsler manifold, and Let L and L be the two Finsler metrics. For a differential one form β(x,dx)=bi(x)dxi on M, G. Randers, in 1941, introduced a special Finsler space defined by the change L =L+β, where L is i Riemannian, to consider a unified field theory. For a β-change of Finsler metric, the differential one-form β plays a very important role. With the above observations, in this article, the authors have tried to study the necessary and sufficient n condition for Finsler space Fn which is transformed by a b-change of Finsler space Fn with (α, β)-metric to be of Douglas type. And also we are discussing the different classes of (α, β)-metrics of Finsler spaces Fn are discussed, which is obtained by a β-change of a Finsler space Fn is of Douglas type. The terminology and notations are referred to the Matsumoto's monograph (Matsumoto, 1992).

Non-Steady Radial Flow of a Viscous Incompressible Liquid in The Porous Medium Around a Radially Oscillating Spherical Surface

Volume 8 Issue 1 January - March 2019

Research Paper

Non-Steady Radial Flow of a Viscous Incompressible Liquid in The Porous Medium Around a Radially Oscillating Spherical Surface

Mohammed Naheed*

Department of Information and Technology (Mathematics Section), Nizwa College of Technology (Nizwa), Sultanate of Oman.

Naheed, M. (2019). Non-Steady Radial Flow of a Viscous Incompressible Liquid in The Porous Medium Around a Radially Oscillating Spherical Surface. i-manager's Journal on Mathematics, 8(1), 16-23 https://doi.org/10.26634/jmat.8.1.16065

Abstract

This paper deals with non-steady radial flow of a viscous, incompressible liquid in the porous medium around a radially oscillating time dependent spherical surface. The momentum equation considered for the flow through the porous medium takes care of the fluid inertia and the Newtonian stresses in addition to the classical Darcy's friction. Expressions for the pressure and velocity distributions have been derived in terms of the expansion rate of sphere radius using analytical method and effects of variation of pressure, velocity of a viscous, incompressible, and homogeneous fluid flow in a porous medium are reported and the results are presented graphically for the two special cases of radius of the sphere.

A Study to Predict Eid Al-Fitr Day in Oman using Markov Chain Technique

Volume 8 Issue 1 January - March 2019

Research Paper

A Study to Predict Eid Al-Fitr Day in Oman using Markov Chain Technique

Mohammed Razeeuddin *, B. V. Senthil Kumar**

*_**Section of Mathematics, Department of Information and Technology, Nizwa College of Technology (Nizwa), Sultanate of Oman.

Razeeuddin, M., Kumar, B. V. S. (2019). A Study to Predict Eid al-Fitr Day in Oman using Markov Chain Technique. i-manager's Journal on Mathematics, 8(1), 8-15 https://doi.org/10.26634/jmat.8.1.16233

Abstract

Markov chain is a powerful technique employed to forecast the variations in the sharemarket, customer behaviour, marketing, customers' brand loyalty, weather, game of golf, weather report, gold rate, conversion of currency rate, etc. This study focuses on research discrete-time Markov chain. Some significant properties of Markov chains are evoked and then the research and knowledge gained on Markov chains is applied to predict Eid al-Fitr day for the succeeding years and also in the long run. The Eid al-Fitr day for each year depends only on the previous year Eid al-Fitr day and not on its previous years' Eid al-Fitr days. The authors have also justified is study that the application of Markov chain is an appropriate process in predicting Eid al-Fitr day in Oman.

Dismantling of Magneto-Hydrodynamic Maxwell Equation in Cylindrical Co-Ordinates

Volume 8 Issue 1 January - March 2019

Research Paper

Dismantling of Magneto-Hydrodynamic Maxwell Equation in Cylindrical Co-Ordinates

M. O. Mosa*

Mathematics Teacher, Sudan International Grammar School, Sudan.

Mosa, M. O. (2019). Dismantling of Magneto-Hydrodynamic Maxwell Equation in Cylindrical Co-Ordinates. i-manager's Journal on Mathematics, 8(1), 1-7 https://doi.org/10.26634/jmat.8.1.15737

Abstract

The Maxwell model is considered to be the simplest of rate type fluids model of viscoelastic fluid, the model describes the blood flow in small vessels. And also the response of some polymeric liquids. The focus of this work is derivation of magneto-hydrodynamic of Maxwell model in cylindrical co-ordinates (r;θ; z), basic equations (equation of continuity and momentum), and the Maxwell model were changed from the vector form to deferential form to derive the model in cylindrical co-ordinates (r; θ ; z). The Maxwell equation has been derived and system of partial differential equations was obtained under effect of magnetic field.

Effect of Inclined Magnetic Field and Radiation Absorption on Mixed Convection Flow of a Chemically Reacting and Radiating Fluid Past a Semi Infinite Porous Plate

Volume 7 Issue 4 October - December 2018

Research Paper

Effect of Inclined Magnetic Field and Radiation Absorption on Mixed Convection Flow of a Chemically Reacting and Radiating Fluid Past a Semi Infinite Porous Plate

M. Obulesu*, R. Siva Prasad**

* Research Scholar, Department of Mathematics, Sri Krishnadevaraya University, Anantapuram, Andhra Pradesh, India.

** Professor and Head, Department of Mathematics, Sri Krishnadevaraya University, Anantapuram, Andhra Pradesh, India.

Obulesu, M., Prasad, R. S. (2018). Effect of Inclined Magnetic Field and Radiation Absorption on Mixed Convection Flow of a Chemically Reacting and Radiating Fluid Past a Semi Infinite Porous Plate, i-manager's Journal on Mathematics, 7(4), 39-49.https://doi.org/10.26634/jmat.7.4.15561

Abstract

In this manuscript, an attempt is made to study the effect of Inclined Magnetic Field and Radiation Absorption on Mixed Convection Flow of a Chemically Reacting and Radiating Fluid Past a Semi Infinite Porous Plate. Analytical solutions are obtained by solving the constituted governing equations by using regular perturbation technique. The impact of various physical parameters on the flow quantities are studied numerically. The expressions for other important physical parameters such as skin friction coefficient, Nusselt number and Sherwood number are also presented and studied with the help of tables. The results of this study are more suitable with the existing literature in the absence of the extended parameters.

Effects of Heat and Mass Transfer on MHD Flow of Viscoelastic Micro-Polar Fluid Through A Porous Medium with Heat Source and Chemical Reaction

Volume 7 Issue 4 October - December 2018

Research Paper

Effects of Heat and Mass Transfer on MHD Flow of Viscoelastic Micro-Polar Fluid Through A Porous Medium with Heat Source and Chemical Reaction

Kuppala R. Sekhar*

Assistant Professor, Department of H & S, Vemu Institute of Technology, P. Kothakota, Chittoor District, Andhra Pradesh, India.

Sekhar, K. R. (2018). Effects of Heat and Mass Transfer on MHD Flow of Viscoelastic Micro-Polar Fluid Through a Porous Medium with Heat Source and Chemical Reaction, i-manager's Journal on Mathematics, 7(4), 27-38.https://doi.org/10.26634/jmat.7.4.15377

Abstract

The present study investigates heat and mass transfer effects on unsteady flow of a visco-elastic fluid over an infinite moving permeable plate in a saturated porous medium in the presence of a transverse magnetic field with chemical reaction and heat sink are studied. The governing equations are solved analytically by using general perturbation technique to obtain the expressions for velocity, micro-rotation, temperature and concentration. The result shows that the effect of the chemical reaction parameter and heat source parameter increases, with increasing in micro-rotation across the boundary layer while visco-elastic parameter decreases in the vicinity of the plate. With the aid of these, the expressions for skin-friction coefficient, Nusselt number and Sherwood numbers are presented in tabular form.

The Iterative Method for Strong Convergence of Variational Inequality with H-Accretive Operator

Volume 7 Issue 4 October - December 2018

Research Paper

The Iterative Method for Strong Convergence of Variational Inequality with H-Accretive Operator

Poonam Mishra*, Shailesh Dhar Diwan**

*Department of Applied Mathematics, Amity School of Engineering and Technology, Amity University, Raipur, Chhattisgarh, India.

**Department of Applied Mathematics, Government Engineering College, Raipur, Chhattisgarh, India.

Mishra, P., Diwan, S. D. (2018). The Iterative Method for Strong Convergence of Variational Inequality with H-Accretive Operator, i-manager's Journal on Mathematics, 7(4), 20-26. https://doi.org/10.26634/jmat.7.4.15278

Abstract

In this paper, we have used a new iterative method given by Thuy (2016), for the class of H-Accretive operator in a q-uniformly smooth Banach space. Further, we have used this method to find a solution for the variational inequalities over the set of common fixed points of a family of nonexpansive mappings in Banach Space. Our result improves and generalizes some recent results in the literature.

On Construction of Discrete Wrapped Lindley Distribution

Volume 7 Issue 4 October - December 2018

Research Paper

On Construction of Discrete Wrapped Lindley Distribution

R. Srinivas*, G. V. L. N. Srihari**, S. V. S. Girija***

*Assistant Professor, Department of Mathematics, Hindu College, Guntur, Andhra Pradesh, Telangana, India.

** Associate Professor, Department of Mathematics, Aurora's Scientific Technological and Research Academy, Hyderabad, Andhra Pradesh, Telangana, India.

*** Associate Professor, Department of Mathematics, Hindu College, Guntur, Andhra Pradesh, Telangana, India.

Srinivas, R., Srihari, G. V. L. N., & Girija, S. V. S. (2008). On Construction of Discrete Wrapped Lindley Distribution, i-manager's Journal on Mathematics, 7(4), 10-19. https://doi.org/10.26634/jmat.7.4.15874

Abstract

In this paper, a new discrete circular distribution is constructed by applying the method of discretization for existing continuous circular distribution. The Wrapped Lindley Distribution is discretized and new circular model is Discrete Wrapped Lindley distribution. The probability mass function, cumulative distribution function, and characteristic function of the Discrete Wrapped Lindley Distribution are derived and population characteristics are studied using first two trigonometric moments. The graphs of the probability mass function and cumulative distribution function are plotted for different values of parameter by using MATLAB.

Chaos Control in a Chaotic Finance System by Lie Algebraic Exact Linearization

Volume 7 Issue 4 October - December 2018

Research Paper

Chaos Control in a Chaotic Finance System by Lie Algebraic Exact Linearization

Mohammad Shahzad*, Mohammed Raziuddin**

*Department of General Studies, College of Applied Sciences, Nizwa, Oman.

**Department of Information Technology, Nizwa College of Technology, Nizwa, Oman.

Shahzad, M., Raziuddin, M. (2018). Chaos Control in a Chaotic Finance System by Lie AlgebraicExact Linearization, i-manager's Journal on Mathematics, 7(4), 1-9. https://doi.org/10.26634/jmat.7.4.14941

Abstract

In this paper, the authors investigate the control of chaotic dynamics of a financesystem by implementing a Lie algebraic exact linearization technique.Controlling of chaos is based on feedback control law in which nonlinearcoordinateis transformed into linear one without the loss of generality. The authors use Mathematica for all simulation. All the analytical and graphical results confirm the robustness of the control in the considered finance system. A comparative graphical study between uncontrolled (original) and controlled trajectories has been presented through various plots.

Common Fixed Point Theorems for Cr-Iteration Scheme in Three Multivalued Mappings

Volume 7 Issue 3 July - September 2018

Research Paper

Common Fixed Point Theorems for Cr-Iteration Scheme in Three Multivalued Mappings

Apurva Kumar Das*, Shailesh Dhar Diwan**, Swati Jain***

* Lecturer, Department of Mathematics, Government Polytechnic College Sukma, Chhattisgarh, India.

** Associate Professor and Head, Department of Mathematics, Government Engineering College, Raipur, Chhattisgarh, India.

*** Assistant Professor and Head, Department of Computer Science, Government J. Yoganandam Chhattisgarh College, Raipur, Chhattisgarh, India.

Das, A. K., Diwan, S. D., & Jain, S. (2018). Common Fixed Point Theorems for Cr-Iteration Scheme in Three Multivalued Mappings, i-manager's Journal on Mathematics, 7(3), 51-60. https://doi.org/10.26634/jmat.7.3.15064

Abstract

The purpose of this paper is to introduce multivalued version of CR iteration process given by Chugh, Kumar, and Kumar (2012) and provecommon fixed point theorem for this iteration in three multivalued ρ-nonexpansive mappings in modular space. Let ρϵη satisfy (UUC1) and C ⊂ Lp be nonempty ρ-bounded and convex set. Let T1, T2, T3: C →Pρ(C) be three multivalued mappings such that PT1ρ, PT2ρ and PT3ρ are ρ-nonexpansive mappings with F = Fρ(T1) ⋂ Fρ(T2) ⋂ Fρ(T3) ≠ φ. Suppose T1 , T2 and T3 satisfy condition (I). Then the sequence {fn} defined by us converges to a point of F.

An Inventory Model for Two Storage System with Stock Dependent Demand

Volume 7 Issue 3 July - September 2018

Research Paper

An Inventory Model for Two Storage System with Stock Dependent Demand

Amit Kumar Attri*, S. R. Singh**, Shweta Choudhary***

* Assistant Professor, Department of Mathematics, Delhi Technical Campus, Greater Noida, Uttar Pradesh, India.

** Professor, Department of Mathematics, CCS University Meerut, Uttar Pradesh, India.

*** Associate Professor and Head, Department of Applied Sciences, ABES Engineering College,.Dr. A. P. J. Abdul Kalam Technical University, Ghaziabad, Uttar Pradesh, India.

Attri, A. K., Singh, S. R., & Choudhary, S. (2018). An Inventory Model for Two Storage System with Stock Dependent Demand, i-manager's Journal on Mathematics, 7(3), 42-50. https://doi.org/10.26634/jmat.7.3.14668

Abstract

In this paper an inventory model to find out the buyer's optimal policy with two storage system has been developed. The buyer purchases a lot of Q units and transfers this stock in the display area in n equal lots. The demand considered here is a function of displayed stock level. The objective of this model is to optimize the total average cost for the buyer and find out the optimal number of shipments. A numerical example is presented to illustrate this study. The sensitivity analysis presented here shows that the model is quite stable and reflects the real life marketing situations.

Application of Multi-State Semi-Markov Models on HIV/AIDS Disease Progression

Volume 7 Issue 3 July - September 2018

Research Paper

Application of Multi-State Semi-Markov Models on HIV/AIDS Disease Progression

Solomon Kalayu Mengesha*, Gebregewergis Alemu Gebremedhn**, Tilahun Ferede***, Cheru Atsmegiorgis ****

*-**Lecturer, Adigrat University, Tigray, Ethiopia.

***-****Hawassa University, Awassa, Ethiopia.

Mengesha, S. K., Gebremedhn, G. A., Tilahun, F., & Atsmegiorgis, C. (2018). Application of Multi-State Semi-Markov Models on HIV/AIDS Disease Progression, i-manager's Journal on Mathematics, 7(3), 30-41. https://doi.org/10.26634/jmat.7.3.14988

Abstract

Although remarkable progress has been made in the control of the global Human Immunodeficiency Virus (HIV/AIDS) epidemic, the burden of HIV has reached contemporary at the shocking level in Sub-Saharan Africa. Understanding the cycle of HIV/AIDS disease progression can have great value on the effectiveness of the therapy. The purpose of this study is to determine factors affecting the progression between different stages of the disease and to model the progression of HIV/AIDS disease of an HIV infected patients under ART follow-up using multistate Semi-Markov model. A cohort of 526 HIV infected patients has been sampled from a Hawassa University Referral Hospital, Hawassa, Ethiopia, who have been under ART follow up from September 2012 to August 2017. States of the Markovian process are defined by the seriousness of the sickness based on the CD4 counts in cells/microliter. The five states of HIV/AIDS disease progression considered in the multi-state Semi-Markov model were defined based on of the following CD4 cell counts. State I, State II, State III, State IV and Death state. The major transiently prognostic factors between different states of HIV/AIDS disease were sex, age, ART adherence level, TB status, functional status, opportunistic infections , and body weight of patients. Hence, the progression of HIV/AIDS was significantly accelerated with poor ART adherence, patient's co-infection with TB, older patients, and patients being bedridden. The conditional probabilities of patients from any good states to worst state are increasing over time. Weibull sojourn time distribution is the appropriate and is preferably used as sojourn time distribution under multistate models. As time elapsed, the transition probability of patients is more likely to be in worse state than to be in better one. This shows that patients should aware the need to initiate therapy at early stages of the virus.

Trioengineering Interapplication and Comprehensive Cohesive Cogitation: The Use of Systemic Neuromathematical Trioinformatics to Create, Define, and Express Trichotomous Research Instrumentation and Tri-Squared Analytics

Volume 7 Issue 3 July - September 2018

Research Paper

Trioengineering Interapplication and Comprehensive Cohesive Cogitation: The Use of Systemic Neuromathematical Trioinformatics to Create, Define, and Express Trichotomous Research Instrumentation and Tri-Squared Analytics

James Edward Osler II*

Associate Professor, Department of Allied Professions, North Carolina Central University, USA.

Osler II, J. E. (2018). Trioengineering Interapplication and Comprehensive Cohesive Cogitation: The Use of Systemic Neuromathematical Trioinformatics to Create, Define, and Express Trichotomous Research Instrumentation and Tri-Squared Analytics, i-manager's Journal on Mathematics, 7(3), 10-29. https://doi.org/10.26634/jmat.7.3.15190

Abstract

This discourse provides a deeper epistemological rational for the novel discipline of “Trioinformatics” through the use of “Trioengineering” to create innovative research instrumentation from trichotomous research questions. Trioengineering uses of the novel mathematical “Ambitation” from “Neuromathematical Neuroengineering Notation” in Trioengineering as a novel operational methodology referred to as “Interapplication”. This specialized operation was first defined in the Trioinformatics article that appeared in the March-May i-manager Journal on Circuits and Systems. Trioengineering's use of the neuromathematics “Ambitation” as an “Interapplication” is the holistic, collaborative, and comprehensive expression of Trioinformatics as a sequential sequence of inquiry into a precise research analysis methodology. Neuroengineering is an innovative way of explaining the transition from trichotomous logic (Osler, 2015) into a trichotomous Triple-I (Osler, 2013d) in which research questions are implemented in a meticulously defined and mathematically associated instrument [first introduced in the i-manager Journal on Mathematics as a part of the Tri- Squared Test (Osler, 2012a)]. Trioinformatics is an in-depth way of symbolically illustrating the law of trichotomy as a mathematically-grounded rational technique for explaining the ternary nature of electronic circuitry (Osler, 2015). The use of the Trioinformatics also adds value to investigative inquiry through the efficacy of digital instruments and tools via eduscientifically - engineered (Osler, 2013) research designs (Osler, 2015).

On Lacunary Statistical Convergence and Some Properties in Fuzzy N-Normed Spaces

Volume 7 Issue 3 July - September 2018

Research Paper

On Lacunary Statistical Convergence and Some Properties in Fuzzy N-Normed Spaces

Muhammed Recai Türkmen*

Assistant Professor, Department of Mathematics and Science Education, The Afyon Kocatepe University, Turkey.

Türkmen, M. R. (2018). On Lacunary Statistical Convergence and Some Properties in Fuzzy N-Normed Spaces, i-manager's Journal on Mathematics, 7(3), 1-9. https://doi.org/10.26634/jmat.7.3.14868

Abstract

In this paper, the author has introduced the concept of lacunary summable and lacunary statistical convergence in fuzzy n-normed spaces. At the same time, the author has introduced condition of being lacunary statistically Cauchy sequence with respect to a fuzzy n-norm. The author has also studied the relation between these concepts and gave some properties of lacunary statistical convergence sequences in fuzzy n-normed spaces.

Thermal Diffusion and Radiation Effects on Magnetocasson Fluid Flow Past A Vertical Porous Plate

Volume 7 Issue 2 April - June 2018

Research Paper

Thermal Diffusion and Radiation Effects on Magnetocasson Fluid Flow Past A Vertical Porous Plate

K. Venkateswara Raju*, M. C. Raju**, V. Ravi Kumar***, G. S. S. Raju****

* Assistant Professor, Department of Mathematics, Sree Vidyanikethan Engineering College (Autonomous), A. Rangampet, Tirupati, Andhra Pradesh, India.

** Coordinator Research and Development, Department of Mathematics, Annamacharya Institute of Technology and Sciences (Autonomous), Rajampet, , Andhra Pradesh, India.

*** Assistant Professor, Department of Mathematics, Annamacharya Institute of Technology and Sciences (Autonomous), Rajampet, Andhra Pradesh, India.

****The Professor and Head, Department of Mathematics, JNTU College of Engineering (Autonomous), Pulivendula, Kadapa (Dt), Andhra Pradesh, India.

Raju. K.V., Raju, M.C., Kumar. V.R., and Raju. G.S.S. (2018). Thermal Diffusion and Radiation Effects on Magnetocasson Fluid Flow Past A Vertical Porous Plate. i-manager’s Journal on Mathematics, 7(2), 32-46. https://doi.org/10.26634/jmat.7.2.14680

Abstract

In this manuscript thermal diffusion and radiation effects on magneto-Casson fluid flow past a vertical porous plate with chemical reaction is studied. The non-dimensional governing equations for momentum, energy and concentration equations have been solved by using perturbation techniques. The expressions for skin friction, Nusselt number and Sherwood number are also obtained. The effects of various physical parameters like chemical reaction parameter, Casson parameter, magnetic parameter, radiation parameter, Soret number, Schmidt number, Grashof number, Prandtl number, and modified Grashof number have been discussed in detailed through graphs and tables.

Influence of Viscous Dissipation on Radiative and Conducting Fluid Past an Accelerated Plate

Volume 7 Issue 2 April - June 2018

Research Paper

Influence of Viscous Dissipation on Radiative and Conducting Fluid Past an Accelerated Plate

D. Ravi Kumar*, K. Jayarami Reddy**

* Research Scholar, Department of Mathematics, Rayalaseema Univesity, Kurnool, Andhra Pradesh, India.

** Professor, Department of Mathematics, K. L. University, Vaddeswaram, Guntur, Andhra Pradesh. India.

Kumar. D.R., and Reddy. K.J. (2018). Influence of Viscous Dissipation on Radiative and Conducting Fluid Past an Accelerated Plate. i-manager’s Journal on Mathematics, 7(2), 24-31. https://doi.org/10.26634/jmat.7.2.14679

Abstract

An unsteady free convective, chemically reactive, radiation absorbing, viscous dissipative fluid past an exponentially accelerated vertical porous plate in the presence of and Soret and Dufour effects is considered. The set of nondimensional governing equations along with boundary conditions are solved numerically using finite difference method. The characteristics of pertinent physical parameters on flow quantities are examined numerically by using graphs. For the substantial interest, the fluctuations in skin friction, Nusselt number and Sherwood number are also deals through tables.

Constrained Scalar Valued Dynamic Games and Symmetric Duality for Multi Objective Variational Problem

Volume 7 Issue 2 April - June 2018

Research Paper

Constrained Scalar Valued Dynamic Games and Symmetric Duality for Multi Objective Variational Problem

0*, Devanandam. Dola**, B. Satyanarayana***

* Professor, Department of Information Technology, Sree Vidyanikethan Engineering College (Autonomous), Tirupati, Andhra Pradesh, India.

** Lecturer and Head, Department of Mathematics, Dharma Apparao College, Nuzivid, Krishna (Dt), Andhra Pradesh, India.

*** Professor, Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar, Andhra Pradesh, India.

Reddy. L.V., Dola. D., and Satyanarayana. B. (2018). Constrained Scalar Valued Dynamic Games and Symmetric Duality for Multi Objective Variational Problem. i-manager’s Journal on Mathematics, 7(2), 17-23. https://doi.org/10.26634/jmat.7.2.14678

Abstract

In this paper, a certain constrained scalar valued dynamic game is formulated and shown to be equivalent to a pair of multi-objective symmetric dual variational problem. These are more generation formulations then those studied easier. Further, various duality results were obtained in this context under generalized invexity conditions.

Strong and Δ - Convergence Theorems using Modified Proximal Point Algorithm in CAt(0) Spaces

Volume 7 Issue 2 April - June 2018

Research Paper

Strong and Δ - Convergence Theorems using Modified Proximal Point Algorithm in CAt(0) Spaces

Apurva Kumar Das*, Shailesh Dhar Diwan**, Samir Dashputre***

* Lecturer, Department of Mathematics, Government Polytechnic Sukma, Chhattisgarh, India.

** Associate Professor, Department of Mathematics, Government Engineering College, Raipur, Chhattisgarh, India.

*** Assistant Professor, Department of Mathematics, Government College Arjunda, Balod, Chhattisgarh, India.

Das. A.K., Diwan. S.D., and Dashputre. S. (2018). Strong and Δ - Convergence Theorems using Modified Proximal Point Algorithm in CAt(0) Spaces. i-manager’s Journal on Mathematics, 7(2), 8-16. https://doi.org/10.26634/jmat.7.2.13999

Abstract

Let (X, d) be a complete CAT(0) space and f∶ X → (-∞, ∞] be a proper convex and lower semi-continuous function. Suppose T be a nonexpansive mapping on X such that Ω=F(T) ⋂ argmin(yϵX) f(y) is nonempty. The purpose of this paper is to define a modified proximal point algorithm and prove the existence of a sequence proposed by the authors converges to Ω. In this paper, they prove strong and Δ-convergence theorems with their proposed modified proximal point algorithm in CAT(0) spaces.

Proof of Beal's Conjecture and Fermat Last Theorem using Contra Positive Method

Volume 7 Issue 2 April - June 2018

Research Article

Proof of Beal's Conjecture and Fermat Last Theorem using Contra Positive Method

Vinay Kumar*

Professor, Vivekananda School of IT, VIPS, GGSIPU, New Delhi, India.

Kumar. V. (2018). Proof of Beal's Conjecture and Fermat Last Theorem using Contra Positive Method. i-manager’s Journal on Mathematics, 7(2), 1-7. https://doi.org/10.26634/jmat.7.2.14127

Abstract

“If Ax + By = Cz , for integers A, B, C ≥2 and integers x, y, z greater than 2 , then A, B, C must have a common prime factor”. The statement is known as Beal's conjecture (Rubin & Silverberg, 1994). Without loss of generality, integers B and C can be expressed in terms of A. Assuming B = A + m and C = A + n, the present study proves the conjecture for all the four cases: i) m = 0, n = 0; ii) m = 0, n≠ 0; iii) m≠0, n = 0; and iv) m≠0, n ≠0. A, B, and C can be ordered (sequenced) in six different ways. A theorem that is proved for one sequence, the same theorem can easily be proved for other five sequences. Contrapositive approach together with integer division algorithm is used to prove the conjecture. Contrapositive statement of Beal's x conjecture is “if A, B, and C have no common prime factor then  no integers A, B, C and integers x, y, z > 2 such that Ax + By = Cz”. Some basic and fundamental properties of quadratic equation are also used in the proof.

A Simple Method of Numerical Integration for a Class of Singularly Perturbed Two Point Boundary Value Problems

Volume 7 Issue 1 January - March 2018

Research Paper

A Simple Method of Numerical Integration for a Class of Singularly Perturbed Two Point Boundary Value Problems

Rakesh Ranjan*, H. S. Prasad**, Md. Javed Alam***

*,*** Research Scholar, Department of Mathematics, National Institute of Technology, Jamshedpur, Jharkhand, India.

** Assistant Professor, Department of Mathematics, National Institute of Technology, Jamshedpur, Jharkhand, India.

Rakesh Ranjan., H. S. Prasad., Md. Javed Alam. (2018). A Simple Method of Numerical Integration for A Class of Singularly Perturbed Two Point Boundary Value Problems. i-manager’s Journal on Mathematics, 7(1), 43-52.https://doi.org/10.26634/jmat.7.1.14031

Abstract

This paper deals with a simple but efficient numerical integration method to solve a class of singularly perturbed twopoint boundary value problems. Using the methods of exact rule of integration with a finite difference approximation of first derivatives, a three-term recurrence relationship is obtained. The authors have employed Thomas algorithm to obtain the solution of the obtained system. Also, the stability and convergence of the proposed scheme are established. Several model example problems have been solved and the results are presented in terms of maximum absolute errors, which show the accuracy and efficiency of the method. The method produces highly accurate results for a fixed value of step size h when the perturbation parameter e tends to zero.

A New Approach to Variant Assignment Problem

Volume 7 Issue 1 January - March 2018

Research Paper

A New Approach to Variant Assignment Problem

Uruturu balakrishna*

Professor of Mathematics, Department of Science & Humanities, Sreenivasa Institute of Technology and Management Studies, Chittoor, India.

Balakrishna, U. (2018). A New Approach to Variant Assignment Problem. i-manager’s Journal on Mathematics, 7(1), 34-42.https://doi.org/10.26634/jmat.7.1.14030

Abstract

It is a two dimensional problem where the time matrix T(i, j) is the time of the j job assigned to i person. The time matrix T(i.j) [i=1,2,3,…, m; j=1,2,3,…,n] is known. Each of the person is constrained to do the specified number of jobs. All the persons start working on the jobs simultaneously, but a person cannot work on more than one job at a time. The problem is to assign the n jobs to m persons, with minimum total time with the restriction that each person to do given specified number of jobs. A Lexi search approach is proposed using pattern recognition technique to find an optimal feasible assignment. For this problem a computer program is developed for the algorithm and is tested. It is observed that it takes less time for solving higher dimension problems also.

Common Fixed Point Theorems for Six occasionally weakly Compatible Mappings in Fuzzy Metric Spaces

Volume 7 Issue 1 January - March 2018

Research Paper

Common Fixed Point Theorems for Six occasionally weakly Compatible Mappings in Fuzzy Metric Spaces

T Rakesh Singh*, P. Srikanth Rao**

* Associate Professor, Department of Mathematics, Aurora's Technological Institute, Hyderabad, Telangana, India.

** Professor, Department of Mathematics, B.V. Raju Institute of Technology, Narsapur, Telangana, India.

Singh, T.R., and Rao, P.S. (2018). Common Fixed Point Theorems for Six Occasionally Weakly Compatible Mappings in Fuzzy Metric Spaces. i-manager’s Journal on Mathematics, 7(1), 28-33. https://doi.org/10.26634/jmat.7.1.14029

Abstract

The fixed point hypotheses in metric spaces are assuming a noteworthy part to develop techniques in arithmetic to take care of issues in connecting applied mathematics and sciences. So the fascination of metric spaces to substantial quantities of mathematicians is understandable. The aim of this paper is to prove common fixed point theorems for Occasionally Weakly Compatible six self mappings. The concept of Occasionally Weakly Compatible Mappings introduced by Al-Thagafi and Shahzad (2008) also generalized the concept of compatible maps and weakly compatible maps in fuzzy metric space. The authors aim to improve the results of Sanodia et al. (2017). Their result generalizes and improves other similar results in the literature.

Finite Element Solution of Viscous Dissipative Effects on Unsteady MHD Flow Past A Parabolic Started Vertical Plate with Mass Diffussion and Variable Temperature

Volume 7 Issue 1 January - March 2018

Research Paper

Finite Element Solution of Viscous Dissipative Effects on Unsteady MHD Flow Past A Parabolic Started Vertical Plate with Mass Diffussion and Variable Temperature

B .Shankar Goud*, Shekar, M.N.R.**

* Research Scholar, Department of Mathematics, JNTUH College of Engineering Kukatpally, Hyderabad, India.

** Professor, Department of Mathematics, JNTUH College of Engineering Nachupally, Hyderabad, India

Goud. B.S., and Shekar, M.N.R. (2018). Finite Element Solution of Viscous Dissipative Effects on Unsteady MHD Flow Past A Parabolic Started Vertical Plate with Mass Diffussion and Variable Temperature. i-manager’s Journal on Mathematics, 7(1), 20-27.https://doi.org/10.26634/jmat.7.1.14028

Abstract

In this paper, the authors have investigated an unsteady magneto hydrodynamic flow past a parabolic starting motion of the infinite vertical plate with variable temperature and variable mass diffusion. The plate temperature and the concentration level close to the plate are raised with time. The dimensionless governing equations are solved by using Galerkin Finite Element Technique. The effect of velocity, temperature and concentration distribution is studied for different physical parameters.

A Homotopy Based Method for Nonlinear Fredholm Integral Equations

Volume 7 Issue 1 January - March 2018

Research Paper

A Homotopy Based Method for Nonlinear Fredholm Integral Equations

Javed Ali*

Senior Lecturer, Department of Mathematics and Statistics, Caledonian (University) College of Engineering, Oman.

Javed Ali. (2018). A Homotopy Based Method For Nonlinear Fredholm Integral Equations. i-manager’s Journal on Mathematics, 7(1), 13-17. https://doi.org/10.26634/jmat.7.1.14027

Abstract

In this work, the author extends the application of the optimal homotopy asymptotic method to the solution of nonlinear Fredholm integral equations of the second kind. Several examples are solved to demonstrate the efficiency of the proposed method. Numerical results are compared with the exact solution.

The Tri–Sigma Test: The Triple–Sigma Trichotomous Summation Triostatistic for the Viability, Verifiability, and Validityof Multiple Tri–Squared Test Outcomes

Volume 7 Issue 1 January - March 2018

Research Paper

The Tri–Sigma Test: The Triple–Sigma Trichotomous Summation Triostatistic for the Viability, Verifiability, and Validityof Multiple Tri–Squared Test Outcomes

James Edward Osler II*

Associate Professor, Department of Curriculum and Instruction, North Carolina Central University, USA.

Osler II, J.E. (2018). The Tri-Sigma Test: The Triple-Sigma Trichotomous Summation Triostatistic for the Viability, Verifiability, and Validity of Multiple Tri-Squared Test Outcomes. i-manager’s Journal on Mathematics, 7(1), 1-12.https://doi.org/10.26634/jmat.7.1.14026

Abstract

This paper provides a novel statistical methodology called “Triple or Tri–Sigma” (“Tri-Σ”) that is designed to conceptually add to the research that has been conducted on and with the Tri–Squared Test (Osler, 2012a). The Tri–Sigma Test is an advanced statistical procedure that is used to analyze multiple Tri–Squared Tests that have been delivered at different times. Tripleseries summation provides an innovative way of investigating the data derived from a series of researchbased investigative instruments that are known as “Trichotomous Tri-Squared Test Triple-I's” (Osler and Mansaray, 2013b). The Triple–I is directly derived from specific research questions as an in-depth associated instrument [first introduced in the i-manager's Journal on Mathematics as a part of the “Tri-Squared Test” (Osler, 2012a)]. This new approach to research inquiry lends additional strength to trichotomous research designs. Trichotomous tests can now be offered at multiple stages, multiple times, and in multiple ways with multiple research questions.