Earthline Journal of Mathematical Sciences

Earthline Journal of Mathematical Sciences

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  • Publisher: Earthline Publishers
  • Country of publisher: india
  • Date added to EuroPub: 2019/Sep/29

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  • Time from submission to publication: weeks

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  • Waiver policy for charges? No

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  • Open Access Statement: No
  • Year open access content began: 2019
  • Does the author retain unrestricted copyright? False
  • Does the author retain publishing rights? False

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This journal has '42' articles

A Note on the Notions of Topological Entropy

A Note on the Notions of Topological Entropy

Authors: Wong Koon Sang, Zabidin Salleh
Year: 2019, Volume: 1, Number: 1
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Abstract

Topological entropy is used to determine the complexity of a dynamical system. This paper aims to serve as a stepping stone for the study of topological entropy. We review the notions of topological entropy, give an overview on the relation between the notions and fundamental properties of topological entropy. Besides, we cover the topological entropy of the induced hyperspaces and its connection with the original systems. We also provide a summary on the latest research topic related with topological entropy.

Keywords: topological entropy, dynamical systems, induced hyperspaces, set-valued functions.
An Almost Periodic Lasota-Wazewska Dynamic Model on Time Scales

An Almost Periodic Lasota-Wazewska Dynamic Model on Time Scales

Authors: Zhijian Yao
Year: 2019, Volume: 1, Number: 1
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Abstract

This paper deals with almost periodicity of Lasota-Wazewska dynamic equation on time scales. By applying a method based on the fixed point theorem of decreasing operator, we establish sufficient conditions for the existence of a unique almost periodic positive solution. We also give iterative sequence which converges to almost periodic positive solution. Moreover, we investigate the exponential stability of almost periodic solution by means of Gronwall inequality. Our study unifies differential and difference equations.

Keywords: Lasota-Wazewska model on time scales, exponential dichotomy, almost periodic solution, exponential stability.
Sensitivity Analysis and Stabilization for Two Dynamical Systems

Sensitivity Analysis and Stabilization for Two Dynamical Systems

Authors: Frank Etin-Osa Bazuaye
Year: 2019, Volume: 1, Number: 1
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Abstract

This paper focuses on the sensitivity analysis for two dominant political parties. In contrast to Misra, Bazuaye and Khan, who developed the model without investigating the impact of varying the initial state of political parties on the solution trajectory of each political parties, we have developed a sound numerical algorithm to analyze the impact of change on the initial data on the behavior of the democratic process which is a rare contribution to knowledge. Two Matlab standard solvers for ordinary differential equations, ode45 and ode23, have been utilized to handle these formidable mathematical problems. Our findings indicate that as the initial data varies, the dynamical system describing the interaction between two political parties is stabilized over a period of eight years. As duration increases, the systems get de-stabilized.

Keywords: dominant political parties, qualitative characterization, stabilization.
Further Generalized Beta Function with Three Parameters Mittag-Leffler Function

Further Generalized Beta Function with Three Parameters Mittag-Leffler Function

Authors: Salem Saleh Barahmah
Year: 2019, Volume: 1, Number: 1
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Abstract

The purpose of the present paper is to introduce a new extension of extended Beta function by product of two Mittag-Leffler functions. Further, we present certain results including summation formulas, integral representations and Mellin transform.

Keywords: extended Beta function, Mittag-Leffler function, summation formulas, integral representations, Mellin transform.
Mathematical Optimization Model Technique for Network Congestion Control in Global System for Mobile Communications

Mathematical Optimization Model Technique for Network Congestion Control in Global System for Mobile Communications

Authors: Remigius Okeke Aja, Emeka Uchendu Agwu, Sussan Ijeoma Ezeh, Udochi John Stephen
Year: 2019, Volume: 1, Number: 1
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Abstract

The introduction of Global System for Mobile Communication (GSM) in Nigeria is responsible for significant tremendous teledensity ratio increment, which results in network congestion in most busy areas. In this paper, we applied a Second Order Necessary Condition (a Mathematical Optimization Technique) as a tool in solving the problem of network congestion. One of the GSM providers; Mobile Telecommunication of Nigeria (MTN), was used to demonstrate the usefulness of Second Order Necessary Condition to the control of network congestion at Michael Okpara University of Agriculture, Umudike (MOUAU). Free flow of connection between mobile phone users at different locations within the area of investigation was established, hence congestion controlled.

Keywords: Global System for Mobile Communication (GSM), network congestion, Mobile Telecommunication of Nigeria (MTN), teledensity ratio, controlled, second order necessary condition, mathematical optimization technique.
On the Modified Optimal Investment Strategy for Annuity Contracts under the Constant Elasticity of Variance (CEV) Model

On the Modified Optimal Investment Strategy for Annuity Contracts under the Constant Elasticity of Variance (CEV) Model

Authors: K. N. C. Njoku, B. O. Osu
Year: 2019, Volume: 1, Number: 1
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Abstract

In this work, the optimal pension wealth investment strategy during the decumulation phase, in a defined contribution (DC) pension scheme is constructed. The pension plan member is allowed to invest in a risk free and a risky asset, under the constant elasticity of variance (CEV) model. The explicit solution of the constant relative risk aversion (CRRA) and constant absolute risk aversion (CARA) utility functions are obtained, using Legendre transform, dual theory, and change of variable methods. It is established herein that the elastic parameter, β, say, must not necessarily be equal to one (β ≠ 1). A theorem is constructed and proved on the wealth investment strategy. Observations and significant results are made and obtained, respectively in the comparison of our various utility functions and some previous results in literature.

Keywords: annuity contracts, CRRA, CARA, DC, CEV, optimal strategy.
A Best Proximity Point Theorem for G-Proximal (delta, 1-delta) Weak Contraction in Complete Metric Space Endowed with a Graph

A Best Proximity Point Theorem for G-Proximal (delta, 1-delta) Weak Contraction in Complete Metric Space Endowed with a Graph

Authors: Clement Boateng Ampadu
Year: 2019, Volume: 1, Number: 1
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Abstract

The notion of (delta, 1-delta) weak contraction appeared in [1]. In this paper, we consider that the map satisfying the (delta, 1-delta) weak contraction is a non-self map, and obtain a best proximity point theorem in complete metric space endowed with a graph.

Keywords: best proximity, G-proximal, (delta, 1-delta) weak contraction, complete metric space, graph.
Fully Homomorphic Cipher Based on Finite Algebraic Structures

Fully Homomorphic Cipher Based on Finite Algebraic Structures

Authors: Y. Ts. Alaverdyan, E. G. Satimova
Year: 2019, Volume: 1, Number: 1
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Abstract

A way to increase the robustness of a cryptographic algorithm toward unauthorized inversion can be obtained through application of non-commutative or non-associative algebraic structures. In this regard, data security became a great issue in adaptation of cloud computing over Internet. While in the traditional encryption methods, security to data in storage state and transmission state is provided, in cloud data processing state, decryption of data is assumed, data being available to cloud provider. In this paper, we propose a special homomorphism between self-distributed and non-associative algebraic structures, which can stand as a premise to construct a homomorphic encryption algorithm aimed at the cloud data security in processing state. Homomorphic encryption so developed will allow users to operate encrypted data directly bypassing the decryption.

Keywords: cryptology, non-associative algebra, self-distributed algebra, homomorphic mapping.
A New Symmetric p-stable Obrechkoff Method with Optimal Phase lag for Oscillatory Problems

A New Symmetric p-stable Obrechkoff Method with Optimal Phase lag for Oscillatory Problems

Authors: I. C. Felix, O. O. Famoofo, S. M. Akintewe
Year: 2019, Volume: 1, Number: 1
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Abstract

In this paper, we derive a class of symmetric p-stable Obrechkoff methods via Padé approximation approach (PAA) for the numerical solution of special second order initial value problems (IVPs) in ordinary differential equations (ODEs). We investigate periodicity analysis on the proposed scheme to verify p-stability property. The new algorithms possess minimum phase-lag error which shows that they can accurately solve oscillatory problems. Reports on several numerical experiments are provided to illustrate the accuracy of the method.

Keywords: p-stability, Obrechkoff method, Padé approximation, symmetric, oscillatory, phase-lag error.
On the Effect of Inflation and Impact of Hedging on Pension Wealth Generation Strategies under the Geometric Brownian Motion Mode

On the Effect of Inflation and Impact of Hedging on Pension Wealth Generation Strategies under the Geometric Brownian Motion Mode

Authors: B. O. Osu, K. N. C. Njoku, Ben I. Oruh
Year: 2019, Volume: 1, Number: 2
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Abstract

This work investigates the effect of Inflation and the impact of hedging on the optimal investment strategies for a prospective investor in a DC pension scheme, using inflation-indexed bond and inflation-linked stock. The model used here permits the plan member to make a defined contribution, as provided in the Nigerian Pension Reform Act of 2004. The pension plan member is allowed to invest in risk-free asset (cash), and two risky assets (i.e., the inflation-indexed bond and inflation-linked stock). A stochastic differential equation of the pension wealth that takes into account certain agreed proportions of the plan member’s salary, paid as contribution towards the pension fund, is constructed and presented. The Hamilton-Jacobi-Bellman (H-J-B) equation, Legendre transformation, and dual theory are used to obtain the explicit solution of the optimal investment strategies for CRRA utility function. Our investigation reveals that the inflation have significant negative effect on wealth investment strategies, particularly, the RRA(w) is not constant with the investment strategy, since the inflation parameters and coefficient of CRRA utility function have insignificant input on the investment strategies, and also the inflation-indexed bond and inflation-linked stock has a positive damping effect (hedging) on the severe effect of inflation.

Keywords: hedging. defined contribution pension. Hamilton-Jacobi Bellman equation. GBM, inflation.
Differential Subordination Results for Fractional Integral Associated with Generalized Mittag-Leffler Function

Differential Subordination Results for Fractional Integral Associated with Generalized Mittag-Leffler Function

Authors: Abbas Kareem Wanas, Alaa Hussein Khaleel
Year: 2019, Volume: 1, Number: 2
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Abstract

In this work, by making use of fractional integral, we define a certain class of holomorphic functions defined by generalized Mittag-Leffler function in the open unit disk U. Also, we establish some results for this class related to integral representation, inclusion relationship and argument estimate.

Keywords: holomorphic functions. generalized Mittag-Leffler function. fractional integral. subordination. integral representation.
The Convex $(\delta,L)$ Weak Contraction Mapping Theorem and its Non-Self Counterpart in Graphic Language

The Convex $(\delta,L)$ Weak Contraction Mapping Theorem and its Non-Self Counterpart in Graphic Language

Authors: Clement Boateng Ampadu
Year: 2019, Volume: 1, Number: 2
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Abstract

Let $(X,d)$ be a metric space. A map $T:X \mapsto X$ is said to be a $(\delta,L)$ weak contraction [1] if there exists $\delta \in (0,1)$ and $L\geq 0$ such that the following inequality holds for all $x,y \in X$: $d(Tx,Ty)\leq \delta d (x,y)+Ld(y,Tx)$ On the other hand, the idea of convex contractions appeared in [2] and [3]. In the first part of this paper, motivated by [1]-[3], we introduce a concept of convex $(\delta,L)$ weak contraction, and obtain a fixed point theorem associated with this mapping. In the second part of this paper, we consider the map is a non-self map, and obtain a best proximity point theorem. Finally, we leave the reader with some open problems.

Keywords: $(\delta,L)$ weak contraction, convex contraction, non-self map, graph, fixed point theorem, best proximity point theorem.
On the Convergence Region of Multi-step Chebyshev-Halley-type Schemes for Solving Equations

On the Convergence Region of Multi-step Chebyshev-Halley-type Schemes for Solving Equations

Authors: Ioannis K. Argyros, Santhosh George
Year: 2019, Volume: 1, Number: 2
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Abstract

The aim of this article is to extend the convergence region of certain multi-step Chebyshev-Halley-type schemes for solving Banach space valued nonlinear equations. In particular, we find an at least as small region as the region of the operator involved containing the iterates. This way the majorant functions are tighter than the ones related to the original region, leading to a finer local as well as a semi-local convergence analysis under the same computational effort. Numerical examples complete this article.

Keywords: Chebyshev method, Halley method, local convergence, semi-local convergence, Fréchet derivative, \omega-conditions
Differential Sandwich Theorems for a Certain Class of Analytic Functions Defined by Differential Operator

Differential Sandwich Theorems for a Certain Class of Analytic Functions Defined by Differential Operator

Authors: Abbas Kareem Wanas, Hala Abbas Mehai
Year: 2019, Volume: 1, Number: 2
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Abstract

In this paper, we establish some applications of first order differential subordination and superordination results involving Hadamard product for a certain class of analytic functions with differential operator defined in the open unit disk. These results are applied to obtain sandwich results.

Keywords: analytic functions, differential subordination, differential superordination, Hadamard product, differential operator.
A Family of Stiffly Stable Second Derivative Block Methods for Initial Value Problems in Ordinary Differential Equations

A Family of Stiffly Stable Second Derivative Block Methods for Initial Value Problems in Ordinary Differential Equations

Authors: Samuel A. Ajayi, Kingsley O. Muka, Oluwasegun M. Ibrahim
Year: 2019, Volume: 1, Number: 2
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Abstract

In this paper, we present a family of stiffly stable second derivative block methods (SDBMs) suitable for solving first-order stiff ordinary differential equations (ODEs). The methods proposed herein are consistent and zero stable, hence, they are convergent. Furthermore, we investigate the local truncation error and the region of absolute stability of the SDBMs. A flowchart, describing this procedure is illustrated. Some of the developed schemes are shown to be A-stable and L-stable, while some are found to be A(\alpha)-stable. The numerical results show that our SDBMs are stiffly stable and give better approximations than the existing methods in the literature.

Keywords: second derivative, A-stability, L-stability, block method, ordinary differential equations.

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