Journal of Mathematics Research

Journal of Mathematics Research

Published by Canadian Center of Science and Education

Online ISSN: 1916-9809

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Print ISSN: 1916-9795

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Various Proofs of the Sylvester Criterion for Quadratic Forms

December 2024

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8,303 Reads

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9 Citations

Giorgio Giorgi

In the first part of the paper we present several proofs of the so-called Sylvester criterion for quadratic forms; some of the said proofs are short and easy. In the second part of the paper we give an algebraic proof of the Sylvester criterion for quadratic forms subject to a linear homogeneous system.

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38 reads in the past 30 days

On Statistical Convergence in Metric Spaces

December 2024

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71 Reads

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1 Citation

The statistical convergence in metric spaces is considered. Its equivalence to the statistical fundamentality in complete metric spaces is proved. Introduced the concept of p-strong convergence, and proved its equivalence to the statistical convergence. Tauberian theorems concerning statistical convergence in metric spaces are given.

Aims and scope


Journal of Mathematics Research publishes high-quality papers covering all areas of pure and applied mathematics. It highlights significant advances in mathematical theories, methods, and applications. Topics include algebra, analysis, geometry, number theory, statistics, and interdisciplinary research. The journal serves as a platform for mathematicians to share innovative solutions and foster international collaboration in advancing mathematical knowledge.

Recent articles


Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 16, No. 6
  • Article

January 2025

Reviewer Acknowledgements for Journal of Mathematics Research, Vol. 16, No. 6


Spatial Dynamics in Prey-Predator Model With Holling type II and Strong Allee Effect in Prey
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January 2025

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4 Reads

In this study, a spatiotemporal prey-predator mathematical model incorporating a Holling type II functional response and a strong Allee effect in the prey population was developed to explore the dynamics of species undergoing diffusion and migration. The stability of the model without diffusion and migration was analyzed, and the influence of the Allee effect on bifurcations was investigated. The spatial dynamics of the model were further examined to understand how diffusion and migration impact the onset of Turing instability under zero-flux boundary conditions. The findings reveal that the inclusion of the Allee effect can generate complex spatial patterns. While diffusion promotes the emergence of Turing instability, advection does not lead to such instabilities.


Type II Topp-Leone Exponentiated Exponential Distribution: Properties and Applications to Failure Data

January 2025

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1 Read

This work presents a flexible three-parameter lifetime distribution with increasing, increasing and decreasing and non-monotonic hazard rate called Type II Topp-Leone Exponentiated Exponential (TIITLEE) distribution. The density function of TIITLEE model has right-skewed and symmetrical shapes. Descriptive properties such as quantile function, moments, incomplete moments, probability weighted moments, moment generating functions, characteristics function, and Renyi and ρ -entropies are theoretically established. Parameters of TIITLEE distribution are estimated using maximum likelihood method. The potentiality/tractability of TIITLEE distribution is demonstrated by its applications to two lifetime data


Analysis of the Well-posedness of a SEIRDS Dynamic Model for the Spread of Infectious Diseases

January 2025

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14 Reads

The goal of this paper is to demonstrate the well-posedness of a nonlinear parabolic reaction-diffusion system modeling the spread of infectious diseases. The considered mathematical model is of the SEIRDS type. We prove the global existence of a weak solution by using an approximation system with a delay operator λ^τ (which we define in the subsection 3.1) , along with a priori estimates and compactness arguments. Additionally, we establish the uniqueness of the solution and its continuous dependence on the contagion rates using Gronwall's lemma. These results not only show the existence of a solution but also ensure that it is unique and responds stably to variations in the model parameters.


Figure 4. Integer Cordial Labeling of Graph 3í µí°¹ í µí±š í µí±– 2í µí±ƒ 2 with í µí±š 1 = í µí±š 2 = 2 and í µí±š 3 = 4 Theorem 3 Graphs í µí±›í µí°¹ í µí±š í µí±– (í µí±› − 1)í µí±ƒ í µí±¡ with í µí±š í µí±– even or odd connected by paths of even length are integer cordial graphs. Proof: For í µí±› even, a function í µí±“: í µí±‰(í µí±›í µí°¹ í µí±š í µí±– (í µí±› − 1)í µí±ƒ í µí±¡ ) → {− ⌊ |í µí±‰(í µí°º)| 2 ⌋ , − ⌊ |í µí±‰(í µí°º)| 2 ⌋ + 1, … , −1,0,1, … , ⌊ |í µí±‰(í µí°º)| 2 ⌋ − 1, ⌊ |í µí±‰(í µí°º)| 2 ⌋}
Figure 5. Integer Cordial Labeling of Graph 3í µí°¹ í µí±š í µí±– 2í µí±ƒ 5 with í µí±š 1 = í µí±š 3 = 3 and í µí±š 2 = 5
Figure 6. Integer Cordial Labeling of Graph 2í µí°¹ í µí±š í µí±– í µí±ƒ 6 with í µí±š 1 = 5 and í µí±š 2 = 3
Integer Cordial Labelling on Graphs nF_(m_i ) (n-1) P_t With m_i Even or Odd

January 2025

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12 Reads

This paper discusses the integer cordial labeling on the graph nF_(m_i)(n-1)P_t when m_i is even or odd. The graph nF_m(n-1)P_t is obtained from n friendship graphs connected by n-1 paths P_t at vertices other than the central vertex of the graph for the i-th and i+1-th graphs where 1≤i≤n. Additionally, m_i denotes the number of copies of the cycle C_3 for each friendship graph. The main result is the integer cordial label for this graph. Furthermore, it was proved that nF_m(n-1)P_t when m_i even or odd is a graph with integer cordial labeling.


Local Entropy Solution of a Convection-Diffusion Type Integro-Differential Equation

January 2025

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1 Read

In this work, we prove existence local entropy solution of a convection-diffusion type integro-differential equation \displaystyle \partial_{t}\bigg(k* (j(v)-j(v_{0}))\bigg) - \nabla\cdot\bigg( a(x,\nabla \varphi (v))+ F(\varphi (v))\bigg) = f in QT:=(0,T)×ΩQ_{T}:= (0,T) \times \Omega with Dirichlet boundary condition v(0,)=v0v(0, \cdot{})= v_{0} in Ω\Omega and L1L^{1}-data fL1((0,T)×Ω), j(v0)L1(Ω)f \in L^{1}((0,T)\times \Omega), \ j(v_{0})\in L^{1}(\Omega). To that end, regularising the data by LL^{\infty}-functions, using the existence result of entropy solution for these more approximate data and a comparison and diagonal principle of the regularised entropy solution, we prove the existence of an local entropy solution.


Liquidity Premiums in a Levy Market

December 2024

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14 Reads

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1 Citation

This paper gives a theorem for the continuous time super-replication cost of European options where the stock price follows an exponential L\'{e}vy process.Under a mild assumption on the legend transform of the trading cost function, the limit of the sequence of the discrete super-replication cost is proved to be greater than or equal to an optimal control problem.The main tool is an approximation multinomial scheme based on a discrete grid on a finite time interval [0,1] for a pure jump L\'{e}vy model.This multinomial model is constructed similar to that proposed by (Szimayer {\&} Maller, Stoch. Proce. {\&} Their Appl., 117, 1422-1447, 2007).Furthermore, it is proved that the existence of a liquidity premium for the continuous-time model under a L\'{e}vy process.This paper concentrates on the L\'{e}vy processes with infinitely many jumps in any finite time interval.The approach overcomes some difficulties that can be encountered when the L\'{e}vy process has infinite activity.


Figure 8. Example 2. Comparison of residual errors for A2DM with the other six methods 
Accelerated Bidirectional Modifications of the Steepest Descent Method for Ill-posed Linear Algebraic Systems with Dynamics-theoretical and Optimization Interpretation

December 2024

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129 Reads

It is well known that the classical numerical algorithm of the steepest descent method (SDM) is effective for well-posed linear systems, but performs poorly for ill-posed ones. In this paper we propose accelerated and/or bidirectional modifications of SDM, namely the accelerated steepest descent method (ASDM), the bidirectional method (2DM), and the accelerated bidirectional method (A2DM). The starting point is a manifold defined in terms of a minimum functional and a fictitious time variable; nevertheless, in the end the fictitious time variable disappears so that we arrive at purely iterative algorithms. The proposed algorithms are justified by dynamics-theoretical and optimization interpretation. The accelerator plays a prominent role of switching from the situation of slow convergence to a new situation that the functional tends to decrease stepwise in an intermittent and ceaseless manner. Three examples of solving ill-posed systems are examined and comparisons are made with exact solutions and with the existing algorithms of the SDM, the Barzilai-Borwein method, and the random SDM, revealing that the new algorithms of ASDM and A2DM have better computational efficiency and accuracy even for the highly ill-posed systems.



Dynamic Selection of Optimal Sub-portfolio - Application in the Regional Stock Exchange of Securities in West Africa (BRVM)

December 2024

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156 Reads

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1 Citation

In this paper, we consider a generalization of the mean-variance model of Markowitz, including a new limiting constraint on marginal returns through the PER(price earnings ratio), that we apply to an optimal portfolio selection in the Regional Stock Exchange of Securities in West africa (BRVM). We study the PER restriction impact through a dynamic selection of optimal sub-portfolios from an initial portfolio. We trace out dynamically the efficient frontiers of the sub-portfolios for different integer values of the PER. The main objective is to provide, for every level of performance (in term of returns) and for a fixed PER, the selection of optimal sub-portfolios that should lead, for a minimal risk, to the same performance as the original portfolio. We show that based on the PER, we can know for each level of performance, the securities to turn down to be able to define the best selection that converge to the optimal portfolio. Moreover, this work is a contribution to the development efforts of our financial systems and our West African stock market environment. The plots of the efficient frontiers of the sub-portfolios were carried out throughout data collected from the BRVM (Regional Stock Exchange Securities) in the period from October 2014 to February 2015.


Accurate Solutions of Initial Value Problems for Ordinary Differential Equations with the Fourth Order Runge Kutta Method

December 2024

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607 Reads

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44 Citations

In this paper, we consider fourth order Runge-Kutta method for solving ordinary differential equations in initial value problems. The proposed methods are quite efficient and are practically well suited for solving these problems. Several examples are presented to demonstrate the accuracy and easy implementation of the proposed methods. The results of numerical experiments are compared with the analytical solution and thereby gain some insight into the accuracy of proposed methods. Finally we investigate and compute the error of proposed methods. This counterintuitive result is analyzed in this paper.


On Different Types of Chaos for Zd\mathbb{Z}^d-Actions

December 2024

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180 Reads

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5 Citations

In this paper we obtain a characterization of k-typetransitivity for a Zd\mathbb{Z}^d-action on certain spaces andthen prove that k-type SDIC is redundant in the definition ofk-type Devaney chaos for Zd\mathbb{Z}^d-actions on infinitemetric spaces. We define different types of chaos forZd\mathbb{Z}^d-actions and prove results related to theirpreservations under conjugacy and uniform conjugacy. Finally wediscuss k-type properties on product spaces.



Figure 5. Comparison of time-histories of solutions to uncontrolled (red lines) and controlled (blue lines) error equations, e(0) = 10 4
Figure 6. Performance test of the state observers which confronts random perturbation of nominal parameter values
Simulation Approach to State Estimation of Complex Systems

December 2024

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5 Reads

Various uncertainties jeopardize predictability of complex systems arising in different application domains which stimulates the efforts to improve the accuracy of numerical forecast by integrating observations and simulations. This paper addresses a simulation driven approach to the design of feedback controlled observer for complex nonlinear systems where application of analytical techniques become cumbersome or impractical. The quality of state estimations of this approach is tested in applications to some time-dependent and stiff nonlinear systems under significant parameter and initial data uncertainty arising in atmospheric chemistry modeling. We demonstrate that this approach yields robust and rapid state estimation for these systems and simultaneously provides denoising if the corresponding measurements are corrupted by noise.


Table 2 . Estimators, biases, MSE and relative bias using one auxiliary variable in Population 1
Table 5 .
Alternative Ratio Estimator of Population Mean in Simple Random Sampling

December 2024

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493 Reads

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7 Citations

An alternative ratio estimator is proposed for a finite population mean of a study variable Y in simple random sampling using information on the mean of an auxiliary variable X, which is highly correlated with Y. Expressions for the bias and the mean square error of the proposed estimator are obtained. Both analytical and numerical comparisons have shown the proposed alternative estimator to be more efficient than some existing ones. The bias of the proposed estimator is also found to be negligible for all populations considered, indicating that the estimator is as good as the regression estimator and better than the other estimators under consideration.



Direct Block Predictor-Corrector Method for the Solution of General Fourth Order Odes

December 2024

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102 Reads

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18 Citations

This article presented the direct block predictor-corrector method for solving general higher order initial value problems of ordinary differential equation. Method of collocation and interpolation of power series approximate solution was used to derive a continuous linear multistep method. Block method was later used to generate the non overlapping solution at selected grid points. The method developed, is self starting, consistent, symmetric, zero-stable and convergent. The performance of the new block method was tested with some fourth order initial value problems and it was found to compare favorably with the existing methods.


Alternating Group A5A_5 Actions on Homotopy $S^2\times S^2

December 2024

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8 Reads

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2 Citations

Let X be a smooth, closed 4-manifold which is homotopy equivalent to S2×S2S^2\times S^2. By the Seiberg-Witten theory, we take IndA5DX\mathrm{Ind}_{A_5}D_X as a virtual A5A_5-representation and give its concrete representation. We also study IndA5DX\mathrm{Ind}_{A_5}D_X when X is homotopy equivalent to nS2×S2\sharp_n S^2 \times S^2. Besides we give an example of our main theorem.


Relationships between Ordered Compositions and Fibonacci Numbers

December 2024

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74 Reads

A sequence of four compositions of 3 is: 1 + 1 + 1, 1 + 2, 2 + 1, 3. By the replacement of the plus signs (+) and commas (,) by the multiplication dots (?) and plus signs (+) respectively, the sequence becomes the summation series: 1?1?1 + 1?2 + 2?1 + 3, which is equal to 8 or 6th number in the famous Fibonacci sequence. It is a curious fact that the sum of a positive integer n and the products of summands corresponding to the compositions of n is equal to (2n)-th Fibonacci number. We establish the proposition after obtaining a special order of the compositions of n; and then obtain some other results. The results show that Fibonacci sequence has close connection with the special order of the compositions of n. Two Fibonacci identities, which we derive from a special recurrence relation, are useful to prove two theorems. The relationships are stated first in the theorems and are then shown in the consequences of the theorems.


Figure 1. E ff ective thicknesses distribution of Xing Fourth Zone 
Figure 2. Sketch of instantaneous oil production curve of the polymer in Xing Fourth Zone 
Figure 3. Sketch of water moisture curve of the polymer in Xing Fourth Zone 
Theory and Application of Characteristic Finite Difference Fractional Step Method of Capillary Force Enhanced Oil Production

December 2024

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107 Reads

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1 Citation

A kind of second-order implicit characteristic fractional steps finite difference method is presented in this paper for the numerical simulation coupled system of enhanced (chemical) oil production on consideration capillary force in porous media. Some techniques, such as the calculus of variations, energy analysis method, commutativity of the products of difference operators, decomposition of high-order difference operators and the theory of a priori estimates are introduced and an optimal order error estimates in l2l^2 norm is derived. This method has been applied successfully the numerical simulation of enhanced oil production in actual oilfields, and the simulation results are quite interesting and satisfactory.


On Co-screen Conformality of 1-lightlike Submanifolds in a Lorentzian Manifold

December 2024

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62 Reads

In this paper, the co-screen conformal 1-lightlike submanifolds of a Lorentzian manifoldare introduced as a generalization of co-screen locally half-lightlike submanifolds in(Wang, Wang {\&} Liu, 2013; Wang {\&} Liu, 2013) and two examples are given whichone is co-screen locally conformal andthe other is not. Some results are obtained on these submanifolds whichthe co-screen distribution is conformal Killing on the ambient manifold.The induced Ricci tensor of co-screen conformal 1-lightlike submanifolds isinvestigated.


Table 2 .
Figure 3.2. Time plot of first differenced data from January 2004 to February 2015  
Figure 3.8. 3-year forecast with ARIMA(1,2,1)(0,0,2) model  
Figure 3.1. Time series plot of monthly mid-rate against time from January 2004 to February 2015  
Figure 3.5. Histogram of ARIMA(1,2,1)(0,0,2) residuals
Time Series Analysis of the Exchange Rate of the Ghanaian Cedi to the American Dollar

December 2024

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4,159 Reads

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8 Citations

In this paper, we consider two univariate time series models of predicting the dynamics of the exchange rate (using mid-rate data) of the Ghana cedi to the US dollar over a 10year 2months period from January 2004, to February 2015. We consider out-of-sample forecast for the next three years of the exchange rate. The time series models considered for this objective are the Autoregressive Integrated Moving Average (ARIMA) and the Random walk model. We find modest differences between these two models based on the out-of-sample forecast. Interestingly, both models perform similarly based on forecast values. Forecast values shows that the exchange rate of the Ghana cedi to the American dollar will increase continuously in the next three (3) years.


Optimal Regulation of Impulsive Fractional Differential Equation with Delay and Application to Nonlinear Fractional Heat Equation

December 2024

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141 Reads

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10 Citations

The purpose of this paper was considering the impulsive fractional differential system with time delay. We investigated the existence of solution corresponding to the regulator in the admissible regulator set describing by the compact semigroup on Banach space. The result was applied to nonlinear fractional heat equation.


On the Irreducibility of Artin's Group of Graphs

December 2024

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74 Reads

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1 Citation

We consider the graph E3,1E_{3,1} with three generators σ1,σ2,δ\sigma_1, \sigma_2, \delta, where σ1\sigma_1 has an edge with each of   σ2\;\sigma_2 and   δ\;\delta. We then define the Artin group of the graph E3,1E_{3,1} and consider its reduced Perron representation of degree three. After we specialize the indeterminates used in defining the representation to non-zero complex numbers, we obtain a necessary and sufficient condition that guarantees the irreducibility of the representation.



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