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The present comment concerns some doubtful mathematical calculation that produced misleading results which are presented in the above paper. [ABSTRACT FROM AUTHOR]

Road traffic conditions exhibit spatial and temporal variations influenced by factors such as construction, speed limits, and accidents. Accurate and efficient modeling of vehicular flow on changing road conditions is crucial for understanding intricate traffic phenomena and analyzing dynamic characteristics in real-world scenarios. In this paper, we develop a rapid numerical approach that computes traffic flow solutions for roads divided into multiple sections with varying traffic conditions, utilizing the Lighthill-Whitham-Richards model as the mathematical framework. The key aspect of our approach lies in solving the flow at the dividing point between consecutive road sections with different traffic conditions. For the two-section road scenario, we integrate the Hamilton-Jacobi formulation of the traffic model with the triangular fundamental diagram, capturing the explicit relationship between flow and density. This integration allows us to derive the spatiotemporal solution for a single dividing point. By accounting for the dynamic interaction between adjacent dividing points, we extend the applicability of our approach to an arbitrary number of road sections based on a semi-analytic Lax-Hopf formula. Our semi-analytical method is distinguished by grid-free computing, reducing computational demands and ensuring exceptional simulation speed. Particularly noteworthy is the formulation's remarkable efficacy in handling the complexities of heterogeneous road traffic conditions, marked by dynamic variations in both time and space, surpassing traditional macroscopic traffic flow simulations. To demonstrate its effectiveness, we apply the proposed approach to an optimization example involving traffic signal timing in a complex road environment. Additionally, we showcase its predictive capabilities by efficiently evaluating the impact of traffic accidents on the surrounding traffic flow. This research provides valuable insights for traffic management, optimization, and decision-making, enabling the analysis of complex scenarios and facilitating the development of strategies to enhance traffic efficiency and safety. • Propose a novel approach for traffic flow computation under changing road conditions. • Extend approach to multiple heterogeneous road sections, accounting for dividing point interactions. • Demonstrate the improved speed and accuracy by eliminating approximations and meshes. • Illustrate the practical applications in signal timing optimization and accident impact prediction. [ABSTRACT FROM AUTHOR]

This paper presents a proposed approach for modeling the life data for system components that have failure modes by different Weibull models. This approach is applied for censored, grouped and ungrouped samples. To support the main idea, numerical applications with exact failure times and censored data are implemented. The parameters are obtained by different computational statistical methods such as graphic method based on Weibull probability plot (WPP), maximum likelihood estimates (MLE), Bayes estimators, non-linear Benard’s median rank regression. This paper also presents a parametric estimation method depends on expectation–maximization (EM) algorithm for estimation the parameters of finite Weibull mixture distributions. GOF is used to determine the best distribution for modeling life data. The performance of the proposed approach to model lifetime data is assessed. It’s an efficient approach for moderate and large samples especially with a heavily censored data and few exact failure times. [ABSTRACT FROM AUTHOR]

As a type of uncertain differential equations, uncertain spring vibration equation is driven by Liu process. This paper proposes a concept of α -path, and shows that the solution of an uncertain spring vibration equation can be expressed by a family of solutions of second-order ordinary differential equations. This paper also proves that the inverse uncertainty distribution of solution of uncertain spring vibration equation is just the α -path of uncertain spring vibration equation, and a numerical algorithm is designed. Moreover, a formula to calculate the expected value of solution of uncertain spring vibration equation is derived. Finally, several numerical examples are provided to illustrate the efficiency of the numerical method. [ABSTRACT FROM AUTHOR]

In this paper we consider a one-dimensional one-phase Stefan problem corresponding to the solidification process of a semi-infinite material with a convective boundary condition at the fixed face. The exact solution of this problem, available recently in the literature, enable us to test the accuracy of the approximate solutions obtained by applying the classical technique of the heat balance integral method and the refined integral method, assuming a quadratic temperature profile in space. We develop variations of these methods which turn out to be optimal in some cases. Throughout this paper, a dimensionless analysis is carried out by using the parameters: Stefan number (Ste) and the generalized Biot number (Bi). In addition it is studied the case when Bi goes to infinity, recovering the approximate solutions when a Dirichlet condition is imposed at the fixed face. Some numerical simulations are provided in order to estimate the errors committed by each approach for the corresponding free boundary and temperature profiles. [ABSTRACT FROM AUTHOR]

The concept of geometrical multiscale modelling of non-Newtonian blood flow in patient-specific models is presented with the aim to provide a methodology for the assessment of hemodynamic significance of carotid artery stenoses. The content of the paper is divided into two consequent parts. In the first one, the principle of the fractional flow reserve (FFR) as an indicator of ischemia-inducing arterial stenoses is tested on three large arterial models containing the aortic arch and both left and right carotid arteries. Using the three-element Windkessel model as an outflow boundary condition, the blood flow simulations are carried out on the basis of data taken from the literature due to unavailable information on patient-specific flow and pressure waveforms. In the second part of the paper, the incorporation of real in-vivo measurements into the multiscale simulations is addressed by presenting a sequential algorithm for the estimation of Windkessel parameters. The ability of the described estimation method, which employs a non-linear state estimator (unscented Kalman filter) on zero-dimensional flow models, is demonstrated on two different patient-specific carotid bifurcation models. [ABSTRACT FROM AUTHOR]

Solar radiation numerical models need the implementation of an accurate method for determining cast shadows on the terrain or on solar collectors. The aim of this work is the development of a new methodology to detect the shadows on a particular terrain. The paper addresses the detection of self and cast shadows produced by the orography as well as those caused by clouds. The paper presents important enhancements on the methodology proposed by the authors in previous works, to detect the shadows caused by the orography. The domain is the terrain surface discretised using an adaptive mesh of triangles. A triangle of terrain will be under cast shadows when, looking at the mesh from the Sun, you can find another triangle that covers all or partially the first one. For each time step, all the triangles should be checked to see if there are cast or self shadows on it. The computational cost of this procedure eventually resulted unaffordable when dealing with complex topography such as that in Canary Islands thus, a new methodology was developed. This one includes a filtering system to identify which triangles are those likely to be shadowed. If there are no self shadowed triangles, the entire mesh will be illuminated and there will not be any shadows. Only triangles that have their backs towards the Sun will be able to cast shadows on other triangles. Detection of shadows generated by clouds is achieved by a shadow algorithm using satellite images. In this paper, Landsat 8 images have been used. The code was done in python programming language. Finally, the outputs of both approaches, shadows generated by the topography and generated by clouds, can be combined in one map. The whole problem has been tested in Gran Canaria and Tenerife Island (Canary Islands – Spain), and in the Tatra Mountains (Poland and Slovakia). [ABSTRACT FROM AUTHOR]

In this paper we consider a discrete-time retrial queueing system with batch arrivals of geometric type and general batch services. The arriving group of customers can decide to go directly to the server expelling out of the system the batch of customers that is currently being served, if any, or to join the orbit. After a successful retrial all the customers in the orbit get service simultaneously. An extensive analysis of the model is carried out, and using a generating functions approach some performance measures of the model, such as the first distribution’s moments of the number of customers in the orbit and in the system, are obtained. The generating functions of the sojourn time of a customer in the orbit and in the system are also given. Finally, in the section of conclusions and research results the main contributions of the paper are commented. [ABSTRACT FROM AUTHOR]

This paper addresses finite-region asynchronous H ∞ filtering for a class of two-dimensional Markov jump systems (2-D MJSs). A mathematical model is established using the Roesser model, and asynchrony is accounted for using a hidden Markov model (HMM). The modes jumping between the target system and the designed filter are determined by the given conditional probability matrix. Sufficient conditions are derived using suitable Lyapunov function and linear matrix inequalities (LMIs) to ensure stable filtering performance. The practical applicability of the approach is illustrated by two examples. Overall, this study offers a method to tackle filtering challenges in 2-D Markov jump systems, incorporating HMM, Lyapunov functions, and LMIs to effectively solve the finite-region asynchronous H ∞ filtering problem. • An HMM is used to describe the asynchronous phenomenon between the system and the filter. • Lyapunov functional and recursive formulas effectively analyze the FRB of filtering error system. • The Darboux equation and the heat exchange process both validate the effectiveness of the filter. [ABSTRACT FROM AUTHOR]

In this paper, we propose an impulsive predator–prey model with communicable disease in the prey species only and investigate its interesting biological dynamics. By the Floquet theory of impulsive differential equation and small amplitude perturbation skills, we have deduced the sufficient conditions for the globally asymptotical stability of the semi-trivial periodic solution and the permanence of the proposed model. We also give the existences of the “infection-free” periodic solution and the “predator-free” solution. Finally, numerical results validate the effectiveness of theoretical analysis for the proposed model in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we present a new iterative method based on the hybrid viscosity approximation method and the hybrid steepest-descent method for finding a common element of the set of solutions of generalized mixed equilibrium problems and the set of common fixed points of a finite family of nonexpansive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative method has strong convergence under some mild conditions imposed on algorithm parameters. The results presented in this paper improve and extend the corresponding results reported by some authors recently. [ABSTRACT FROM AUTHOR]

The paper deals with the scheduler for virtualization of links with the partial performance isolation between the virtual links, meaning that the traffic on one virtual link may influence the performance of other virtual links only up to limited extent – every virtual link has guaranteed performance even in the worst case scenario. In this paper the analysis of the scheduler is carried out using the polling model of time-limited type. In particular, the queue size distribution and throughput of both privileged and normal virtual links are obtained. [ABSTRACT FROM AUTHOR]

Behind Medicine (M) is Physiology (P), behind Physiology is Physics (P) and behind Physics is always Mathematics (M), for which I expect that the symmetry of the quadruplet MPPM will be compatible with the characteristic bias of hyperbolic partial differential equations, a theme of this paper. I start with a description of several idiopathic brain pathologies that appear to have a strong vascular dimension, of which the most prominent example considered here is multiple sclerosis, the most common neurodegenerative, disabling disease in young adults. Other pathologies surveyed here include retinal abnormalities, Transient Global Amnesia, Transient Monocular Blindness, Ménière’s disease and Idiopathic Parkinson’s disease. It is the hypothesised vascular aspect of these conditions that links medicine to mathematics, through fluid mechanics in very complex networks of moving boundary blood vessels. The second part of this paper is about mathematical modelling of the human cardiovascular system, with particular reference to the venous system and the brain. A review of a recently proposed multi-scale mathematical model then follows, consisting of a one-dimensional hyperbolic description of blood flow in major arteries and veins, coupled to a lumped parameter description of the remaining main components of the human circulation. Derivation and analysis of the hyperbolic equations is carried out for blood vessels admitting variable material properties and with emphasis on the venous system, a much neglected aspect of cardiovascular mathematics. Veins, unlike their arterial counterparts, are highly deformable, even collapsible under mild physiological conditions. We address mathematical and numerical challenges. Regarding the numerical analysis of the hyperbolic PDEs, we deploy a modern non-linear finite volume method of arbitrarily high order of accuracy in both space and time, the ADER methodology. In vivo validation examples and brain haemodynamics computations are shown. We also point out two, preliminary but important new findings through the use of mathematical models, namely that extracranial venous strictures produce chronic intracranial venous hypertension and that augmented pressure increases the blood vessel wall permeability. [ABSTRACT FROM AUTHOR]

• Incorporating time delay has a considerable impact on the dynamics of prey– predator interactions with fading memory and Allee effect. • Different values of time delays in competition and cooperation can lead to or eliminate chaos. • Predator density depends not only on the current density of prey but also on the recent past density of prey. • The stability of the system switches from stable (unstable) to unstable (stable) through Hopf bifurcation in the presence of time delays. This paper deals with a model of population dynamics comprising Allee effect and weakening memory with constant time delays. Since predator density depends on the prey density in current time and in past, a two-component model of prey-predator interactions is complemented with a third differential equation for the influence of recent past. The role of constant time delays incorporated in the functional form of Allee effect (referred as delays in competition and cooperation) is investigated analytically and numerically. Steady states of the model are obtained and the local stability analysis around the coexisting state is calculated in the presence of both delays. The critical threshold for time delays, above which the stability of the system switches from stable (unstable) to unstable (stable), is computed for various cases. Analytical findings of this paper are supported with numerical simulations, where time evolution as well as numerical bifurcation diagrams are presented. The results of this paper demonstrate that the influence of past on the prey-predator density in the present of time delay may have a considerable effect upon the system behaviour and can give important insights into underlying biological mechanism. [ABSTRACT FROM AUTHOR]

Air pollution models plays a critical role in atmospheric environment research. Chemical kinetic equations is an important component of air pollution models. The chemical equations is numerically sticky because of its stiffness, nonlinearity, coupling and nonnegativity of the exact solutions. Over the past decades, numerous papers about chemical equation solvers have been published. However, these solvers cannot preserve the nonnegativity of the exact solutions. Therefore, in the calculation, the negative numerical concentration values are usually set to zero artificially, which may cause simulation errors. To obtain real nonnegative numerical concentration values, very small step-size has to be adopted. Then enormous amount of CPU time is consumed to solve the chemical equations. In this paper, we revisit this topic and derive a new algorithm. Our algorithm Modified-Backward-Euler (MBE) Method can unconditionally preserve the nonnegativity of the exact solutions. MBE is a simple, robust and efficient solver. It is much faster and more precise than the traditional solvers such as LSODE and QSSA. The numerical results and parameter suggestions are shown at the end of the paper. MBE is based on the P-L structure of the chemical equations and a deeper view into the nature of Euler Methods. It cannot only be used to solve chemical equations, but can also be applied to conquer ordinary differential equations (ODEs) with similar P-L structure. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of damped vibration problems with superquadratic terms at infinity. By using variational methods, we obtain infinitely many nontrivial periodic solutions under conditions weaker than those previously assumed. To the best of our knowledge, there is no published result focusing on this case by the method used in this paper. [ABSTRACT FROM AUTHOR]

In this paper, neural algorithms, including the multi-layered perceptron (MLP) differential approximator, generalized hybrid power series, discrete Hopfield neural network, and the hybrid numerical, are used for constructing models that incorporate a priori knowledge in the form of differential equations for dynamic engineering processes. The properties of these approaches are discussed and compared to each other in terms of efficiency and accuracy. The presented algorithms have a number of advantages over other traditional mesh-based methods such as reduction of the computational cost, speed up of the execution time, and data integration with the a priori knowledge. Furthermore, the presented techniques are applicable when the differential equations governing a system or dynamic engineering process are not fully understood. The proposed algorithms learn to compute the unknown or free parameters of the equation from observations of the process behavior, hence a more precise theoretical description of the process is obtained. Additionally, there will be no need to solve the differential equation each time the free parameters change. The parallel nature of the approaches outlined in this paper make them attractive for parallel implementation in dynamic engineering processes. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish some new Hermite–Hadamard type inequalities for harmonic h -convex functions involving hypergeometric functions. We also discuss some new and known special cases, which can be deduced from our results. The ideas and techniques of this paper may inspire further research in this field. [ABSTRACT FROM AUTHOR]

This paper is devoted to analyzing the instantaneous availability of a typical software system with intrusion tolerance. By formulating the system with a couple of ordinary differential and partial differential equations, this paper describes the system as a time-delay partial differential equation. Based on the time-delay model, both steady-state availability and instantaneous availability are investigated. The optimal policy for preventive patch management to maximize the steady-state availability of the software system is obtained, and its related availability criterions are also presented. Employing the finite difference scheme and Trotter–Kato theorem, we converted the time-delay partial equation into a time-delay ordinary equation. As a result, the instantaneous availability of the system is derived. Some numerical results are given to show the effectiveness of the method presented in the paper. [ABSTRACT FROM AUTHOR]

This paper presents adaptive wavelet collocation methods for the numerical solutions to partial integro-differential equations (PIDEs) arising from option pricing in a market driven by jump-diffusion process. The first contribution of this paper lies in the formulation of the wavelet collocation schemes: the integral and differential operators are formulated in the collocation setting exactly and efficiently in both adaptive and non-adaptive wavelet settings. The wavelet compression technique is employed to replace the full matrix corresponding to the nonlocal integral term by a sparse matrix. An adaptive algorithm is developed, which automatically obtains the solution on a near-optimal grid. The second contribution of this paper is the theoretical analysis of the wavelet collocation schemes: due to the possible degeneracy of the parabolic operators, classical solutions of the jump-diffusion models may not exist. In this paper we first prove the convergence and stability of the proposed numerical schemes under the framework of viscosity solution theory, and then the numerical experiments demonstrate the accuracy and computational efficiency of the methods we developed. [ABSTRACT FROM AUTHOR]

Abstract: The importance of electric power in today’s world cannot be overemphasized, for it is the key energy source for industrial, commercial and domestic activities. Its availability in the right quantity is essential to advancement of civilization. Electrical energy produced at power stations is transmitted to load centres from where it is distributed to the consumers through the use of transmission lines run from one place to another. As a result of the physical properties of the transmission medium, some of the transmitted power are lost to the surroundings. The power losses could take off a sizeable portion of the transmitted power since the transmission lines usually span a long distance, sometimes several hundred kilometers. The overall effect of power losses on the system is a reduction in the quantity of power available to the consumers. As such, adequate measures must be put in place to reduce power losses to the barest minimum. Thus, in this paper, we developed a mathematical model for determining power losses over typical transmission lines, as the resultant effect of ohmic and corona power losses, taking into cognizance the flow of current and voltage along the lines. Application of the classical optimization technique aided the formulation of an optimal strategy for minimization of power losses on transmission lines. With the aid of the new models it is possible to determine current and voltage along the transmission lines. In addition, we note that the analytical method does not involve any design or construction and so is less expensive than other models reported in the literature. Hence, the goal of this paper is to address a very well-known engineering problem – reducing the power losses on transmission lines to the barest minimum. [Copyright &y& Elsevier]

Abstract: Li and Lim (2011) [8] proposed a three-dimensional system of ordinary differential equations modeling the role of Tax expression in the persistence of Human T-lymphotropic virus Type I and presented a mathematical analysis and its immunovirological explanation. The previous paper shows that three-dimensional system is a cooperative system if a sharp condition is satisfied. By means of the theory of cooperative dynamical systems, they studied the global dynamics. If the sharp condition is not satisfied, they leave it an open problem. The present paper is to provide a complete classification of global dynamics for this ODE model. In particular, our global analysis establishes that the dynamics of the HTLV-I infection are completely determined by a basic reproductive number, which completely solves the open problem above. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a variable-territory predator–prey model with Dirichlet boundary condition. We establish a necessary and sufficient condition for the existence of positive solutions to steady state. Furthermore, we also prove that the local bifurcation positive solutions are unconditional stable. By regular perturbation theorem, we investigate the convergence and stability of positive solutions when handling time m is large enough. At the end of this paper, there are some numerical simulations and biological significance to check and complement our theoretical analysis results. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to present a critical review on the paper “The common Re-nnd and Re-pd solutions to the matrix equations and ” by authors Xiong and Qin (2011) [1]. We point out that the conditions given by Theorem 2.1 are not enough to ensure the existence of common Re-nnd solution to and , and the proofs are unacceptable. Finally, the corrected results are given. [Copyright &y& Elsevier]

Abstract: The research in this paper presents a new approach for the modeling of epidemic spread by using a set of connected social networks. The purpose of this work is to simulate the spreading of the well know A/H1N1 pandemic virus. The case study analyzed in this paper refers to the spreading of A/H1N1 in Romania. The epidemic is followed from its beginning throughout its evolution in Romania, i.e. between May 2009 and February 2010. The evolution is performed in a hierarchical way, taking into account the state divisions, the influences among them, national level as well as influences from abroad (from other infected countries). Numerical experiments performed analyze the monthly evolution of the infection in each county and at the country level and compare the results with the real ones (collected during and at the end of the epidemic spread). The simulations results are closer to the reality than the ones provided by the Health Ministry in Romania. [Copyright &y& Elsevier]

Abstract: The study of the numerical solutions of PDEs with wavelet collocation has yielded a number of substantial results. However, the existence and uniqueness of solution has not been discussed yet. In this paper, the existence and uniqueness of solution to wavelet collocation for elliptic equations is established and discussed. Moreover, wavelet collocation is applied to numerical example to examine its appropriateness. According to numerical example and analysis, it is seen that the existence and uniqueness of solution of this paper is feasible, and the new theory is meaningful for developing wavelet collocation. [Copyright &y& Elsevier]

Abstract: This paper studies the impact of inaccurate demand beliefs on dynamic quantity-setting market games. The conventional assumption that players share a uniform and accurate demand model in game is relaxed by a more realistic model—players individually make their subjective demand estimation possibly with errors. A dynamic game with such subjective demand belief for two heterogeneous players is built. Based on this model, the impact of demand belief errors on the game’s equilibriums and their stability is investigated. The results shows that the stability region is not only determined by the parameters of the system configuration and the bidding adjustment-as pointed out in conventional model, but also by the player’s imperfect knowledge about the market. Thus new dynamic behaviors and instability may arise given an original error-free system (where all players are assumed to have perfect and uniform knowledge about the market). It is suggested that in order to avoid possible system instability, the design of players’s adjustment speed, and the possible demand belief errors from different players must be taken into account. Moreover, this paper points out that the various behavior patterns of players have different influence on the stability regions and corresponding dynamic characteristics of system equilibriums. The changes of players’s profits and customer surplus induced by inaccurate beliefs are also studied. The stability analyses, dynamics behaviors, and system performance in steady state are validated with a set of numerical experiments. [Copyright &y& Elsevier]

Abstract: In this paper, we have proposed and mathematically modeled an epidemic problem with vector-borne disease. We have taken three different classes for the trees, namely susceptible, exposed and infected, and two different classes for the vector population, namely susceptible and infected. In the first part of our paper, we rigorously analyze our model using the dynamical systems approach. Global stability of equilibria is resolved by using Lyapunov functional. In the second part, the model is reformulated as an optimal control problem in order to determine the significance of certain control measures on the model. We apply four control parameters, namely the tree injection control to the trees, deforestation of infected trees, eradication effort of aerial insecticide spraying and the effort of restrain of mating. Both numerical and analytical methods are employed to ascertain the existence of cost effective control measures. [Copyright &y& Elsevier]

Abstract: This paper introduces a saturated treatment function into an SIS model with saturated incidence rate. The treatment function is a continuous and differential function which describes the effect of delayed treatment when the medical condition is limited and the number of infected individuals is large. Sufficient conditions for the existence and global asymptotical stability of the disease-free and endemic equilibria are given in this paper, and the nonexistence of limit cycles is also demonstrated. A backward bifurcation is found when the capacity of the treatment is low. It indicates that we should improve the efficiency and enlarge the capacity of the treatment to control the spread of diseases. By mathematical analysis and numerical simulations, it is shown that the system undergoes Hopf bifurcation and Bogdanov–Takens bifurcation. [Copyright &y& Elsevier]

• A real option is a contract which gives its holder the flexibility to expand the scale of an investment project or production. Real options are often used to hedge risks or capture opportunities in investments. In this paper, we establish a mathematical model for pricing a real option of expansion whose underlying asset price and its volatility/variance satisfy two separate stochastic equations. Based on Ito's lemma and a hedging technique, we show that the option price satisfies a 2 nd -order parabolic partial differential equation (PDE) in two spatial dimensions. We also derive the boundary and terminal conditions for the PDE and some of these conditions are also determined by PDEs. • We propose a novel 9-point finite difference scheme with a upwind technique is designed for solving the PDE system, as well that for determining the terminal (payoff) condition, established. We show that the coefficient matrix of the system from this discretization is an M-matrix and the numerical solution generated by the finite difference scheme converge to the exact one by proving that the scheme is consistent, monotone and stable. • Extensive numerical experiments on the model and numerical methods using a model investment problem in an iron-ore industry have been performed. The numerical results show that our model and numerical methods for solving the model are able to produce numerical results which are financially meaningful. In this paper we develop a PDE-based mathematical model for valuing real options on the expansion of an investment project whose underlying commodity price and its volatility follow their respective geometric Brownian motions. This mathematical model is of the form of a 2-dimensional Black-Scholes equation whose payoff condition is determined also by a PDE system. A novel 9-point finite difference scheme is proposed for the discretization of the spatial derivatives and the fully implicit time-stepping scheme is used for the time discretization of the PDE systems. We show that the coefficient matrix of the fully discretized system is an M -matrix and prove that the solution generated by this finite difference scheme converges to the exact one when the mesh sizes approach zero. To demonstrate the usefulness and effectiveness of the mathematical model and numerical method, we present a case study on a real option pricing problem in the iron-ore mining industry. Numerical experiments show that our model and methods are able to produce numerical results which are financially meaningful. [ABSTRACT FROM AUTHOR]

Abstract: The time-dependent solution of a kind of repairable system with preventive maintenance is investigated in the paper. With total probability formula, we show that the behavior of the system can be described as a group of ordinary differential equations coupled with partial differential equations, which can be formulated as a time delay equation in an appropriate Banach space. Based on the time-delay equation, this paper presents a difference scheme as an approximating method to solve the time-dependent solution which is necessary for analyzing the instantaneous availability of the repairable system. Some numerical examples are shown to illustrate the effectiveness of this approach. [Copyright &y& Elsevier]

Abstract: This paper is devoted to the identification of a pollution source in a river. A simple mathematical model of such a problem is given by a one-dimensional linear advection–dispersion–reaction equation with a right hand side spatially supported in a point (the source) and a time varying intensity, both unknown. There exist some identifiability results about this distributed system. But the numerical estimation of the unknown quantities require the introduction of an approximated model, whose identifiability properties are not analyzed usually. This paper has a double purpose: – to do the identifiability analysis of the differential system considered for estimating the parameters, – to propose a new numerical global search of these parameters, based on the previous analysis. Another consequence of this approach is to give the unknown pollution intensity directly as the solution of a differential equation. Lastly, the numerical algorithm is described in detail, completed with some applications. [Copyright &y& Elsevier]

Abstract: This paper reviews three articles, namely “A note on the inventory model for deteriorating items with trapezoidal type demand rate” by Cheng and Wang (2009) [1], “Inventory models with managerial policy independent of demand” by Lin (2011) [7], and “Optimal policy for deteriorating items with trapezoidal type demand and partial backlogging” by Chen et al. (2011) [2]. This paper extends their models with a generalized demand, a generalized deteriorated rate, and an extended backlogged rate. The findings of this study can provide references on important inventory models. [Copyright &y& Elsevier]

Abstract: This paper presents an analysis of some selection methods used in memory consideration of Harmony search (HS) Algorithm. The selection process in memory consideration entails selecting the value of the decision variable from any solution in the Harmony memory (HM). Quite recently, there has been a tendency to adopt novel selection methods that mimic the natural phenomena of the ‘survival of the fittest’ to replace the random selection method in memory consideration. Consequently, the value of decision variable selected using memory consideration is chosen from the higher promising solutions in HM. The adopted selection methods include: proportional, tournament, linear rank, and exponential rank. It has been demonstrated that experimenting with any of these methods in memory consideration directly affects the performance of HS. However, the success of these methods is based on choosing the optimal parameter value of each. The wrong parameter settings might affect the balance between exploration and exploitation of the search space. Accordingly, this paper studies the effect of the selection method parameters in order to show their effect on HS behavior. The evaluation is conducted using standard mathematical functions used in the literature for HS adoptions. The results suggest that the optimal setting of the selection method parameters is crucial to improve the HS performance. [Copyright &y& Elsevier]

Abstract: Singular perturbation problems with turning points arise as mathematical models for various physical phenomena. The problem with interior turning point represent one-dimensional version of stationary convection–diffusion problems with a dominant convective term and a speed field that changes its sign in the catch basin. Boundary turning point problems, on the other hand, arise in geophysics and in modeling thermal boundary layers in laminar flow. In this paper, we review some existing literature on asymptotic and numerical analysis of singularly perturbed turning point and interior layer problems. The purpose is to find out what problems are treated and what numerical/asymptotic methods are employed, with an eye towards the goal of developing general methods to solve such problems. Since major work in this area started after 1970 so this paper limits its coverage to the work done by numerous researchers between 1970 and 2011. [Copyright &y& Elsevier]

Abstract: In stochastic differential equations (SDEs), there is a class of stochastic functional differential equations with random jump magnitudes, which aries in many financial models. In general most equations of stochastic age-dependent capital system do not have explicit solutions. Thus numerical approximation schemes are invaluable tools for exploring their properties. In this paper, the numerical approximation is established for a class of stochastic age-dependent capital system with random jump magnitudes. The main aim of this paper is to investigate the convergence of the numerical approximation for a class of stochastic age-dependent capital system with random jump magnitudes. It is proved that the numerical approximate solutions converge to the analytical solutions of the equations under given conditions. The numerical approximate results in Zhang et al. (2011) [2] are improved. An example is given for illustration. [Copyright &y& Elsevier]

Abstract: The paper is devoted to an extended Lotka–Volterra system of differential equations of predator–prey model. The extension is proposed with perturbation terms, which are null for the positive equilibrium state. In the original Lotka–Volterra system, the equilibrium state is not asymptotically stable due to the fact that perturbations are periodic in time. The aim of the paper is to characterize a form of perturbation terms guaranteeing the asymptotic stability or instability of equilibrium state. The reason of the proposed model is that for large time scale, the Lotka–Volterra model is too simple to be realistic. In the paper, the non-autonomous perturbations do not change the equilibrium state but introduce functions of time as well as for additional perturbed terms as for the main part of the equations modified from Lotka–Volterra model. Theorems are proposed in a renormalized form of the differential equations for time and the two variables. The key point of the paper comes from the use of a Liapunov function introduced in Section 2 which allows to obtain conditions for the asymptotic stability (Section 3) and instability (Section 4) by using a Cetaiev instability theorem following conditions on the renormalized coefficients in time of System (6). An appendix recalls the main results of the Liapunov Direct Method for non-autonomous binary systems of ordinary differential equations. [Copyright &y& Elsevier]

Abstract: Although a large number of different methods for establishing the fitting parameters of PH distributions to data traces (PH fitting) have been developed, most of these approaches lack efficiency and numerical stability. In the present paper, a restricted class of PH distribution, called the hyper-Erlang distribution (HErD), is used to establish a maximum likelihood estimation model for data tracing. To fit the parameters, a hybrid algorithm based on the scatter search algorithm, the improved adaptive genetic algorithm, and the expectation maximization algorithm was developed to obtain the SS&IAGA-EM algorithm, which has a polynomial time complexity. In the data tracing tests for different distribution functions, the results obtained from SS&IAGA-EM and from the G-FIT, which is currently the best software for PH fitting, were compared. The present paper demonstrates that (a) the fitting effect of G-FIT does not positively correlate with the number of states of a HErD; thus, G-FIT repeatedly has to test the number of states manually to achieve a satisfactory fitting effect; (b) although setting range of the number of branches in G-FIT could mitigate the aforementioned deficiency, the combinations of the number of phases per branch grow exponentially; and (c) on SS&IAGA-EM can optimize the number of states and the number of phases automatically, aside from being slightly faster than G-FIT for a small number of branches and is significantly faster for a large number of branches. Moreover, in all tests, SS&IAGA-EM can achieve the same fitting quality as G-FIT for the same number of states. [Copyright &y& Elsevier]

Abstract: This paper develops a model for determining ordering/trade-credit policy of a supply chain, where one supplier sells a product to a retailer, who faces a deterministic demand, and may offer the retailer two types of trade credit contracts: a “one-part” or a “two-part” contract. We discuss the existence of the optimal solution to the model, and provide a simple algorithm for finding the optimal ordering and trade credit policy of two members. We specify the conditions under which it is beneficial in reducing operational cost for the supplier to offer the two trade credit contracts. Through numerical experiments, we reveal that it is more superior in reducing operational cost for the supplier to offer a two-part credit than to offer a one-part credit, which can be extended to a multi-part credit. The sensitivity analysis is presented at the end of the paper. [Copyright &y& Elsevier]

Abstract: In this paper we proposed and analyzed a prey predator system with stage-structured for the predator population. A time delay is incorporated due to the gestation for the matured predator. All the possible non-negative equilibria are obtained and their local as well as global behavior are studied. Choosing delay as a bifurcation parameter, the existence of the Hopf bifurcation of the system has been investigated. Moreover, we use the normal form method and the center manifold theorem to examine the direction of the Hopf bifurcation and the nature of the bifurcating periodic solution. Some numerical simulations are given to support the analytical results. Some interesting conclusions are obtained from our analysis and it is given at the end of the paper. [Copyright &y& Elsevier]

Abstract: The paper deals with the analysis of the mathematical model of the two dimensional stationary viscous incompressible flow through a rotating radial blade machine. The flow is described and studied in the rotating frame. The paper provides the classical and weak formulation of the corresponding boundary value problem. The boundary condition on the outflow is the so called “natural” boundary condition, with the nonlinear term proposed by Bruneau and Fabrie (1996) [1], and also modified by a term arising from the rotation of the machine. The existence of a weak solution is proved. [Copyright &y& Elsevier]

Abstract: In this paper, a delayed HIV-1 infection model with nonlinear incidence of infection is reinvestigated. It is shown that if the reproduction number , then the system is permanent, and the infective equilibrium of the system is globally asymptotically stable. Thus, the global dynamics of the system is completely determined by the reproduction number . The results obtained enrich and improve the corresponding results given by Wang et al. [X. Wang, Y. Tao, X. Song, A delayed HIV-1 infection model with Beddington–DeAngelis functional response, Nonlinear Dynamics 62 (2010) 67–72]. The conclusions we established also verify the numerical simulation results on the global asymptotic stability of the infective equilibrium in the paper [D. Li, W. Ma, Asymptotic properties of an HIV-1 infection model with time delay, J. Math. Anal. Appl. 335 (2007) 683–691]. [Copyright &y& Elsevier]

Abstract: By suitably combining the investigations by Ghare and Schrader (1963) , Dolan (1987) and Huang and Chung (2003) , Kreng and Tan (2011) consider and analyze the optimal inventory policies with order-size dependent trade credit under delayed payment and cash discount. The mathematical analysis of Kreng and Tan (2011) is based upon an inventory model for deteriorating items with trade credit and cash discount linked to the order quantity. Motivated by the potential for practical applications of such inventory models as those that are considered in (for example) the aforecited works, we address some shortcomings in the 2011 paper by Kreng and Tan (2011) . We emphasize upon the invalidity of an important assumption by Kreng and Tan (2011) , namely that the deterioration rate is small, provide a counterexample to Kreng and Tan’s and question the results of Kreng and Tan’s . We present our own observations and results as theorems and proofs. We thus have not only removed the aforementioned shortcomings in the paper by Kreng and Tan (2011) , but we have also provided the complete solution procedures for some of the aforementioned models. Finally, some numerical examples are used to compare the results, which are presented in this paper, with those of the aforecited earlier investigations. [Copyright &y& Elsevier]

Abstract: This paper describes an approach to modeling and analysis of time-dependent system specifications which is based on the Time Stream Petri Nets (TSPNs) formalism. The work argues that although TSPNs were originally proposed for modeling multimedia/hypermedia systems, they are well suited for expressing timing constraints in general time-dependent systems. The approach is assisted by some developed tools based on model checking in terms of Uppaal timed automata, which permit behavioural analysis and in particular schedulability analysis of task executions in real-time specifications. Property analysis rests on the construction of a (hopefully finite) zone state graph of a TSPN model and its efficient traversal by Uppaal verifier, which in turn represents an effective approach for dealing with infinite computations in a compact way. The paper introduces the TSPN formalism and focuses on the implemented structural translation onto Uppaal which is assisted by a library of reusable template processes. The modeling/analysis techniques are demonstrated by two examples. The first example deals with project management, i.e. the exhaustive analysis of general CPM/PERT project models where an activity duration is expressed by a time interval. The second example is related to a thoroughly analysis of the temporal behaviour of a complex embedded real-time system with timing constraints. An indication of on-going and future work is, finally, given in the conclusions. Soundness of the structural translation is shown by a formal proof reported in appendix. [Copyright &y& Elsevier]

Highlights • We develop a multi-strain dengue model assuming reinfection with the same dengue serotype. • We found a novel criteria for the stability of endemic equilibrium. • The reinfection parameter contributes to an increasing number of primary and secondary infections. Abstract Dengue is worldwide problem with around 390 million cases annually. Dengue is caused by four dengue serotypes: DEN1, DEN2, DEN3, DEN4. Individuals obtain lifelong immunity to the serotype they are infected with. This becomes the main underlying assumptions of most modeling work on dengue. However, data from West Java, Indonesia, showed that there is a possibility for individuals to be reinfected by the same strain, which may result in significantly different dengue transmission dynamics. In this paper, we develop a novel multi-strain dengue model taking into account the reinfection with the same dengue serotype. We examine the effects of reinfection with the same serotype, study symmetric epidemiological characteristics and investigate the effects of antibody-dependent enhancement on dengue transmission dynamics by using a mathematical model. We analyse the stability of the model and perform global sensitivity analysis to determine the most influential parameters. We found that the model has four equilibrium points: disease-free, two partially endemic and coexistence equilibria. We also presented two Basic Reproductive Ratio R i associated with the first and the second strain of the viruses. The stability of the model is determined by the condition of basic reproductive ratio. We found that when the degree of immunity to the same strain, κ , is between zero and one, the existence of endemic equilibrium is determined by κ ℜ i , where ℜ i is the basic reproductive ratio. Furthermore, we found that reinfection with the same serotype contributes an increase in the number of primary and secondary dengue cases. The results suggest that it is likely that reinfection with the same serotype may be one of the underlying factors causing an increase in the number of secondary infection. [ABSTRACT FROM AUTHOR]

Abstract Let G be a connected graph. The edge k -partiteness of G is the minimum number of edges whose deletion from G yields a k -partite graph. The Kirchhoff index Kf (G) of G is the sum of the resistance distance between all unordered pairs of vertices. In this paper, we study the problem to determine the minimum Kirchhoff index of graphs with a given edge k -partiteness. First, we theoretically characterize the graphs with minimum Kirchhoff index in this graph family when the edge k -partiteness is not big compared to the number of vertices of G. Then we propose an exhaustive search algorithm to find the optimal graphs. At last, three strategies are used to reduce the computation complexity of our algorithm and several performance comparisons of these strategies are given. [ABSTRACT FROM AUTHOR]

Abstract The Preisach model of hysteresis has two parts: a geometrical staircase and a density or weighting function. In typical applications, the underlying density function of hysteresis operators is estimated through partial derivatives of first order reversal curves, or a priori assumed to obey simple functional forms like Gaussian, Lorenzian etc. Here we take a more agnostic and empirical approach, and expand the density in a general form using the spectrum of the Laplace operator on a bounded triangular domain. Transforming the input to the same bounded domain, we have a nonlinear parameter fitting problem. We fit parameters to our own magnetic hysteresis data directly using complex waveforms, for both soft and hard loops. For hard loops, if the Preisach density is to be kept strictly nonnegative (as is usual), a nonlinear transformation of the Preisach output is needed. Additionally, the Preisach density is consists of a single hump for soft loops and three distinct humps for hard loops. Our fitted density function, based on a general expansion, contains several coefficients, but subsequent simulation is quick. The main contribution of this paper is a direct demonstration of fitting the density function without making a priori assumptions about the functional form. [ABSTRACT FROM AUTHOR]

Abstract Investors often co-invest in the same project together. As the payoff of the project realizes, how to share the total payoff is in consideration. With this inspiration, an investor sharing game is proposed in this paper, where investors’ payoffs relate to their investing amount and the degree of monopoly in the industry market. Economically, the degree of monopoly in the market is introduced in the game by a parameter α that affects the evolutionary process. The distribution of investing amounts is assumed to satisfy the Pareto distribution in terms of the empirical wealth distribution. The simulation on WS small-world networks shows that cooperative behaviors will prosper by the union of investors who invest less amounts in a less monopolized market. The higher power of the Pareto distribution of investing amounts also results in more cooperators in equilibriums. Furthermore, as the degree of monopoly swings, the density of cooperators is higher and more stable in a more random small-world network. The findings may be helpful in understanding the effect of network structure on the emergence of cooperation. [ABSTRACT FROM AUTHOR]

Highlights • A time delay model of the complex interaction between Tumor, CD8+T cells and T - helper cells. • The model undergoes Hopf bifurcation in which time delay plays an important role to destabilize the system. • Extensive numerical simulations are performed to validate our analytical findings. Abstract In this paper, we consider a three-dimensional nonlinear delay differential system (tumor cells, cytotoxic-T lymphocytes, T-helper cells) with single interaction delay. We perform linear stability of the equilibria and the existence of Hopf bifurcation in which the discrete time delay is used as a bifurcation parameter. We estimate the length of delay to preserve the stability of period-1 limit cycle. We also investigate the direction, period, and the stability of bifurcated periodic solutions by applying normal form method and center manifold theory. We observe that the discrete time delay plays an important role in stability switching. Numerical simulations are presented to illustrate the rich dynamical behavior of the model with different values for the time delay τ including the existence of periodic oscillations, which demonstrate the phenomena of long-term tumor relapse. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we propose a new method for pricing double-barrier options with moving barriers under the Black–Scholes and the CEV models. First of all, by applying a variational technique typical of the boundary element method, we derive an integral representation of the double-barrier option price in which two of the integrand functions are not given explicitly but must be obtained solving a system of Volterra integral equations of the first kind. Second, we develop an ad hoc numerical method to regularize and solve the system of integral equations obtained. Several numerical experiments are carried out showing that the overall algorithm is extraordinarily fast and accurate, even if the barriers are not differentiable functions. Moreover the numerical method presented in this paper performs significantly better than the finite difference approach. [Copyright &y& Elsevier]