Applications and Applied Mathematics: An International Journal (AAM)Copyright (c) 2021 Prairie View A&M University All rights reserved.
https://digitalcommons.pvamu.edu/aam
Recent documents in Applications and Applied Mathematics: An International Journal (AAM)en-usSat, 11 Dec 2021 01:41:59 PST3600(R1513) The Dynamical Study of Variable Mass Test Particle in Nonlinear Sense of Restricted 3-body Problem with Heterogeneous Primaries
https://digitalcommons.pvamu.edu/aam/vol16/iss2/28
https://digitalcommons.pvamu.edu/aam/vol16/iss2/28Thu, 09 Dec 2021 11:08:33 PST
The main idea of this paper is to study the non-linear stability property of the motion of the test particle which is moving under the influence of heterogeneous primaries having N-layers with different densities as well as varying its mass according to Jeans law. The system is also perturbed by the small perturbations in Coriolis as well as centrifugal forces. We evaluate the equations of motion of the test particle under the influence of the above said perturbations. From this system of equations of motion, we reveal analytically the locations of stationary points as well as the non-linear stability.
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Sada Nand Prasad et al.(R1412) Stability and Bifurcation of a Cholera Epidemic Model with Saturated Recovery Rate
https://digitalcommons.pvamu.edu/aam/vol16/iss2/27
https://digitalcommons.pvamu.edu/aam/vol16/iss2/27Thu, 09 Dec 2021 11:08:30 PST
In this paper, a Cholera epidemic model is proposed and studied analytically as well as numerically. It is assumed that the disease is transmitted by contact with Vibrio cholerae and infected person according to dose-response function. However, the saturated treatment function is used to describe the recovery process. Moreover, the vaccine against the disease is assumed to be utterly ineffective. The existence, uniqueness and boundedness of the solution of the proposed model are discussed. All possible equilibrium points and the basic reproduction number are determined. The local stability and persistence conditions are established. Lyapunov method and the second additive compound matrix are used to study the global stability of the system. The conditions that guarantee the occurrence of local bifurcation and backward bifurcation are determined. Finally, numerical simulation is used to investigate the global dynamical behavior of the Cholera epidemic model and understand the effects of parameters on evolution of the disease in the environment. It is observed that the solution of the model is very sensitive to varying in parameters values and different types of bifurcations are obtained including backward bifurcation.
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Huda Abdul-Satar et al.(R1523) Abundant Natural Resources, Ethnic Diversity and Inclusive Growth in Sub-Saharan Africa: A Mathematical Approach
https://digitalcommons.pvamu.edu/aam/vol16/iss2/26
https://digitalcommons.pvamu.edu/aam/vol16/iss2/26Mon, 06 Dec 2021 10:33:58 PST
The sub-Saharan African region is blessed with abundant natural resources and diverse ethnic groups, yet the region is dominated by the largest number of poor people worldwide due to inequitable distribution of national income. Existing statistics forecast decay in the quality of lives over the years compared to the continent of Asia that shares similar history with the region. In this paper, a-five dimensional first-order nonlinear ordinary differential equations was formulated to give insight into various factors that shaped dynamics of inclusive growth in sub-Saharan Africa. The validity test was performed based on ample mathematical theorems and the model was found to be valid. The model was then studied qualitatively and quantitatively via stability theory of nonlinear differential equations which depended on the policy success ratio and classical fourth-order Runge-Kutta scheme implemented in maple respectively. The results from the analysis showed that inclusive growth from abundant natural resources and ethnic diversity in sub-Saharan Africa was a function of policy reform whereby an increase in both equitable distribution of national income and accessibility of common man to the goods and services provided by the state to narrow inequality gap was accompanied with a low level of nepotism.
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Juliet I. Adenuga et al.(R1494) Approximate Solutions of the Telegraph Equation
https://digitalcommons.pvamu.edu/aam/vol16/iss2/25
https://digitalcommons.pvamu.edu/aam/vol16/iss2/25Mon, 06 Dec 2021 10:33:55 PST
In this paper the initial boundary value problems for the linear telegraph equation in one and two space dimensions are considered. To find approximate solutions, a recently proposed optimization-free approach that utilizes artificial neural networks with one hidden layer is used, in which the connecting weights from the input layer to the hidden layer are chosen randomly and the weights from the hidden layer to the output layer are found by solving a system of linear equations. One of the advantages of this method, in comparison to the usual discretization methods for the two-dimensional linear telegraph equation, is that this artificial neural network method does not require time discretization and it produces the approximate solution in a closed analytic form. A numerical study on several examples for which the exact solutions are known is conducted and the dependence of the maximum absolute error and the root-mean-square deviation error on the size of the training set and on the number of nodes in the hidden layer is explored. It is shown numerically that, in general, both errors tend to decrease with the increase of the size of the training set and the size of the hidden layer.
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Ilija Jegdić(R1499) Family of Surfaces with a Common Bertrand D-Curve as Isogeodesic, Isoasymptotic and Line of Curvature
https://digitalcommons.pvamu.edu/aam/vol16/iss2/24
https://digitalcommons.pvamu.edu/aam/vol16/iss2/24Mon, 06 Dec 2021 10:33:53 PST
In this paper, we establish the necessary and sufficient conditions to parameterize a surface family on which the Bertrand D-partner of any given curve lies as isogeodesic, isoasymptotic or curvature line in \mathbb{E}^3. Then, we calculate the fundamental forms of these surfaces and determine the developability and minimality conditions with the Gaussian and mean curvatures. We also extend this idea on ruled surfaces and provide the required conditions for those to be developable. Finally, we present some examples and graph the corresponding surfaces.
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Süleyman Şenyurt et al.(R1458) A New Finite Difference Scheme for High-Dimensional Heat Equation
https://digitalcommons.pvamu.edu/aam/vol16/iss2/23
https://digitalcommons.pvamu.edu/aam/vol16/iss2/23Mon, 06 Dec 2021 10:33:50 PST
In this research, a new second-order finite difference scheme is proposed to solve two and three- dimensional heat equation. Finite difference equations are determined via a discretization approach in which spatial second order partial derivatives in x and y directions are approximated simultaneously while in the classic method, each spatial partial derivative is replaced by a central finite difference approximation, separately. By this new discretization scheme and also using the forward difference to the first-order time derivative, a finite difference equation is obtained for the parabolic equation. This approach is explicit and similar to other explicit approaches, an interval for the Courant number, r is determined. This region for r is obtained through Fourier stability analysis. The advantage of this approach is that its stability interval is larger than the interval for traditional methods. Numerical experiments are presented to confirm the theoretical results. It is shown that more accurate approximations can be obtained by the new scheme.
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Jafar Biazar et al.(R1454) On Reducing the Linearization Coefficients of Some Classes of Jacobi Polynomials
https://digitalcommons.pvamu.edu/aam/vol16/iss2/22
https://digitalcommons.pvamu.edu/aam/vol16/iss2/22Mon, 06 Dec 2021 10:33:48 PST
This article is concerned with establishing some new linearization formulas of the modified Jacobi polynomials of certain parameters. We prove that the linearization coefficients involve hypergeometric functions of the type _{4}F_{3}(1). Moreover, we show that the linearization coefficients can be reduced in several cases by either utilizing certain standard formulas, and in particular Pfaff-Saalschütz identity and Watson’s theorem, or via employing the symbolic algebraic algorithms of Zeilberger, Petkovsek, and van Hoeij. New formulas for some definite integrals are obtained with the aid of the developed linearization formulas.
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Waleed Abd-Elhameed et al.(R1466) Ideals and Filters on a Lattice in Neutrosophic Setting
https://digitalcommons.pvamu.edu/aam/vol16/iss2/21
https://digitalcommons.pvamu.edu/aam/vol16/iss2/21Mon, 06 Dec 2021 10:33:45 PST
The notions of ideals and filters have studied in many algebraic (crisp) fuzzy structures and used to study their various properties, representations and characterizations. In addition to their theoretical roles, they have used in some areas of applied mathematics. In a recent paper, Arockiarani and Antony Crispin Sweety have generalized and studied these notions with respect to the concept of neutrosophic sets introduced by Smarandache to represent imprecise, incomplete and inconsistent information. In this article, we aim to deepen the study of these important notions on a given lattice in the neutrosophic setting. We show their various properties and characterizations, in particular, we pay attention to their characterizations based on of the lattice min and max operations. In addition, we study the notion of prime single-valued neutrosophic ideal (resp. filter) as interesting kind and we discuss some its set-operations, complement and associate sets.
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Lemnaouar Zedam et al.(R1519) On Some Geometric Properties of Non-null Curves via its Position Vectors in \mathbb{R}_1^3
https://digitalcommons.pvamu.edu/aam/vol16/iss2/20
https://digitalcommons.pvamu.edu/aam/vol16/iss2/20Mon, 06 Dec 2021 10:33:42 PST
In this work, the geometric properties of non-null curves lying completely on spacelike surface via its position vectors in the dimensional Minkowski 3-space \mathbb{R}_1^3 are studied. Also, we give a few portrayals for the spacelike curves which lie on certain subspaces of \mathbb{R}_1^3. Finally, we present an application to demonstrate our insights.
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Emad Solouma et al.(R1506) Generalized cr3b Problem with Heterogeneous Primary and Secondary as Finite Straight Segment
https://digitalcommons.pvamu.edu/aam/vol16/iss2/19
https://digitalcommons.pvamu.edu/aam/vol16/iss2/19Mon, 06 Dec 2021 10:33:40 PST
The existence and stability of stationary points are investigated under the effects of heterogeneous primary having N-layers with different densities, radiating finite straight segment and the Coriolis as well as centrifugal forces in the frame of cr3bp. The equations of motion are determined with the help of which we evaluate five stationary points analytically as well as graphically, and examine their stability.
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Abdullah A. Ansari et al.(R1514) Nano Continuous Mappings via Nano M Open Sets
https://digitalcommons.pvamu.edu/aam/vol16/iss2/18
https://digitalcommons.pvamu.edu/aam/vol16/iss2/18Mon, 06 Dec 2021 10:33:37 PST
Nano M open sets are a union of nano θ semi open sets and nano δ pre open sets. The properties of nano M open sets with their interior and closure operators are discussed in a previous paper. In this paper, we discuss about nano M-continuous and nano M-irresolute functions are introduced in a nano topological spaces along with their continuous and irresolute mappings. Also, nano M-open and nano M-closed functions are introduced and compare with their near open and closed mappings in a nano topological spaces. Further, nano M homeomorphism is also discussed in nano topological spaces. Also, we discuss nano e-Cts, nano e-Irr, nano eo and nano ec functions and nano eHom in nano topological spaces. Also some of their properties are well discussed.
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A. Vadivel et al.(R1056) Effect of Rotation on Plane Waves of Generalized Magneto-thermoelastic Medium with Voids under Thermal Loading due to Laser Pulse
https://digitalcommons.pvamu.edu/aam/vol16/iss2/17
https://digitalcommons.pvamu.edu/aam/vol16/iss2/17Mon, 06 Dec 2021 10:33:34 PST
The investigation in this paper deals with the rotation of the magneto-thermoelastic solid and with voids subjected to thermal loading due to laser pulse. The problem is studied in the context of three theories of generalized magneto thermoelasticity: Lord-Schulman (L-S), Green-Lindsay (G-L) and the coupled theory (CD) with the effect of rotation, magnetic field, thermal loading and voids. The methodology applied here is using the normal mode analysis to solve the physical problem to obtain the exact expressions for the displacement components, the stresses, the temperature, and the change in the volume fraction field have been shown graphically by comparison between three theories, in the presence and the absence of rotation, magnetic field and for two different values of time on thermoelastic material in the presence of voids.
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Mohamed I.A. Othman et al.(R1480) Heat Transfer in Peristaltic Motion of Rabinowitsch Fluid in a Channel with Permeable Wall
https://digitalcommons.pvamu.edu/aam/vol16/iss2/16
https://digitalcommons.pvamu.edu/aam/vol16/iss2/16Mon, 06 Dec 2021 10:33:32 PST
This paper is intended to investigate the effect of heat transfer on the peristaltic flow of Rabinowitsch fluid in a channel lined with a porous material. The Navier -Stokes equation governs the channel's flow, and Darcy's law describes the permeable boundary. The Rabinowitsch fluid model's governing equations are solved by utilizing approximations of the long-wavelength and small number of Reynolds. The expressions for axial velocity, temperature distribution, pressure gradient, friction force, stream function are obtained. The influence on velocity, pressure gradient, friction force, and temperature on pumping action of different physical parameters is explored via graphs.
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Mahadev M. Channakote et al.(R1471) MHD Reiner-Rivlin Liquid Flow Through a Porous Cylindrical Annulus
https://digitalcommons.pvamu.edu/aam/vol16/iss2/15
https://digitalcommons.pvamu.edu/aam/vol16/iss2/15Mon, 06 Dec 2021 10:33:29 PST
The present work concerns the steady and unsteady flow of an incompressible Reiner- Rivlin liquid in the porous annular region of two concentric rotating cylinders, which is moving parallel to their axis, about the common axis of these cylinders under uniform magnetic field acted in perpendicular direction of the axis. The electrically conducting flow of Reiner-Rivlin liquid in the annular porous region is governed by the Brinkman equation with the consideration that the effective viscosity of liquid is same as viscosity of the liquid. Analytical expressions for velocity components, pressure gradient and volumetric flow rate are established. Effects of the magnetic field and other flow parameters on the axial and rotational velocity components and flow rate are discussed graphically.
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Satya Deo et al.(R1496) Impact of Electronic States of Conical Shape of Indium Arsenide/Gallium Arsenide Semiconductor Quantum Dots
https://digitalcommons.pvamu.edu/aam/vol16/iss2/14
https://digitalcommons.pvamu.edu/aam/vol16/iss2/14Mon, 06 Dec 2021 10:33:26 PST
Semiconductor quantum dots (QDs) have unique atom-like properties. In this work, the electronic states of quantum dot grown on a GaAs substrate has been studied. The analytical expressions of electron wave function for cone-like quantum dot on the semiconductor surface has been obtained and the governing eigen value equation has been solved, thereby obtaining the dependence of ground state energy on radius and height of the cone-shaped -dots. In addition, the energy of eigenvalues is computed for various length and thickness of the wetting layer (WL). We discovered that the eigen functions and energies are nearly associated with the GaAs potential.
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Md. Fayz-Al-Asad et al.(R1508) Stability and Zero Velocity Curves in the Perturbed Restricted Problem of 2 + 2 Bodies
https://digitalcommons.pvamu.edu/aam/vol16/iss2/13
https://digitalcommons.pvamu.edu/aam/vol16/iss2/13Mon, 06 Dec 2021 10:33:24 PST
The present study investigates the existence and linear stability of the equilibrium points in the restricted problem of 2+2 bodies including the effect of small perturbations epsilon-1 and espilon-2 in the Coriolis and centrifugal forces respectively. The less massive primary is considered as a straight segment and the more massive primary a point mass. The equations of motion of the infinitesimal bodies are derived.We obtain fourteen equilibrium points of the model, out of which six are collinear and rest non-collinear with the centers of the primaries. The position of the equilibrium points are affected by the small perturbation in centrifugal force, length and mass parameters, but there is no impact of small perturbation in Coriolis force on them. In addition, the obtained results are applied to Earth-22 Kalliope-dual satellite system. For this system, we calculate collinear and non-collinear equilibrium points and observed that the number of non-collinear equilibrium points depends on epsilon-2. Furthermore, for a set of values of the parameters epsilon-1 and epsilon-2, we have checked the stability of all the equilibrium points and concluded that all the equilibrium points are found to be unstable. The permissible regions of motion for the Earth-22 Kalliope-dual satellite system are also studied.
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Rajiv Aggarwal et al.(R1493) Discussion on Stability and Hopf-bifurcation of an Infected Prey under Refuge and Predator
https://digitalcommons.pvamu.edu/aam/vol16/iss2/12
https://digitalcommons.pvamu.edu/aam/vol16/iss2/12Mon, 06 Dec 2021 10:33:21 PST
The paper deals with the case of non-selective predation in a partially infected prey-predator system, where both the susceptible prey and predator follow the law of logistic growth and some preys avoid predation by hiding. The disease-free preys get infected in due course of time by a certain rate. However, the carrying capacity of the predator population is considered proportional to the sum-total of the susceptible and infected prey. The positivity and boundedness of the solutions of the system are studied and the existence of the equilibrium points and stability of the system are analyzed at these points. The effect of the infected prey-refuge on each population density is also discussed. It is observed that a Hopf-bifurcation may occur about the interior equilibrium, where the refuge parameter is considered as the bifurcation parameter. The analytical findings are illustrated through computer simulation using MAPLE that show the reliability of the model from the ecological point of view.
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Moulipriya Sarkar et al.(R1464) Stability of the Artificial Equilibrium Points in the Low-Thrust Restricted Three-Body Problem with Variable Mass
https://digitalcommons.pvamu.edu/aam/vol16/iss2/11
https://digitalcommons.pvamu.edu/aam/vol16/iss2/11Mon, 06 Dec 2021 10:33:19 PST
In this article, we have investigated the existence and stability of the artificial equilibrium points (AEPs) in the low-thrust restricted three-body problem with variable mass. In this model of the low-thrust restricted three-body problem, we have considered both the primaries as point masses. The mass of the spacecraft varies with time according to Jeans’ law (1928). We have introduced a new concept for creating the AEPs in the restricted three-body problem with variable mass using continuous constant acceleration. We have derived the equations of motion of the spacecraft after using the space-time transformations of Meshcherskii. The AEPs have been created by cancelling the gravitational and centrifugal forces with the constant continuous low-thrust at the non-equilibrium points. The positions of these AEPs will depend not only on magnitude but also on the constant directions of the low-thrust acceleration. We have analyzed the linear stability of the AEPs and found that all the AEPs are unstable. Finally, we have drawn the zero velocity curves (ZVCs) to determine the possible regions of motion in which the spacecraft is free to move.
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Amit Mittal et al.(R1488) Transformation of Glucokinase under Variable Rate Constants and Thermal Conditions: A Mathematical Model
https://digitalcommons.pvamu.edu/aam/vol16/iss2/10
https://digitalcommons.pvamu.edu/aam/vol16/iss2/10Mon, 06 Dec 2021 10:33:16 PST
The glucokinase (GK) in cells plays a pivotal role in the regulation of carbohydrate metabolism and acts as a sensor of glucose. It helps us to control glucose levels during fast and food intake conditions through triggering shifts in metabolism or cell functions. Various forms of hypoglycaemia and hyperglycaemia occur due to the transformations of the gene of the Glucokinase. The mathematical modelling of enzyme dynamics is an emerging research area to serve its role in biological investigations. Thus, it is imperative to establish a mathematical model to understand the kinetics of native and denatured forms of enzyme-GK under thermal stress with respect to time. The formulation of the current model is based on the number of non-linear ordinary differential equations with suitable initial and boundary conditions. The transformations of glucokinase were studied using mathematical and computational simulations in order to estimate the concentration of native and denatured enzyme forms with respect to different rate constants and under various thermal changes. The results obtained in this model were verified with the empirical outcome of Sanchez Ruiz et al. and Weinhouse for the validity and efficacy of the formulated model.
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Mukhtar Ahmad Khanday et al.(R1468) Global Analysis of an SEIRS Model for COVID-19 Capturing Saturated Incidence with Treatment Response
https://digitalcommons.pvamu.edu/aam/vol16/iss2/9
https://digitalcommons.pvamu.edu/aam/vol16/iss2/9Mon, 06 Dec 2021 10:33:14 PST
In this work, a new SEIRS model with saturated incidence rate and piecewise linear treatment response is proposed to describe the dynamics of COVID-19. It is assumed that the treatment response is proportional to the number of infected people as long as the incidence cases are within the capacity of the healthcare system, after which the value becomes constant, when the number of confirmed cases exceeds the carrying capacity of the available medical facilities. Thus, the basic reproduction number of the model is obtained. It is proved that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number is less than a critical value. Moreover, sufficient conditions are obtained to guarantee the local and global stability of the equilibrium points of the model. The numerical analysis reveals that multiple endemic equilibria may exist even when the basic reproduction number is less than one, and some interesting dynamics can be observed when the treatment parameter and immunity waning rate are varied.
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David A. Oluyori et al.(R1497) On the Invariant Subspaces of the Fractional Integral Operator
https://digitalcommons.pvamu.edu/aam/vol16/iss2/8
https://digitalcommons.pvamu.edu/aam/vol16/iss2/8Mon, 06 Dec 2021 10:33:11 PST
In operator theory, there is an important problem called the invariant subspace problem. This important problem of mathematics has been clear for more than half a century. However the solution seems to be nowhere in sight. With this motivation, we investigate the invariant subspaces of the fractional integral operator in the Banach space with certain conditions in this paper. Also by using the Duhamel product method, unicellularity of the fractional integral operator on some space is obtained and the description of the invariant subspaces is given.
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Mehmet Gürdal et al.(R1524) The Existence and Uniqueness of Solution for Fractional Newel-Whitehead-Segel Equation within Caputo-Fabrizio Fractional Operator
https://digitalcommons.pvamu.edu/aam/vol16/iss2/7
https://digitalcommons.pvamu.edu/aam/vol16/iss2/7Mon, 06 Dec 2021 10:33:09 PST
In this paper, we introduce and study the existence and uniqueness theorem of the solution for the fractional Newell-Whitehead-Segel equation within Caputo-Fabrizio fractional operator. Also, we propose a new numerical method known as natural reduced differential transform method (NRDTM) for solving this equation. We confirm our theoretical discussion with two numerical examples in order to achieve the validity and accuracy of the proposed method. The computations, associated with these examples, are performed by MATLAB software package.
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Ali Khalouta(R1491) Numerical Solution of the Time-space Fractional Diffusion Equation with Caputo Derivative in Time by a-polynomial Method
https://digitalcommons.pvamu.edu/aam/vol16/iss2/6
https://digitalcommons.pvamu.edu/aam/vol16/iss2/6Mon, 06 Dec 2021 10:33:06 PST
In this paper, a novel type of polynomial is defined which is equipped with an auxiliary parameter a. These polynomials are a combination of the Chebyshev polynomials of the second kind. The approximate solution of each equation is assumed as the sum of these polynomials and then, with the help of the collocation points, the unknown coefficients of each polynomial, as well as auxiliary parameter, is obtained optimally. Now, by placing the optimal value of a in polynomials, the polynomials are obtained without auxiliary parameter, which is the restarted step of the present method. The time discretization is performed on fractional partial differential equations by L1 method. In the following, the convergence theorem of the method is proved.
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Saeid Abbasbandy et al.(R1505) A Note on Large Deviations in Insurance Risk
https://digitalcommons.pvamu.edu/aam/vol16/iss2/5
https://digitalcommons.pvamu.edu/aam/vol16/iss2/5Mon, 06 Dec 2021 10:33:04 PST
We study large and moderate deviations for an insurance portfolio, with the number of claims tending to infinity, without assuming identically distributed claims. The crucial assumption is that the centered claims are bounded, and that variances are bounded below. From a general large deviations upper bound, we obtain an exponential bound for the probability of the average loss exceeding a threshold. A counterexample shows that a full large deviation principle, including also a lower bound, does not follow from our assumptions. We argue that our assumptions make sense, in particular, for life insurance portfolios and discuss how to apply our upper bound in this context. Finally, we use a moderate deviations result by Petrov (1954) to estimate the probability of exceeding a threshold that depends on portfolio size. In this asymptotic regime, the rate function that determines the asymptotic behavior is explicit and thus very easy to compute numerically, without solving an optimization problem.
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Stefan Gerhold(R1463) On the Central Limit Theorem for Conditional Density Estimator In the Single Functional Index Model
https://digitalcommons.pvamu.edu/aam/vol16/iss2/4
https://digitalcommons.pvamu.edu/aam/vol16/iss2/4Mon, 06 Dec 2021 10:33:01 PST
The main objective of this paper is to investigate the nonparametric estimation of the conditional density of a scalar response variable Y, given the explanatory variable X taking value in a Hilbert space when the sample of observations is considered as an independent random variables with identical distribution (i.i.d.) and are linked with a single functional index structure. First of all, a kernel type estimator for the conditional density function (cond-df) is introduced. Afterwards, the asymptotic properties are stated for a conditional density estimator when the observations are linked with a single-index structure from which we derive an central limit theorem (CLT) of the conditional density estimator to show the asymptotic normality of the kernel estimate of this model. As an application the conditional mode in functional single-index model is presented. As an application the conditional mode in functional single-index model is presented as well as the asymptotic ( 1 - \xi) confidence interval of the conditional mode function is given for 0 < \xi < 1. Simulation study is also presented to illustrate the validity and finite sample performance of the considered estimator.
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Abbes Rabhi et al.(R1239) A New Type II Half Logistic-G family of Distributions with Properties, Regression Models, System Reliability and Applications
https://digitalcommons.pvamu.edu/aam/vol16/iss2/3
https://digitalcommons.pvamu.edu/aam/vol16/iss2/3Mon, 06 Dec 2021 10:32:58 PST
This study proposes a new family of distributions based on the half logistic distribution. With the new family, the baseline distributions gain flexibility through additional shape parameters. The important statistical properties of the proposed family are derived. A new generalization of the Weibull distribution is used to introduce a location-scale regression model for the censored response variable. The utility of the introduced models is demonstrated in survival analysis and estimation of the system reliability. Three data sets are analyzed. According to the empirical results, it is observed that the proposed family gives better results than other existing models.
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Emrah Altun et al.(R1887) Inferring Trends of Point Processes from Non-iid Samples
https://digitalcommons.pvamu.edu/aam/vol16/iss2/2
https://digitalcommons.pvamu.edu/aam/vol16/iss2/2Mon, 06 Dec 2021 10:32:56 PST
We discuss unprecedented, albeit rudimentary, tools to infer the evolution of a point process where the available samples are both truncated and non independently drawn. To achieve this goal, we lay in an intermediate domain between probability models and fuzzy sets, still maintaining probabilistic features of the employed statistics as the reference KPI of the tools. The overall strategy is to frame the problem within the Algorithmic Inference framework and use a sort of kernel trick to distort the seeds of the observed variable so as to render them an iid sample of a random variable in a proper feature space. Numerical results highlight the suitability of the proposed tools.
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Bruno Appolloni(R1504) Second-order Modified Nonstandard Runge-Kutta and Theta Methods for One-dimensional Autonomous Differential Equations
https://digitalcommons.pvamu.edu/aam/vol16/iss2/1
https://digitalcommons.pvamu.edu/aam/vol16/iss2/1Mon, 06 Dec 2021 10:32:53 PST
Nonstandard finite difference methods (NSFD) are used in physical sciences to approximate solutions of ordinary differential equations whose analytical solution cannot be computed. Traditional NSFD methods are elementary stable but usually only have first order accuracy. In this paper, we introduce two new classes of numerical methods that are of second order accuracy and elementary stable. The methods are modified versions of the nonstandard two-stage explicit Runge-Kutta methods and the nonstandard one-stage theta methods with a specific form of the nonstandard denominator function. Theoretical analysis of the stability and accuracy of both modified NSFD methods is presented. Numerical simulations that concur with the theoretical findings are also presented, which demonstrate the computational advantages of the proposed new modified nonstandard finite difference methods.
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Madhu Gupta et al.