Journal Description
AppliedMath
AppliedMath
is an international, peer-reviewed, open access journal on applied mathematics published quarterly online by MDPI.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 30.7 days after submission; acceptance to publication is undertaken in 6.6 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: APC discount vouchers, optional signed peer review, and reviewer names published annually in the journal.
- AppliedMath is a companion journal of Mathematics.
Latest Articles
The Reliability Inference for Multicomponent Stress–Strength Model under the Burr X Distribution
AppliedMath 2024, 4(1), 394-426; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010021 - 17 Mar 2024
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The reliability of the multicomponent stress–strength system was investigated under the two-parameter Burr X distribution model. Based on the structure of the system, the type II censored sample of strength and random sample of stress were obtained for the study. The maximum likelihood
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The reliability of the multicomponent stress–strength system was investigated under the two-parameter Burr X distribution model. Based on the structure of the system, the type II censored sample of strength and random sample of stress were obtained for the study. The maximum likelihood estimators were established by utilizing the type II censored Burr X distributed strength and complete random stress data sets collected from the multicomponent system. Two related approximate confidence intervals were achieved by utilizing the delta method under the asymptotic normal distribution theory and parametric bootstrap procedure. Meanwhile, point and confidence interval estimators based on alternative generalized pivotal quantities were derived. Furthermore, a likelihood ratio test to infer the equality of both scalar parameters is provided. Finally, a practical example is provided for illustration.
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Open AccessArticle
Inverses for Fourth-Degree Permutation Polynomials Modulo 32Ψ or 96Ψ, with Ψ as a Product of Different Prime Numbers Greater than Three
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Lucian Trifina, Daniela Tărniceriu and Ana-Mirela Rotopănescu
AppliedMath 2024, 4(1), 383-393; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010020 - 16 Mar 2024
Abstract
In this paper, we address the inverse of a true fourth-degree permutation polynomial (4-PP), modulo a positive integer of the form , where and is a product of different prime
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In this paper, we address the inverse of a true fourth-degree permutation polynomial (4-PP), modulo a positive integer of the form , where and is a product of different prime numbers greater than three. Some constraints are considered for the 4-PPs to avoid some complicated coefficients’ conditions. With the fourth- and third-degree coefficients of the form and , respectively, we prove that the inverse PP is (I) a 4-PP when and or when and (II) a 5-PP when and .
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Open AccessReview
Four Measures of Association and Their Representations in Terms of Copulas
by
Michel Adès, Serge B. Provost and Yishan Zang
AppliedMath 2024, 4(1), 363-382; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010019 - 02 Mar 2024
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Four measures of association, namely, Spearman’s , Kendall’s , Blomqvist’s and Hoeffding’s , are expressed in terms of copulas. Conveniently, this article also includes explicit expressions for their empirical counterparts. Moreover, copula representations of the four coefficients are
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Four measures of association, namely, Spearman’s , Kendall’s , Blomqvist’s and Hoeffding’s , are expressed in terms of copulas. Conveniently, this article also includes explicit expressions for their empirical counterparts. Moreover, copula representations of the four coefficients are provided for the multivariate case, and several specific applications are pointed out. Additionally, a numerical study is presented with a view to illustrating the types of relationships that each of the measures of association can detect.
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Open AccessArticle
Pricing Contingent Claims in a Two-Interest-Rate Multi-Dimensional Jump-Diffusion Model via Market Completion
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Alexander Melnikov and Pouneh Mohammadi Nejad
AppliedMath 2024, 4(1), 348-362; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010018 - 02 Mar 2024
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This paper investigates a financial market where asset prices follow a multi-dimensional Brownian motion process and a multi-dimensional Poisson process characterized by diverse credit and deposit rates where the credit rate is higher than the deposit rate. The focus extends to evaluating European
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This paper investigates a financial market where asset prices follow a multi-dimensional Brownian motion process and a multi-dimensional Poisson process characterized by diverse credit and deposit rates where the credit rate is higher than the deposit rate. The focus extends to evaluating European options by establishing upper and lower hedging prices through a transition to a suitable auxiliary market. Introducing a lemma elucidates the same solution to the pricing problem in both markets under specific conditions. Additionally, we address the minimization of shortfall risk and determine no-arbitrage price bounds within the framework of incomplete markets. This study provides a comprehensive understanding of the challenges posed by the multi-dimensional jump-diffusion model and varying interest rates in financial markets.
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A Block Hybrid Method with Equally Spaced Grid Points for Third-Order Initial Value Problems
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Salma A. A. Ahmedai Abd Allah, Precious Sibanda, Sicelo P. Goqo, Uthman O. Rufai, Hloniphile Sithole Mthethwa and Osman A. I. Noreldin
AppliedMath 2024, 4(1), 320-347; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010017 - 01 Mar 2024
Abstract
In this paper, we extend the block hybrid method with equally spaced intra-step points to solve linear and nonlinear third-order initial value problems. The proposed block hybrid method uses a simple iteration scheme to linearize the equations. Numerical experimentation demonstrates that equally spaced
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In this paper, we extend the block hybrid method with equally spaced intra-step points to solve linear and nonlinear third-order initial value problems. The proposed block hybrid method uses a simple iteration scheme to linearize the equations. Numerical experimentation demonstrates that equally spaced grid points for the block hybrid method enhance its speed of convergence and accuracy compared to other conventional block hybrid methods in the literature. This improvement is attributed to the linearization process, which avoids the use of derivatives. Further, the block hybrid method is consistent, stable, and gives rapid convergence to the solutions. We show that the simple iteration method, when combined with the block hybrid method, exhibits impressive convergence characteristics while preserving computational efficiency. In this study, we also implement the proposed method to solve the nonlinear Jerk equation, producing comparable results with other methods used in the literature.
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(This article belongs to the Special Issue Contemporary Iterative Methods with Applications in Applied Sciences)
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Open AccessArticle
Comparative Study of Monte Carlo Simulation and the Deterministic Model to Analyze Thermal Insulation Costs
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Marco Antonio Montufar Benítez, Jaime Mora Vargas, José Raúl Castro Esparza, Héctor Rivera Gómez and Oscar Montaño Arango
AppliedMath 2024, 4(1), 305-319; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010016 - 01 Mar 2024
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The main purpose of this paper is to implement a simulation model in @RISKTM and study the impact of incorporating random variables, such as the degree days in a traditional deterministic model, for calculating the optimum thickness of thermal insulation in walls.
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The main purpose of this paper is to implement a simulation model in @RISKTM and study the impact of incorporating random variables, such as the degree days in a traditional deterministic model, for calculating the optimum thickness of thermal insulation in walls. Currently, green buildings have become important because of the increasing worldwide interest in the reduction of environmental pollution. One method of saving energy is to use thermal insulation. The optimum thickness of these insulators has traditionally been calculated using deterministic models. With the information generated from real data using the degree days required in a certain zone in Palestine during winter, random samples of the degree days required annually in this town were generated for periods of 10, 20, 50, and 70 years. The results showed that the probability of exceeding the net present value of the cost calculated using deterministic analysis ranges from 0% to 100%, without regard to the inflation rate. The results also show that, for design lifetimes greater than 40 years, the risk of overspending is lower if the building lasts longer than the period for which it was designed. Moreover, this risk is transferred to whomever will pay the operating costs of heating the building. The contribution of this research is twofold: (a) a stochastic approach is incorporated into the traditional models that determine the optimum thickness of thermal insulation used in buildings, by introducing the variability of the degree days required in a given region; (b) a measure of the economic risk incurred by building heating is established as a function of the years of use for which the building is designed and the number of years it is actually used.
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Open AccessArticle
A Strange Result Regarding Some MHD Motions of Generalized Burgers’ Fluids with a Differential Expression of Shear Stress on the Boundary
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Constantin Fetecau, Costică Moroşanu and Shehraz Akhtar
AppliedMath 2024, 4(1), 289-304; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010015 - 01 Mar 2024
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In this work, we investigate isothermal MHD motions of a large class of rate type fluids through a porous medium between two infinite horizontal parallel plates when a differential expression of the non-trivial shear stress is prescribed on the boundary. Exact expressions are
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In this work, we investigate isothermal MHD motions of a large class of rate type fluids through a porous medium between two infinite horizontal parallel plates when a differential expression of the non-trivial shear stress is prescribed on the boundary. Exact expressions are provided for the dimensionless steady state velocities, shear stresses and Darcy’s resistances. Obtained solutions can be used to find the necessary time to touch the steady state or to bring to light certain characteristics of the fluid motion. Graphical representations showed the fluid moves slower in presence of a magnetic field or porous medium. In addition, contrary to our expectations, the volume flux across a plane orthogonal to the velocity vector per unit width of this plane is zero. Finally, based on a simple remark regarding the governing equations of velocity and shear stress for MHD motions of incompressible generalized Burgers’ fluids between infinite parallel plates, provided were the first exact solutions for MHD motions of these fluids when the two plates apply oscillatory or constant shear stresses to the fluid. This important remark offers the possibility to solve any isothermal MHD motion of these fluids between infinite parallel plates or over an infinite plate when the non-trivial shear stress is prescribed on the boundary. As an application, steady state solutions for MHD motions of same fluids have been developed when a differential expression of the fluid velocity is prescribed on the boundary.
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Open AccessArticle
Exploratory Analysis of Distributional Data Using the Quantile Method
by
Manabu Ichino
AppliedMath 2024, 4(1), 261-288; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010014 - 17 Feb 2024
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The quantile method transforms each complex object described by different histogram values to a common number of quantile vectors. This paper retraces the authors’ research, including a principal component analysis, unsupervised feature selection using hierarchical conceptual clustering, and lookup table regression model. The
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The quantile method transforms each complex object described by different histogram values to a common number of quantile vectors. This paper retraces the authors’ research, including a principal component analysis, unsupervised feature selection using hierarchical conceptual clustering, and lookup table regression model. The purpose is to show that this research is essentially based on the monotone property of quantile vectors and works cooperatively in the exploratory analysis of the given distributional data.
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Open AccessArticle
On Some Properties of a Complete Quadrangle
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Vladimir Volenec, Marija Šimić Horvath and Ema Jurkin
AppliedMath 2024, 4(1), 250-260; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010013 - 05 Feb 2024
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In this paper, we study the properties of a complete quadrangle in the Euclidean plane. The proofs are based on using rectangular coordinates symmetrically on four vertices and four parameters . Here, many properties of the
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In this paper, we study the properties of a complete quadrangle in the Euclidean plane. The proofs are based on using rectangular coordinates symmetrically on four vertices and four parameters . Here, many properties of the complete quadrangle known from earlier research are proved using the same method, and some new results are given.
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Open AccessFeature PaperArticle
Convection of Physical Quantities of Random Density
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Elisabetta Barletta, Sorin Dragomir and Francesco Esposito
AppliedMath 2024, 4(1), 225-249; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010012 - 05 Feb 2024
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We study the random flow, through a thin cylindrical tube, of a physical quantity of random density, in the presence of random sinks and sources. We model convection in terms of the expectations of the flux and density and solve the initial value
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We study the random flow, through a thin cylindrical tube, of a physical quantity of random density, in the presence of random sinks and sources. We model convection in terms of the expectations of the flux and density and solve the initial value problem for the resulting convection equation. We propose a difference scheme for the convection equation, that is both stable and satisfies the Courant–Friedrichs–Lewy test, and estimate the difference between the exact and approximate solutions.
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Open AccessArticle
Decompositions of the λ-Fold Complete Mixed Graph into Mixed 6-Stars
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Robert Gardner and Kazeem Kosebinu
AppliedMath 2024, 4(1), 211-224; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010011 - 05 Feb 2024
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Graph and digraph decompositions are a fundamental part of design theory. Probably the best known decompositions are related to decomposing the complete graph into 3-cycles (which correspond to Steiner triple systems), and decomposing the complete digraph into orientations of a 3-cycle (the two
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Graph and digraph decompositions are a fundamental part of design theory. Probably the best known decompositions are related to decomposing the complete graph into 3-cycles (which correspond to Steiner triple systems), and decomposing the complete digraph into orientations of a 3-cycle (the two possible orientations of a 3-cycle correspond to directed triple systems and Mendelsohn triple systems). Decompositions of the -fold complete graph and the -fold complete digraph have been explored, giving generalizations of decompositions of complete simple graphs and digraphs. Decompositions of the complete mixed graph (which contains an edge and two distinct arcs between every two vertices) have also been explored in recent years. Since the complete mixed graph has twice as many arcs as edges, an isomorphic decomposition of a complete mixed graph into copies of a sub-mixed graph must involve a sub-mixed graph with twice as many arcs as edges. A partial orientation of a 6-star with two edges and four arcs is an example of such a mixed graph; there are five such mixed stars. In this paper, we give necessary and sufficient conditions for a decomposition of the -fold complete mixed graph into each of these five mixed stars for all .
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Open AccessArticle
Cell-Cycle Synchronization Prior to Radiotherapy: A Mathematical Model of the Use of Gemcitabine on Melanoma Xenografts
by
Frederika Rentzeperis, Benjamin Coleman and Dorothy Wallace
AppliedMath 2024, 4(1), 197-210; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010010 - 04 Feb 2024
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Radiotherapy can differentially affect the phases of the cell cycle, possibly enhancing suppression of tumor growth, if cells are synchronized in a specific phase. A model is designed to replicate experiments that synchronize cells in the S phase using gemcitabine before radiation at
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Radiotherapy can differentially affect the phases of the cell cycle, possibly enhancing suppression of tumor growth, if cells are synchronized in a specific phase. A model is designed to replicate experiments that synchronize cells in the S phase using gemcitabine before radiation at various doses, with the goal of quantifying this effect. The model is used to simulate a clinical trial with a cohort of 100 individuals receiving only radiation and another cohort of 100 individuals receiving radiation after cell synchronization. The simulations offered in this study support the statement that, at suitably high levels of radiation, synchronizing melanoma cells with gemcitabine before treatment substantially reduces the final tumor size. The improvement is statistically significant, and the effect size is noticeable, with the near suppression of growth at 8 Gray and 92% synchronization.
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Open AccessArticle
A Model of Hepatitis B Viral Dynamics with Delays
by
Benito Chen-Charpentier
AppliedMath 2024, 4(1), 182-196; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010009 - 01 Feb 2024
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Hepatitis B is a liver disease caused by the human hepatitis B virus (HBV). Mathematical models help further the understanding of the processes involved and help make predictions. The basic reproduction number, , is an index that predicts whether the disease
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Hepatitis B is a liver disease caused by the human hepatitis B virus (HBV). Mathematical models help further the understanding of the processes involved and help make predictions. The basic reproduction number, , is an index that predicts whether the disease will be chronic or not. This is the single most-important information that a mathematical model can give. Within-host virus processes involve delays. We study two within-host hepatitis B virus infection models without and with delay. One is a standard one, and the other considering additional processes and with two delays is new. We analyze the basic reproduction number and alternative threshold indices. The values of and the alternative indices change depending on the model. All these indices predict whether the infection will persist or not, but they do not give the same rate of growth of the infection when it is starting. Therefore, the choice of the model is very important in establishing whether the infection is chronic or not and how fast it initially grows. We analyze these indices to see how to decrease their value. We study the effect of adding delays and how the threshold indices depend on how the delays are included. We do this by studying the local asymptotic stability of the disease-free equilibrium or by using an equivalent method. We show that, for some models, the indices do not change by introducing delays, but they change when the delays are introduced differently. Numerical simulations are presented to confirm the results. Finally, some conclusions are presented.
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Open AccessArticle
Convergence and Stability Improvement of Quasi-Newton Methods by Full-Rank Update of the Jacobian Approximates
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Peter Berzi
AppliedMath 2024, 4(1), 143-181; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010008 - 26 Jan 2024
Abstract
A system of simultaneous multi-variable nonlinear equations can be solved by Newton’s method with local q-quadratic convergence if the Jacobian is analytically available. If this is not the case, then quasi-Newton methods with local q-superlinear convergence give solutions by approximating the Jacobian in
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A system of simultaneous multi-variable nonlinear equations can be solved by Newton’s method with local q-quadratic convergence if the Jacobian is analytically available. If this is not the case, then quasi-Newton methods with local q-superlinear convergence give solutions by approximating the Jacobian in some way. Unfortunately, the quasi-Newton condition (Secant equation) does not completely specify the Jacobian approximate in multi-dimensional cases, so its full-rank update is not possible with classic variants of the method. The suggested new iteration strategy (“T-Secant”) allows for a full-rank update of the Jacobian approximate in each iteration by determining two independent approximates for the solution. They are used to generate a set of new independent trial approximates; then, the Jacobian approximate can be fully updated. It is shown that the T-Secant approximate is in the vicinity of the classic quasi-Newton approximate, providing that the solution is evenly surrounded by the new trial approximates. The suggested procedure increases the superlinear convergence of the Secant method to super-quadratic and the quadratic convergence of the Newton method to cubic in one-dimensional cases. In multi-dimensional cases, the Broyden-type efficiency (mean convergence rate) of the suggested method is an order higher than the efficiency of other classic low-rank-update quasi-Newton methods, as shown by numerical examples on a Rosenbrock-type test function with up to 1000 variables. The geometrical representation (hyperbolic approximation) in single-variable cases helps explain the basic operations, and a vector-space description is also given in multi-variable cases.
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(This article belongs to the Special Issue Contemporary Iterative Methods with Applications in Applied Sciences)
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A Mathematical Structure Underlying Sentences and Its Connection with Short–Term Memory
by
Emilio Matricciani
AppliedMath 2024, 4(1), 120-142; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010007 - 18 Jan 2024
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The purpose of the present paper is to further investigate the mathematical structure of sentences—proposed in a recent paper—and its connections with human short–term memory. This structure is defined by two independent variables which apparently engage two short–term memory buffers in a series.
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The purpose of the present paper is to further investigate the mathematical structure of sentences—proposed in a recent paper—and its connections with human short–term memory. This structure is defined by two independent variables which apparently engage two short–term memory buffers in a series. The first buffer is modelled according to the number of words between two consecutive interpunctions—variable referred to as the word interval, —which follows Miller’s law; the second buffer is modelled by the number of word intervals contained in a sentence, , ranging approximately for one to seven. These values result from studying a large number of literary texts belonging to ancient and modern alphabetical languages. After studying the numerical patterns (combinations of and ) that determine the number of sentences that theoretically can be recorded in the two memory buffers—which increases with the use of and —we compare the theoretical results with those that are actually found in novels from Italian and English literature. We have found that most writers, in both languages, write for readers with small memory buffers and, consequently, are forced to reuse sentence patterns to convey multiple meanings.
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Open AccessArticle
A Co-Infection Model for Onchocerciasis and Lassa Fever with Optimal Control Analysis
by
Kabiru Michael Adeyemo, Kayode Oshinubi, Umar Muhammad Adam and Adejimi Adeniji
AppliedMath 2024, 4(1), 89-119; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010006 - 10 Jan 2024
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A co-infection model for onchocerciasis and Lassa fever (OLF) with periodic variational vectors and optimal control is studied and analyzed to assess the impact of controls against incidence infections. The model is qualitatively examined in order to evaluate its asymptotic behavior in relation
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A co-infection model for onchocerciasis and Lassa fever (OLF) with periodic variational vectors and optimal control is studied and analyzed to assess the impact of controls against incidence infections. The model is qualitatively examined in order to evaluate its asymptotic behavior in relation to the equilibria. Employing a Lyapunov function, we demonstrated that the disease-free equilibrium (DFE) is globally asymptotically stable; that is, the related basic reproduction number is less than unity. When it is bigger than one, we use a suitable nonlinear Lyapunov function to demonstrate the existence of a globally asymptotically stable endemic equilibrium (EE). Furthermore, the necessary conditions for the presence of optimum control and the optimality system for the co-infection model are established using Pontryagin’s maximum principle. The model is quantitatively analyzed by studying how sensitive the basic reproduction number is to the model parameters and the model simulation using Runge–Kutta technique of order 4 is also presented to study the effects of the treatments. We deduced from the quantitative analysis that, if there is an effective treatment and diagnosis of those exposed to and infected with the disease, the spread of the viral disease can be effectively managed. The results presented in this work will be useful for the proper mitigation of the disease.
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Open AccessArticle
Informational Updates and the Derivative Pricing Kernel
by
Ayan Bhattacharya
AppliedMath 2024, 4(1), 79-88; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010005 - 03 Jan 2024
Abstract
It is common in financial markets for market makers to offer prices on derivative instruments even though they are uncertain about the underlying asset’s value. This paper studies the mathematical problem that arises as a result. Derivatives are priced in the risk-neutral framework,
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It is common in financial markets for market makers to offer prices on derivative instruments even though they are uncertain about the underlying asset’s value. This paper studies the mathematical problem that arises as a result. Derivatives are priced in the risk-neutral framework, so as the market maker acquires more information about the underlying asset, the change of measure for transition to the risk-neutral framework (the pricing kernel) evolves. This evolution takes a precise form when the market maker is Bayesian. It is shown that Bayesian updates can be characterized as additional informational drift in the underlying asset’s stochastic process. With Bayesian updates, the change of measure needed for pricing derivatives is two-fold: the first change is from the prior probability measure to the posterior probability measure, and the second change is from the posterior probability measure to the risk-neutral measure. The relation between the regular pricing kernel and the pricing kernel under this two-fold change of measure is characterized.
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Open AccessArticle
Dynamics of the Isotropic Star Differential System from the Mathematical and Physical Point of Views
by
Joan-Carles Artés, Jaume Llibre and Nicolae Vulpe
AppliedMath 2024, 4(1), 70-78; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010004 - 02 Jan 2024
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The following differential quadratic polynomial differential system
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The following differential quadratic polynomial differential system when the parameter models the structure equations of an isotropic star having a linear barotropic equation of state, being where is the mass inside the sphere of radius r of the star, where is the density of the star, and where R is the radius of the star. First, we classify all the topologically non-equivalent phase portraits in the Poincaré disc of these quadratic polynomial differential systems for all values of the parameter . Second, using the information of the different phase portraits obtained we classify the possible limit values of and of an isotropic star when r decreases.
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Open AccessArticle
Life at the Landau Pole
by
Paul Romatschke
AppliedMath 2024, 4(1), 55-69; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010003 - 01 Jan 2024
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If a quantum field theory has a Landau pole, the theory is usually called ‘sick’ and dismissed as a candidate for an interacting UV-complete theory. In a recent study on the interacting 4d O(N) model at large N, it was shown that at
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If a quantum field theory has a Landau pole, the theory is usually called ‘sick’ and dismissed as a candidate for an interacting UV-complete theory. In a recent study on the interacting 4d O(N) model at large N, it was shown that at the Landau pole, observables remain well-defined and finite. In this work, I investigate both relevant and irrelevant deformations of the said model at the Landau pole, finding that physical observables remain unaffected. Apparently, the Landau pole in this theory is benign. As a phenomenological application, I compare the O(N) model to QCD by identifying with the Landau pole in the O(N) model.
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Open AccessArticle
Measuring the Risk of Vulnerabilities Exploitation
by
Maria de Fátima Brilhante, Dinis Pestana, Pedro Pestana and Maria Luísa Rocha
AppliedMath 2024, 4(1), 20-54; https://0-doi-org.brum.beds.ac.uk/10.3390/appliedmath4010002 - 24 Dec 2023
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Modeling the vulnerabilities lifecycle and exploitation frequency are at the core of security of networks evaluation. Pareto, Weibull, and log-normal models have been widely used to model the exploit and patch availability dates, the time to compromise a system, the time between compromises,
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Modeling the vulnerabilities lifecycle and exploitation frequency are at the core of security of networks evaluation. Pareto, Weibull, and log-normal models have been widely used to model the exploit and patch availability dates, the time to compromise a system, the time between compromises, and the exploitation volumes. Random samples (systematic and simple random sampling) of the time from publication to update of cybervulnerabilities disclosed in 2021 and in 2022 are analyzed to evaluate the goodness-of-fit of the traditional Pareto and log-normal laws. As censoring and thinning almost surely occur, other heavy-tailed distributions in the domain of attraction of extreme value or geo-extreme value laws are investigated as suitable alternatives. Goodness-of-fit tests, the Akaike information criterion (AIC), and the Vuong test, support the statistical choice of log-logistic, a geo-max stable law in the domain of attraction of the Fréchet model of maxima, with hyperexponential and general extreme value fittings as runners-up. Evidence that the data come from a mixture of differently stretched populations affects vulnerabilities scoring systems, specifically the common vulnerabilities scoring system (CVSS).
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