Math. Comput. Appl., Volume 26, Issue 4 (December 2021) – 17 articles

In this article, Burr III distribution is proposed with a significantly improved functional form. This new modification has enhanced the flexibility of the classical distribution with the ability to model all shapes of hazard rate function including increasing, decreasing, bathtub, upside-down bathtub, and nearly constant. Some of its elementary properties, such as rth moments, sth incomplete moments, moment generating function, skewness, kurtosis, mode, ith order statistics, and stochastic ordering, are presented in a clear and concise manner. The well-established technique of maximum likelihood is employed to estimate model parameters. Middle-censoring is considered as a modern general scheme of censoring. The efficacy of the proposed model is asserted through three applications consisting of complete and censored samples. Full article

The paper contributes majorly in the development of a flexible trigonometric extension of the well-known modified Lindley distribution. More precisely, we use features from the sine generalized family of distributions to create an original one-parameter survival distribution, called the sine modified Lindley distribution. As the main motivational fact, it provides an attractive alternative to the Lindley and modified Lindley distributions; it may be better able to model lifetime phenomena presenting data of leptokurtic nature. In the first part of the paper, we introduce it conceptually and discuss its key characteristics, such as functional, reliability, and moment analysis. Then, an applied study is conducted. The usefulness, applicability, and agility of the sine modified Lindley distribution are illustrated through a detailed study using simulation. Two real data sets from the engineering and climate sectors are analyzed. As a result, the sine modified Lindley model is proven to have a superior match to important models, such as the Lindley, modified Lindley, sine exponential, and sine Lindley models, based on goodness-of-fit criteria of importance. Full article

Let $G=\left(V\right(G),E(G\left)\right)$ be a connected graph with n vertices and m edges. A bijection $f:E\left(G\right)\to \{1,2,\cdots ,m\}$ is an edge labeling of G. For any vertex x of G, we define $\omega \left(x\right)={\sum }_{e\in E\left(x\right)}f\left(e\right)$ as the vertex label or weight of x, where $E\left(x\right)$ is the set of edges incident to x, and f is called a local antimagic labeling of G, if $\omega \left(u\right)\ne \omega \left(v\right)$ for any two adjacent vertices $u,v\in V\left(G\right)$. It is clear that any local antimagic labelling of G induces a proper vertex coloring of G by assigning the vertex label $\omega \left(x\right)$ to any vertex x of G. The local antimagic chromatic number of G, denoted by ${\chi }_{la}\left(G\right)$, is the minimum number of different vertex labels taken over all colorings induced by local antimagic labelings of G. In this paper, we present explicit local antimagic chromatic numbers of $F_n\vee \overline{K_2}$ and $F_n-v$, where $F_n$ is the friendship graph with n triangles and v is any vertex of $F_n$. Moreover, we explicitly construct an infinite class of connected graphs G such that ${\chi }_{la}\left(G\right)={\chi }_{la}(G\vee \overline{K_2})$, where $G\vee \overline{K_2}$ is the join graph of G and the complement graph of complete graph $K_2$. This fact leads to a counterexample to a theorem of Arumugam et al. in 2017, and our result also provides a partial solution to Problem 3.19 in Lau et al. in 2021. Full article

SEIR models are typically conjured for populations in open environments; however, there seems to be a lack of these types of models that deal with infection rates amongst enclosed spaces. We have also seen certain age groups struggle to deal with COVID-19 more than others, and to this end, we have constructed an age-structured SEIR model that incorporates the Gammaitoni–Nucci model, which is used for infective material in an enclosed space with ventilation. We apply some sensitivity analysis to better understand which parameters have the biggest impact on overall infection rates, as well as create a realistic scenario in which we apply our model to see the comparison in sickness rates amongst four different age groups with different ventilation filtration systems (UVGI, HEPA) and differing quanta production rates. Full article

In this work, fractional-order strain theory was applied to construct a novel model that introduces a thermal analysis of a thermoelastic, isotropic, and homogeneous nanobeam. Under supported conditions of fixed aspect ratios, a two-temperature generalized thermoelasticity theory based on one relaxation time was used. The governing differential equations were solved using the Laplace transform, and their inversions were found by applying the Tzou technique. The numerical solutions and results for a thermoelastic rectangular silicon nitride nanobeam were validated and supported in the case of ramp-type heating. Graphs were used to present the numerical results. The two-temperature model parameter, beam size, ramp-type heat, and beam thickness all have a substantial influence on all of the investigated functions. Moreover, the parameter of the ramp-type heat might be beneficial for controlling the damping of nanobeam energy. Full article

In this paper, we study the dynamics of HIV under gene therapy and latency reversing agents. While previous works modeled either the use of gene therapy or latency reversing agents, we consider the effects of a combination treatment strategy. For constant treatment controls, we establish global stability of the disease-free equilibrium and endemic equilibrium based on the value of ${\mathcal{R}}_0.$ We then consider time-dependent controls and formulate an associated optimal control problem that emphasizes reduction of the latent reservoir. Characterizations for the optimal control profiles are found using Pontryagin’s Maximum Principle. We perform numerical simulations of the optimal control model using the fourth-order Runge–Kutta forward-backward sweep method. We find that a combination treatment of gene therapy with latency reversing agents provides better remission times than gene therapy alone. We conclude with a discussion of our findings and future work. Full article

In this paper, we introduce a discrete version of the Pseudo Lindley (PsL) distribution, namely, the discrete Pseudo Lindley (DPsL) distribution, and systematically study its mathematical properties. Explicit forms gathered for the properties such as the probability generating function, moments, skewness, kurtosis and stress–strength reliability made the distribution favourable. Two different methods are considered for the estimation of unknown parameters and, hence, compared with a broad simulation study. The practicality of the proposed distribution is illustrated in the first-order integer-valued autoregressive process. Its empirical importance is proved through three real datasets. Full article

The Korteweg–de Vries equation (KdV) is a mathematical model of waves on shallow water surfaces. It is given as third-order nonlinear partial differential equation and plays a very important role in the theory of nonlinear waves. It was obtained by Boussinesq in 1877, and a detailed analysis was performed by Korteweg and de Vries in 1895. In this article, by using multi-linear estimates in Bourgain type spaces, we prove the local well-posedness of the initial value problem associated with the Korteweg–de Vries equations. The solution is established online for analytic initial data $w_0$ that can be extended as holomorphic functions in a strip around the x-axis. A procedure for constructing a global solution is proposed, which improves upon earlier results. Full article

This paper reviews the interdisciplinary collaboration between Environmental Sciences and Statistics. The usage of statistical methods as a problem-solving tool for handling environmental problems is the key element of this approach. This paper enhances a clear pavement for environmental scientists as well as quantitative researchers for their further collaborative learning with an analytical base. Full article

Nonlocal models are ubiquitous in all branches of science and engineering, with a rapidly expanding range of mathematical and computational applications due to the ability of such models to capture effects and phenomena that traditional models cannot. While spatial nonlocalities have received considerable attention in the research community, the same cannot be said about nonlocality in time, in particular when nonlocal initial conditions are present. This paper aims at filling this gap, providing an overview of the current status of nonlocal models and focusing on the mathematical treatment of such models when nonlocal initial conditions are at the heart of the problem. Specifically, our representative example is given for a nonlocal-in-time problem for the abstract Schrödinger equation. By exploiting the linear nature of nonlocal conditions, we derive an exact representation of the solution operator under assumptions that the spectrum of Hamiltonian is contained in the horizontal strip of the complex plane. The derived representation permits us to establish the necessary and sufficient conditions for the problem’s well-posedness and the existence of its solution under different regularities. Furthermore, we present new sufficient conditions for the existence of the solution that extend the existing results in this field to the case when some nonlocal parameters are unbounded. Two further examples demonstrate the developed methodology and highlight the importance of its computer algebra component in the reduction procedures and parameter estimations for nonlocal models. Finally, a connection of the considered models and developed analysis is discussed in the context of other reduction techniques, concentrating on the most promising from the viewpoint of data-driven modelling environments, and providing directions for further generalizations. Full article

The World Food Studies Simulation Model (WOFOST) model is a daily crop growth and yield forecast model with interactions with the environment, including soil, agricultural management, and especially climate conditions. An El Niño–Southern Oscillation (ENSO) phenomenon directly affected climate change and indirectly affected the rice yield in Thailand. This study aims to simulate rice production in central Thailand using the WOFOST model and to find the relationship between rice yield and ENSO. The meteorological data and information on rice yields of Suphan Buri 1 variety from 2011 to 2018 in central Thailand were used to study the rice yields. The study of rice yield found that the WOFOST model was able to simulate rice yield with a Root Mean Square Error (RMSE) value of 752 kg ha${}^{-1}$, with approximately 16% discrepancy. The WOFOST model was able to simulate the growth of Suphan Buri 1 rice, with an average discrepancy of 16.205%, and Suphan Buri province had the least discrepancy at 6.99%. Most rice yield simulations in the central region were overestimated (except Suphan Buri) because the model did not cover crop damage factors such as rice disease or insect damage. The WOFOST model had good relative accuracy and could respond to estimates of rice yields. When an El Niño phenomenon occurs at Niño 3.4, it results in lower-than-normal yields of Suphan Buri 1 rice in the next 8 months. On the other hand, when a La Niña phenomenon occurs at Niño 3.4, Suphan Buri 1 rice yields are higher than normal in the next 8 months. An analysis of the rice yield data confirms the significant impact of ENSO on rice yields in Thailand. This study shows that climate change leads to impacts on rice production, especially during ENSO years. Full article

In the present paper, we consider an important problem from the application perspective in science and engineering, namely, one-dimensional porous–elastic systems with nonlinear damping, infinite memory and distributed delay terms. A new minimal conditions, placed on the nonlinear term and the relationship between the weights of the different damping mechanisms, are used to show the well-posedness of the solution using the semigroup theory. The solution energy has an explicit and optimal decay for the cases of equal and nonequal speeds of wave propagation. Full article

Providing uninterrupted response service is of paramount importance for emergency medical services, regardless of the operating scenario. Thus, reliable estimates of the time to the critical condition, under which there will be no available servers to respond to the next incoming call, become very useful measures of the system’s performance. In this contribution, we develop a key performance indicator by providing an explicit formula for the average time to the shortage condition. Our analytical expression for this average time is a function of the number of parallel servers and the inter-arrival and service times. We assume exponential distributions of times in our analytical expression, but for evaluating the mean first-passage time to the critical condition under more realistic scenarios, we validate our result through exhaustive simulations with lognormal service time distributions. For this task, we have implemented a simulator in R. Our results indicate that our analytical formula is an acceptable approximation under any situation of practical interest. Full article

When using boundary integral equation methods, we represent solutions of a linear partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor resolution when evaluated closed to (but not on) the boundary. To address this challenge, we provide modified representations of the problem’s solution. Similar to Gauss’s law used to modify Laplace’s double-layer potential, we use modified representations of Laplace’s single-layer potential and Helmholtz layer potentials that avoid the close evaluation problem. Some techniques have been developed in the context of the representation formula or using interpolation techniques. We provide alternative modified representations of the layer potentials directly (or when only one density is at stake). Several numerical examples illustrate the efficiency of the technique in two and three dimensions. Full article

Forest fires have been a major threat to the environment throughout history. In order to mitigate its consequences, we present, in a first of a series of works, a mathematical model with the purpose of predicting fire spreading in a given land portion divided into patches, considering the area and the rate of spread of each patch as inputs. The rate of spread can be estimated from previous knowledge on fuel availability, weather and terrain conditions. We compute the time duration of the spreading process in a land patch in order to construct and parametrize a landscape network, using cellular automata simulations. We use the multilayer network model to propose a network of networks at the landscape scale, where the nodes are the local patches, each with their own spreading dynamics. We compute some respective network measures and aim, in further work, for the establishment of a fire-break structure according to increasing accuracy simulation results. Full article

A serious and ubiquitous issue in existing mapped WENO schemes is that most of them can hardly preserve high resolutions, but in the meantime prevent spurious oscillations in the solving of hyperbolic conservation laws with long output times. Our goal for this article was to address this widely known problem. In our previous work, the order-preserving (OP) criterion was originally introduced and carefully used to devise a new mapped WENO scheme that performs satisfactorily in long simulations, and hence it was indicated that the OP criterion plays a critical role in the maintenance of low-dissipation and robustness for mapped WENO schemes. Thus, in our present work, we firstly defined the family of mapped WENO schemes, whose mappings meet the OP criterion, as OP-Mapped WENO. Next, we attentively took a closer look at the mappings of various existing mapped WENO schemes and devised a general formula for them. That helped us to extend the OP criterion to the design of improved mappings. Then, we created a generalized implementation of obtaining a group of OP-Mapped WENO schemes, named MOP-WENO-X, as they are developed from the existing mapped WENO-X schemes, where the notation “X” is used to identify the version of the existing mapped WENO scheme. Finally, extensive numerical experiments and comparisons with competing schemes were conducted to demonstrate the enhanced performances of the MOP-WENO-X schemes. Full article

A method recently advanced as the conformable Euler method (CEM) for the finite difference discretization of fractional initial value problem $D_t^{\alpha }y\left(t\right)=f\left(t;\mathrm{y}\left(t\right)\right),y\left(t_0\right)=y_0,a\le t\le b$, and used to describe hyperchaos in a financial market model, is shown to be valid only for $\alpha =1$. The property of the conformable fractional derivative (CFD) used to show this limitation of the method is used, together with the integer definition of the derivative, to derive a modified conformable Euler method for the initial value problem considered. A method of constructing generalized derivatives from the solution of the non-integer relaxation equation is used to motivate an alternate definition of the CFD and justify alternative generalizations of the Euler method to the CFD. The conformable relaxation equation is used in numerical experiments to assess the performance of the CEM in comparison to that of the alternative methods. Full article