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
SIRS Epidemic Models with Delays, Partial and Temporary Immunity and Vaccination
AppliedMath 2024, 4(2), 666-689; https://doi.org/10.3390/appliedmath4020036 - 28 May 2024
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The basic reproduction, or reproductive number, is a useful index that indicates whether or not there will be an epidemic. However, it is also very important to determine whether an epidemic will eventually decrease and disappear or persist as an endemic. Different infectious
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The basic reproduction, or reproductive number, is a useful index that indicates whether or not there will be an epidemic. However, it is also very important to determine whether an epidemic will eventually decrease and disappear or persist as an endemic. Different infectious diseases have different behaviors and mathematical models used to simulated them should capture the most important processes; however, the models also involve simplifications. Influenza epidemics are usually short-lived and can be modeled with ordinary differential equations without considering demographics. Delays such as the infection time can change the behavior of the solutions. The same is true if there is permanent or temporary immunity, or complete or partial immunity. Vaccination, isolation and the use of antivirals can also change the outcome. In this paper, we introduce several new models and use them to find the effects of all the above factors paying special attention to whether the model can represent an infectious process that eventually disappears. We determine the equilibrium solutions and establish the stability of the disease-free equilibrium using various methods. We also show that many models of influenza or other epidemics with a short duration do not have solutions with a disappearing epidemic. The main objective of the paper is to introduce different ways of modeling immunity in epidemic models. Several scenarios with different immunities are studied since a person may not be re-infected because he/she has total or partial immunity or because there were no close contacts. We show that some relatively small changes, such as in the vaccination rate, can significantly change the dynamics; for example, the existence and number of the disease-free equilibria. We also illustrate that while introducing delays makes the models more realistic, the dynamics have the same qualitative behavior.
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Open AccessArticle
New Bivariate Copulas via Lomax Distribution Generated Distortions
by
Fadal Abdullah Ali Aldhufairi and Jungsywan H. Sepanski
AppliedMath 2024, 4(2), 641-665; https://doi.org/10.3390/appliedmath4020035 - 17 May 2024
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We develop a framework for creating distortion functions that are used to construct new bivariate copulas. It is achieved by transforming non-negative random variables with Lomax-related distributions. In this paper, we apply the distortions to the base copulas of independence, Clayton, Frank, and
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We develop a framework for creating distortion functions that are used to construct new bivariate copulas. It is achieved by transforming non-negative random variables with Lomax-related distributions. In this paper, we apply the distortions to the base copulas of independence, Clayton, Frank, and Gumbel copulas. The properties of the tail dependence coefficient, tail order, and concordance ordering are explored for the new families of distorted copulas. We conducted an empirical study using the daily net returns of Amazon and Google stocks from January 2014 to December 2023. We compared the popular Clayton, Gumbel, Frank, and Gaussian copula models to their corresponding distorted copula models induced by the unit-Lomax and unit-inverse Pareto distortions. The new families of distortion copulas are equipped with additional parameters inherent in the distortion function, providing more flexibility, and are demonstrated to perform better than the base copulas. After analyzing the data, we have found that the joint extremes of Amazon and Google stocks are more likely for high daily net returns than for low daily net returns.
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Open AccessFeature PaperArticle
Three-Body 3D-Kepler Electromagnetic Problem—Existence of Periodic Solutions
by
Vasil Georgiev Angelov
AppliedMath 2024, 4(2), 612-640; https://doi.org/10.3390/appliedmath4020034 - 16 May 2024
Abstract
The main purpose of the present paper is to prove the existence of periodic solutions of the three-body problem in the 3D Kepler formulation. We have solved the same problem in the case when the three particles are considered in an external inertial
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The main purpose of the present paper is to prove the existence of periodic solutions of the three-body problem in the 3D Kepler formulation. We have solved the same problem in the case when the three particles are considered in an external inertial system. We start with the three-body equations of motion, which are a subset of the equations of motion (previously derived by us) for any number of bodies. In the Minkowski space, there are 12 equations of motion. It is proved that three of them are consequences of the other nine, so their number becomes nine, as much as the unknown trajectories are. The Kepler formulation assumes that one particle (the nucleus) is placed at the coordinate origin. The motion of the other two particles is described by a neutral system with respect to the unknown velocities. The state-dependent delays arise as a consequence of the finite vacuum speed of light. We obtain the equations of motion in spherical coordinates and split them into two groups. In the first group all arguments of the unknown functions are delays. We take their solutions as initial functions. Then, the equations of motion for the remaining two particles must be solved to the right of the initial point. To prove the existence–uniqueness of a periodic solution, we choose a space consisting of periodic infinitely smooth functions satisfying some supplementary conditions. Then, we use a suitable operator which acts on these spaces and whose fixed points are periodic solutions. We apply the fixed point theorem for the operators acting on the spaces of periodic functions. In this manner, we show the stability of the He atom in the frame of classical electrodynamics. In a previous paper of ours, we proved the existence of spin functions for plane motion. Thus, we confirm the Bohr and Sommerfeld’s hypothesis for the He atom.
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Open AccessArticle
A Study of Singular Similarity Solutions to Laplace’s Equation with Dirichlet Boundary Conditions
by
Chao-Kang Feng and Jyh-Haw Tang
AppliedMath 2024, 4(2), 596-611; https://doi.org/10.3390/appliedmath4020033 - 6 May 2024
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The infinite series solution to the boundary-value problems of Laplace’s equation with discontinuous Dirichlet boundary conditions was found by using the basic method of separation of variables. The merit of this paper is that the closed-form solution, or the singular similarity solution in
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The infinite series solution to the boundary-value problems of Laplace’s equation with discontinuous Dirichlet boundary conditions was found by using the basic method of separation of variables. The merit of this paper is that the closed-form solution, or the singular similarity solution in the semi-infinite strip domain and the first-quadrant domain, can be generated from the basic infinite series solution in the rectangular domain. Moreover, based on the superposition principle, the infinite series solution in the rectangular domain can be related to the singular similarity solution in the semi-infinite strip domain. It is proven that the analytical source-type singular behavior in the infinite series solution near certain singular points in the rectangular domain can be revealed from the singular similarity solution in the semi-infinite strip domain. By extending the boundary of the rectangular domain, the infinite series solution to Laplace’s equation in the first-quadrant domain can be derived to obtain the analytical singular similarity solution in a direct and much easier way than by using the methods of Fourier transform, images, and conformal mapping.
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Open AccessFeature PaperArticle
A G-Modified Helmholtz Equation with New Expansions for the Earth’s Disturbing Gravitational Potential, Its Functionals and the Study of Isogravitational Surfaces
by
Gerassimos Manoussakis
AppliedMath 2024, 4(2), 580-595; https://doi.org/10.3390/appliedmath4020032 - 4 May 2024
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The G-modified Helmholtz equation is a partial differential equation that enables us to express gravity intensity g as a series of spherical harmonics having radial distance r in irrational powers. The Laplace equation in three-dimensional space (in Cartesian coordinates, is the sum of
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The G-modified Helmholtz equation is a partial differential equation that enables us to express gravity intensity g as a series of spherical harmonics having radial distance r in irrational powers. The Laplace equation in three-dimensional space (in Cartesian coordinates, is the sum of the second-order partial derivatives of the unknown quantity equal to zero) is used to express the Earth’s gravity potential (disturbing and normal potential) in order to represent other useful quantities—which are also known as functionals of the disturbing potential—such as gravity disturbance, gravity anomaly, and geoid undulation as a series of spherical harmonics. We demonstrate that by using the G-modified Helmholtz equation, not only gravity intensity but also disturbing potential and its functionals can be expressed as a series of spherical harmonics. Having gravity intensity represented as a series of spherical harmonics allows us to create new Global Gravity Models. Furthermore, a more detailed examination of the Earth’s isogravitational surfaces is conducted. Finally, we tabulate our results, which makes it clear that new Global Gravity Models for gravity intensity g will be very useful for many geophysical and geodetic applications.
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Open AccessArticle
Quantum Mixtures and Information Loss in Many-Body Systems
by
Diana Monteoliva, Angelo Plastino and Angel Ricardo Plastino
AppliedMath 2024, 4(2), 570-579; https://doi.org/10.3390/appliedmath4020031 - 2 May 2024
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In our study, we investigate the phenomenon of information loss, as measured by the Kullback–Leibler divergence, in a many-fermion system, such as the Lipkin model. Information loss is introduced as the number N of particles increases, particularly when the system is in
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In our study, we investigate the phenomenon of information loss, as measured by the Kullback–Leibler divergence, in a many-fermion system, such as the Lipkin model. Information loss is introduced as the number N of particles increases, particularly when the system is in a mixed state. We find that there is a significant loss of information under these conditions. However, we observe that this loss nearly disappears when the system is in a pure state. Our analysis employs tools from information theory to quantify and understand these effects.
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Open AccessArticle
Approximating a Function with a Jump Discontinuity—The High-Noise Case
by
Qusay Muzaffar, David Levin and Michael Werman
AppliedMath 2024, 4(2), 561-569; https://doi.org/10.3390/appliedmath4020030 - 2 May 2024
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This paper presents a novel deep-learning network designed to detect intervals of jump discontinuities in single-variable piecewise smooth functions from their noisy samples. Enhancing the accuracy of jump discontinuity estimations can be used to find a more precise overall approximation of the function,
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This paper presents a novel deep-learning network designed to detect intervals of jump discontinuities in single-variable piecewise smooth functions from their noisy samples. Enhancing the accuracy of jump discontinuity estimations can be used to find a more precise overall approximation of the function, as traditional approximation methods often produce significant errors near discontinuities. Detecting intervals of discontinuities is relatively straightforward when working with exact function data, as finite differences in the data can serve as indicators of smoothness. However, these smoothness indicators become unreliable when dealing with highly noisy data. In this paper, we propose a deep-learning network to pinpoint the location of a jump discontinuity even in the presence of substantial noise.
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(This article belongs to the Special Issue Application of Machine Learning and Deep Learning Methods in Science)
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Open AccessArticle
Modeling the Impact of Misinformation on the Transmission Dynamics of COVID-19
by
Ziyi Su and Ephraim Agyingi
AppliedMath 2024, 4(2), 544-560; https://doi.org/10.3390/appliedmath4020029 - 30 Apr 2024
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The threat posed by the COVID-19 pandemic has been accompanied by an epidemic of misinformation, causing confusion and mistrust among the public. Misinformation about COVID-19 whether intentional or unintentional takes many forms, including conspiracy theories, false treatments, and inaccurate information about the origins
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The threat posed by the COVID-19 pandemic has been accompanied by an epidemic of misinformation, causing confusion and mistrust among the public. Misinformation about COVID-19 whether intentional or unintentional takes many forms, including conspiracy theories, false treatments, and inaccurate information about the origins and spread of the virus. Though the pandemic has brought to light the significant impact of misinformation on public health, mathematical modeling emerged as a valuable tool for understanding the spread of COVID-19 and the impact of public health interventions. However, there has been limited research on the mathematical modeling of the spread of misinformation related to COVID-19. In this paper, we present a mathematical model of the spread of misinformation related to COVID-19. The model highlights the challenges posed by misinformation, in that rather than focusing only on the reproduction number that drives new infections, there is an additional threshold parameter that drives the spread of misinformation. The equilibria of the model are analyzed for both local and global stability, and numerical simulations are presented. We also discuss the model’s potential to develop effective strategies for combating misinformation related to COVID-19.
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Open AccessArticle
Minimal Terracini Loci in a Plane and Their Generalizations
by
Edoardo Ballico
AppliedMath 2024, 4(2), 529-543; https://doi.org/10.3390/appliedmath4020028 - 17 Apr 2024
Abstract
We study properties of the minimal Terracini loci, i.e., families of certain zero-dimensional schemes, in a projective plane. Among the new results here are: a maximality theorem and the existence of arbitrarily large gaps or non-gaps for the integers x for which the
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We study properties of the minimal Terracini loci, i.e., families of certain zero-dimensional schemes, in a projective plane. Among the new results here are: a maximality theorem and the existence of arbitrarily large gaps or non-gaps for the integers x for which the minimal Terracini locus in degree d is non-empty. We study similar theorems for the critical schemes of the minimal Terracini sets. This part is framed in a more general framework.
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Open AccessArticle
Spontaneous Imbibition and an Interface-Electrostatics-Based Model of the Transition Zone Thickness of Hydrocarbon Reservoirs and Their Theoretical Interpretations
by
Mumuni Amadu and Adango Miadonye
AppliedMath 2024, 4(2), 517-528; https://doi.org/10.3390/appliedmath4020027 - 16 Apr 2024
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The transition zone (TZ) of hydrocarbon reservoirs is an integral part of the hydrocarbon pool which contains a substantial fraction of the deposit, particularly in carbonate petroleum systems. Consequently, knowledge of its thickness and petrophysical properties, viz. its pore size distribution and wettability
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The transition zone (TZ) of hydrocarbon reservoirs is an integral part of the hydrocarbon pool which contains a substantial fraction of the deposit, particularly in carbonate petroleum systems. Consequently, knowledge of its thickness and petrophysical properties, viz. its pore size distribution and wettability characteristic, is critical to optimizing hydrocarbon production in this zone. Using classical formation evaluation techniques, the thickness of the transition zone has been estimated, using well logging methods including resistivity and Nuclear Magnetic Resonance, among others. While hydrocarbon fluids’ accumulation in petroleum reservoirs occurs due to the migration and displacement of originally water-filled potential structural and stratigraphic traps, the development of their TZ integrates petrophysical processes that combine spontaneous capillary imbibition and wettability phenomena. In the literature, wettability phenomena have been shown to also be governed by electrostatic phenomena. Therefore, given that reservoir rocks are aggregates of minerals with ionizable surface groups that facilitate the development of an electric double layer, a definite theoretical relationship between the TZ and electrostatic theory must be feasible. Accordingly, a theoretical approach to estimating the TZ thickness, using the electrostatic theory and based on the electric double layer theory, is attractive, but this is lacking in the literature. Herein, we fill the knowledge gap by using the interfacial electrostatic theory based on the fundamental tenets of the solution to the Poisson–Boltzmann mean field theory. Accordingly, we have used an existing model of capillary rise based on free energy concepts to derive a capillary rise equation that can be used to theoretically predict observations based on the TZ thickness of different reservoir rocks, using well-established formation evaluation methods. The novelty of our work stems from the ability of the model to theoretically and accurately predict the TZ thickness of the different lithostratigraphic units of hydrocarbon reservoirs, because of the experimental accessibility of its model parameters.
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Open AccessArticle
Sums of Independent Circular Random Variables and Maximum Likelihood Circular Uniformity Tests Based on Nonnegative Trigonometric Sums Distributions
by
Juan José Fernández-Durán and María Mercedes Gregorio-Domínguez
AppliedMath 2024, 4(2), 495-516; https://doi.org/10.3390/appliedmath4020026 - 9 Apr 2024
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The sum of independent circular uniformly distributed random variables is also circular uniformly distributed. In this study, it is shown that a family of circular distributions based on nonnegative trigonometric sums (NNTS) is also closed under summation. Given the flexibility of NNTS circular
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The sum of independent circular uniformly distributed random variables is also circular uniformly distributed. In this study, it is shown that a family of circular distributions based on nonnegative trigonometric sums (NNTS) is also closed under summation. Given the flexibility of NNTS circular distributions to model multimodality and skewness, these are good candidates for use as alternative models to test for circular uniformity to detect different deviations from the null hypothesis of circular uniformity. The circular uniform distribution is a member of the NNTS family, but in the NNTS parameter space, it corresponds to a point on the boundary of the parameter space, implying that the regularity conditions are not satisfied when the parameters are estimated by using the maximum likelihood method. Two NNTS tests for circular uniformity were developed by considering the standardised maximum likelihood estimator and the generalised likelihood ratio. Given the nonregularity condition, the critical values of the proposed NNTS circular uniformity tests were obtained via simulation and interpolated for any sample size by the fitting of regression models. The validity of the proposed NNTS circular uniformity tests was evaluated by generating NNTS models close to the circular uniformity null hypothesis.
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Open AccessArticle
A New Approach to Understanding Quantum Mechanics: Illustrated Using a Pedagogical Model over ℤ2
by
David Ellerman
AppliedMath 2024, 4(2), 468-494; https://doi.org/10.3390/appliedmath4020025 - 9 Apr 2024
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The new approach to quantum mechanics (QM) is that the mathematics of QM is the linearization of the mathematics of partitions (or equivalence relations) on a set. This paper develops those ideas using vector spaces over the field
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The new approach to quantum mechanics (QM) is that the mathematics of QM is the linearization of the mathematics of partitions (or equivalence relations) on a set. This paper develops those ideas using vector spaces over the field as a pedagogical or toy model of (finite-dimensional, non-relativistic) QM. The -vectors are interpreted as sets, so the model is “quantum mechanics over sets” or QM/Sets. The key notions of partitions on a set are the logical-level notions to model distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. Those pairs of concepts are the key to understanding the non-classical ‘weirdness’ of QM. The key non-classical notion in QM is the notion of superposition, i.e., the notion of a state that is indefinite between two or more definite- or eigen-states. As Richard Feynman emphasized, all the weirdness of QM is illustrated in the double-slit experiment, so the QM/Sets version of that experiment is used to make the key points.
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Open AccessArticle
Analyzing Small-Signal Stability in a Multi-Source Single-Area Power System with a Load-Frequency Controller Coordinated with a Photovoltaic System
by
Ghazanfar Shahgholian and Arman Fathollahi
AppliedMath 2024, 4(2), 452-467; https://doi.org/10.3390/appliedmath4020024 - 3 Apr 2024
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The frequency deviation from the nominal working frequency in power systems is a consequence of the imbalance between total electrical loads and the aggregate power supplied by production units. The sensitivity of energy system frequency to both minor and major load variations underscore
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The frequency deviation from the nominal working frequency in power systems is a consequence of the imbalance between total electrical loads and the aggregate power supplied by production units. The sensitivity of energy system frequency to both minor and major load variations underscore the need for effective frequency load control mechanisms. In this paper, frequency load control in single-area power system with multi-source energy is analysed and simulated. Also, the effect of the photovoltaic system on the frequency deviation changes in the energy system is shown. In the single area energy system, the dynamics of thermal turbine with reheat, thermal turbine without reheat and hydro turbine are considered. The simulation results using Simulink/Matlab and model analysis using eigenvalue analysis show the dynamic behaviour of the power system in response to changes in the load.
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Open AccessArticle
An Explicit Form of Ramp Function
by
John Constantine Venetis
AppliedMath 2024, 4(2), 442-451; https://doi.org/10.3390/appliedmath4020023 - 2 Apr 2024
Abstract
In this paper, an analytical exact form of the ramp function is presented. This seminal function constitutes a fundamental concept of the digital signal processing theory and is also involved in many other areas of applied sciences and engineering. In particular, the ramp
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In this paper, an analytical exact form of the ramp function is presented. This seminal function constitutes a fundamental concept of the digital signal processing theory and is also involved in many other areas of applied sciences and engineering. In particular, the ramp function is performed in a simple manner as the pointwise limit of a sequence of real and continuous functions with pointwise convergence. This limit is zero for strictly negative values of the real variable , whereas it coincides with the independent variable for strictly positive values of the variable . Here, one may elucidate beforehand that the pointwise limit of a sequence of continuous functions can constitute a discontinuous function, on the condition that the convergence is not uniform. The novelty of this work, when compared to other research studies concerning analytical expressions of the ramp function, is that the proposed formula is not exhibited in terms of miscellaneous special functions, e.g., gamma function, biexponential function, or any other special functions, such as error function, hyperbolic function, orthogonal polynomials, etc. Hence, this formula may be much more practical, flexible, and useful in the computational procedures, which are inserted into digital signal processing techniques and other engineering practices.
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Open AccessArticle
Enhancing COVID-19 Prevalence Forecasting: A Hybrid Approach Integrating Epidemic Differential Equations and Recurrent Neural Networks
by
Liang Kong, Yanhui Guo and Chung-wei Lee
AppliedMath 2024, 4(2), 427-441; https://doi.org/10.3390/appliedmath4020022 - 1 Apr 2024
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Accurate forecasting of the coronavirus disease 2019 (COVID-19) spread is indispensable for effective public health planning and the allocation of healthcare resources at all levels of governance, both nationally and globally. Conventional prediction models for the COVID-19 pandemic often fall short in precision,
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Accurate forecasting of the coronavirus disease 2019 (COVID-19) spread is indispensable for effective public health planning and the allocation of healthcare resources at all levels of governance, both nationally and globally. Conventional prediction models for the COVID-19 pandemic often fall short in precision, due to their reliance on homogeneous time-dependent transmission rates and the oversight of geographical features when isolating study regions. To address these limitations and advance the predictive capabilities of COVID-19 spread models, it is imperative to refine model parameters in accordance with evolving insights into the disease trajectory, transmission rates, and the myriad economic and social factors influencing infection. This research introduces a novel hybrid model that combines classic epidemic equations with a recurrent neural network (RNN) to predict the spread of the COVID-19 pandemic. The proposed model integrates time-dependent features, namely the numbers of individuals classified as susceptible, infectious, recovered, and deceased (SIRD), and incorporates human mobility from neighboring regions as a crucial spatial feature. The study formulates a discrete-time function within the infection component of the SIRD model, ensuring real-time applicability while mitigating overfitting and enhancing overall efficiency compared to various existing models. Validation of the proposed model was conducted using a publicly available COVID-19 dataset sourced from Italy. Experimental results demonstrate the model’s exceptional performance, surpassing existing spatiotemporal models in three-day ahead forecasting. This research not only contributes to the field of epidemic modeling but also provides a robust tool for policymakers and healthcare professionals to make informed decisions in managing and mitigating the impact of the COVID-19 pandemic.
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Open AccessArticle
The Reliability Inference for Multicomponent Stress–Strength Model under the Burr X Distribution
by
Yuhlong Lio, Ding-Geng Chen, Tzong-Ru Tsai and Liang Wang
AppliedMath 2024, 4(1), 394-426; https://doi.org/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
by
Lucian Trifina, Daniela Tărniceriu and Ana-Mirela Rotopănescu
AppliedMath 2024, 4(1), 383-393; https://doi.org/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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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://doi.org/10.3390/appliedmath4010019 - 2 Mar 2024
Cited by 1
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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
by
Alexander Melnikov and Pouneh Mohammadi Nejad
AppliedMath 2024, 4(1), 348-362; https://doi.org/10.3390/appliedmath4010018 - 2 Mar 2024
Abstract
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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Open AccessArticle
A Block Hybrid Method with Equally Spaced Grid Points for Third-Order Initial Value Problems
by
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://doi.org/10.3390/appliedmath4010017 - 1 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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