This paper summarizes an investigation of certain operating parameters on the viscosity of petroleum emulsions. The production of crude oil is accompanied by emulsified water production, which comes along with various challenges like corroding the transport systems and catalysts poisoning during petroleum refining in the downstream. Several process variables are believed to affect the ease with which emulsified water can be separated from emulsions. Some of the issues have not been extensively examined in the literature. The simplicity with which water is separated from petroleum changes with age (after formation) of the emulsion; notwithstanding, this subject has not been investigated broadly in literature. This study tries to assess the correlation between aging time, water cut, crude oil viscosity, water viscosity and amount of solids and viscosity of petroleum emulsions. To achieve that, a response surface methodology (RSM) based on Box-Behnken design (BBD) was used to design the experiment. Synthetic emulsions were prepared from an Offshore Malaysian Crude oil based on the DoE design and were aged for 7 days. The emulsions viscosities were measured at 60-degree Celsius using an electromagnetic viscometer (EV100). The broad pressure and temperature range of the HPHT viscometer permit the imitation of acute conditions under which such emulsions may form. The data obtained from the RSM analysis was used to develop a prediction model using gene expression programming (GEP). It was discovered that the viscosity of water has no effect on the viscosities of the studied emulsions, as does the water cut and amount of solids. The most significant factor that affects emulsion viscosity is the aging time, with the emulsion becoming more viscous over time. This is believed to be imminent because of variations in the interfacial film structure. This is followed by the amount of solids, also believed to be as a result of increasing coverage at the interface of the water droplets, limiting the movements of the dispersed droplets (reduced coalescence), thereby increasing the viscosity of the emulsions.

The indefinite inner product defined by $J=\text{diag}\left(j_1,\dots ,j_n\right),j_k\in \left\{-1,+1\right\}$, arises frequently in some applications, such as the theory of relativity and the research of the polarized light. This indefinite scalar product is referred to as hyperbolic inner product. In this paper, we introduce three indefinite iterative methods: indefinite Arnoldi’s method, indefinite Lanczos method (ILM), and indefinite full orthogonalization method (IFOM). The indefinite Arnoldi’s method is introduced as a process that constructs a J-orthonormal basis for the nondegenerated Krylov subspace. The ILM method is introduced as a special case of the indefinite Arnoldi’s method for J-Hermitian matrices. IFOM is mentioned as a process for solving linear systems of equations with J-Hermitian coefficient matrices. Finally, by providing numerical examples, the FOM, IFOM, and ILM processes have been compared with each other in terms of the required time for solving linear systems and also from the point of the number of iterations.

We consider functional data analysis when the observations at each location are functional rather than scalar. When the dynamic of underlying functional-valued process at each location is of interest, it is desirable to recover partial derivatives of a sample function, especially from sparse and noise-contaminated measures. We propose a novel approach based on estimating derivatives of eigenfunctions of marginal kernels to obtain a representation for functional-valued process and its partial derivatives in a unified framework in which the number of locations and number of observations at each location for each individual can be any rate relative to the sample size. We derive almost sure rates of convergence for the procedures and further establish consistency results for recovered partial derivatives.

In a previous paper, we have shown that forward use of the steady-state difference equations arising from homogeneous discrete-state space Markov chains may be subject to inherent numerical instability. More precisely, we have proven that, under some appropriate assumptions on the transition probability matrix P, the solution space S of the difference equation may be partitioned into two subspaces $S=S_1\oplus S_2$, where the stationary measure of P is an element of $S_1$, and all solutions in $S_1$ are asymptotically dominated by the solutions corresponding to $S_2$. In this paper, we discuss the analogous problem of computing hitting probabilities of Markov chains, which is affected by the same numerical phenomenon. In addition, we have to fulfill a somewhat complicated side condition which essentially differs from those conditions one is usually confronted with when solving initial and boundary value problems. To extract the desired solution, an efficient and numerically stable generalized-continued-fraction-based algorithm is developed.

In this paper, we propose and study a diagonal inexact version of Bregman proximal methods, to solve convex optimization problems with and without constraints. The proposed method forms a unified framework for existing algorithms by providing others.

In this paper, we study the resolution of a permutation flow shop problem with sequence-independent setup time. The objective is to minimize the maximum of job completion time, also called the makespan. In this contribution, we propose three methods of resolution, a mixed-integer linear programming (MILP) model; two heuristics, the first based on Johnson’s rule and the second based on the NEH algorithm; and finally two metaheuristics, the iterative local search algorithm and the iterated greedy algorithm. A set of test problems is simulated numerically to validate the effectiveness of our resolution approaches. For relatively small-size problems, it has been revealed that the adapted NEH heuristic has the best performance than that of the Johnson-based heuristic. For the relatively medium and large problems, the comparative study between the two metaheuristics based on the exploration of the neighborhood shows that the iterated greedy algorithm records the best performances.

In this paper, analytic approximation to the heat and mass transfer characteristics of a two-dimensional time-dependent flow of Williamson nanofluids over a permeable stretching sheet embedded in a porous medium has been presented by considering the effects of magnetic field, thermal radiation, and chemical reaction. The governing partial differential equations along with the boundary conditions were reduced to dimensionless forms by using suitable similarity transformation. The resulting system of ordinary differential equations with the corresponding boundary conditions was solved via the homotopy analysis method. The results of the study show that velocity, temperature, and concentration boundary layer thicknesses generally decrease as we move away from the surface of the stretching sheet and the Williamson parameter was found to retard the velocity but it enhances the temperature and concentration profiles near the surface. It was also found that increasing magnetic field strength, thermal radiation, or rate of chemical reaction speeds up the mass transfer but slows down the heat transfer rates in the boundary layer. The results of this study were compared with some previously published works under some restrictions, and they are found in excellent agreement.

In this paper, a collocation method using sinc functions and Chebyshev wavelet method is implemented to solve linear systems of Volterra integro-differential equations. To test the validity of these methods, two numerical examples with known exact solution are presented. Numerical results indicate that the convergence and accuracy of these methods are in good a agreement with the analytical solution. However, according to comparison of these methods, we conclude that the Chebyshev wavelet method provides more accurate results.

In this paper, an initial value method for solving a weakly coupled system of two second-order singularly perturbed Convection–diffusion problems exhibiting a boundary layer at one end is proposed. In this approach, the approximate solution for the given problem is obtained by solving, a coupled system of initial value problem (namely, the reduced system), and two decoupled initial value problems (namely, the layer correction problems), which are easily deduced from the given system of equations. Both the reduced system and the layer correction problems are independent of perturbation parameter, $\epsilon$. These problems are then solved analytically and/or numerically, and those solutions are combined to give an approximate solution to the problem. Further, error estimates are derived and examples are provided to illustrate the method.

Pneumocccal pneumonia, a secondary bacterial infection that follows influenza A infection, is responsible for morbidity and mortality in children, elderly, and immunocomprised groups. A mathematical model to study the global stability of pneumococcal pneumonia with awareness and saturated treatment is presented. The basic reproduction number, $R_0$, is computed using the next generation matrix method. The results show that if , the disease-free steady state is locally asymptotically stable; thus, pneumococcal pneumonia would be eradicated in the population. On the other hand, if $R_0>1$ the endemic steady state is globally attractive; thus, the disease would persist in the population. The quadratic-linear and Goh–Voltera Lyapunov functionals approach are used to prove the global stabilities of the disease-free and endemic steady states, respectively. The sensitivity analysis of $R_0$ on model parameters shows that, it is positively sensitive to the maximal effective rate before antibiotic resistance awareness, rate of relapse encountered in administering treatment, and loss of information by aware susceptible individuals. Contrarily, the sensitivity analysis of $R_0$ on model parameters is negatively sensitive to recovery rate due to treatment and the rate at which unaware susceptible individuals become aware. The numerical analysis of the model shows that awareness about antibiotic resistance and treatment plays a significant role in the control of pneumococcal pneumonia.

This paper is concerned with an optimal control problem governed by a Kirchhoff-type variational inequality. The existence of multiplicity solutions for the Kirchhoff-type variational inequality is established by using some nonlinear analysis techniques and the variational method, and the existence results of an optimal control for the optimal control problem governed by a Kirchhoff-type variational inequality are derived.

In this paper, we propose a discrete mathematical model that describes the interaction between the classes of drinkers, namely, potential drinkers $\left(P\right)$, moderate drinkers $\left(M\right)$, heavy drinkers $\left(H\right)$, poor heavy drinkers $\left(T^p\right)$, rich heavy drinkers $\left(T^r\right)$, and quitters of drinking $\left(Q\right)$. We also focus on the importance of treatment within addiction treatment centers aiming to find the optimal strategies to minimize the number of drinkers and maximize the number of heavy drinkers who join addiction treatment centers. We use three controls which represent awareness programs through media and education for the potential drinkers, efforts to encourage the heavy drinkers to join addiction treatment centers, and psychological support with follow-up for the individuals who quit drinking. We use Pontryagin’s maximum principle in discrete time to characterize these optimal controls. The resulting optimality system is solved numerically by Matlab. Consequently, the obtained results confirm the performance of the optimization strategy.

Magnetohydrodynamics free convection flow of incompressible fluids over corrugated vibrating bottom surface with Hall currents and heat and mass transfers considering heat flux is discussed. The corrugation patterns suggested are sinusoidal in nature. The governing equations are solved by the explicit finite difference numerical method of the forward-time backward-space scheme to obtain the analytical results for velocity, concentration, and temperature profiles. The unsteady resultant velocities, concentration, and temperature for various values of physical parameters are discussed in detail, and it is shown that they have significant effects on the fluid flow, and heat and mass transfers are shown graphically.

Sub-Saharan Africa harbours the majority of the burden of Lassa fever. Clinical diseases, as well as high seroprevalence, have been documented in Nigeria, Sierra Leone, Liberia, Guinea, Ivory Coast, Ghana, Senegal, Upper Volta, Gambia, and Mali. Deaths from Lassa fever occur all year round but naturally peak during the dry season. Annually, the number of people infected is estimated at 100,000 to 300,000, with approximately 5,000 deaths. There have been some work done on the dynamics of Lassa fever disease transmission, but to the best of our knowledge, none has been able to capture the seasonal variation of Mastomys rodent population and its impact on the transmission dynamics. In this work, a periodically forced seasonal nonautonomous system of a nonlinear ordinary differential equation is developed that captures the dynamics of Lassa fever transmission and seasonal variation in the birth of Mastomys rodents where time was measured in days to capture seasonality. It was shown that the model is epidemiologically meaningful and mathematically well posed by using the results from the qualitative properties of the solution of the model. A time-dependent basic reproduction number $R_L\left(t\right)$ is obtained such that its yearly average is written as , when the disease does not invade the population (means that the number of infected humans always decreases in the seasons of transmission), and ${\tilde{R}}_L>1$, when the disease remains constantly and is invading the population, and it was detected that ${\tilde{R}}_L\ne R_L$. We also performed some evaluation of the Lassa fever disease intervention strategies using the elasticity of the equilibrial prevalence in order to predict the optimal intervention strategies that can be useful in guiding the local national control program on Lassa fever disease to make a proper decision on the intervention packages. Numerical simulations were carried out to illustrate the analytical results, and we found that the numerical simulations of the model showed that possible combined intervention strategies would reduce the spread of the disease. It was established that, to eliminate Lassa fever disease, treatments with ribavirin must be provided early to reduce mortality and other preventive measures like an educational campaign, community hygiene, isolation of infected humans, and culling/destruction of rodents must be applied to also reduce the morbidity of the disease. Finally, the obtained results gave a primary framework for planning and designing cost-effective strategies for good interventions in eliminating Lassa fever.

A mathematical model is proposed to study the dynamics of the transmission of rabies, incorporating predation of dogs by humans. The model is shown to have a unique disease-free equilibrium which is globally asymptotically stable whenever ${\mathrm{ℛ}}_0\le 1$. Local sensitivity analysis suggests that the disease can be controlled through reducing contact with infected dogs, increasing immunization of dogs, screening recruited dogs, culling of infected dogs, and use of dog meat as a delicacy.

The study of pollution movement is an important basis for solving water quality problems, which is of vital importance in almost every country. This research proposes the motion of flowing pollution by using a mathematical model in one-dimensional advection-dispersion equation which includes terms of decay and enlargement process. We are assuming an added pollutant sources along the river in two cases: uniformly and exponentially increasing terms. The unsteady state analytical solutions are obtained by using the Laplace transformation, and the finite difference technique is utilized for numerical solutions. Solutions are compared by relative error values. The result appears acceptable between the analytical and numerical solutions. Varying the value of the rate of pollutant addition along the river $\left(q\right)$ and the arbitrary constant of exponential pollution source term $\mathrm{(\lambda )}$ is displayed to explain the behavior of the incremental concentration. It is shown that the concentration increases as $q$ and $\lambda$ increase, and the exponentially increasing pollution source is a suitable model for the behavior of incremental pollution along the river. The results are presented and discussed graphically. This work can be applied to other physical situations described by advection-dispersion phenomena which are affected by the increase of those source concentrations.

In this paper, we suggest a new patch condition for nonconforming mixed finite elements (MFEs) on parallelepiped and provide a framework for the convergence. Also, we introduce a new family of nonconforming MFE space satisfying the new patch condition. The numerical experiments show that the new MFE shows optimal order convergence in $H\left(\text{div}\right)$ and $L^2$-norm for various problems with discontinuous coefficient case.

The focus of this work lies on proving the existence theorem of a unique state vector solution (Stvs) of the triple nonlinear hyperbolic boundary value problem (TNHBVP) when the classical continuous control vector (CCCVE) is fixed by using the Galerkin method (Galm), proving the existence theorem of a unique constraints classical continuous optimal control vector (CCCOCVE) with vector state constraints (equality EQVC and inequality INEQVC). Also, it consists of studying for the existence and uniqueness adjoint vector solution (Advs) of the triple adjoint vector equations (TAEqs) associated with the considered triple state equations (Tsteqs). The Fréchet Derivative (Frde.) of the Hamiltonian (HAM) is found. At the end, the theorems for the necessary conditions and the sufficient conditions of optimality (Necoop and Sucoop) are achieved.

Let $G=\left(V,E\right)$ be a graph, and two players Alice and Bob alternate turns coloring the vertices of the graph $G$ a proper coloring where no two adjacent vertices are signed with the same color. Alice's goal is to color the set of vertices using the minimum number of colors, which is called game chromatic number and is denoted by ${\chi }_g\left(G\right)$, while Bob's goal is to prevent Alice's goal. In this paper, we investigate the game chromatic number ${\chi }_g\left(G\right)$ of Generalized Petersen Graphs $GP\left(n,k\right)$ for $k\ge 3$ and arbitrary $n$, $n$-Crossed Prism Graph, and Jahangir Graph $J_{n,m}$.

In this paper, we study the solvability of a class of nonlinear multiorder Caputo fractional differential equations with integral and antiperiodic boundary conditions. By using some fixed point theorems including the Banach contraction mapping principle and Schaefer’s fixed point theorem, we obtain new existence and uniqueness results for our given problem. Also, we give some examples to illustrate our main results.

A Value-at-Risk (VaR) forecast may be calculated for the case of a random loss alone and/or of a random loss that depends on another random loss. In both cases, the VaR forecast is obtained by employing its (conditional) probability distribution of loss data, specifically the quantile of loss distribution. In practice, we have an estimative VaR forecast in which the distribution parameter vector is replaced by its estimator. In this paper, the quantile-based estimative VaR forecast for dependent random losses is explored through a simulation approach. It is found that the estimative VaR forecast is more accurate when a copula is employed. Furthermore, the stronger the dependence of a random loss to the target loss, in linear correlation, the larger/smaller the conditional mean/variance. In any dependence measure, generally, stronger and negative dependence gives a higher forecast. When there is a tail dependence, the use of upper and lower tail dependence provides a better forecast instead of the single correlation coefficient.

This paper is concerned with binary quadratic programs (BQPs), which are among the most well-studied classes of nonlinear integer optimization problems because of their wide variety of applications. While a number of different solution approaches have been proposed for tackling BQPs, practitioners need techniques that are both efficient and easy to implement. We revisit two of the most widely used linearization strategies for BQPs and examine the effectiveness of enhancements to these formulations that have been suggested in the literature. We perform a detailed large-scale computational study over five different classes of BQPs to compare these two linearizations with a more recent linear reformulation and direct submission of the nonlinear integer program to an optimization solver. The goal is to provide practitioners with guidance on how to best approach solving BQPs in an effective and easily implemented manner.

Time series analysis and prediction are major scientific challenges that find their applications in fields as diverse as finance, biology, economics, meteorology, and so on. Obtaining the method with the least prediction error is one of the difficult problems of financial market and investment analysts. State space modelling is an efficient and flexible method for statistical inference of a broad class of time series and other data. The neural network is an important tool for analyzing time series especially when it is nonlinear and nonstationary. Essential tools for the study of Box-Jenkins methodology, neural networks, and extended Kalman filter were put together. We examine the use of the nonlinear autoregressive neural network method as a prediction technique for financial time series and the application of the extended Kalman filter algorithm to improve the accuracy of the model. As application on a real example, we are analyzing the time series of the daily price of steel over a 790-day period for establishing the superiority of this method over other existing methods. The simulation results using MATLAB and R software show that the model is capable of producing a reasonable accuracy.

A collection of oscillatory basis functions generated via an integral equation is investigated here. This is a new approach in the harmonic analysis as we are able to interpret phenomena with damping and amplifying oscillations other than classical Fourier-like periodic waves. The proposed technique is tested with a data set of dengue incidence, where different types of influences prevail. An intermediate transform supported by the Laplace transform is available. It facilitates parameter estimation and strengthens the extraction of hidden influencing accumulations. This mechanistic work can be extended as a tool in signal processing that encounters oscillatory and accumulated effects.

In this paper, an alternative strategy for real-time control of active distribution network voltage is developed, not by controlling the bus voltage as in the various centralized, decentralized, and local approaches presented in literature but rather by only eliminating the impact produced by active and reactive power of distributed generation (DG) units on the voltage of all network nodes and keeping the traditional voltage control systems dealing with the same constraints of passive systems. In literature, voltage deterioration introduced by DGs has been reported as one of the main obstacles for the interconnection of large amounts of DG units to the existing networks. In this paper, the novel control strategy is based on a sensitivity formula developed to calculate the compensation needed for additional distributed flexible AC transmission system (D-FACTS) devices to push and pull the exact reactive power and to eliminate the impact produced by DGs on the network voltage profile. The criteria of the allocation of the var devices and the required network reinforcement are developed in this paper, considering all possible topology structures, and an innovative codification method is introduced to reduce the needed computation time and communication data to actualize the sensitivity coefficients and get the proposed control approach flexible with network topology reconfiguration. The risk of the conflict of the proposed control system with the traditional voltage equipment is reduced due to the fast capability of D-FACTS devices to regulate their reactive power in finer granularity. A case study of two meshed IEEE 15-bus feeders is introduced to compare the voltage behavior with and without the presence of DG units and to evaluate the total system losses. The proposed method could be used for the interconnection of the first generation units in emerging networks, which does not yet have an active voltage control strategy, as it could be used for DG units not able to be connected to existing centralized control systems and it could also be used as the principal voltage control strategy, with the extension for several neighboring units and the preservation of the traditional voltage control systems.

This paper is aimed at presenting thermal slip flow driven by oscillatory pressure gradient in a deformable microchannel of elliptic cross-section. The fully developed flow of Newtonian fluid is considered, and Navier slip is applied on the boundary. The boundary value problem is formulated and applied to the coronary blood flow-heat transfer phenomenon during thermotherapy treatment. Its semianalytical solutions of velocity and temperature fields are carried out by the Ritz method. The effects of oscillatory wall and slip length on velocity and temperature fields of blood are investigated.

The importance of soft separation axioms comes from their vital role in classifications of soft spaces, and their interesting properties are studied. This article is devoted to introducing the concepts of $tt$-soft semi-$T_i\left(i=0,1,2,3,4\right)$ and $tt$-soft semiregular spaces with respect to ordinary points. We formulate them by utilizing the relations of total belong and total nonbelong. The advantages behind using these relations are, first, generalization of existing comparable properties on general topology and, second, eliminating the stability shape of soft open and closed subsets of soft semiregular spaces. By some examples, we show the relationships between them as well as with soft semi-$T_i\left(i=0,1,2,3,4\right)$ and soft semiregular spaces. Also, we explore under what conditions they are kept between soft topology and its parametric topologies. We characterize a $tt$-soft semiregular space and demonstrate that it guarantees the equivalence of $tt$-soft semi-$T_i\left(i=0,1,2\right)$. Further, we investigate some interrelations of them and some soft topological notions such as soft compactness, product soft spaces, and sum of soft topological spaces. Finally, we define a concept of semifixed soft point and study its main properties.

We propose an optimal control strategy by conducting awareness campaigns for diabetics about the severity of complications of diabetes and the negative impact of an unbalanced lifestyle and the surrounding environment, as well as treatment and psychological follow-up. Pontryagin’s maximum principle is used to characterize the optimal controls, and the optimality system is solved by an iterative method. Finally, some numerical simulations are performed to verify the theoretical analysis using MATLAB.

This study examined the applicability of artificial neural network models in modelling univariate time series ambulance demand for short-term forecasting horizons in Zimbabwe. Bulawayo City Councils’ ambulance services department was used as a case study. Two models, feed-forward neural network (FFNN) and seasonal autoregressive integrated moving average, (SARIMA) were developed using monthly historical data from 2010 to 2017 and compared against observed data for 2018. The mean absolute error (MAE), root mean square error (RMSE), and paired sample $t$-test were used as performance measures. Calculated performance measures for FFNN were MAE (94.0), RMSE (137.19), and the test statistic value whilst corresponding values for SARIMA were 105.71, 125.28, and $p=0.005\left(<0.05\right)$, respectively. Findings of this study suggest that the FFNN model is inclined to value estimation whilst the SARIMA model is directional with a linear pattern over time. Based on the performance measures, the parsimonious FFNN model was selected to predict short-term annual ambulance demand. Demand forecasts with FFNN for 2019 reflected the expected general trends in Bulawayo. The forecasts indicate high demand during the months of January, March, September, and December. Key ambulance logistic activities such as vehicle servicing, replenishment of essential equipment and drugs, staff training, leave days scheduling, and mock drills need to be planned for April, June, and July when low demand is anticipated. This deliberate planning strategy would avoid a dire situation whereby ambulances are available but without adequate staff, essential drugs, and equipment to respond to public emergency calls.

Lassa fever is an animal-borne acute viral illness caused by Lassa virus. It poses a serious health challenge around the world today, especially in West African countries like Ghana, Benin, Guinea, Liberia, Mali, Sierra Leone, and Nigeria. In this work, we formulate a multiple-patch Lassa fever model, where each patch denotes a socioeconomic class (SEC). Some of the important epidemiological features such as basic reproduction number of the model were determined and analysed accordingly. We further investigated how varying SECs affect the transmission dynamics of Lassa fever. We analysed the required state at which each SEC is responsible in driving the Lassa fever disease outbreak. Sensitivity analyses were carried out to determine the importance of model parameters to the disease transmission and prevalence. We carried out numerical simulation to support our analytical results. Finally, we extend some of the results of the 2-patch model to the general $n$-patch model.

Health insurance is considered to be a special type of nonlife insurance with two important features. First, compared with property insurance, health insurance provides valuable hedge against unpredictable shocks to health status, instead of loss on property. Therefore, a modified utility function that describes the trade-off between health and wealth should be applied in optimal indemnity design. Second, in the case that the insured is severely or critically ill, with necessary medical treatment, the insured may not fully recover from an illness or an injury. The doctor usually communicates with the patient to set up a personalized treatment plan and explains clearly about the expected outcome beforehand. Hence, there is some probability that health insurance helps to rescue the insured from disastrous financial burden, but it still yields a lower utility of health. By taking these special features into account, we formulate the optimization problem and characterize the optimal solutions via the Lagrange multiplier method and optimal control technique. Finally, we examine our optimal contracts by numerical illustration. Our research work gives new insights into health insurance design.

For dealing numerically with the infinite-state-space Markov chains, a truncation of the state space is inevitable, that is, an approximation by a finite-state-space Markov chain has to be performed. In this paper, we consider level-dependent quasi-birth-death processes, and we focus on the computation of stationary expectations. In previous literature, efficient methods for computing approximations to these characteristics have been suggested and established. These methods rely on truncating the process at some level $N$, and for $N\to \infty$, convergence of the approximation to the desired characteristic is guaranteed. This paper’s main goal is to quantify the speed of convergence. Under the assumption of an $f$-modulated drift condition, we derive terms for a lower bound and an upper bound on stationary expectations which converge quickly to the same value and which can be efficiently computed.

In this paper, we proposed a new four-parameter Extended Gumbel type-2 distribution which can further be split into the Lehman type I and type II Gumbel type-2 distribution by using a generalized exponentiated $G$ distribution. The distributional properties of the proposed distribution have been studied. We derive the $p$th moment; thus, we generalize some results in the literature. Expressions for the density, moment-generating function, and $r$th moment of the order statistics are also obtained. We discuss estimation of the parameters by maximum likelihood and provide the information matrix of the developed distribution. Two life data, which consist of data on cancer remission times and survival times of pigs, were used to show the applicability of the Extended Gumbel type-2 distribution in modelling real life data, and we found out that the new model is more flexible than its submodels.

In order to bring the new coronavirus pandemic in the country under control, the government of Sri Lanka implemented a set of control strategies including social distancing, quarantine, lockdowns, travel restrictions, and isolation of villages. The aim of this study is to investigate the effectiveness of the overall control process with the aid of classical compartment models and network models. Our results indicate that the prevailing control strategies are effective with at least 50% contact rate reduction or with at least 40% isolation of the contact history of infected population.

A set of linear second-order differential equations is converted into a semigroup, whose algebraic structure is used to generate novel equations. The Lagrangian formalism based on standard, null, and nonstandard Lagrangians is established for all members of the semigroup. For the null Lagrangians, their corresponding gauge functions are derived. The obtained Lagrangians are either new or generalization of those previously known. The previously developed Lie group approach to derive some equations of the semigroup is also described. It is shown that certain equations of the semigroup cannot be factorized, and therefore, their Lie groups cannot be determined. A possible solution of this problem is proposed, and the relationship between the Lagrangian formalism and the Lie group approach is discussed.

In this paper, we present a new family of methods for finding simple roots of nonlinear equations. The convergence analysis shows that the order of convergence of all these methods is three. The originality of this family lies in the fact that these sequences are defined by an explicit expression which depends on a parameter $p$ where $p$ is a nonnegative integer. A first study on the global convergence of these methods is performed. The power of this family is illustrated analytically by justifying that, under certain conditions, the method convergence’s speed increases with the parameter $p$. This family’s efficiency is tested on a number of numerical examples. It is observed that our new methods take less number of iterations than many other third-order methods. In comparison with the methods of the sixth and eighth order, the new ones behave similarly in the examples considered.

This work considers the model order reduction approach for parametrized viscous fingering in a horizontal flow through a 2D porous media domain. A technique for constructing an optimal low-dimensional basis for a multidimensional parameter domain is introduced by combining $K$-means clustering with proper orthogonal decomposition (POD). In particular, we first randomly generate parameter vectors in multidimensional parameter domain of interest. Next, we perform the $K$-means clustering algorithm on these parameter vectors to find the centroids. POD basis is then generated from the solutions of the parametrized systems corresponding to these parameter centroids. The resulting POD basis is then used with Galerkin projection to construct reduced-order systems for various parameter vectors in the given domain together with applying the discrete empirical interpolation method (DEIM) to further reduce the computational complexity in nonlinear terms of the miscible flow model. The numerical results with varying different parameters are demonstrated to be efficient in decreasing simulation time while maintaining accuracy compared to the full-order model for various parameter values.

In this paper, the analyses of traffic evolution on the road network of a roundabout having three entrances and three exiting legs are conducted from macroscopic point of view. The road networks of roundabouts are modeled as a merging and diverging types $1\times 2$ and $2\times 1$ junctions. To study traffic evolution at junction, two cases have been considered, namely, demand and supply limited cases. In each case, detailed mathematical analysis and numerical tests have been presented. The analysis in the case of demand limited showed that rarefaction wave fills the portion of the road network in time. In the contrary, in supply limited case, traffic congestion occurs at merging junctions and shock wave propagating back results in reducing the performance of a roundabout to control traffic dynamics. Also, we illustrate density and flux profiles versus space discretization at different time steps via numerical simulation with the help of Godunov scheme.

This paper deals with the computation of invariant measures and stationary expectations for discrete-time Markov chains governed by a block-structured one-step transition probability matrix. The method generalizes in some respect Neuts’ matrix-geometric approach to vector-state Markov chains. The method reveals a strong relationship between Markov chains and matrix continued fractions which can provide valuable information for mastering the growing complexity of real-world applications of large-scale grid systems and multidimensional level-dependent Markov models. The results obtained are extended to continuous-time Markov chains.

The study scrutinizes the effects of thermal radiation, heat generation, and induced magnetic field on steady, fully developed hydromagnetic free convection flow of an incompressible viscous and electrically conducting couple stress fluid in a vertical channel. The channel walls are maintained at an isoflux-isothermal condition, such that the left channel wall is maintained at a constant heat flux. In contrast, the right channel wall is maintained at a constant temperature. The governing simultaneous equations are solved analytically utilizing the method of undetermined coefficient, and closed form solutions in dimensionless form have been acquired for the velocity field, the induced magnetic field, and the temperature field. The expression for the induced current density has been also obtained. A parametric study for the velocity, temperature, and induced magnetic field profiles, as well as for the skin-friction coefficient, Nusselt number, and induced current density, is conducted and discussed graphically.

In this research, the color system was analyzed according to the International Lighting Commission (CIE) standard by studying the theoretical aspect of the general color system according to the latest communication theories of the visual image supported by mathematical equations and illustrations supporting the relevant hypotheses and then a comparison of evolution. There is an enormous use in color spaces and systems according to their own use, where the use of colors has become in various areas including television systems; computer systems; industry and product colors; printing of all kinds of black and white and color; paint colors for buildings, houses, and cities; and many other color-related uses. The development of color spaces and systems from 1931 to the present day has expanded a lot, and this led to the emergence of new areas of color systems characterized by accuracy and beauty and became the color of the subcolors according to the desire of the customer and the quality of use. The development of color systems has an impact on visual communication such as television broadcasting systems, medical image processing, and video signal processing, as well as in the field of computer such as graphic equipment and printing.

The purpose of this paper is to prove some new fixed point theorem and common fixed point theorems of a commuting family of order-preserving mappings defined on an ordered set, which unify and generalize some relevant fixed point theorems.

In this paper, a nonlinear deterministic model for the dynamics of corruption is proposed and analysed qualitatively using the stability theory of differential equations. The basic reproduction number with respect to the corruption-free equilibrium is obtained using next-generation matrix method. The conditions for local and global asymptotic stability of corruption-free and endemic equilibria are established. From the analysis using center manifold theory, the model exhibits forward bifurcation. Then, the model was extended by reformulating it as an optimal control problem, with the use of two time-dependent controls to assess the impact of corruption on human population, namely, campaigning about corruption through media and advertisement and exposing corrupted individuals to jail and giving punishment. By using Pontryagin’s maximum principle, necessary conditions for the optimal control of the transmission of corruption were derived. From the numerical simulation, it was found that the integrated control strategy must be taken to fight against corruption.

Finding the solutions of nonlinear operator equations has been a subject of research for decades but has recently attracted much attention. This paper studies the convergence of a newly introduced viscosity implicit iterative algorithm to a fixed point of a nonexpansive mapping in Banach spaces. Our technique is indispensable in terms of explicitly clarifying the associated concepts and analysis. The scheme is effective for obtaining the solutions of various nonlinear operator equations as it involves the generalized contraction. The results are applied to obtain a fixed point of $\lambda$-strictly pseudocontractive mappings, solution of $\alpha$-inverse-strongly monotone mappings, and solution of integral equations of Fredholm type.

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics.

It has been reported that unprotected contact with the dead bodies of infected individuals is a plausible way of Nipah virus transmission. An SIRD model is proposed in this paper to investigate the impact of unprotected contact with dead bodies of infected individuals before burial or cremation and their disposal rate on the dynamics of Nipah virus infection. The model is analyzed, and the reproduction number is computed. It is established that the disease-free state is globally asymptotically stable when the reproduction number is less than unity and unstable if it is greater than unity. By using the central manifold theory, we observe that the endemic equilibrium is locally stable near to unity. It is concluded that minimizing unsafe contact with the infected dead body and/or burial or cremation as fast as possible contributes positively. Further, the numerical simulations for the given choice of data and initial conditions illustrate that the endemic state is stable and the disease persists in the community when the reproduction number is greater than one.

This work is aimed at formulating a mathematical model for the control of mosquito population using sterile insect technology (SIT). SIT is an environmental friendly method, which depends on the release of sterile male mosquitoes that compete with wild male mosquitoes and mate with wild female mosquitoes, which leads to the production of no offspring. The basic offspring number of the mosquitoes’ population was computed, after which we investigated the existence of two equilibrium points of the model. When the basic offspring number of the model $\left(M_0\right)$, is less than or equal to 1, a mosquito extinction equilibrium point $\left(E_2\right)$, which is often biologically unattainable, was shown to exits. On the other hand, if $\left(M_0>1\right)$, we have the nonnegative equilibrium point $\left(E_1\right)$ which is shown to be both locally and globally asymptotically stable whenever $\left(M_0>1\right)$. Local sensitivity analysis was then performed to know the parameters that should be targeted by control intervention strategies and result shows that female mating probability to be with the sterile male mosquitoes $\left({\rho }_S\right)$, mating rate of the sterile mosquito $\left({\beta }_2\right)$, and natural death rates of both aquatic and female mosquitoes $\left({\mu }_A+{\mu }_F\right)$ have greater impacts on the reduction and elimination of mosquitoes from a population. Simulation of the model shows that enough release of sterile male mosquitoes into the population of the wild mosquitoes controls the mosquito population and as such can reduce the spread of mosquito borne disease such as Zika.

A linear operator on a Hilbert space may be approximated with finite matrices by choosing an orthonormal basis of thez Hilbert space. In this paper, we establish an approximation of the $q$-numerical range of bounded and unbounnded operator matrices by variational methods. Application to Schrödinger operator, Stokes operator, and Hain-Lüst operator is given.

Tridiagonal matrices appear frequently in mathematical models. In this paper, we derive the positive integer powers of special tridiagonal matrices of arbitrary order.

This paper proposes a statistical mechanical model for the energy conservation behaviour of energy users. The model was inspired by the multipopulation Curie-Weiss model and the discrete choice with social interaction model. We demonstrate that the model integrates the sociopsychological, the economic, and the energy technologist viewpoints to energy management, allowing us to subject these perspectives to an empirical study.

The dynamic behavior of structures with piezoelectric patches is governed by partial differential equations with strong singularities. To directly deal with these equations, well adapted numerical procedures are required. In this work, the differential quadrature method (DQM) combined with a regularization procedure for space and implicit scheme for time discretization is used. The DQM is a simple method that can be implemented with few grid points and can give results with a good accuracy. However, the DQM presents some difficulties when applied to partial differential equations involving strong singularities. This is due to the fact that the subsidiaries of the singular functions cannot be straightforwardly discretized by the DQM. A methodological approach based on the regularization procedure is used here to overcome this difficulty and the derivatives of the Dirac-delta function are replaced by regularized smooth functions. Thanks to this regularization, the resulting differential equations can be directly discretized using the DQM. The efficiency and applicability of the proposed approach are demonstrated in the computation of the dynamic behavior of beams for various boundary conditions and excited by impulse and Multiharmonics piezoelectric actuators. The obtained numerical results are well compared to the developed analytical solution.

In this paper, a recent and reliable method, named the fractional reduced differential transform method (FRDTM) is employed to solve one-dimensional time-fractional Beam equation subject to the appropriate initial conditions. This method provides the solutions very accurately and efficiently in convergent series form with easily computable coefficients. The efficacy and accuracy of this method are verified by means of three illustrative examples which indicate that the present method is very effective, simple, and easy to implement. Finally, it is observed that the FRDTM is the prevailing and convergent method for the solutions of linear and nonlinear fractional-order partial differential equations.

In this paper, we propose and analyze a fuzzy model for the health risk challenges associated with alcoholism. The fuzziness gets into the system by assuming uncertainty condition in the measure of influence of the risky individual and the additional death rate. Specifically, the fuzzy numbers are defined functions of the degree of peer influence of a susceptible individual into drinking behavior. The fuzzy basic risk reproduction number ${\mathcal{R}}_0^f$ is computed by means of Next-Generation Matrix and analyzed. The analysis of ${\mathcal{R}}_0^f$ reveals that health risk associated with alcoholism can be effectively controlled by raising the resistance of susceptible individuals and consequently reducing their chances of initiation of drinking behavior. When perceived respectable individuals in the communities are involved in health education campaign, the public awareness about prevailing risks increases rapidly. Consequently, a large population proportion will gain protection from initiation of drinks which would accelerate their health condition into more risky states. In a situation where peer influence is low, the health risks are likely to be reduced by natural factors that provide virtual protection from alcoholism. However, when the perceived most influential people in the community engage in alcoholism behavior, it implies an increase in the force of influence, and as such, the system will be endemic.

In this paper, a model for the transmission dynamics of cystic echinococcosis in the dog, sheep, and human populations is developed and analyzed. We first model and analyze the predator-prey interaction model in these populations; then, we propose a mathematical model of the transmission dynamics of cystic echinococcosis. We calculate the basic reproduction number $R_0$ and prove that the disease-free equilibrium is globally asymptotically stable, and hence, the disease dies out if $R_0<1$. We further show that the endemic equilibrium is globally asymptotically stable, and hence, the disease persists if . Numerical simulations are performed to illustrate our analytic results. We give sensitivity analysis of the key parameters and give strategies that are helpful to control the transmission of cystic echinococcosis, from which the most sensitive parameter is the transmission rate of Echinococcus’ eggs from the environment to sheep $\left({\beta }_{\mathrm{es}}\right)$. Thus, the effective controlling strategies are associated with this parameter.

Optimization techniques have been used in this paper to obtain an optimal investment in a selected portfolio that gives maximum returns with minimal inputs based on the secondary data supplied by a particular firm that is examined. Sensitivity analysis is done to ascertain the robustness of the resulting model towards the changes in input parameters to determine a redundant constraint using linear programming. The challenge of determining the available funds and allocating each component of the portfolio to maximize returns and minimize inputs by portfolio holders and managers who are the major decision-makers in allocating their resources cannot be quantified. This optimization technique is used to obtain an optimal investment portfolio including financial risks of a firm with disposable of $15,000,000.00 invested in crude oil, mortgage securities, cash crop, certificate of deposit, fixed deposit, treasury bills, and construction loans. The model is a single-objective model that maximizes the return on the portfolio as the interests on the original data reduces by 5%; then, the return on investments also reduced by almost 15%, with the quantum of money on treasury bills and construction loans posing a significant reduction for the maximum return. The investment in the other options saw a slight decrease. Also, as the interest rates of the original data increase by 5%, the return on investments also grows by almost 17% while the quantum of money on the treasury bills and construction loans increases, and the quantum of money on the other options experienced a decrease except for mortgage securities which recorded a slight increase.

Malaria is one of the world’s most prevalent epidemics. Current control and eradication efforts are being frustrated by rapid changes in climatic factors such as temperature and rainfall. This study is aimed at assessing the impact of temperature and rainfall abundance on the intensity of malaria transmission. A human host-mosquito vector deterministic model which incorporates temperature and rainfall dependent parameters is formulated. The model is analysed for steady states and their stability. The basic reproduction number is obtained using the next-generation method. It was established that the mosquito population depends on a threshold value $\theta$, defined as the number of mosquitoes produced by a female Anopheles mosquito throughout its lifetime, which is governed by temperature and rainfall. The conditions for the stability of the equilibrium points are investigated, and it is shown that there exists a unique endemic equilibrium which is locally and globally asymptotically stable whenever the basic reproduction number exceeds unity. Numerical simulations show that both temperature and rainfall affect the transmission dynamics of malaria; however, temperature has more influence.

This article presents the implementation of a learning environment for the teaching of control systems. This environment integrates physical equipment and simulation, monitoring, and control through a network. A software platform based on ROS (Robotic Operating System) grants access to the system through intranet and Internet, facilitating the integration of new test equipment. The environment developed can be used in didactic experiences both inside and outside the classroom, enhancing the learning of four main study topics: modeling, analysis, parameter estimation, and controller design.

Analyzing and improving mathematical models for water quality investigation are imperative for water quality issues around the world. This study is aimed at presenting the 1D unsteady state regarding analytical and numerical solutions of dissolved oxygen (DO) concentration in a river, in which the increase of pollution from a source is considered as an exponential term. Laplace transformation was utilized to obtain analytical solutions, while the finite difference technique was selected for numerical solutions. The results show that the rate of pollutant addition along the river ($q$) and the arbitrary constants of an exponentially increasing pollution source term ($\lambda$) affected inversely, while the initial concentration $X_i$ affected directly, DO in the river. These solutions and simulations can be enabled for testing in various scenarios in terms of the behavior of oxygen depletion in polluted rivers.

The Löwner partial order is taken into consideration in order to define Löwner majorants for a given finite set of symmetric matrices. A special class of Löwner majorants is analyzed based on two specific matrix parametrizations: a two-parametric form and a four-parametric form, which arise in the context of so-called zeroth-order bounds of the effective linear behavior in the field of solid mechanics in engineering. The condensed explicit conditions defining the convex parameter sets of Löwner majorants are derived. Examples are provided, and potential application to semidefinite programming problems is discussed. Open-source MATLAB software is provided to support the theoretical findings and for reproduction of the presented results. The results of the present work offer in combination with the theory of zeroth-order bounds of mechanics a highly efficient approach for the automated material selection for future engineering applications.

Face recognition has gained prominence among the various biometric-based methods (such as fingerprint and iris) due to its noninvasive characteristics. Modern face recognition modules/algorithms have been successful in many application areas (access control, entertainment/leisure, security system based on biometric data, and user-friendly human-machine interfaces). In spite of these achievements, the performance of current face recognition algorithms/modules is still inhibited by varying environmental constraints such as occlusions, expressions, varying poses, illumination, and ageing. This study assessed the performance of Principal Component Analysis with singular value decomposition using Fast Fourier Transform (FFT-PCA/SVD) for preprocessing the face recognition algorithm on left and right reconstructed face images. The study found that average recognition rates for the FFT-PCA/SVD algorithm were 95% and 90% when the left and right reconstructed face images are used as test images, respectively. The result of the paired sample $t$-test revealed that the average recognition distances for the left and right reconstructed face images are not significantly different when FFT-PCA/SVD is used for recognition. FFT-PCA/SVD is recommended as a viable algorithm for recognition of left and right reconstructed face images.

In this paper, we aim to estimate and predict the situation of the new coronavirus pandemic (COVID-19) in countries under quarantine measures. First, we present a new discrete-time mathematical model describing the evolution of the COVID-19 in a population under quarantine. We are motivated by the growing numbers of infections and deaths in countries under quarantine to investigate potential causes. We consider two new classes of people, those who respect the quarantine and stay at home, and those who do not respect the quarantine and leave their homes for one or another reason. Second, we use real published data to estimate the parameters of the model, and then, we estimate these populations in Morocco. We investigate the impact of people who underestimate the quarantine by considering an optimal control strategy to reduce this category and then reducing the number of the population at risk in Morocco. We provide several simulations to support our findings.