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 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 EDTPredicting the Viscosity of Petroleum Emulsions Using Gene Expression Programming (GEP) and Response Surface Methodology (RSM)https://projecteuclid.org/euclid.jam/1589421620<strong>Abubakar A. Umar</strong>, <strong>Ismail M. Saaid</strong>, <strong>Aliyu A. Sulaimon</strong>, <strong>Rashidah M. Pilus</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 9 pages.</p><p><strong>Abstract:</strong><br/>
This paper summarizes an investigation of certain operating parameters on the viscosity of petroleum emulsions. The production of crude oil is accompanied by emulsified water production, which comes along with various challenges like corroding the transport systems and catalysts poisoning during petroleum refining in the downstream. Several process variables are believed to affect the ease with which emulsified water can be separated from emulsions. Some of the issues have not been extensively examined in the literature. The simplicity with which water is separated from petroleum changes with age (after formation) of the emulsion; notwithstanding, this subject has not been investigated broadly in literature. This study tries to assess the correlation between aging time, water cut, crude oil viscosity, water viscosity and amount of solids and viscosity of petroleum emulsions. To achieve that, a response surface methodology (RSM) based on Box-Behnken design (BBD) was used to design the experiment. Synthetic emulsions were prepared from an Offshore Malaysian Crude oil based on the DoE design and were aged for 7 days. The emulsions viscosities were measured at 60-degree Celsius using an electromagnetic viscometer (EV100). The broad pressure and temperature range of the HPHT viscometer permit the imitation of acute conditions under which such emulsions may form. The data obtained from the RSM analysis was used to develop a prediction model using gene expression programming (GEP). It was discovered that the viscosity of water has no effect on the viscosities of the studied emulsions, as does the water cut and amount of solids. The most significant factor that affects emulsion viscosity is the aging time, with the emulsion becoming more viscous over time. This is believed to be imminent because of variations in the interfacial film structure. This is followed by the amount of solids, also believed to be as a result of increasing coverage at the interface of the water droplets, limiting the movements of the dispersed droplets (reduced coalescence), thereby increasing the viscosity of the emulsions.
</p>projecteuclid.org/euclid.jam/1589421620_20200513220106Wed, 13 May 2020 22:01 EDTSome Hyperbolic Iterative Methods for Linear Systemshttps://projecteuclid.org/euclid.jam/1589421621<strong>K. Niazi Asil</strong>, <strong>M. Ghasemi Kamalvand</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 8 pages.</p><p><strong>Abstract:</strong><br/>
The indefinite inner product defined by $J=\text{diag}({j}_{1},\dots ,{j}_{n}),\text{\hspace\{0.17em\}}{j}_{k}\in \{-1,+1\}$ , arises frequently in some applications, such as the theory of relativity and the research of the polarized light. This indefinite scalar product is referred to as hyperbolic inner product. In this paper, we introduce three indefinite iterative methods: indefinite Arnoldi’s method, indefinite Lanczos method (ILM), and indefinite full orthogonalization method (IFOM). The indefinite Arnoldi’s method is introduced as a process that constructs a J -orthonormal basis for the nondegenerated Krylov subspace. The ILM method is introduced as a special case of the indefinite Arnoldi’s method for J -Hermitian matrices. IFOM is mentioned as a process for solving linear systems of equations with J -Hermitian coefficient matrices. Finally, by providing numerical examples, the FOM, IFOM, and ILM processes have been compared with each other in terms of the required time for solving linear systems and also from the point of the number of iterations.
</p>projecteuclid.org/euclid.jam/1589421621_20200513220106Wed, 13 May 2020 22:01 EDTPartial Derivative Estimation for Underlying Functional-Valued Process in a Unified Frameworkhttps://projecteuclid.org/euclid.jam/1589421622<strong>Yunbei Ma</strong>, <strong>Fanyin Zhou</strong>, <strong>Xuan Luo</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 17 pages.</p><p><strong>Abstract:</strong><br/>
We consider functional data analysis when the observations at each location are functional rather than scalar. When the dynamic of underlying functional-valued process at each location is of interest, it is desirable to recover partial derivatives of a sample function, especially from sparse and noise-contaminated measures. We propose a novel approach based on estimating derivatives of eigenfunctions of marginal kernels to obtain a representation for functional-valued process and its partial derivatives in a unified framework in which the number of locations and number of observations at each location for each individual can be any rate relative to the sample size. We derive almost sure rates of convergence for the procedures and further establish consistency results for recovered partial derivatives.
</p>projecteuclid.org/euclid.jam/1589421622_20200513220106Wed, 13 May 2020 22:01 EDTComputing Hitting Probabilities of Markov Chains: Structural Results with regard to the Solution Space of the Corresponding System of Equationshttps://projecteuclid.org/euclid.jam/1589421623<strong>Hendrik Baumann</strong>, <strong>Thomas Hanschke</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 9 pages.</p><p><strong>Abstract:</strong><br/>
In a previous paper, we have shown that forward use of the steady-state difference equations arising from homogeneous discrete-state space Markov chains may be subject to inherent numerical instability. More precisely, we have proven that, under some appropriate assumptions on the transition probability matrix P , the solution space S of the difference equation may be partitioned into two subspaces $S={S}_{1}\oplus {S}_{2}$ , where the stationary measure of P is an element of ${S}_{1}$ , and all solutions in ${S}_{1}$ are asymptotically dominated by the solutions corresponding to ${S}_{2}$ . In this paper, we discuss the analogous problem of computing hitting probabilities of Markov chains, which is affected by the same numerical phenomenon. In addition, we have to fulfill a somewhat complicated side condition which essentially differs from those conditions one is usually confronted with when solving initial and boundary value problems. To extract the desired solution, an efficient and numerically stable generalized-continued-fraction-based algorithm is developed.
</p>projecteuclid.org/euclid.jam/1589421623_20200513220106Wed, 13 May 2020 22:01 EDTTheoretical Aspect of Diagonal Bregman Proximal Methodshttps://projecteuclid.org/euclid.jam/1589421624<strong>S. Kabbadj</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 9 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we propose and study a diagonal inexact version of Bregman proximal methods, to solve convex optimization problems with and without constraints. The proposed method forms a unified framework for existing algorithms by providing others.
</p>projecteuclid.org/euclid.jam/1589421624_20200513220106Wed, 13 May 2020 22:01 EDTSolving Permutation Flow Shop Scheduling Problem with Sequence-Independent Setup Timehttps://projecteuclid.org/euclid.jam/1589421625<strong>Jabrane Belabid</strong>, <strong>Said Aqil</strong>, <strong>Karam Allali</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 11 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we study the resolution of a permutation flow shop problem with sequence-independent setup time. The objective is to minimize the maximum of job completion time, also called the makespan. In this contribution, we propose three methods of resolution, a mixed-integer linear programming (MILP) model; two heuristics, the first based on Johnson’s rule and the second based on the NEH algorithm; and finally two metaheuristics, the iterative local search algorithm and the iterated greedy algorithm. A set of test problems is simulated numerically to validate the effectiveness of our resolution approaches. For relatively small-size problems, it has been revealed that the adapted NEH heuristic has the best performance than that of the Johnson-based heuristic. For the relatively medium and large problems, the comparative study between the two metaheuristics based on the exploration of the neighborhood shows that the iterated greedy algorithm records the best performances.
</p>projecteuclid.org/euclid.jam/1589421625_20200513220106Wed, 13 May 2020 22:01 EDTHeat and Mass Transfer in Unsteady Boundary Layer Flow of Williamson Nanofluidshttps://projecteuclid.org/euclid.jam/1589421626<strong>Tesfaye Kebede</strong>, <strong>Eshetu Haile</strong>, <strong>Gurju Awgichew</strong>, <strong>Tadesse Walelign</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 13 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, analytic approximation to the heat and mass transfer characteristics of a two-dimensional time-dependent flow of Williamson nanofluids over a permeable stretching sheet embedded in a porous medium has been presented by considering the effects of magnetic field, thermal radiation, and chemical reaction. The governing partial differential equations along with the boundary conditions were reduced to dimensionless forms by using suitable similarity transformation. The resulting system of ordinary differential equations with the corresponding boundary conditions was solved via the homotopy analysis method. The results of the study show that velocity, temperature, and concentration boundary layer thicknesses generally decrease as we move away from the surface of the stretching sheet and the Williamson parameter was found to retard the velocity but it enhances the temperature and concentration profiles near the surface. It was also found that increasing magnetic field strength, thermal radiation, or rate of chemical reaction speeds up the mass transfer but slows down the heat transfer rates in the boundary layer. The results of this study were compared with some previously published works under some restrictions, and they are found in excellent agreement.
</p>projecteuclid.org/euclid.jam/1589421626_20200513220106Wed, 13 May 2020 22:01 EDTApproximation Techniques for Solving Linear Systems of Volterra Integro-Differential Equationshttps://projecteuclid.org/euclid.jam/1589421627<strong>Ahmad Issa</strong>, <strong>Naji Qatanani</strong>, <strong>Adnan Daraghmeh</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 13 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, a collocation method using sinc functions and Chebyshev wavelet method is implemented to solve linear systems of Volterra integro-differential equations. To test the validity of these methods, two numerical examples with known exact solution are presented. Numerical results indicate that the convergence and accuracy of these methods are in good a agreement with the analytical solution. However, according to comparison of these methods, we conclude that the Chebyshev wavelet method provides more accurate results.
</p>projecteuclid.org/euclid.jam/1589421627_20200513220106Wed, 13 May 2020 22:01 EDTSolving Systems of Singularly Perturbed Convection Diffusion Problems via Initial Value Methodhttps://projecteuclid.org/euclid.jam/1589421628<strong>Wondwosen Gebeyaw Melesse</strong>, <strong>Awoke Andargie Tiruneh</strong>, <strong>Getachew Adamu Derese</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 8 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, an initial value method for solving a weakly coupled system of two second-order singularly perturbed Convection–diffusion problems exhibiting a boundary layer at one end is proposed. In this approach, the approximate solution for the given problem is obtained by solving, a coupled system of initial value problem (namely, the reduced system), and two decoupled initial value problems (namely, the layer correction problems), which are easily deduced from the given system of equations. Both the reduced system and the layer correction problems are independent of perturbation parameter, $\epsilon $ . These problems are then solved analytically and/or numerically, and those solutions are combined to give an approximate solution to the problem. Further, error estimates are derived and examples are provided to illustrate the method.
</p>projecteuclid.org/euclid.jam/1589421628_20200513220106Wed, 13 May 2020 22:01 EDTGlobal Stability of Pneumococcal Pneumonia with Awareness and Saturated Treatmenthttps://projecteuclid.org/euclid.jam/1589421629<strong>Fulgensia Kamugisha Mbabazi</strong>, <strong>J. Y. T. Mugisha</strong>, <strong>Mark Kimathi</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 12 pages.</p><p><strong>Abstract:</strong><br/>
Pneumocccal pneumonia, a secondary bacterial infection that follows influenza A infection, is responsible for morbidity and mortality in children, elderly, and immunocomprised groups. A mathematical model to study the global stability of pneumococcal pneumonia with awareness and saturated treatment is presented. The basic reproduction number, ${R}_{0}$ , is computed using the next generation matrix method. The results show that if ${R}_{0}<1$ , the disease-free steady state is locally asymptotically stable; thus, pneumococcal pneumonia would be eradicated in the population. On the other hand, if ${R}_{0}>1$ the endemic steady state is globally attractive; thus, the disease would persist in the population. The quadratic-linear and Goh–Voltera Lyapunov functionals approach are used to prove the global stabilities of the disease-free and endemic steady states, respectively. The sensitivity analysis of ${R}_{0}$ on model parameters shows that, it is positively sensitive to the maximal effective rate before antibiotic resistance awareness, rate of relapse encountered in administering treatment, and loss of information by aware susceptible individuals. Contrarily, the sensitivity analysis of ${R}_{0}$ on model parameters is negatively sensitive to recovery rate due to treatment and the rate at which unaware susceptible individuals become aware. The numerical analysis of the model shows that awareness about antibiotic resistance and treatment plays a significant role in the control of pneumococcal pneumonia.
</p>projecteuclid.org/euclid.jam/1589421629_20200513220106Wed, 13 May 2020 22:01 EDTAn Optimal Control Problem Governed by a Kirchhoff-Type Variational Inequalityhttps://projecteuclid.org/euclid.jam/1589421630<strong>Chengfu Wang</strong>, <strong>Pengcheng Wu</strong>, <strong>Yuying Zhou</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 8 pages.</p><p><strong>Abstract:</strong><br/>
This paper is concerned with an optimal control problem governed by a Kirchhoff-type variational inequality. The existence of multiplicity solutions for the Kirchhoff-type variational inequality is established by using some nonlinear analysis techniques and the variational method, and the existence results of an optimal control for the optimal control problem governed by a Kirchhoff-type variational inequality are derived.
</p>projecteuclid.org/euclid.jam/1589421630_20200513220106Wed, 13 May 2020 22:01 EDTA Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Controlhttps://projecteuclid.org/euclid.jam/1589421631<strong>Bouchaib Khajji</strong>, <strong>Abderrahim Labzai</strong>, <strong>Abdelfatah Kouidere</strong>, <strong>Omar Balatif</strong>, <strong>Mostafa Rachik</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 13 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we propose a discrete mathematical model that describes the interaction between the classes of drinkers, namely, potential drinkers $(P)$ , moderate drinkers $(M)$ , heavy drinkers $(H)$ , poor heavy drinkers $({T}^{p})$ , rich heavy drinkers $({T}^{r})$ , and quitters of drinking $(Q)$ . We also focus on the importance of treatment within addiction treatment centers aiming to find the optimal strategies to minimize the number of drinkers and maximize the number of heavy drinkers who join addiction treatment centers. We use three controls which represent awareness programs through media and education for the potential drinkers, efforts to encourage the heavy drinkers to join addiction treatment centers, and psychological support with follow-up for the individuals who quit drinking. We use Pontryagin’s maximum principle in discrete time to characterize these optimal controls. The resulting optimality system is solved numerically by Matlab. Consequently, the obtained results confirm the performance of the optimization strategy.
</p>projecteuclid.org/euclid.jam/1589421631_20200513220106Wed, 13 May 2020 22:01 EDTMagnetohydrodynamics Free Convection Flow of Incompressible Fluids over Corrugated Vibrating Bottom Surface with Hall Currents and Heat and Mass Transfershttps://projecteuclid.org/euclid.jam/1589421632<strong>Vincent M. Bulinda</strong>, <strong>Giterere P. Kang’ethe</strong>, <strong>Phineas R. Kiogora</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 10 pages.</p><p><strong>Abstract:</strong><br/>
Magnetohydrodynamics free convection flow of incompressible fluids over corrugated vibrating bottom surface with Hall currents and heat and mass transfers considering heat flux is discussed. The corrugation patterns suggested are sinusoidal in nature. The governing equations are solved by the explicit finite difference numerical method of the forward-time backward-space scheme to obtain the analytical results for velocity, concentration, and temperature profiles. The unsteady resultant velocities, concentration, and temperature for various values of physical parameters are discussed in detail, and it is shown that they have significant effects on the fluid flow, and heat and mass transfers are shown graphically.
</p>projecteuclid.org/euclid.jam/1589421632_20200513220106Wed, 13 May 2020 22:01 EDTMathematical Modelling and Analysis of Transmission Dynamics of Lassa Feverhttps://projecteuclid.org/euclid.jam/1589421633<strong>E. A. Bakare</strong>, <strong>E. B. Are</strong>, <strong>O. E. Abolarin</strong>, <strong>S. A. Osanyinlusi</strong>, <strong>Benitho Ngwu</strong>, <strong>Obiaderi N. Ubaka</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 18 pages.</p><p><strong>Abstract:</strong><br/>
Sub-Saharan Africa harbours the majority of the burden of Lassa fever. Clinical diseases, as well as high seroprevalence, have been documented in Nigeria, Sierra Leone, Liberia, Guinea, Ivory Coast, Ghana, Senegal, Upper Volta, Gambia, and Mali. Deaths from Lassa fever occur all year round but naturally peak during the dry season. Annually, the number of people infected is estimated at 100,000 to 300,000, with approximately 5,000 deaths. There have been some work done on the dynamics of Lassa fever disease transmission, but to the best of our knowledge, none has been able to capture the seasonal variation of Mastomys rodent population and its impact on the transmission dynamics. In this work, a periodically forced seasonal nonautonomous system of a nonlinear ordinary differential equation is developed that captures the dynamics of Lassa fever transmission and seasonal variation in the birth of Mastomys rodents where time was measured in days to capture seasonality. It was shown that the model is epidemiologically meaningful and mathematically well posed by using the results from the qualitative properties of the solution of the model. A time-dependent basic reproduction number ${R}_{L}(t)$ is obtained such that its yearly average is written as ${\widetilde{R}}_{L}<1$ , when the disease does not invade the population (means that the number of infected humans always decreases in the seasons of transmission), and ${\widetilde{R}}_{L}>1$ , when the disease remains constantly and is invading the population, and it was detected that ${\widetilde{R}}_{L}\ne {R}_{L}$ . We also performed some evaluation of the Lassa fever disease intervention strategies using the elasticity of the equilibrial prevalence in order to predict the optimal intervention strategies that can be useful in guiding the local national control program on Lassa fever disease to make a proper decision on the intervention packages. Numerical simulations were carried out to illustrate the analytical results, and we found that the numerical simulations of the model showed that possible combined intervention strategies would reduce the spread of the disease. It was established that, to eliminate Lassa fever disease, treatments with ribavirin must be provided early to reduce mortality and other preventive measures like an educational campaign, community hygiene, isolation of infected humans, and culling/destruction of rodents must be applied to also reduce the morbidity of the disease. Finally, the obtained results gave a primary framework for planning and designing cost-effective strategies for good interventions in eliminating Lassa fever.
</p>projecteuclid.org/euclid.jam/1589421633_20200513220106Wed, 13 May 2020 22:01 EDTMathematical Analysis of Rabies Infectionhttps://projecteuclid.org/euclid.jam/1589421634<strong>C. S. Bornaa</strong>, <strong>Baba Seidu</strong>, <strong>M. I. Daabo</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 17 pages.</p><p><strong>Abstract:</strong><br/>
A mathematical model is proposed to study the dynamics of the transmission of rabies, incorporating predation of dogs by humans. The model is shown to have a unique disease-free equilibrium which is globally asymptotically stable whenever ${\mathrm{\scr R}}_{0}\le 1$ . Local sensitivity analysis suggests that the disease can be controlled through reducing contact with infected dogs, increasing immunization of dogs, screening recruited dogs, culling of infected dogs, and use of dog meat as a delicacy.
</p>projecteuclid.org/euclid.jam/1589421634_20200513220106Wed, 13 May 2020 22:01 EDTAnalytical and Numerical Solutions of Pollution Concentration with Uniformly and Exponentially Increasing Forms of Sourceshttps://projecteuclid.org/euclid.jam/1589421635<strong>N. Manitcharoen</strong>, <strong>B. Pimpunchat</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 9 pages.</p><p><strong>Abstract:</strong><br/>
The study of pollution movement is an important basis for solving water quality problems, which is of vital importance in almost every country. This research proposes the motion of flowing pollution by using a mathematical model in one-dimensional advection-dispersion equation which includes terms of decay and enlargement process. We are assuming an added pollutant sources along the river in two cases: uniformly and exponentially increasing terms. The unsteady state analytical solutions are obtained by using the Laplace transformation, and the finite difference technique is utilized for numerical solutions. Solutions are compared by relative error values. The result appears acceptable between the analytical and numerical solutions. Varying the value of the rate of pollutant addition along the river $(q)$ and the arbitrary constant of exponential pollution source term $(\lambda)$ is displayed to explain the behavior of the incremental concentration. It is shown that the concentration increases as $q$ and $\lambda $ increase, and the exponentially increasing pollution source is a suitable model for the behavior of incremental pollution along the river. The results are presented and discussed graphically. This work can be applied to other physical situations described by advection-dispersion phenomena which are affected by the increase of those source concentrations.
</p>projecteuclid.org/euclid.jam/1589421635_20200513220106Wed, 13 May 2020 22:01 EDTA Framework for Nonconforming Mixed Finite Element Method for Elliptic Problems in ${\Bbb R}^{3}$https://projecteuclid.org/euclid.jam/1589421636<strong>Gwanghyun Jo</strong>, <strong>J. H. Kim</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 8 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we suggest a new patch condition for nonconforming mixed finite elements (MFEs) on parallelepiped and provide a framework for the convergence. Also, we introduce a new family of nonconforming MFE space satisfying the new patch condition. The numerical experiments show that the new MFE shows optimal order convergence in $H(\text{div})$ and ${L}^{2}$ -norm for various problems with discontinuous coefficient case.
</p>projecteuclid.org/euclid.jam/1589421636_20200513220106Wed, 13 May 2020 22:01 EDTConstraints Optimal Control Governing by Triple Nonlinear Hyperbolic Boundary Value Problemhttps://projecteuclid.org/euclid.jam/1589421637<strong>Jamil A. Ali Al-Hawasy</strong>, <strong>Lamyaa H. Ali</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 14 pages.</p><p><strong>Abstract:</strong><br/>
The focus of this work lies on proving the existence theorem of a unique state vector solution (Stvs) of the triple nonlinear hyperbolic boundary value problem (TNHBVP) when the classical continuous control vector (CCCVE) is fixed by using the Galerkin method (Galm), proving the existence theorem of a unique constraints classical continuous optimal control vector (CCCOCVE) with vector state constraints (equality EQVC and inequality INEQVC). Also, it consists of studying for the existence and uniqueness adjoint vector solution (Advs) of the triple adjoint vector equations (TAEqs) associated with the considered triple state equations (Tsteqs). The Fréchet Derivative (Frde.) of the Hamiltonian (HAM) is found. At the end, the theorems for the necessary conditions and the sufficient conditions of optimality (Necoop and Sucoop) are achieved.
</p>projecteuclid.org/euclid.jam/1589421637_20200513220106Wed, 13 May 2020 22:01 EDTGame Chromatic Number of Generalized Petersen Graphs and Jahangir Graphshttps://projecteuclid.org/euclid.jam/1589421638<strong>Ramy Shaheen</strong>, <strong>Ziad Kanaya</strong>, <strong>Khaled Alshehada</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 4 pages.</p><p><strong>Abstract:</strong><br/>
Let $G=(V,E)$ be a graph, and two players Alice and Bob alternate turns coloring the vertices of the graph $G$ a proper coloring where no two adjacent vertices are signed with the same color. Alice's goal is to color the set of vertices using the minimum number of colors, which is called game chromatic number and is denoted by ${\chi }_{g}(G)$ , while Bob's goal is to prevent Alice's goal. In this paper, we investigate the game chromatic number ${\chi }_{g}(G)$ of Generalized Petersen Graphs $GP(n,k)$ for $k\ge 3$ and arbitrary $n$ , $n$ -Crossed Prism Graph, and Jahangir Graph ${J}_{n,m}$ .
</p>projecteuclid.org/euclid.jam/1589421638_20200513220106Wed, 13 May 2020 22:01 EDTExistence Results for Nonlinear Multiorder Fractional Differential Equations with Integral and Antiperiodic Boundary Conditionshttps://projecteuclid.org/euclid.jam/1589421641<strong>HuiChol Choi</strong>, <strong>YongSim Sin</strong>, <strong>KumSong Jong</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 9 pages.</p><p><strong>Abstract:</strong><br/>
In this paper, we study the solvability of a class of nonlinear multiorder Caputo fractional differential equations with integral and antiperiodic boundary conditions. By using some fixed point theorems including the Banach contraction mapping principle and Schaefer’s fixed point theorem, we obtain new existence and uniqueness results for our given problem. Also, we give some examples to illustrate our main results.
</p>projecteuclid.org/euclid.jam/1589421641_20200513220106Wed, 13 May 2020 22:01 EDTQuantile-Based Estimative VaR Forecast and Dependence Measure: A Simulation Approachhttps://projecteuclid.org/euclid.jam/1589421642<strong>Khreshna Syuhada</strong>, <strong>Risti Nur’aini</strong>, <strong> Mahfudhotin</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 14 pages.</p><p><strong>Abstract:</strong><br/>
A Value-at-Risk (VaR) forecast may be calculated for the case of a random loss alone and/or of a random loss that depends on another random loss. In both cases, the VaR forecast is obtained by employing its (conditional) probability distribution of loss data, specifically the quantile of loss distribution. In practice, we have an estimative VaR forecast in which the distribution parameter vector is replaced by its estimator. In this paper, the quantile-based estimative VaR forecast for dependent random losses is explored through a simulation approach. It is found that the estimative VaR forecast is more accurate when a copula is employed. Furthermore, the stronger the dependence of a random loss to the target loss, in linear correlation, the larger/smaller the conditional mean/variance. In any dependence measure, generally, stronger and negative dependence gives a higher forecast. When there is a tail dependence, the use of upper and lower tail dependence provides a better forecast instead of the single correlation coefficient.
</p>projecteuclid.org/euclid.jam/1589421642_20200513220106Wed, 13 May 2020 22:01 EDTComputational Comparison of Exact Solution Methods for 0-1 Quadratic Programs: Recommendations for Practitionershttps://projecteuclid.org/euclid.jam/1589421647<strong>Richard J. Forrester</strong>, <strong>Noah Hunt-Isaak</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 21 pages.</p><p><strong>Abstract:</strong><br/>
This paper is concerned with binary quadratic programs (BQPs), which are among the most well-studied classes of nonlinear integer optimization problems because of their wide variety of applications. While a number of different solution approaches have been proposed for tackling BQPs, practitioners need techniques that are both efficient and easy to implement. We revisit two of the most widely used linearization strategies for BQPs and examine the effectiveness of enhancements to these formulations that have been suggested in the literature. We perform a detailed large-scale computational study over five different classes of BQPs to compare these two linearizations with a more recent linear reformulation and direct submission of the nonlinear integer program to an optimization solver. The goal is to provide practitioners with guidance on how to best approach solving BQPs in an effective and easily implemented manner.
</p>projecteuclid.org/euclid.jam/1589421647_20200513220106Wed, 13 May 2020 22:01 EDTNonlinear Autoregressive Neural Network and Extended Kalman Filters for Prediction of Financial Time Serieshttps://projecteuclid.org/euclid.jam/1589421648<strong>Ghassane Benrhmach</strong>, <strong>Khalil Namir</strong>, <strong>Abdelwahed Namir</strong>, <strong>Jamal Bouyaghroumni</strong>. <p><strong>Source: </strong>Journal of Applied Mathematics, Volume 2020, 6 pages.</p><p><strong>Abstract:</strong><br/>
Time series analysis and prediction are major scientific challenges that find their applications in fields as diverse as finance, biology, economics, meteorology, and so on. Obtaining the method with the least prediction error is one of the difficult problems of financial market and investment analysts. State space modelling is an efficient and flexible method for statistical inference of a broad class of time series and other data. The neural network is an important tool for analyzing time series especially when it is nonlinear and nonstationary. Essential tools for the study of Box-Jenkins methodology, neural networks, and extended Kalman filter were put together. We examine the use of the nonlinear autoregressive neural network method as a prediction technique for financial time series and the application of the extended Kalman filter algorithm to improve the accuracy of the model. As application on a real example, we are analyzing the time series of the daily price of steel over a 790-day period for establishing the superiority of this method over other existing methods. The simulation results using MATLAB and R software show that the model is capable of producing a reasonable accuracy.
</p>projecteuclid.org/euclid.jam/1589421648_20200513220106Wed, 13 May 2020 22:01 EDT