Journal of Applied Mathematics Articles (Project Euclid)
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The latest articles from Journal of Applied Mathematics on Project Euclid, a site for mathematics and statistics resources.en-usCopyright 2010 Cornell University LibraryEuclid-L@cornell.edu (Project Euclid Team)Thu, 05 Aug 2010 15:41 EDTMon, 01 Nov 2010 10:04 EDThttp://projecteuclid.org/collection/euclid/images/logo_linking_100.gifProject Euclid
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An Analytic Solution for a Vasicek Interest Rate Convertible Bond Model
http://projecteuclid.org/euclid.jam/1267538827
<strong>A. S. Deakin</strong>, <strong>Matt Davison</strong><p><strong>Source: </strong>J. Appl. Math., Volume 2010, 5 pages.</p><p><strong>Abstract:</strong><br/>
This paper provides the analytic solution to the partial differential equation for the value of a convertible bond. The equation assumes a Vasicek model for the interest rate and a geometric Brownian motion model for the stock price. The solution is obtained using integral transforms.
</p>projecteuclid.org/euclid.jam/1267538827_Thu, 05 Aug 2010 15:41 EDTThu, 05 Aug 2010 15:41 EDTAnalytical Approach for Solving the Internal Waves Problems Involving the Tidal Forcehttps://projecteuclid.org/euclid.jam/1537322592<strong> Jaharuddin</strong>, <strong>Hadi Hermansyah</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 5 pages.</p><p><strong>Abstract:</strong><br/>
The mathematical model for describing internal waves of the ocean is derived from the assumption of ideal fluid; i.e., the fluid is incompressible and inviscid. These internal waves are generated through the interaction between the tidal currents and the basic topography of the fluid. Basically the mathematical model of the internal wave problem of the ocean is a system of nonlinear partial differential equations (PDEs). In this paper, the analytical approach used to solve nonlinear PDE is the Homotopy Analysis Method (HAM). HAM can be applied to determine the resolution of almost any internal wave problem involving tidal forces. The use of HAM in the solution to basic fluid equations is efficient and simple, since it involves only modest calculations using the common integral.
</p>projecteuclid.org/euclid.jam/1537322592_20180918220322Tue, 18 Sep 2018 22:03 EDTSome Properties of the Strong Primitivity of Nonnegative Tensorshttps://projecteuclid.org/euclid.jam/1537322593<strong>Lihua You</strong>, <strong>Yafei Chen</strong>, <strong>Pingzhi Yuan</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 9 pages.</p><p><strong>Abstract:</strong><br/>
We show that an order $m$ dimension 2 tensor is primitive if and only if its majorization matrix is primitive, and then we obtain the characterization of order $m$ dimension 2 strongly primitive tensors and the bound of the strongly primitive degree. Furthermore, we study the properties of strongly primitive tensors with $n\ge \mathrm{3}$ and propose some problems for further research.
</p>projecteuclid.org/euclid.jam/1537322593_20180918220322Tue, 18 Sep 2018 22:03 EDTParameter Estimation in Ordinary Differential Equations Modeling via Particle Swarm Optimizationhttps://projecteuclid.org/euclid.jam/1539136831<strong>Devin Akman</strong>, <strong>Olcay Akman</strong>, <strong>Elsa Schaefer</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 9 pages.</p><p><strong>Abstract:</strong><br/>
Researchers using ordinary differential equations to model phenomena face two main challenges among others: implementing the appropriate model and optimizing the parameters of the selected model. The latter often proves difficult or computationally expensive. Here, we implement Particle Swarm Optimization, which draws inspiration from the optimizing behavior of insect swarms in nature, as it is a simple and efficient method for fitting models to data. We demonstrate its efficacy by showing that it outstrips evolutionary computing methods previously used to analyze an epidemic model.
</p>projecteuclid.org/euclid.jam/1539136831_20181009220138Tue, 09 Oct 2018 22:01 EDTAccessing the Power of Tests Based on Set-Indexed Partial Sums of Multivariate Regression Residualshttps://projecteuclid.org/euclid.jam/1539136832<strong>Wayan Somayasa</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 13 pages.</p><p><strong>Abstract:</strong><br/>
The intention of the present paper is to establish an approximation method to the limiting power functions of tests conducted based on Kolmogorov-Smirnov and Cramér-von Mises functionals of set-indexed partial sums of multivariate regression residuals. The limiting powers appear as vectorial boundary crossing probabilities. Their upper and lower bounds are derived by extending some existing results for shifted univariate Gaussian process documented in the literatures. The application of multivariate Cameron-Martin translation formula on the space of high dimensional set-indexed continuous functions is demonstrated. The rate of decay of the power function to a presigned value $\alpha $ is also studied. Our consideration is mainly for the trend plus signal model including multivariate set-indexed Brownian sheet and pillow. The simulation shows that the approach is useful for analyzing the performance of the test.
</p>projecteuclid.org/euclid.jam/1539136832_20181009220138Tue, 09 Oct 2018 22:01 EDTThe Evaluation of the Number and the Entropy of Spanning Trees on Generalized Small-World Networkshttps://projecteuclid.org/euclid.jam/1539136833<strong>Raihana Mokhlissi</strong>, <strong>Dounia Lotfi</strong>, <strong>Joyati Debnath</strong>, <strong>Mohamed El Marraki</strong>, <strong>Noussaima EL Khattabi</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 7 pages.</p><p><strong>Abstract:</strong><br/>
Spanning trees have been widely investigated in many aspects of mathematics: theoretical computer science, combinatorics, so on. An important issue is to compute the number of these spanning trees. This number remains a challenge, particularly for large and complex networks. As a model of complex networks, we study two families of generalized small-world networks, namely, the Small-World Exponential and the Koch networks, by changing the size and the dimension of the cyclic subgraphs. We introduce their construction and their structural properties which are built in an iterative way. We propose a decomposition method for counting their number of spanning trees and we obtain the exact formulas, which are then verified by numerical simulations. From this number, we find their spanning tree entropy, which is lower than that of the other networks having the same average degree. This entropy allows quantifying the robustness of the networks and characterizing their structures.
</p>projecteuclid.org/euclid.jam/1539136833_20181009220138Tue, 09 Oct 2018 22:01 EDTInfinitely Many Trees with Maximum Number of Holes Zero, One, and Twohttps://projecteuclid.org/euclid.jam/1539136834<strong>Srinivasa Rao Kola</strong>, <strong>Balakrishna Gudla</strong>, <strong>P. K. Niranjan</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 14 pages.</p><p><strong>Abstract:</strong><br/>
An $L(\mathrm{2,1})$ -coloring of a simple connected graph $G$ is an assignment $f$ of nonnegative integers to the vertices of $G$ such that $|f(u)-f(v)|\geqslant\mathrm{2}$ if $d(u,v)=\mathrm{1}$ and $|f(u)-f(v)|\geqslant\mathrm{1}$ if $d(u,v)=\mathrm{2}$ for all $u,v\in V(G)$ , where $d(u,v)$ denotes the distance between $u$ and $v$ in $G$ . The span of $f$ is the maximum color assigned by $f$ . The span of a graph $G$ , denoted by $\lambda (G)$ , is the minimum of span over all $L(\mathrm{2,1})$ -colorings on $G$ . An $L(\mathrm{2,1})$ -coloring of $G$ with span $\lambda (G)$ is called a span coloring of $G$ . An $L(\mathrm{2,1})$ -coloring $f$ is said to be irreducible if there exists no $L(\mathrm{2,1})$ -coloring g such that $g(u)⩽f(u)$ for all $u\in V(G)$ and $g(v)<f(v)$ for some $v\in V(G)$ . If $f$ is an $L(\mathrm{2,1})$ -coloring with span $k$ , then $h\in \{\mathrm{0,1},\mathrm{2},\dots ,k\}$ is a hole if there is no $v\in V(G)$ such that $f(v)=h$ . The maximum number of holes over all irreducible span colorings of $G$ is denoted by ${H}_{\lambda }(G)$ . A tree $T$ with maximum degree $\mathrm{\Delta }$ having span $\mathrm{\Delta }+\mathrm{1}$ is referred to as Type-I tree; otherwise it is Type-II. In this paper, we give a method to construct infinitely many trees with at least one hole from a one-hole tree and infinitely many two-hole trees from a two-hole tree. Also, using the method, we construct infinitely many Type-II trees with maximum number of holes one and two. Further, we give a sufficient condition for a Type-II tree with maximum number of holes zero.
</p>projecteuclid.org/euclid.jam/1539136834_20181009220138Tue, 09 Oct 2018 22:01 EDTNumerical Solution to Coupled Burgers’ Equations by Gaussian-Based Hermite Collocation Schemehttps://projecteuclid.org/euclid.jam/1539136835<strong>Nissaya Chuathong</strong>, <strong>Sayan Kaennakham</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 18 pages.</p><p><strong>Abstract:</strong><br/>
One of the most challenging PDE forms in fluid dynamics namely Burgers equations is solved numerically in this work. Its transient, nonlinear, and coupling structure are carefully treated. The Hermite type of collocation mesh-free method is applied to the spatial terms and the 4 th -order Runge Kutta is adopted to discretize the governing equations in time. The method is applied in conjunction with the Gaussian radial basis function. The effect of viscous force at high Reynolds number up to 1,300 is investigated using the method. For the purpose of validation, a conventional global collocation scheme (also known as “Kansa” method) is applied parallelly. Solutions obtained are validated against the exact solution and also with some other numerical works available in literature when possible.
</p>projecteuclid.org/euclid.jam/1539136835_20181009220138Tue, 09 Oct 2018 22:01 EDTA Note on Caputo’s Derivative Operator Interpretation in Economyhttps://projecteuclid.org/euclid.jam/1542337249<strong>Hameed Ur Rehman</strong>, <strong>Maslina Darus</strong>, <strong>Jamal Salah</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 7 pages.</p><p><strong>Abstract:</strong><br/>
We propound the economic idea in terms of fractional derivatives, which involves the modified Caputo’s fractional derivative operator. The suggested economic interpretation is based on a generalization of average count and marginal value of economic indicators. We use the concepts of $T-indicators$ which analyses the economic performance with the presence of memory. The reaction of economic agents due to recurrence identical alteration is minimized by using the modified Caputo’s derivative operator of order $\lambda $ instead of integer order derivative $n$ . The two sides of Caputo’s derivative are expressed by a brief time-line. The degree of attenuation is further depressed by involving the modified Caputo’s operator.
</p>projecteuclid.org/euclid.jam/1542337249_20181115220140Thu, 15 Nov 2018 22:01 ESTA Theoretical Consideration on the Estimation of Interphase Poisson’s Ratio for Fibrous Polymeric Compositeshttps://projecteuclid.org/euclid.jam/1542337250<strong>J. Venetis</strong>, <strong>E. Sideridis</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 9 pages.</p><p><strong>Abstract:</strong><br/>
An analytical approach on the evaluation of interphase Poisson’s ratio for fibrous composites, consisting of polymeric matrix and unidirectional continuous fibers, is performed. The simulation of the microstructure of the composite was carried out by means of a modified form of Hashin-Rosen cylinder assemblage model. Next, by the use of this three-phase model the authors impose some limitations to the polynomial variation laws which are commonly adopted to approximate the thermomechanical properties of the interphase layer of this type of polymeric composites and then propose an nth-degree polynomial function to approximate the Poisson’s ratio of this layer.
</p>projecteuclid.org/euclid.jam/1542337250_20181115220140Thu, 15 Nov 2018 22:01 ESTRobust Nonlinear Partial Least Squares Regression Using the BACON Algorithmhttps://projecteuclid.org/euclid.jam/1542337251<strong>Abdelmounaim Kerkri</strong>, <strong>Jelloul Allal</strong>, <strong>Zoubir Zarrouk</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 5 pages.</p><p><strong>Abstract:</strong><br/>
Partial least squares regression (PLS regression) is used as an alternative for ordinary least squares regression in the presence of multicollinearity. This occurrence is common in chemical engineering problems. In addition to the linear form of PLS, there are other versions that are based on a nonlinear approach, such as the quadratic PLS (QPLS2). The difference between QPLS2 and the regular PLS algorithm is the use of quadratic regression instead of OLS regression in the calculations of latent variables. In this paper we propose a robust version of QPLS2 to overcome sensitivity to outliers using the Blocked Adaptive Computationally Efficient Outlier Nominators (BACON) algorithm. Our hybrid method is tested on both real and simulated data.
</p>projecteuclid.org/euclid.jam/1542337251_20181115220140Thu, 15 Nov 2018 22:01 ESTAdomian Decomposition Method with Modified Bernstein Polynomials for Solving Ordinary and Partial Differential Equationshttps://projecteuclid.org/euclid.jam/1542337252<strong>Ahmed Farooq Qasim</strong>, <strong>Ekhlass S. AL-Rawi</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 9 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we used Bernstein polynomials to modify the Adomian decomposition method which can be used to solve linear and nonlinear equations. This scheme is tested for four examples from ordinary and partial differential equations; furthermore, the obtained results demonstrate reliability and activity of the proposed technique. This strategy gives a precise and productive system in comparison with other traditional techniques and the arrangements methodology is extremely straightforward and few emphasis prompts high exact solution. The numerical outcomes showed that the acquired estimated solutions were in appropriate concurrence with the correct solution.
</p>projecteuclid.org/euclid.jam/1542337252_20181115220140Thu, 15 Nov 2018 22:01 ESTA Comparison of Algorithms for Finding an Efficient Theme Park Tourhttps://projecteuclid.org/euclid.jam/1542337253<strong>Elizabeth L. Bouzarth</strong>, <strong>Richard J. Forrester</strong>, <strong>Kevin R. Hutson</strong>, <strong>Rahul Isaac</strong>, <strong>James Midkiff</strong>, <strong>Danny Rivers</strong>, <strong>Leonard J. Testa</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 14 pages.</p><p><strong>Abstract:</strong><br/>
The problem of efficiently touring a theme park so as to minimize the amount of time spent in queues is an instance of the Traveling Salesman Problem with Time-Dependent Service Times (TSP-TS). In this paper, we present a mixed-integer linear programming formulation of the TSP-TS and describe a branch-and-cut algorithm based on this model. In addition, we develop a lower bound for the TSP-TS and describe two metaheuristic approaches for obtaining good quality solutions: a genetic algorithm and a tabu search algorithm. Using test instances motivated by actual theme park data, we conduct a computational study to compare the effectiveness of our algorithms.
</p>projecteuclid.org/euclid.jam/1542337253_20181115220140Thu, 15 Nov 2018 22:01 ESTExplicit Solutions to the (3+1)-Dimensional Kudryashov-Sinelshchikov Equations in Bubbly Flow Dynamicshttps://projecteuclid.org/euclid.jam/1544756443<strong>Y. B. Chukkol</strong>, <strong>M. N. B. Mohamad</strong>, <strong>Mukhiddin Muminov</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 9 pages.</p><p><strong>Abstract:</strong><br/>
A modified tanh-coth method with Riccati equation is used to construct several explicit solutions of (3+1)-dimensional Kudryashov-Sinelshchikov equations in bubble gas liquid flow. The solutions include solitons and periodic solutions. The method applied can be used in further works to obtain entirely new solutions to many other nonlinear evolution equations.
</p>projecteuclid.org/euclid.jam/1544756443_20181213220144Thu, 13 Dec 2018 22:01 ESTBasic Properties and Qualitative Dynamics of a Vector-Borne Disease Model with Vector Stages and Vertical Transmissionhttps://projecteuclid.org/euclid.jam/1544756444<strong>Sansao A. Pedro</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 16 pages.</p><p><strong>Abstract:</strong><br/>
This work systematically discusses basic properties and qualitative dynamics of vector-borne disease models, particularly those with vertical transmission in the vector population. Examples of disease include Dengue and Rift Valley fever which are endemic in Sub-Saharan Africa, and understanding of the dynamics underlying their transmission is central for providing critical informative indicators useful for guiding control strategies. Of particular interest is the applicability and derivation of relevant population and epidemic thresholds and their relationships with vertical infection. This study demonstrates how the failure of ${R}_{\mathrm{0}}$ derived using the next-generation method compounds itself when varying vertical transmission efficiency, and it shows that the host type reproductive number gives the correct ${R}_{\mathrm{0}}$ . Further, novel relationships between the host type reproductive number, vertical infection, and ratio of female mosquitoes to host are established and discussed. Analytical results of the model with vector stages show that the quantities ${Q}_{\mathrm{0}}$ , ${Q}_{\mathrm{0}}^{v}$ , and ${R}_{\mathrm{0}}^{c}$ , which represent the vector colonization threshold, the average number of female mosquitoes produced by a single infected mosquito, and effective reproductive number, respectively, provide threshold conditions that determine the establishment of the vector population and invasion of the disease. Numerical simulations are also conducted to confirm and extend the analytical results. The findings imply that while vertical infection increases the size of an epidemic, it reduces its duration, and control efforts aimed at reducing the critical thresholds ${Q}_{\mathrm{0}}$ , ${Q}_{\mathrm{0}}^{v}$ , and ${R}_{\mathrm{0}}^{c}$ to below unity are viable control strategies.
</p>projecteuclid.org/euclid.jam/1544756444_20181213220144Thu, 13 Dec 2018 22:01 ESTA Dynamic Model of PI3K/AKT Pathways in Acute Myeloid Leukemiahttps://projecteuclid.org/euclid.jam/1544756445<strong>Yudi Ari Adi</strong>, <strong>Fajar Adi-Kusumo</strong>, <strong>Lina Aryati</strong>, <strong>Mardiah S. Hardianti</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 9 pages.</p><p><strong>Abstract:</strong><br/>
Acute myeloid leukemia (AML) is a malignant hematopoietic disorder characterized by uncontrolled proliferation of immature myeloid cells. In the AML cases, the phosphoinositide 3-kinases (PI3K)/AKT signaling pathways are frequently activated and strongly contribute to proliferation and survival of these cells. In this paper, a mathematical model of the PI3K/AKT signaling pathways in AML is constructed to study the dynamics of the proteins in these pathways. The model is a 5-dimensional system of the first-order ODE which describes the interaction of the proteins in AML. The interactions between those components are assumed to follow biochemical reactions, which are modelled by Hill’s equation. From the numerical simulations, there are three potential components targets in PI3K/AKT pathways to therapy in the treatment of AML patient.
</p>projecteuclid.org/euclid.jam/1544756445_20181213220144Thu, 13 Dec 2018 22:01 ESTAnalysis and Optimal Control Intervention Strategies of a Waterborne Disease Model: A Realistic Case Studyhttps://projecteuclid.org/euclid.jam/1544756446<strong>Obiora Cornelius Collins</strong>, <strong>Kevin Jan Duffy</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 14 pages.</p><p><strong>Abstract:</strong><br/>
A mathematical model is formulated that captures the essential dynamics of waterborne disease transmission under the assumption of a homogeneously mixed population. The important mathematical features of the model are determined and analysed. The model is extended by introducing control intervention strategies such as vaccination, treatment, and water purification. Mathematical analyses of the control model are used to determine the possible benefits of these control intervention strategies. Optimal control theory is utilized to determine how to reduce the spread of a disease with minimum cost. The model is validated using a cholera outbreak in Haiti.
</p>projecteuclid.org/euclid.jam/1544756446_20181213220144Thu, 13 Dec 2018 22:01 ESTTwo Proofs and One Algorithm Related to the Analytic Hierarchy Processhttps://projecteuclid.org/euclid.jam/1547089318<strong>Miron Pavluš</strong>, <strong>Rostislav Tomeš</strong>, <strong>Lukáš Malec</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 9 pages.</p><p><strong>Abstract:</strong><br/>
36 years ago, Thomas Saaty introduced a new mathematical methodology, called Analytic Hierarchy Process (AHP), regarding the decision-making processes. The methodology was widely applied by Saaty and by other authors in the different human activity areas, like planning, business, education, healthcare, etc. but, in general, in the area of management. In this paper, we provide two new proofs for well-known statement that the maximal eigenvalue ${\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is equal to $n$ for the eigenvector problem $Aw=\lambda w$ , where $A$ is, so-called, the consistent matrix of pairwise comparisons of type $n\timesn$ ( $n$ $\ge $ 2) with the solution vector $w$ that represents the probability components of disjoint events. Moreover, we suggest an algorithm for the determination of the eigenvalue problem solution $Aw=nw$ as well as the corresponding flowchart. The algorithm for arbitrary consistent matrix $A$ can be simply programmed and used.
</p>projecteuclid.org/euclid.jam/1547089318_20190109220250Wed, 09 Jan 2019 22:02 ESTA Study of a Diseased Prey-Predator Model with Refuge in Prey and Harvesting from Predatorhttps://projecteuclid.org/euclid.jam/1547089319<strong>Ahmed Sami Abdulghafour</strong>, <strong>Raid Kamel Naji</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 17 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, a mathematical model of a prey-predator system with infectious disease in the prey population is proposed and studied. It is assumed that there is a constant refuge in prey as a defensive property against predation and harvesting from the predator. The proposed mathematical model is consisting of three first-order nonlinear ordinary differential equations, which describe the interaction among the healthy prey, infected prey, and predator. The existence, uniqueness, and boundedness of the system’ solution are investigated. The system's equilibrium points are calculated with studying their local and global stability. The persistence conditions of the proposed system are established. Finally the obtained analytical results are justified by a numerical simulation.
</p>projecteuclid.org/euclid.jam/1547089319_20190109220250Wed, 09 Jan 2019 22:02 ESTModelling In Vivo HIV Dynamics under Combined Antiretroviral Treatmenthttps://projecteuclid.org/euclid.jam/1547089320<strong>B. Mobisa</strong>, <strong>G. O. Lawi</strong>, <strong>J. K. Nthiiri</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 11 pages.</p><p><strong>Abstract:</strong><br/>
In this paper a within host mathematical model for Human Immunodeficiency Virus (HIV) transmission incorporating treatment is formulated. The model takes into account the efficacy of combined antiretroviral treatment on viral growth and T cell population in the human blood. The existence of an infection free and positive endemic equilibrium is established. The basic reproduction number ${R}_{\mathrm{0}}$ is derived using the method of next generation matrix. We perform local and global stability analysis of the equilibria points and show that if ${R}_{\mathrm{0}}<\mathrm{1}$ , then the infection free equilibrium is globally asymptotically stable and theoretically the virus is cleared and the disease dies out and if ${R}_{\mathrm{0}}>\mathrm{1}$ , then the endemic equilibrium is globally asymptotically stable implying that the virus persists within the host. Numerical simulations are carried out to investigate the effect of treatment on the within host infection dynamics.
</p>projecteuclid.org/euclid.jam/1547089320_20190109220250Wed, 09 Jan 2019 22:02 ESTA Modified Artificial Bee Colony Algorithm with Firefly Algorithm Strategy for Continuous Optimization Problemshttps://projecteuclid.org/euclid.jam/1547089321<strong>Amnat Panniem</strong>, <strong>Pikul Puphasuk</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 9 pages.</p><p><strong>Abstract:</strong><br/>
Artificial Bee Colony (ABC) algorithm is one of the efficient nature-inspired optimization algorithms for solving continuous problems. It has no sensitive control parameters and has been shown to be competitive with other well-known algorithms. However, the slow convergence, premature convergence, and being trapped within the local solutions may occur during the search. In this paper, we propose a new Modified Artificial Bee Colony (MABC) algorithm to overcome these problems. All phases of ABC are determined for improving the exploration and exploitation processes. We use a new search equation in employed bee phase, increase the probabilities for onlooker bees to find better positions, and replace some worst positions by the new ones in onlooker bee phase. Moreover, we use the Firefly algorithm strategy to generate a new position replacing an unupdated position in scout bee phase. Its performance is tested on selected benchmark functions. Experimental results show that MABC is more effective than ABC and some other modifications of ABC.
</p>projecteuclid.org/euclid.jam/1547089321_20190109220250Wed, 09 Jan 2019 22:02 ESTAnalytical Synthesis of Regulators for Nonlinear Systems with a Terminal State Method on Examples of Motion Control of a Wheeled Robot and a Vesselhttps://projecteuclid.org/euclid.jam/1547089322<strong>E. A. Shushlyapin</strong>, <strong>A. E. Bezuglaya</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2018, 13 pages.</p><p><strong>Abstract:</strong><br/>
The paper is devoted to several examples of control algorithm development for two-wheeled double-track robot and low-tonnage vessel-catamaran with two Azipods that show practical aspects of the application of one nonlinear system control method — terminal state method. This method, developed by the authors of the present paper, belongs to the class of methods for inverse dynamics problem solving. Mathematical models of control objects in the form of normal systems of third-order nonlinear differential equations for the wheeled robot and seventh-order ones for the vessel are presented. Design formulas of the method in general form for terminal and stabilizing controls are shown. A routine of obtaining calculation expressions for control actions is shown. Results of computer simulation of bringing the robot to a given point in a given time, as well as bringing the vessel to a given course during a “strong” maneuver, are described.
</p>projecteuclid.org/euclid.jam/1547089322_20190109220250Wed, 09 Jan 2019 22:02 ESTA New Approximate Analytical Solutions for Two- and Three-Dimensional Unsteady Viscous Incompressible Flows by Using the Kinetically Reduced Local Navier-Stokes Equationshttps://projecteuclid.org/euclid.jam/1551150320<strong>Abdul-Sattar J. Al-Saif</strong>, <strong>Assma J. Harfash</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 19 pages.</p><p><strong>Abstract:</strong><br/>
In this work, the kinetically reduced local Navier-Stokes equations are applied to the simulation of two- and three-dimensional unsteady viscous incompressible flow problems. The reduced differential transform method is used to find the new approximate analytical solutions of these flow problems. The new technique has been tested by using four selected multidimensional unsteady flow problems: two- and three-dimensional Taylor decaying vortices flow, Kovasznay flow, and three-dimensional Beltrami flow. The convergence analysis was discussed for this approach. The numerical results obtained by this approach are compared with other results that are available in previous works. Our results show that this method is efficient to provide new approximate analytic solutions. Moreover, we found that it has highly precise solutions with good convergence, less time consuming, being easily implemented for high Reynolds numbers, and low Mach numbers.
</p>projecteuclid.org/euclid.jam/1551150320_20190225220540Mon, 25 Feb 2019 22:05 ESTOptimal Homotopy Asymptotic and Multistage Optimal Homotopy Asymptotic Methods for Solving System of Volterra Integral Equations of the Second Kindhttps://projecteuclid.org/euclid.jam/1551150321<strong>Jafar Biazar</strong>, <strong>Roya Montazeri</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 17 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, optimal homotopy asymptotic method (OHAM) and its implementation on subinterval, called multistage optimal homotopy asymptotic method (MOHAM), are presented for solving linear and nonlinear systems of Volterra integral equations of the second kind. To illustrate these approaches two examples are presented. The results confirm the efficiency and ability of these methods for such equations. The results will be compared to find out which method is more accurate. Advantages of applying MOHAM are also illustrated.
</p>projecteuclid.org/euclid.jam/1551150321_20190225220540Mon, 25 Feb 2019 22:05 ESTAn Iterative Method for Finding Common Solution of the Fixed Point Problem of a Finite Family of Nonexpansive Mappings and a Finite Family of Variational Inequality Problems in Hilbert Spacehttps://projecteuclid.org/euclid.jam/1551150323<strong>Shamshad Husain</strong>, <strong>Nisha Singh</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 11 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, a hybrid iterative algorithm is proposed for finding a common element of the set of common fixed points of finite family of nonexpansive mappings and the set of common solutions of the variational inequality for an inverse strongly monotone mapping on the real Hilbert space. We establish the strong convergence of the proposed method for approximating a common element of the above defined sets under some suitable conditions. The results presented in this paper extend and improve some well-known corresponding results in the earlier and recent literature.
</p>projecteuclid.org/euclid.jam/1551150323_20190225220540Mon, 25 Feb 2019 22:05 ESTMathematical Modelling of the Transmission Dynamics of Contagious Bovine Pleuropneumonia with Vaccination and Antibiotic Treatmenthttps://projecteuclid.org/euclid.jam/1552615280<strong>Achamyelesh Amare Aligaz</strong>, <strong>Justin Manango W. Munganga</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 10 pages.</p><p><strong>Abstract:</strong><br/>
In this paper we present a mathematical model for the transmission dynamics of Contagious Bovine Pleuropneumonia (CBPP) by considering antibiotic treatment and vaccination. The model is comprised of susceptible, vaccinated, exposed, infectious, persistently infected, and recovered compartments. We analyse the model by deriving a formula for the control reproduction number ${\mathcal{R}}_{c}$ and prove that, for ${\mathcal{R}}_{c}<\mathrm{1}$ , the disease free equilibrium is globally asymptotically stable; thus CBPP dies out, whereas for ${\mathcal{R}}_{c}>\mathrm{1}$ , the unique endemic equilibrium is globally asymptotically stable and hence the disease persists. Thus, ${\mathcal{R}}_{c}=\mathrm{1}$ acts as a sharp threshold between the disease dying out or causing an epidemic. As a result, the threshold of antibiotic treatment is ${\alpha }_{t}^{⁎}=\mathrm{0.1049}$ . Thus, without using vaccination, more than $\mathrm{85.45}\mathrm{%}$ of the infectious cattle should receive antibiotic treatment or the period of infection should be reduced to less than 8.15 days to control the disease. Similarly, the threshold of vaccination is ${\rho }^{⁎}=\mathrm{0.0084}$ . Therefore, we have to vaccinate at least $\mathrm{80}\mathrm{%}$ of susceptible cattle in less than 49.5 days, to control the disease. Using both vaccination and antibiotic treatment, the threshold value of vaccination depends on the rate of antibiotic treatment, ${\alpha }_{t},$ and is denoted by ${\rho }_{{\alpha }_{t}}$ . Hence, if $\mathrm{50}\mathrm{%}$ of infectious cattle receive antibiotic treatment, then at least $\mathrm{50}\mathrm{%}$ of susceptible cattle should get vaccination in less than 73.8 days in order to control the disease.
</p>projecteuclid.org/euclid.jam/1552615280_20190314220142Thu, 14 Mar 2019 22:01 EDTDifferent Physical Structures of Solutions for a Generalized Resonant Dispersive Nonlinear Schrödinger Equation with Power Law Nonlinearityhttps://projecteuclid.org/euclid.jam/1552615281<strong>K. S. Al-Ghafri</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 8 pages.</p><p><strong>Abstract:</strong><br/>
In this work, we investigate various types of solutions for the generalised resonant dispersive nonlinear Schrödinger equation (GRD-NLSE) with power law nonlinearity. Based on simple mathematical techniques, the complicated form of the GRD-NLSE is reduced to an ordinary differential equation (ODE) which has a variety of solutions. The analytic solution of the resulting ODE gives rise to bright soliton, singular soliton, peaked soliton, compacton solutions, solitary pattern solutions, rational solution, Weierstrass elliptic periodic type solutions, and some other types of solutions. Constraint conditions for the existence of solitons and other solutions are given.
</p>projecteuclid.org/euclid.jam/1552615281_20190314220142Thu, 14 Mar 2019 22:01 EDTParameter Estimation and Sensitivity Analysis of Dysentery Diarrhea Epidemic Modelhttps://projecteuclid.org/euclid.jam/1552615282<strong>Hailay Weldegiorgis Berhe</strong>, <strong>Oluwole Daniel Makinde</strong>, <strong>David Mwangi Theuri</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 13 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, dysentery diarrhea deterministic compartmental model is proposed. The local and global stability of the disease-free equilibrium is obtained using the stability theory of differential equations. Numerical simulation of the system shows that the backward bifurcation of the endemic equilibrium exists for ${R}_{\mathrm{0}}>\mathrm{1}$ . The system is formulated as a standard nonlinear least squares problem to estimate the parameters. The estimated reproduction number, based on the dysentery diarrhea disease data for Ethiopia in 2017, is ${R}_{\mathrm{0}}=\mathrm{1.1208}$ . This suggests that elimination of the dysentery disease from Ethiopia is not practical. A graphical method is used to validate the model. Sensitivity analysis is carried out to determine the importance of model parameters in the disease dynamics. It is found out that the reproduction number is the most sensitive to the effective transmission rate of dysentery diarrhea ( ${\beta }_{h}$ ). It is also demonstrated that control of the effective transmission rate is essential to stop the spreading of the disease.
</p>projecteuclid.org/euclid.jam/1552615282_20190314220142Thu, 14 Mar 2019 22:01 EDTApplication of Optimal Control Theory to Newcastle Disease Dynamics in Village Chicken by Considering Wild Birds as Reservoir of Disease Virushttps://projecteuclid.org/euclid.jam/1557972260<strong>Furaha Chuma</strong>, <strong>Gasper Godson Mwanga</strong>, <strong>Verdiana Grace Masanja</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 14 pages.</p><p><strong>Abstract:</strong><br/>
In this study, an optimal control theory was applied to a nonautonomous model for Newcastle disease transmission in the village chicken population. A notable feature of this model is the inclusion of environment contamination and wild birds, which act as reservoirs of the disease virus. Vaccination, culling, and environmental hygiene and sanitation time dependent control strategies were adopted in the proposed model. This study proved the existence of an optimal control solution, and the necessary conditions for optimality were determined using Pontryagin’s Maximum Principle. The numerical simulations of the optimal control problem were performed using the forward–backward sweep method. The results showed that the use of only the environmental hygiene and sanitation control strategy has no significant effect on the transmission dynamics of the Newcastle disease. Additionally, the combination of vaccination and environmental hygiene and sanitation strategies reduces more number of infected chickens and the concentration of the Newcastle disease virus in the environment than any other combination of control strategies. Furthermore, a cost-effective analysis was performed using the incremental cost-effectiveness ratio method, and the results showed that the use of vaccination alone as the control measure is less costly compared to other control strategies. Hence, the most effective way to minimize the transmission rate of the Newcastle disease and the operational costs is concluded to be the timely vaccination of the entire population of the village chicken, improvement in the sanitation of facilities, and the maintenance of a hygienically clean environment.
</p>projecteuclid.org/euclid.jam/1557972260_20190515220435Wed, 15 May 2019 22:04 EDTRainbow Connectivity Using a Rank Genetic Algorithm: Moore Cages with Girth Sixhttps://projecteuclid.org/euclid.jam/1557972261<strong>J. Cervantes-Ojeda</strong>, <strong>M. Gómez-Fuentes</strong>, <strong>D. González-Moreno</strong>, <strong>M. Olsen</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 7 pages.</p><p><strong>Abstract:</strong><br/>
A rainbow $t$ -coloring of a $t$ -connected graph $G$ is an edge coloring such that for any two distinct vertices $u$ and $v$ of $G$ there are at least $t$ internally vertex-disjoint rainbow $(u,v)$ -paths. In this work, we apply a Rank Genetic Algorithm to search for rainbow $t$ -colorings of the family of Moore cages with girth six $(t;\mathrm{6})$ -cages. We found that an upper bound in the number of colors needed to produce a rainbow 4-coloring of a $(\mathrm{4};\mathrm{6})$ -cage is 7, improving the one currently known, which is 13. The computation of the minimum number of colors of a rainbow coloring is known to be NP-Hard and the Rank Genetic Algorithm showed good behavior finding rainbow $t$ -colorings with a small number of colors.
</p>projecteuclid.org/euclid.jam/1557972261_20190515220435Wed, 15 May 2019 22:04 EDTA Multicurve Cross-Currency LIBOR Market Modelhttps://projecteuclid.org/euclid.jam/1557972262<strong>Charity Wamwea</strong>, <strong>Philip Ngare</strong>, <strong>Martin Le Doux Mbele Bidima</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 17 pages.</p><p><strong>Abstract:</strong><br/>
After the dawn of the August 2007 financial crisis, banks became more aware of financial risk leading to the appearance of nonnegligible spreads between LIBOR and OIS rates and also between LIBOR of different tenors. This consequently led to the birth of multicurve models. This study establishes a new model; the multicurve cross-currency LIBOR market model (MCCCLMM). The model extends the initial LIBOR Market Model (LMM) from the single-curve cross-currency economy into the multicurve cross-currency economy. The model incorporates both the risk-free OIS rates and the risky forward LIBOR rates of two different currencies. The established model is suitable for pricing different quanto interest rate derivatives. A brief illustration is given on the application of the MCCCLMM on pricing quanto caplets and quanto floorlets using a Black-like formula derived from the MCCCLMM.
</p>projecteuclid.org/euclid.jam/1557972262_20190515220435Wed, 15 May 2019 22:04 EDTA Novel Algorithm for Studying the Effects of Squeezing Flow of a Casson Fluid between Parallel Plates on Magnetic Fieldhttps://projecteuclid.org/euclid.jam/1557972263<strong>Abdul-Sattar J. A. Al-Saif</strong>, <strong>Abeer Majeed Jasim</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 19 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, the magneto hydrodynamic (MHD) squeezing flow of a non-Newtonian, namely, Casson, fluid between parallel plates is studied. The suitable one of similarity transformation conversion laws is proposed to obtain the governing MHD flow nonlinear ordinary differential equation. The resulting equation has been solved by a novel algorithm. Comparisons between the results of the novel algorithm technique and other analytical techniques and one numerical Range-Kutta fourth-order algorithm are provided. The results are found to be in excellent agreement. Also, a novel convergence proof of the proposed algorithm based on properties of convergent series is introduced. Flow behavior under the changing involved physical parameters such as squeeze number, Casson fluid parameter, and magnetic number is discussed and explained in detail with help of tables and graphs.
</p>projecteuclid.org/euclid.jam/1557972263_20190515220435Wed, 15 May 2019 22:04 EDTA New Hybrid Algorithm for Convex Nonlinear Unconstrained Optimizationhttps://projecteuclid.org/euclid.jam/1557972264<strong>Eman T. Hamed</strong>, <strong>Huda I. Ahmed</strong>, <strong>Abbas Y. Al-Bayati</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 6 pages.</p><p><strong>Abstract:</strong><br/>
In this study, we tend to propose a replacement hybrid algorithmic rule which mixes the search directions like Steepest Descent (SD) and Quasi-Newton (QN). First, we tend to develop a replacement search direction for combined conjugate gradient (CG) and QN strategies. Second, we tend to depict a replacement positive CG methodology that possesses the adequate descent property with sturdy Wolfe line search. We tend to conjointly prove a replacement theorem to make sure global convergence property is underneath some given conditions. Our numerical results show that the new algorithmic rule is powerful as compared to different standard high scale CG strategies.
</p>projecteuclid.org/euclid.jam/1557972264_20190515220435Wed, 15 May 2019 22:04 EDTDynamic Credit Quality Evaluation with Social Network Datahttps://projecteuclid.org/euclid.jam/1557972265<strong>Stanley Sewe</strong>, <strong>Philip Ngare</strong>, <strong>Patrick Weke</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 11 pages.</p><p><strong>Abstract:</strong><br/>
We investigate the filtering problem where the borrower’s time varying credit quality process is estimated using continuous time observation process and her (in this paper we refer to the borrower as female and the lender as male) ego-network data. The hidden credit quality is modeled as a hidden Gaussian mean-reverting process whilst the social network is modeled as a continuous time latent space network model. At discrete times, the network data provides unbiased estimates of the current credit state of the borrower and her ego-network. Combining the continuous time observed behavioral data and network information, we provide filter equations for the hidden credit quality and show how the network information reduces information asymmetry between the borrower and the lender. Further, we consider the case when the network information arrival times are random and solve stochastic optimal control problem for a lender having linear quadratic utility function.
</p>projecteuclid.org/euclid.jam/1557972265_20190515220435Wed, 15 May 2019 22:04 EDTA Truncation Method for Solving the Time-Fractional Benjamin-Ono Equationhttps://projecteuclid.org/euclid.jam/1563933633<strong>Mohamed R. Ali</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 7 pages.</p><p><strong>Abstract:</strong><br/>
We deem the time-fractional Benjamin-Ono (BO) equation out of the Riemann–Liouville (RL) derivative by applying the Lie symmetry analysis (LSA). By first using prolongation theorem to investigate its similarity vectors and then using these generators to transform the time-fractional BO equation to a nonlinear ordinary differential equation (NLODE) of fractional order, we complete the solutions by utilizing the power series method (PSM).
</p>projecteuclid.org/euclid.jam/1563933633_20190723220146Tue, 23 Jul 2019 22:01 EDTParameter Estimation for p-Order Random Coefficient Autoregressive (RCA) Models Based on Kalman Filterhttps://projecteuclid.org/euclid.jam/1563933634<strong>Mohammed Benmoumen</strong>, <strong>Jelloul Allal</strong>, <strong>Imane Salhi</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 5 pages.</p><p><strong>Abstract:</strong><br/>
In this paper we elaborate an algorithm to estimate p-order Random Coefficient Autoregressive Model (RCA(p)) parameters. This algorithm combines quasi-maximum likelihood method, the Kalman filter, and the simulated annealing method. In the aim to generalize the results found for RCA(1), we have integrated a subalgorithm which calculate the theoretical autocorrelation. Simulation results demonstrate that the algorithm is viable and promising.
</p>projecteuclid.org/euclid.jam/1563933634_20190723220146Tue, 23 Jul 2019 22:01 EDTAlternating Projections Filtering Algorithm to Track Moving Objectshttps://projecteuclid.org/euclid.jam/1563933635<strong>Youssef Qranfal</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 8 pages.</p><p><strong>Abstract:</strong><br/>
An interest is often present in knowing evolving variables that are not directly observable; this is the case in aerospace, engineering control, medical imaging, or data assimilation. What is at hand, though, are time-varying measured data, a model connecting them to variables of interest, and a model of how to evolve the variables over time. However, both models are only approximation and the observed data are tainted with noise. This is an ill-posed inverse problem. Methods, such as Kalman filter (KF), have been devised to extract the time-varying quantities of interest. These methods applied to this inverse problem, nonetheless, are slow, computation wise, since they require large matrices multiplications and even matrix inversion. Furthermore, these methods are not usually suitable to impose some constraints. This article introduces a new iterative filtering algorithm based on alternating projections. Experiments were run with simulated moving projectiles and were compared with results using KF. The new optimization algorithm proves to be slightly more accurate than KF, but, more to the point, it is much faster in terms of CPU time.
</p>projecteuclid.org/euclid.jam/1563933635_20190723220146Tue, 23 Jul 2019 22:01 EDTMapping a Multilayer Air Transport Network with the Integration of Airway, Route, and Flight Networkhttps://projecteuclid.org/euclid.jam/1563933636<strong>Qinyan Zhou</strong>, <strong>Wendong Yang</strong>, <strong>Jinfu Zhu</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 10 pages.</p><p><strong>Abstract:</strong><br/>
This paper develops a mapping approach to explore the relationship between different layers of a multilayer air transport network composed of airway, route, and flight network. A two-step methodology is adopted to investigate the hierarchical structure and mapping relationship of the integrated network. First, the relationship between airway and route network is characterized by a multisource multisink shortest path method based on a generalized incidence matrix. Second, the relationship between route and flight network is formulated by a two-dimension array. A case study of an en route airspace in Lanzhou air traffic control area in China verifies the feasibility of the proposed two-step methodology.
</p>projecteuclid.org/euclid.jam/1563933636_20190723220146Tue, 23 Jul 2019 22:01 EDTA Class of Two-Derivative Two-Step Runge-Kutta Methods for Non-Stiff ODEshttps://projecteuclid.org/euclid.jam/1563933637<strong>I. B. Aiguobasimwin</strong>, <strong>R. I. Okuonghae</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 9 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, a new class of two-derivative two-step Runge-Kutta (TDTSRK) methods for the numerical solution of non-stiff initial value problems (IVPs) in ordinary differential equation (ODEs) is considered. The TDTSRK methods are a special case of multi-derivative Runge-Kutta methods proposed by Kastlunger and Wanner (1972). The methods considered herein incorporate only the first and second derivatives terms of ODEs. These methods possess large interval of stability when compared with other existing methods in the literature. The experiments have been performed on standard problems, and comparisons were made with some standard explicit Runge-Kutta methods in the literature.
</p>projecteuclid.org/euclid.jam/1563933637_20190723220146Tue, 23 Jul 2019 22:01 EDTMixed Optimal Scheduling Model of Flexible Service System Based on Inverted Trianglehttps://projecteuclid.org/euclid.jam/1563933638<strong>Shipei Hu</strong>, <strong>Yujun Sun</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 20 pages.</p><p><strong>Abstract:</strong><br/>
In the study presented in this paper, we built a nonlinear binary integer programming model of a flexible scheduling problem for the Department of Zhejiang Provincial Local Tax Services. One difference between our model and typical ones is that whereas in the latter the number of open windows within each working day is fixed, in our model it is not. We used a variety of integer programming software in an attempt to solve our scheduling model; however, unfortunately we could not find an optimal solution. Thus, we tested all the combinations of different numbers of employees to construct the optimal solution. When we tested our model in the tax office of Lishui City, China, the average waiting time of taxpayers was less than 15 min and the employees working hours were clearly reduced. Thus, a noteworthy improvement in the quality of the service is achieved by the model.
</p>projecteuclid.org/euclid.jam/1563933638_20190723220146Tue, 23 Jul 2019 22:01 EDTModeling Dynamics of Prey-Predator Fishery Model with Harvesting: A Bioeconomic Modelhttps://projecteuclid.org/euclid.jam/1563933639<strong>Charles Raymond</strong>, <strong>Alfred Hugo</strong>, <strong>Monica Kung’aro</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 13 pages.</p><p><strong>Abstract:</strong><br/>
A mathematical model is proposed and analysed to study the dynamics of two-prey one predator system of fishery model with Holling type II function response. The effect of harvesting was incorporated to both populations and thoroughly analysed. We study the ecological dynamics of the Nile perch, cichlid, and tilapia fishes as prey-predator system of lake Victoria fishery in Tanzania. In both cases, by nondimensionalization of the system, the equilibrium points are computed and conditions for local and global stability of the system are obtained. Condition for local stability was obtained by eigenvalue approach and Routh-Hurwitz Criterion. Moreover, the global stability of the coexistence equilibrium point is proved by defining appropriate Lyapunov function. Bioeconomic equilibrium is analysed and numerical simulations are also carried out to verify the analytical results. The numerical results indicate that the three species would coexist if cichlid and tilapia fishes will not be overharvested as these populations contribute to the growth rates of Nile perch population. The fishery control management should be exercised to avoid overharvesting of cichlid and tilapia fishes.
</p>projecteuclid.org/euclid.jam/1563933639_20190723220146Tue, 23 Jul 2019 22:01 EDTA Smoothed ${l}_{0}$ -Norm and ${l}_{1}$ -Norm Regularization Algorithm for Computed Tomographyhttps://projecteuclid.org/euclid.jam/1563933640<strong>Jiehua Zhu</strong>, <strong>Xiezhang Li</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 8 pages.</p><p><strong>Abstract:</strong><br/>
The nonmonotone alternating direction algorithm (NADA) was recently proposed for effectively solving a class of equality-constrained nonsmooth optimization problems and applied to the total variation minimization in image reconstruction, but the reconstructed images suffer from the artifacts. Though by the ${l}_{\mathrm{0}}$ -norm regularization the edge can be effectively retained, the problem is NP hard. The smoothed ${l}_{\mathrm{0}}$ -norm approximates the ${l}_{\mathrm{0}}$ -norm as a limit of smooth convex functions and provides a smooth measure of sparsity in applications. The smoothed ${l}_{\mathrm{0}}$ -norm regularization has been an attractive research topic in sparse image and signal recovery. In this paper, we present a combined smoothed ${l}_{\mathrm{0}}$ -norm and ${l}_{\mathrm{1}}$ -norm regularization algorithm using the NADA for image reconstruction in computed tomography. We resolve the computation challenge resulting from the smoothed ${l}_{\mathrm{0}}$ -norm minimization. The numerical experiments demonstrate that the proposed algorithm improves the quality of the reconstructed images with the same cost of CPU time and reduces the computation time significantly while maintaining the same image quality compared with the ${l}_{\mathrm{1}}$ -norm regularization in absence of the smoothed ${l}_{\mathrm{0}}$ -norm.
</p>projecteuclid.org/euclid.jam/1563933640_20190723220146Tue, 23 Jul 2019 22:01 EDTLump and Lump-Type Solutions of the Generalized (3+1)-Dimensional Variable-Coefficient B-Type Kadomtsev-Petviashvili Equationhttps://projecteuclid.org/euclid.jam/1563933641<strong>Yanni Zhang</strong>, <strong>Jing Pang</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 5 pages.</p><p><strong>Abstract:</strong><br/>
Based on the Hirota bilinear form of the generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation, the lump and lump-type solutions are generated through symbolic computation, whose analyticity can be easily achieved by taking special choices of the involved parameters. The property of solutions is investigated and exhibited vividly by three-dimensional plots and contour plots.
</p>projecteuclid.org/euclid.jam/1563933641_20190723220146Tue, 23 Jul 2019 22:01 EDTAn Approximation of Minimum Initial Capital of Investment Discrete Time Surplus Process with Weibull Distribution in a Reinsurance Companyhttps://projecteuclid.org/euclid.jam/1563933650<strong>Soontorn Boonta</strong>, <strong>Somchit Boonthiem</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 9 pages.</p><p><strong>Abstract:</strong><br/>
Catastrophe is a loss that has a low probability of occurring but can lead to high-cost claims. This paper uses the data of fire accidents from a reinsurance company in Thailand for an experiment. Our study is in two parts. First, we approximate the parameters of a Weibull distribution. We compare the parameter estimation using a direct search method with other frequently used methods, such as the least squares method, the maximum likelihood estimation, and the method of moments. The results show that the direct search method approximates the parameters more precisely than other frequently used methods (to four-digit accuracy). Second, we approximate the minimum initial capital (MIC) a reinsurance company has to hold under a given ruin probability (insolvency probability) by using parameters from the first part. Finally, we show MIC with varying the premium rate.
</p>projecteuclid.org/euclid.jam/1563933650_20190723220146Tue, 23 Jul 2019 22:01 EDTOn a 2D Model of Avascular Tumor with Weak Allee Effecthttps://projecteuclid.org/euclid.jam/1566439645<strong>Peng Feng</strong>, <strong>Zhewei Dai</strong>, <strong>Dorothy Wallace</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 13 pages.</p><p><strong>Abstract:</strong><br/>
Recent studies reveal that Allee effect may play important roles in the growth of tumor. We present one of the first mathematical models of avascular tumor that incorporates the weak Allee effect. The model considers the densities of tumor cells in three stages: proliferating cells, quiescent cells, and necrotic cells. We investigate how Allee effect impacts the growth of the avascular tumor. We also investigate the effect of apoptosis of proliferating cells and necrosis of quiescent cells. The system is numerically solved in 2D using different sets of parameters. We show that Allee effect and apoptosis play important roles in the growth of tumor and the formation of necrotic core.
</p>projecteuclid.org/euclid.jam/1566439645_20190821220741Wed, 21 Aug 2019 22:07 EDTFinite Element Method Solution of Boundary Layer Flow of Powell-Eyring Nanofluid over a Nonlinear Stretching Surfacehttps://projecteuclid.org/euclid.jam/1566439646<strong>Wubshet Ibrahim</strong>, <strong>Gosa Gadisa</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 16 pages.</p><p><strong>Abstract:</strong><br/>
The nonlinear convective flow of Eyring-Powell nanofluid using Catteneo-Christov model with heat generation or absorption term and chemical reaction rate over nonlinear stretching surface is analyzed. The simultaneous nonlinear partial differential equations governing the boundary layer flow are transformed to the corresponding nonlinear ordinary differential equations using similarity solution and then solved using Galerkin finite element method (GFEM). The impacts of pertinent governing parameters like Brownian diffusion, thermophoresis, mixed convection, heat generation or absorption, chemical reaction rate, Deborah numbers, Prandtl number, magnetic field parameter, Lewis number, nonlinear stretching sheet, and Eyring-Powell fluid parameters on velocity field, temperature, and nanoparticle concentration are given in both figures and tabular form. The result shows that the rise in chemical reaction rate will improve mass transfer rate and reduce heat transfer rate and local buoyancy parameter has quit opposite effect. The attributes of local skin friction coefficient, Nusselt number, and Sheer wood number are investigated and validated with existing literatures.
</p>projecteuclid.org/euclid.jam/1566439646_20190821220741Wed, 21 Aug 2019 22:07 EDTEvaluation of Some Sums of Polynomials in ${\mathbb{F}}_{q}[t]$https://projecteuclid.org/euclid.jam/1566439647<strong>Adama Diene</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 7 pages.</p><p><strong>Abstract:</strong><br/>
We prove the polynomial analogues of some Liouville identities from elementary number theory. Consequently several sums defined over the finite fields ${\mathbb{F}}_{q}[t]$ are evaluated by combining the results obtained and some of the results from sums of reciprocals of polynomials over ${\mathbb{F}}_{q}[t]$ .
</p>projecteuclid.org/euclid.jam/1566439647_20190821220741Wed, 21 Aug 2019 22:07 EDTStatistical Distributions of Physical Characteristics of Molecules with Casimir Force in the Transfer of Admixtures in Nanoscale Volumeshttps://projecteuclid.org/euclid.jam/1566439648<strong>Liudmila Uvarova</strong>, <strong>Sergey Babarin</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 8 pages.</p><p><strong>Abstract:</strong><br/>
In this work, we study the statistical properties of molecular systems of admixtures, which are placed in nanoscale volumes like cube or parallelepiped with impermeable surfaces on their walls. We simulate interactions of free motion of molecules of admixtures with molecules on the surfaces of walls: we modeled them in the form of atomic structure grid using SiO 2 as a material. This type of substance allows us to take into account the manifestation of one of the important quantum effects: Casimir force. We used its general expression in terms of interaction energy, with the assumption of dependence on distance and projected area between atoms of the wall and atoms of the admixtures. To model surface roughness we used uniform random distribution function for surface heights (z coordinates). The results of computational experiments can be used to estimate the distribution of chemical bond lengths, valence, and dihedral angles lengths deviations in polyatomic molecules. Our model can be useful to determine the stable configuration properties of the system, to solve practical problems in the conditions of physical limitations of nanoscale devices, filtration of admixtures in highly dispersed systems, in the development of mechanisms in structures that have parallel plates or membranes, including porous structures. Also we compute radial distribution function for multicomponent admixtures including atoms of inert gases, water vapor, and ethanol. And we took into account the influence of Casimir force on admixtures for cube and parallelepiped type volumes. In results, we showed distributions of deviations of lengths from their equilibrium values.
</p>projecteuclid.org/euclid.jam/1566439648_20190821220741Wed, 21 Aug 2019 22:07 EDTCorrigendum to “Study of Two-Sided Similarity Methods Using a Radiation “Switch on” Imploding Shock in a Magnetic Field”https://projecteuclid.org/euclid.jam/1566439649<strong>J. R. A. J. NiCastro</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 1 page.</p><p><strong>Abstract:</strong><br/>
In the article titled “Study of Two-Sided Similarity Methods Using a Radiation “Switch on” Imploding Shock in a Magnetic Field” [1], there were errors in the equation formatting that should be corrected as follows.
</p>projecteuclid.org/euclid.jam/1566439649_20190821220741Wed, 21 Aug 2019 22:07 EDTSurfaces Modelling Using Isotropic Fractional-Rational Curveshttps://projecteuclid.org/euclid.jam/1568858739<strong>Igor V. Andrianov</strong>, <strong>Nataliia M. Ausheva</strong>, <strong>Yuliia B. Olevska</strong>, <strong>Viktor I. Olevskyi</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 13 pages.</p><p><strong>Abstract:</strong><br/>
The problem of building a smooth surface containing given points or curves is actual due to development of industry and computer technology. Previously used for those purposes, shells of zero Gaussian curvature and minimal surfaces based on isotropic analytic curves are restricted in their consumer properties. To expand the possibilities regarding the shaping of surfaces we propose the method of constructing surfaces based on isotropic fractional-rational curves. The surfaces are built using flat isothermal and orthogonal grids and on the basis of the Weierstrass method. In the latter case, the surfaces are minimal. Examples of surfaces that were built according to the proposed method are given.
</p>projecteuclid.org/euclid.jam/1568858739_20190918220623Wed, 18 Sep 2019 22:06 EDTFinite Integral Formulas Involving Multivariable Aleph-Functionshttps://projecteuclid.org/euclid.jam/1568858740<strong>Hagos Tadesse</strong>, <strong>D. L. Suthar</strong>, <strong>Minilik Ayalew</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 10 pages.</p><p><strong>Abstract:</strong><br/>
The integrals evaluated are the products of multivariable Aleph-functions with algebraic functions, Jacobi polynomials, Legendre functions, Bessel-Maitland functions, and general class of polynomials. The main results of our paper are quite general in nature and competent at yielding a very large number of integrals involving polynomials and various special functions occurring in the problem of mathematical analysis and mathematical physics.
</p>projecteuclid.org/euclid.jam/1568858740_20190918220623Wed, 18 Sep 2019 22:06 EDTOn the Location of a Constrained $k-$ Tree Facility in a Tree Network with Unreliable Edgeshttps://projecteuclid.org/euclid.jam/1568858741<strong>Abdallah W. Aboutahoun</strong>, <strong>Eman Fares</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2019, 16 pages.</p><p><strong>Abstract:</strong><br/>
Given a tree network $T$ with $n$ vertices where each edge has an independent operational probability, we are interested in finding the optimal location of a reliable service provider facility in a shape of subtree with exactly $k$ leaves and with a diameter of at most $l$ which maximizes the expected number of nodes that are reachable from the selected subtree by operational paths. Demand requests for service originate at perfectly reliable nodes. So, the major concern of this paper is to find a location of a reliable tree-shaped facility on the network in order to provide a maximum access to network services by ensuring the highest level of network connectivity between the demand nodes and the facility. An efficient algorithm for finding a reliable $(k,l)$ – tree core of $T$ is developed. The time complexity of the proposed algorithm is $O(lkn).$ Examples are provided to illustrate the performance of the proposed algorithm.
</p>projecteuclid.org/euclid.jam/1568858741_20190918220623Wed, 18 Sep 2019 22:06 EDT