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Abstract: This special issue contains the revised and extended versions of three papers presented in the 4th Workshop on Advances in Model-Based Testing (A-MOST 2008). In addition to an executive summary of these three papers, this preface briefly reviews the papers published in the four editions of the A-MOST workshop. We hope that the reader will find this special issue interesting and informative. [Copyright &y& Elsevier]

Compared with the two-valued memristor, the three-valued memristor has higher data density, richer dynamic characteristics, and more potential in digital logic and chaotic circuit. The present model of the three-valued memristor has several limitations. It doesn't perform well enough in three-valued applications since its hysteresis loops are linear and asymmetric. The mathematical model of the three-valued memristor with nonlinear and symmetric hysteresis loops is proposed in this research. To further investigate the electrical characteristics of the three-valued memristor, a circuit emulator of the memristor has been constructed with fundamental components. Multisim simulations and hardware experiments demonstrate the emulator's effectiveness. The three-valued memristor application in chaotic circuits shows fascinating dynamic characteristics and lays the foundation for future research. • The mathematical model of the three-valued memristor with nonlinear and symmetric hysteresis loops is proposed in this paper. • A circuit emulator of the three-valued memristor is proposed and verified using hardware and software. • The three-valued memristor application in chaotic circuits shows fascinating dynamic characteristics. [ABSTRACT FROM AUTHOR]

In this article, we consider a 4-dimensional predator–prey chemostat model of nitrogen-phytoplankton-rotifer interactions with staged structure proposed by Blasius et al. (2020). Although it is still difficult to prove the simulation observations in Blasius et al. (2020) by mathematical arguments, we explore the dynamics in order to better understand the dynamical mechanism of cyclic persistence for this model. We firstly investigate the corresponding system without staged structure, i.e., when the juvenile is absent, the asymptotical behavior of the solutions is given. When the juvenile is present, a threshold condition for the uniform persistence of the 4-dimensional system is provided. Finally, by choosing the life development time delay as a bifurcation parameter, we show that the system admits periodic solutions near one semi-equilibrium undergoing Hopf bifurcation. The rigorous theoretical analytic work in this paper provides some helpful transient information between coherent oscillation and non-coherent oscillation described by the experimental data of Blasius et al. (2020). [ABSTRACT FROM AUTHOR]

In wet-lab experiments, the slime mold Physarum polycephalum has demonstrated its ability to tackle a variety of computing tasks, among them the computation of shortest paths and the design of efficient networks. For the shortest path problem, a mathematical model for the evolution of the slime is available and it has been shown in computer experiments and through mathematical analysis that the dynamics solves the shortest path problem. In this paper, we generalize the dynamics to the network design problem. We formulate network design as the problem of constructing a network that efficiently supports a multi-commodity flow problem. We investigate the dynamics in computer simulations and analytically. The simulations show that the dynamics is able to construct efficient and elegant networks. In the theoretical part we show that the dynamics minimizes an objective combining the cost of the network and the cost of routing the demands through the network. We also give alternative characterizations of the optimum solution. [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]

For a Tychonoff space X , we denote by C p ( X ) the space of all real-valued continuous functions on X with the topology of pointwise convergence. In this paper we continue to study different selectors for sequences of dense sets of C p ( X ) started to study in the paper [14] . A set A ⊆ C p ( X ) will be called 1 -dense in C p ( X ) , if for each x ∈ X and an open set W in R there is f ∈ A such that f ( x ) ∈ W . We give the characterizations of selection principles S 1 ( A , A ) , S f i n ( A , A ) and S 1 ( S , A ) where • A — the family of 1-dense subsets of C p ( X ) ; • S — the family of sequentially dense subsets of C p ( X ) , through the selection principles of a space X . In particular, we give the functional characterizations of the Rothberger and Menger properties. [ABSTRACT FROM AUTHOR]

Typed models of connector/component composition specify interfaces describing ports of components and connectors. Typing ensures that these ports are plugged together appropriately, so that data can flow out of each output port and into an input port. These interfaces typically consider the direction of data flow and the type of values flowing. Components, connectors, and systems are often parameterised in such a way that the parameters affect the interfaces. Typing such connector families is challenging. This paper takes a first step towards addressing this problem by presenting a calculus of connector families with integer and boolean parameters. The calculus is based on monoidal categories, with a dependent type system that describes the parameterised interfaces of these connectors. We use families of Reo connectors as running examples, and show how this calculus can be applied to Petri Nets and to BIP systems. The paper focuses on the structure of connectors— well-connectedness —and less on their behaviour, making it easily applicable to a wide range of coordination and component-based models. A type-checking algorithm based on constraints is used to analyse connector families, supported by a proof-of-concept implementation. [ABSTRACT FROM AUTHOR]

In this paper, it is addressed by mathematical analysis how network-oriented modeling relates to the dynamical systems perspective on mental processes. It has been mathematically proven that any dynamical system can be modeled as a temporal-causal network model and that any adaptive dynamical system (of any order) can be modeled by a self-modeling network (of the same order). [ABSTRACT FROM AUTHOR]

Tumor growth models have proved as an important tool to produce an engineering background for cancer therapy either by designing therapeutic procedures combined with control engineering or by using the models for simulations and evaluation of treatment procedures. Mathematical modeling has been critical for the description of tumor growth, which is a highly complex process, as a finely chiseled tumor growth model always outlines the measurements and the physiological processes of the tumors. Therefore, a mathematical model involving partial differential equations for the growth of tumor have been studied, modified and developed in this paper. It is based on the deterministic model of an avascular tumor growth which is framed in a system of nonlinear coupled PDEs, describing the proliferating, quiescent, necrotic, and surrounding cells densities, accompanied by a supply of the nutrients. These equations are explained numerically by the Finite Difference Method. Furthermore, the simulations are carried out by introducing the Gompertz growth rate function for mitosis rate function g(c) of proliferating cells in the model. The discretization forms a system of coupled nonlinear difference equations which are solved at each iteration. The algorithm is implemented sequentially in MATLAB 2018a and numerical results suggest that the employed model is an authentic tool for analyzing the dynamics of tumor. [ABSTRACT FROM AUTHOR]

Matt Blum conjectured that the- number of tilings of a hexagonal dungeon with side-lengths a , 2 a , b , a , 2 a , b (for b ≥ 2 a ) equals 1 3 2 a 2 1 4 ⌊ a 2 ∕ 2 ⌋ . Ciucu and the author of the present paper proved the conjecture by using Kuo’s graphical condensation method. In this paper, we investigate a 3-parameter refinement of the conjecture and its application to enumeration of tilings of several new types of the hexagonal dungeons. [ABSTRACT FROM AUTHOR]

Strict distinguishability is the property of two systems to generate identical output signals only for the zero control input and the zero initial state vector. The objective of this paper is to characterize this property for single-output nonlinear control-affine systems. In this context, we first introduce the indistinguishability zone of the systems. This zone represents the set of control inputs and initial state vectors that make the output signals of the systems indistinguishable. The explicit identification of the elements of this set is proposed in the paper. From this result, necessary and sufficient conditions for strict distinguishability are then established under suitable assumptions. [ABSTRACT FROM AUTHOR]

This paper proposes a novel optimization algorithm for grouping problems, the Grouping Coral Reefs Optimization algorithm, and describes its application to a Mobile Network Deployment Problem (MNDP) under four optimization criteria. These criteria include economical cost and coverage, and also electromagnetic pollution control and capacity constraints imposed at the base stations controllers, which are novel in this study. The Coral Reefs Optimization algorithm (CRO) is a recently-proposed bio-inspired approach for optimization, based on the simulation of the processes that occur in coral reefs, including reproduction, fight for space or depredation. This paper presents a grouping version of the CRO, which has not previously evaluated before. Grouping meta-heuristics are characterized by variable-length encoding solutions, and have been successfully applied to a number of different optimization and assignment problems. The GCRO proposed is a novel contribution to the intelligent systems field, which is able to improve results obtained by two alternative grouping algorithms such as grouping genetic algorithms and grouping Harmony Search. The performance of the proposed GCRO and the algorithms for comparison has been tested with real data in a case study of a MNDP in Alcalá de Henares, Madrid, Spain. [ABSTRACT FROM AUTHOR]

Our paper introduces a new methodology to solve group decision-making problems under fuzzy and dynamic environment. The methodology takes group members’ linguistically defined pair wise preferences of alternatives in different time intervals and aggregates them across the intervals to obtain each member's net preference levels. Each member's net preference levels are again aggregated across the members to obtain the group's preference. Our paper attaches higher importance to the members whose involvement in the decision process is more recent than the members who opined their views in the past. The fuzzy aggregation operator, IOWA (Induced Ordered Weighted Average) is used to aggregate their views in accordance to their importance in the group. The Ranked_List algorithm, introduced in our paper, inputs the aggregated views of the members in pair wise form and produces the set of sequences of ranked list of alternatives representing the group's consensus view as output. The Ranked_List algorithm is validated and analyzed through a series of synthetic data sets and its results are compared with a movie selection case study. The methodology is illustrated with a numerical example. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to connect R-fuzzy sets and type-2 fuzzy sets, so as to provide a practical means to express complex uncertainty without the associated difficulty of a type-2 fuzzy set. The paper puts forward a significance measure, to provide a means for understanding the importance of the membership values contained within an R-fuzzy set. The pairing of an R-fuzzy set and the significance measure allows for an intermediary approach to that of a type-2 fuzzy set. By inspecting the returned significance degree of a particular membership value, one is able to ascertain its true significance in relation, relative to other encapsulated membership values. An R-fuzzy set coupled with the proposed significance measure allows for a type-2 fuzzy equivalence, an intermediary, all the while retaining the underlying sentiment of individual and general perspectives, and with the adage of a significantly reduced computational burden. Several human based perception examples are presented, wherein the significance degree is implemented, from which a higher level of detail can be garnered. The results demonstrate that the proposed research method combines the high capacity in uncertainty representation of type-2 fuzzy sets, together with the simplicity and objectiveness of type-1 fuzzy sets. This in turn provides a practical means for problem domains where a type-2 fuzzy set is preferred but difficult to construct due to the subjective type-2 fuzzy membership. [ABSTRACT FROM AUTHOR]

The presence of the golden mussel in Brazil is a matter of great concern and causes harm to the country, particularly affecting the power generation sector. Infestation control represents a challenge, and there is a need to mathematically describe the dynamics of the problem. This work proposes to analyze a mathematical model based on differential equations that relate the populations of larvae, mussels, and algae. For this model, the critical points and stationary states are determined, seeking steady-state conditions stability, through the basic reproduction rate. In addition, it presents the sensitivity analysis of the parameters involved. The paper results are relevant as they allow mathematical interpretation of the golden mussel infestation potential through the basic reproduction rate. Furthermore, the sensitivity analysis suggests how important the parameters are for this potential. For that matter, this work can provide baseline information to guide future control strategies as it provides quantification of the species involved over time as well as a condition for infestation. • Mussel-algae interaction model. • Stability analysis of stationary solutions of the model. • Basal reproduction rate for the golden mussel model. [ABSTRACT FROM AUTHOR]

This paper shows that a hazard function can be additively decomposed, and with the additively decomposed hazard function, it shows that one can identify the others' effects which come from interactions between potential adopters and the adopters who bought at every adoption time interval. Also, from the additive decomposition of the discrete Bass hazard function, it derives the discrete Bass model which is consistent with the continuous version of Bass model. Furthermore, the coefficients of the derived discrete Bass model are expressed as the functions of coefficients of the continuous Bass model. Based on the derived discrete Bass model, thus, this paper presents a valuation scheme (calculator) for adopter groups which are classified by every observation time. The valuation calculator allows managers to calculate adopters' values only with the estimates of the continuous Bass model. [ABSTRACT FROM AUTHOR]

This paper studies zeros of networked linear systems with time-invariant interconnection topology. While the characterization of zeros is given for both heterogeneous and homogeneous networks, homogeneous networks are explored in greater detail. In the current paper, for homogeneous networks with time-invariant interconnection dynamics, it is illustrated how the zeros of each individual agent’s system description and zeros definable from the interconnection dynamics contribute to generating zeros of the whole network. We also demonstrate how zeros of networked systems and those of their associated blocked versions are related. [ABSTRACT FROM AUTHOR]

In this paper we continue work from a previous paper on the fragility and indestructibility of the tree property. We present the following: (1) A preservation lemma implicit in Mitchell's PhD thesis, which generalizes all previous versions of Hamkins' Key lemma. (2) A new proof of the ‘superdestructibility’ theorems of Hamkins and Shelah. (3) An answer to a question from our previous paper on the apparent consistency strength of the assertion “The tree property at ℵ 2 is indestructible under ℵ 2 -directed closed forcing”. (4) Two models for successive failures of weak square on long intervals of cardinals. [ABSTRACT FROM AUTHOR]

In the last decades, gain-scheduling control techniques have consolidated as an efficient answer to analysis and synthesis problems for non-linear systems. Among the approaches proposed in the literature, the linear parameter varying (LPV) and Takagi–Sugeno (TS) paradigms have proved to be successful in dealing with the different trials that the analyzer, or the designer, of a gain-scheduled control system has to face. Despite the strong similarities between the two paradigms, research on LPV and TS systems has been performed in an independent way and some results that could be useful for both paradigms were obtained only for one of them. However, in recent works, some clues that there is a very close connection between LPV and TS worlds have been presented. The present paper openly addresses the presence of strong analogies between LPV and TS models, in an attempt to establish a bridge between these two worlds, so far considered different. In particular, this paper addresses the modeling problem, presenting two methods for the automated generation of LPV and TS systems, and introducing some measures in order to compare the obtained models. A mathematical example is used to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

The paper presents results of analysis of existing mathematical models for orbital debris fragments breakup in high velocity collisions. The breakup models are modified and updated taking into account the latest breakup criteria, experimental data and basic conservation laws. The model examples are analyzed, the criterion is developed for distinguishing fragments, which will stay in orbit after collision event. • Analysis of mathematical models for orbital debris fragments breakup is presented. • The breakup models are modified and updated. • Criterion for distinguishing fragments, which will stay in orbit, is developed. [ABSTRACT FROM AUTHOR]

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research. [ABSTRACT FROM AUTHOR]

In this paper, a new mathematical model related to a mining extraction project under uncertainty is proposed. The underlying stochastic factors are the commodity price and the remaining resource, the dynamics of which are introduced. In the stochastic differential equation satisfied by the remaining resource, the extraction rate is involved. The main innovative modelling feature, comes from considering the extraction rate to be proportional to the commodity price, which is more realistic. In this way, an ultraparabolic hypoelliptic differential operator governs the associated PDE of the mathematical model. The mathematical analysis allows to obtain the existence and uniqueness of a classical solution. Uniqueness follows from a suitable Feynman–Kac representation formula. Existence of a classical solution is obtained after a suitable change of variables, the determination of sub and supersolutions and passing to the limit from problems in bounded domains to the unbounded one. For the numerical solution, after justifying the required boundary conditions on the computational bounded domain, the proposed numerical techniques mainly consist of a Crank–Nicolson characteristics method for the time discretization to cope with the convection dominating setting and Lagrange finite elements for the discretization in the commodity and resource variables. Finally, some numerical examples are discussed to illustrate the good performance of the new model and the proposed numerical methods. [ABSTRACT FROM AUTHOR]

• A meta-plate with high-static-low-dynamic stiffness local resonators is proposed. • Mathematical modeling of the meta-plate is established and solved by plane-wave expansion method. • The band gaps are predicted analytically and validated by numerical simulations. • The meta-plate with HSLD resonators can generate very low-frequency band gaps. Aiming to attenuate very low-frequency flexural wave in a thin plate, this paper proposes a meta-plate model by periodically attaching high-static-low-dynamic-stiffness (HSLDS) resonators onto the thin plate. The HSLDS resonator consists of a linear spring with a negative stiffness mechanism (NSM) in parallel, and thus its stiffness can be adjusted to any low values within a range from zero to the stiffness of the linear spring. Using the plane-wave expansion (PWE) method, and considering the linearized stiffness of the resonator, the dispersion relation of the meta-plate can be derived and the band structure can be obtained. A dynamic model of the meta-plate with the original nonlinear stiffness under external excitations is also established. The numerical simulations are carried out by the Galerkin method to evaluate the band structure and study the propagation of the flexural wave along the meta-plate with different azimuth angles. The analytical results exhibit good agreement with the numerical ones, which indicates that the proposed meta-plate can create a very low-frequency band gap. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we present a multipoint machining method for the 5-axis machining of triangulated surfaces with radiused end mills. The main idea is to drop the tool onto the surface to find an initial point of contact, and then rotate the tool while maintaining tangency with this initial point of contact until a second point of contact is found. The proposed procedure ensures a gouge-free position with two points of contact, allowing for a larger side step than a single point of contact method. This proof of concept paper presents the mathematical equations that must be solved to position the tool with two points of contacts on an STL surface. The paper further verifies the concept with simulations and presents experimental results to confirm the simulations. [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: Wireless Sensor Networks (WSNs) have been utilized by many critical applications such as military and health care monitoring. Such applications require special Quality of Service (QoS) treatment. However, the components of sensor nodes suffer from different limitations including the scarce energy source, limited processing capabilities, and limited storage space. At the same time, nodes are supposed to live for long time. This could occur when the energy is balanced on the active nodes in the network. This paper handles the problem of QoS in Wireless Sensor Networks (WSNs). The paper considers the limitation of the nodes in handling many messages at the same time especially the sink node. Therefore, nodes can coordinate with each other to minimize the number of dropped message. Defining some nodes to send to the sink node at certain time allows other nodes to go to sleep. Certainly, this QoS control enhances the operation of the network and positively affect the nodes’ consumed energy. This work applies one of the game theory schemes which is Gur game. The paper proposes two QoS control techniques with Quick Convergence called Periodic Gur Game (PGur) and Adaptive Periodic Gur Game (APGur). These two approaches are evaluated using different sets of experiments. [Copyright &y& Elsevier]

Abstract: Most components undergo tests after they are designed and are redesigned if necessary. Tests help designers find unsafe and overly conservative designs, and redesign can restore safety or increase performance. In general, the expected changes to the performance and reliability of the design after the test and redesign are not considered. In this paper, we explore how modeling a future test and redesign provides a company an opportunity to balance development costs versus performance by simultaneously designing the design and the post-test redesign rules during the initial design stage. Due to regulations and tradition, safety margin and safety factor based design is a common practice in industry as opposed to probabilistic design. In this paper, we show that it is possible to continue to use safety margin based design, and employ probability solely to select safety margins and redesign criteria. In this study, we find the optimum safety margins and redesign criterion for an integrated thermal protection system. These are optimized in order to find a minimum mass design with minimal redesign costs. We observed that the optimum safety margin and redesign criterion call for an initially conservative design and use the redesign process to trim excess weight rather than restore safety. This would fit well with regulatory constraints, since regulations usually impose minimum safety margins. [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]

Abstract: The decision problem considered in this paper is a hierarchical workforce scheduling problem in which a higher qualified worker can substitute for a lower qualified one, but not vice versa, labour requirements may vary, and each worker must receive n off-days a week. Within this context, five mathematical models are discussed. The first two of these five models are previously published. Both of them are for the case where the work is indivisible. The remaining three models are developed by the authors of this paper. One of these new models is for the case where the work is indivisible and the other two are for the case where the work is divisible. The three new models are proposed with the purpose of removing the shortcomings of the previously published two models. All of the five models are applied on the same illustrative example. Additionally, a total of 108 test problems are solved within the context of two computational experiments. [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: Two similar stability notions are considered; one is the long established notion of convergent systems, the other is the younger notion of incremental stability. Both notions require that any two solutions of a system converge to each other. Yet these stability concepts are different, in the sense that none implies the other, as is shown in this paper using two examples. It is shown under what additional assumptions one property indeed implies the other. Furthermore, this paper contains necessary and sufficient characterizations of both properties in terms of Lyapunov functions. [Copyright &y& Elsevier]

Abstract: This paper focuses on two major issues in cellular manufacturing, namely manpower allocation and cell loading. Although significant work has been done in both of these fields, research to minimize the Total Tardiness (TT) within a multi-cell environment has been limited. The methodology adopted in this paper is a two-step one. First, manpower allocation for operations within a cell is determined using mathematical models. This step also includes variations of the mathematical model for sharing of operators between operations and sharing of operators with restrictions. The models with little or no restrictions have found to yield a higher production rate than the model with no operator sharing allowed. The next step involves a mathematical model for cell loading. The performance measure examined in this phase is the total tardiness subject to total Crew Size restriction. The total tardiness is reduced as the total crew size increases. However, it was also found that selection of alternative cell configurations affect the results as well total crew size. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce the concept of -fuzzy frame and study the relationships between the categories of -fuzzy frames and -fuzzy topological spaces. We also introduce separation axioms for -fuzzy frames and study their properties as well as the relationships between them and the separation axioms of -fuzzy topological spaces. At the end of the paper, the concept of the degree of fuzzy compactness is presented. [Copyright &y& Elsevier]

Abstract: Designing materials for targeted performance requirements as required in Integrated Computational Materials Engineering (ICME) demands a combined strategy of bottom–up and top–down modeling and simulation which treats various levels of hierarchical material structure as a mathematical representation, with infusion of systems engineering and informatics to deal with differing model degrees of freedom and uncertainty. Moreover, with time, the classical materials selection approach is becoming generalized to address concurrent design of microstructure or mesostructure to satisfy product-level performance requirements. Computational materials science and multiscale mechanics models play key roles in evaluating performance metrics necessary to support materials design. The interplay of systems-based design of materials with multiscale modeling methodologies is at the core of materials design. In high performance alloys and composite materials, maximum performance is often achieved within a relatively narrow window of process path and resulting microstructures. Much of the attention to ICME in the materials community has focused on the role of generating and representing data, including methods for characterization and digital representation of microstructure, as well as databases and model integration. On the other hand, the computational mechanics of materials and multidisciplinary design optimization communities are grappling with many fundamental issues related to stochasticity of processes and uncertainty of data, models, and multiscale modeling chains in decision-based design. This paper explores computational and information aspects of design of materials with hierarchical microstructures and identifies key underdeveloped elements essential to supporting ICME. One of the messages of this overview paper is that ICME is not simply an assemblage of existing tools, for such tools do not have natural interfaces to material structure nor are they framed in a way that quantifies sources of uncertainty and manages uncertainty in representing physical phenomena to support decision-based design. [Copyright &y& Elsevier]

Abstract: Recently, exploiting the centroids of stability regions (admissible regions) to be used in tuning two-parameter controllers has been considered as an approach to obtain non-fragile two-parameter controllers. Such an approach can be extended for three-dimensional stability spaces (admissible spaces) by considering the center of mass of these spaces in tuning three-parameter controllers. In this paper, the mentioned approach is used to tune PID controllers for controlling integrator plus dead-time (IPDT) and first order plus dead-time (FOPDT) processes. It is shown that the tuning method resulted from this approach is very similar to the Ziegler–Nichols step response tuning method. Consequently, this paper presents an analytic non-fragility justification for the mentioned tuning method. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce and consider a new class of equilibrium variational inequalities, called the mixed general equilibrium bifunction variational inequalities. We suggest and analyze some proximal methods for solving mixed general equilibrium bifunction variational inequalities using the auxiliary principle technique. Convergence of these methods is considered under some mild suitable conditions. Several cases are also discussed. Results in this paper include some new and known results as special cases. [Copyright &y& Elsevier]

Abstract: Since the celebrated Mackey–Glass model of respiratory dynamics was introduced in 1977, many results on its qualitative behavior have been obtained, including oscillation, stability and chaos. The paper reviews some known properties and presents new results for more general models: equations with time-dependent parameters, several delays, a positive periodic equilibrium and distributed delays. The problems considered in the paper involve existence, positivity and permanence of solutions, oscillation and global asymptotic stability. In addition, some general approaches to the study of nonlinear nonautonomous scalar delay equations are outlined. The paper generalizes and unifies existing results and provides an outlook on further studies. [Copyright &y& Elsevier]

Abstract: This paper is to illustrate that the main result of the paper [R.U. Verma, Generalized over-relaxed proximal algorithm based on -maximal monotonicity framework and applications to inclusion problems, Mathematical and Computer Modelling 49 (2009) 1587–1594] is incorrect. The convergence rate of the over-relaxed proximal point algorithm should be greater than 1. Moreover, the strong convergence and the unique solution may not be proved accordingly in the paper by Verma. [Copyright &y& Elsevier]

Abstract: There exist a number of definitions of the concept of risk. Very few of them directly express how “exposure” and “risk exposure” are connected to the risk. Clearly there is a connection, but it is not evident how these concepts are related. In this paper we provide an in-depth study of this issue. A model is presented which links risk sources, hazards/threats and exposed systems. Using this model, it is shown how the concepts of exposure and risk exposure can be given plausible explanations for some common risk perspectives. The model provides new insights on some main perspectives on risk used for risk assessment and risk management. A set of adjusted risk definitions, all reflecting the exposure dimension, is considered. The principal aim of this paper is to contribute to a clarification of the issue in order to strengthen the foundations of the meaning and characterisation of risk, and in this way provide a basis for improved risk management. [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: Publishing papers in the area of forecasting natural gas consumption has begun in the middle of last century and led to a tremendous surge in research activities in the past decade. This paper presents a state-of-the-art survey of forecasting natural gas consumption. Purpose of this paper is to provide analysis and synthesis of published research in this area from beginning to the end of 2010, insights on applied area, used data, models and tools to achieve usable results, in order to be helpful base for future researchers. [Copyright &y& Elsevier]

Abstract: A two-component reaction–diffusion system modelling a class of spatially structured epidemic systems is considered. The system describes the spatial spread of infectious diseases mediated by environmental pollution. A relevant problem, related to the possible eradication of the epidemic, is the so called zero stabilization. In a series of papers, necessary conditions, and sufficient conditions of stabilizability have been obtained. It has been proved that it is possible to diminish exponentially the epidemic process in the whole habitat, just by reducing the concentration of the pollutant in a nonempty and sufficiently large subset of the spatial domain. The stabilizability with a feedback control of the harvesting type is related to the magnitude of the principal eigenvalue of a certain operator which is not selfadjoint. In this paper, we have proposed an approximating method for this principal eigenvalue. Further, we have faced the problem of finding the optimal position (by translation) of the support of the feedback stabilizing control in order to minimize both the infected population and the pollutant at a certain finite time. [Copyright &y& Elsevier]