Mathematical Modeling

The variety of catastrophe bond issuances can be used for portfolio diversification. However, the structure of catastrophe bonds differs from traditional bonds in that the face value and coupons depend on triggering events. This study aims to build a diversification strategy model framework using probabilistic–possibilistic bijective transformation (PPBT) and credibility measures in fuzzy environments based on the payoff function. The stages of modeling include identifying the trigger distribution; determining the membership degrees for the face value and coupons using PPBT; calculating the average face value and coupons using the fuzzy quantification theory; formulating the fuzzy variables for the yield; defining the function of triangular fuzzy membership for the yield; defining the credibility distribution for the triangular fuzzy variables for the yield; determining the expectation and total variance for the yield; developing a model of the catastrophe bond diversification strategy; the numerical simulation of the catastrophe bond strategy model; and formulating a solution to the simulation model of the diversification strategy using the sequential method, quadratic programming, transformation, and linearization techniques. The simulation results show that the proposed model can overcome the self-duality characteristic not possessed by the possibilistic measures in the fuzzy variables. The results obtained are expected to contribute to describing the yield uncertainty of investing in catastrophe bond assets so that investors can make wise decisions. Full article

A bimodal double log-normal distribution on the real line is proposed using the random sign mixture transform. Its associated statistical inferences are derived. Its parameters are estimated by the maximum likelihood method. The performance of the estimators and the corresponding confidence intervals is checked by simulation studies. Application of the proposed distribution to a real data set from a DNA microarray is presented. Full article

The negative multinomial distribution appears in many areas of applications such as polarimetric image processing and the analysis of longitudinal count data. In previous studies, general formulas for the falling factorial moments and cumulants of the negative multinomial distribution were obtained. However, despite the availability of the moment generating function, no comprehensive formulas for the moments have been calculated thus far. This paper addresses this gap by presenting general formulas for both central and non-central moments of the negative multinomial distribution. These formulas are expressed in terms of binomial coefficients and Stirling numbers of the second kind. Utilizing these formulas, we provide explicit expressions for all central moments up to the fourth order and all non-central moments up to the eighth order. Full article

In this study, a modified anisotropic elastic Weiskopf model for a sandy medium was introduced, satisfying the highest rotational symmetry compatible with a Weiskopf sandiness parameter greater than the unity. The developed approach was applied for computing and comparing head SP waves propagating along the free surface of the halfspace. The comparison revealed a substantial discrepancy in the SP wave pulses detected at the points of observation. The developed models for the generation and detection of SP waves are based on the FEA (finite element analysis) of the inner Lamb problem. Full article

Bioventing is a widely recognized technique for the remediation of petroleum hydrocarbon-contaminated soil. In this study, the objective was to identify an optimal mathematical model that balances accuracy and ease of implementation. A comprehensive review of various models developed for bioventing was conducted wherein the advantages and disadvantages of each model were evaluated and compared regarding the different numerical methods used to solve relevant bioventing equations. After investigating the various assumptions and methods from the literature, an improved foundational bioventing model was developed that characterizes gas flow in unsaturated zones where water and non-aqueous phase liquid (NAPL) are present and immobile, accounting for interphase mass transfer and biodegradation, incorporating soil properties through a rate constant correlation. The proposed model was solved using the finite volume method in OpenFOAM, an independent dimensional open-source coding toolbox. The preliminary simulation results of a simple case indicate good agreement with the exact analytical solution of the same equations. This improved bioventing model has the potential to enhance predictions of the remediation process and support the development of efficient remediation strategies for petroleum hydrocarbon-contaminated soil. Full article

This paper addresses serialized approaches of the routing, modulation level, and spectrum assignment (RMLSA) problem in elastic optical networks, using multiple sequential sub-sets of requests, under Integer Linear Programming (ILP). The literature has reported two-stage serial optimization methods referred to as RML+SA, which retain computational efficiency when the problem grows, compared to the classical one-stage RMLSA optimization approach. However, there still remain numerous issues in terms of the spectrum used that can be improved when compared to the RMLSA solution. Consequently, this paper proposes RML+SA solutions considering multiple sequential sub-sets of requests, split traffic flow, as well as path-oriented and link-oriented routing models. Simulation results on different test scenarios determine that: (a) the multiple sequential sub-sets of request-based models improve computation time without worsening the spectrum usage when compared to just one set of requests optimization approaches, (b) divisible traffic flow approaches show promise in cases where the number of request sub-sets is low compared to the non-divisible counterpart, and (c) path-oriented routing succeeds in improving the used spectrum by increasing the number of candidate routes compared to link-oriented routing. Full article

The unique structural characteristics and special symmetry of columnar jointed rock mass result in its complex mechanical properties and strong anisotropy, which seriously affects the safety of engineering construction. To better simulate natural columnar jointed rock mass, a geometric model reconstruction method based on a single-random movement Voronoi diagram of uniform seed points using the feasible geological parameters of horizontal polygon density, irregular factor, dip angle, strike angle, transverse joint spacing, and transverse joint penetration rate is proposed in this paper. Based on this method, numerical simulation of CJRM models with varying strike angles, dip angles, and irregular factors under uniaxial compression were conducted. The results show that the uniaxial compression strengths versus strike angle and dip angle both decrease with the increase in the irregular factor, showing a U-shape and a gentle W-shape, respectively. The strength anisotropy of the strike angle decreases from 1.1057 to 1.0395 with the increase in the irregular factor, indicating relatively isotropy. With the increase int the irregular factor, the strength anisotropy of the dip angle increases from 4.3381 to 6.7953, indicating an increasing strong anisotropy at a high degree, and the effect of the irregular factor on strength behavior has the strongest and weakest impact at the dip angles of 60° and 90°, respectively. Full article

This article deals with oscillations that occur with a certain combination of parameters in a nonlinear system with elastic bonds, formed by three cylinders pulled together by an elastic thread. The aim of this work was to develop a methodology for studying nonlinear oscillatory systems based on the analysis of the potential energy of a system and the balance of the forces acting on it. The novelty of the work lies in the proposed methods for determining the conditions for the occurrence of vibrations and in those for calculating the threshold value of the elasticity coefficient of an elastic thread, at which an oscillatory process is guaranteed to occur. The differential equations of oscillations were compiled and numerically solved both with and without allowance for friction forces. The critical value of the elasticity coefficient of the thread at which periodic oscillations occurred was determined. A study of the motion of the system was carried out. Full article

We focus on the dual interval control problem of multidimensional objects with delay. We propose a new nonparametric algorithm. In such a case, it is not necessary to determine a parametric structure of the investigated object. Another difficulty lies in the complex nature of the decision-making field as it might not be flexible or convenient for decision-makers to exactly quantify their opinions with crisp numbers. Due to this fact, we introduce the interval-valued observations into the algorithm by means of the single-level constraint interval arithmetic. The results of computational experiments illustrate the effectiveness of the algorithm in the case of using intervals instead of crisp values. Full article

The deterioration rate is a significant aspect of perishable goods. Since perishable items will always deteriorate, there are effective methods for reducing the rate of deterioration. Furthermore, in the existing inventory control literature, the deterioration rate is often viewed as an exogenous component. Keeping this problem in mind, this article develops the perishable inventory control system from the retailer’s perspective in which: (i) the deterioration rate is a controllable factor and suggests a new fresh quality technology (FQT) indicator, (ii) demand is determined by the perishable product’s quality, that is controlled by its rate of deterioration, (iii) the credit duration is predefined, and (iv) shortages are expected. The key goal is to demonstrate that there is an ideal quantity of the order that minimizes the retailer’s overall cost in terms of cycle time and deterioration rate. Finally, theoretical results are validated by solving two numerical illustrations and conducting a sensitivity analysis of the main factors resulting from the following managerial implications: (i) if the range of deterioration is between zero and one then the retailer should invest in the preservation factor to preserve the perishable product and if greater than one the retailer should not invest in the preservation factor, (ii) credit period significantly reduces the total cost. Hence, this trade credit strategy is more beneficial to the model. Full article

The main purpose of this study is to investigate solutions of some integral equations of different classes using a new scheme. This research introduces and implements the new double ARA transform to solve integral and partial integro-differential equations. We introduce basic theorems and properties of the double ARA transform in two dimensions, and some results related to the double convolution theorem and partial derivatives are presented. In addition, to show the validity of the proposed technique, we introduce and solve some examples using the new approach. Full article

The intelligent driver (ID) model characterizes traffic behavior with a constant acceleration exponent and does not follow traffic physics. This results in unrealistic traffic behavior. In this paper, a new microscopic heterogeneous traffic flow model is proposed which improves the performance of the ID model. The forward and lateral distance headways are used to characterize traffic behavior. The stability of the ID and proposed models is examined over a 1000 m circular road with a traffic disturbance after 30 s. The results obtained show that the proposed model is more stable than the ID model. The performance of the proposed and ID models is evaluated over an 1800 m circular road for 150 s with a platoon of 51 vehicles. Results are presented which indicate that traffic evolves realistically with the proposed model. This is because it is based on the lateral distance headway. Full article

Tuberculosis (TB), caused by Mycobacterium tuberculosis is one of the treacherous infectious diseases of global concern. In this paper, we consider a deterministic model of TB infection with the public health education and hospital treatment impact. The effective reproductive number, $R_{ph},$ that measures the potential spread of TB is presented by employing the next generation matrix approach. We investigate local and global stability of the TB-free equilibrium point, endemic equilibrium point, and sensitivity analysis. The analyses of the proposed model show that the model undergoes the phenomenon of backward bifurcation when the effective reproduction number $\left(R_{ph}\right)$ is less than one, where two stable equilibria, namely, the DFE and an EEP coexist. Further, we compute the sensitivity of the impact of each parameter on the effective reproductive number of the model by employing a normalized sensitivity index formula. Numerical simulation of the proposed model was conducted using Maple 2016 and MatLab R2020b software and compared with the theoretical results for illustration purposes. The investigation results can be useful in providing information to policy makers and public health authorities in mitigating the spread of TB infection by public health education and hospital treatment. Full article

This paper describes our construction of a new double transform, which we call the double ARA transform (DARAT). Our novel double-integral transform can be used to solve partial differential equations and other problems. We discuss some fundamental characteristics of our approach, including existence, linearity, and several findings relating to partial derivatives and the double convolution theorem. DARAT can be used to precisely solve a variety of partial differential equations, including the heat equation, wave equation, telegraph equation, Klein–Gordon equation, and others, all of which are crucial for physical applications. Herein, we use DARAT to solve model integral equations to obtain exact solutions. We conclude that our novel method is easier to use than comparable transforms. Full article

In this study, an interactive Ising model having the nearest and prolonged next-nearest neighbors defined on a Cayley tree is considered. Inspired by the results obtained for the one-dimensional Ising model, we will construct the partition function and then calculate the free energy of the Ising model having the prolonged next nearest and nearest neighbor interactions and external field on a two-order Cayley tree using the self-similarity of the semi-infinite Cayley tree. The phase transition problem for the Ising system is investigated under the given conditions. Full article

Well-posedness and generalized well-posedness results are examined for a class of commanded variational inequality problems. In this regard, by using the concepts of hemicontinuity, monotonicity, and pseudomonotonicity of the considered functional, and by introducing the set of approximating solutions of the considered commanded variational inequality problems, we establish several well-posedness and generalized well-posedness results. Moreover, some illustrative examples are provided to highlight the effectiveness of the results obtained in the paper. Full article

Diphtheria is a vaccine-preventable disease in which the outbreaks will not occur if a high enough proportion of individuals in a population are immune. Recent reports reveal that vaccinated individuals with low coverage levels of immunity may be at risk of subclinical diphtheria infection. Therefore, the development of an epidemiology model that will predict the optimal vaccine coverage level needed to prevent the spread of these diseases is crucial. In this paper, a mathematical model for diphtheria transmission with asymptomatic infection, logistic growth, and vaccination is formulated and rigorously analyzed to gain insights into its global dynamical features. The study results show that the disease is eradicated whenever the vaccination coverage is greater than the optimal vaccination coverage level needed for diphtheria eradication. The reported cases of diphtheria in Thailand are applied to estimate the appropriate parameters of the model. Sensitivity analysis reveals the rate of vaccination and the asymptomatic infection are influential factors in controlling and preventing diphtheria. Numerical simulations are illustrated in the theoretical results and show that the incubation period of asymptomatic individuals has an impact on the optimal vaccination coverage level needed for diphtheria eradication. Full article