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Abstract: The purpose of this paper is to obtain the risk-neutral drift of the state variables directly from market data in a multifactor commodity futures model. Note that the risk-neutral drift is a key factor in the general asset pricing theory but it is not observable. In this paper, we derive some exact results which relate the risk-neutral drifts to the slope of the commodity futures price jointly with the factors. This fact allows us to estimate some of the coefficients of the pricing partial differential equation directly from the futures data available in the markets. Moreover, we do not have to estimate either the physical drift or the market price of risk. Therefore we considerably reduce the number of functions to estimate and, as a consequence, we reduce the computational cost as well as the misspecification error. In order to investigate the finite sample properties of this approach we carry out some numerical experiments. Finally, an application to crude oil and natural gas futures contracts traded at the New York Mercantile Exchange (NYMEX) is also illustrated. [Copyright &y& Elsevier]

Abstract: The aim of this paper is the evaluation and validation of the Eulerian–Lagrangian Spray Atomization (ELSA) model implemented in a CFD code by Renault. ELSA is an integrated model for capturing the whole spray evolution, in particular including primary break-up and secondary atomization. Two-dimensional simulations have been performed during the study, which is in fact enough to capture some of the main features of the spray, such as the spray penetration and the axial velocity. A mesh independence study has also been carried out in order to characterize the lowest mesh size that can be used to correctly characterize the spray. Furthermore, the two-equation turbulence model has been adjusted by changing some of the parameters of the dissipation rate transport equation in order to accurately characterize the spray. Finally some analyses of the results obtained, in terms of penetration, liquid mass fraction and droplet number and size, are presented in the last section of the paper. [Copyright &y& Elsevier]

Abstract: In this paper we investigate an interesting subclass of analytic univalent functions in the open unit disc on the complex plane. This class was introduced by Sokół [J. Sokół, On starlike functions connected with Fibonacci numbers, Folia Scient. Univ. Tech. Resoviensis 175 (1999) 111–116]. The class is strongly related to the class considered earlier by the authors of the present work in their paper [J. Dziok, R. K. Raina, J. Sokół, Certain results for a class of convex functions related to shell-like curve connected with Fibonacci Numbers, Comput. Math. Appl. 61 (2011) 2606–2613]. Apart from furnishing some genuine remarks, we present certain new results for the class of functions, and also mention some relevant cases for this function class. [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: 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 investigate the optimal risk control and dividend distribution problem for a diffusion model with a terminal value. Usually the insurer cedes risk by means of a reinsurance contract, and pays dividends out dynamically from the surplus. Consider that the insurer is trying to balance risk control and dividend payout in terms of reinsurance and dividend distribution policies. Then the objective is set to make a dynamic choice of reinsurance policy and dividend distribution policy, which maximizes the sum of the expected discounted dividends up to ruin time and the expected discounted terminal value. There are two novelties in this paper. Firstly, we formulate the optimal control problem in terms of general reinsurance control policies. Each of the proportional reinsurance, the excess-of-loss reinsurance and combination of the two can be treated as a special case. It is shown that, under an expected premium principle, the dynamic excess-of-loss reinsurance is of optimal type within the general reinsurance contracts. Secondly, considering the excess-of-loss reinsurance policy and terminal value, we obtain the explicit expressions for the value function and optimal control policies by solving the HJB equation method. At the end of this paper numerical calculations are done to illustrate the influence of the terminal value on the value function and optimal policies as well. [Copyright &y& Elsevier]

Abstract: In this paper, a novel computer virus propagation model with dual delays and multi-state antivirus measures is considered. Using theories of stability and bifurcation, it is proven that there exists a critical value of delay for the stability of virus prevalence. When the delay exceeds the critical value, the system loses its stability and a Hopf bifurcation occurs. Furthermore, the explicit formulas determining the stability and direction of bifurcating periodic solutions are obtained by applying the center manifold theorem and the normal form theory. Finally, some numerical simulations are performed to verify the theoretical analysis. The conclusions of this paper can contribute to a better theoretical basis for understanding the long-term actions of virus propagation in networks. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to design a neural network based adaptive control scheme for redundant manipulators in the presence of model uncertainties and external disturbances together with multiple self-motion criteria. With reference to the paper (N. Kumar, V. Panwar, N. Sukavanam, S.P. Sharma, J.H. Borm, Neural network based nonlinear tracking control of kinematically redundant robot manipulators, Mathematical and Computer Modelling 53 (2011) 1889–1901), an adaptive mechanism is also developed to estimate the uncertain bound of external disturbances and neural network approximation error etc. without requirement of known bounds. By Lyapunov method asymptotic error convergence can be guaranteed for both task-space and sub-task tracking errors. A comparative simulation study with a robust controller and the proposed controller are included for a 3 link planar robot manipulator. [Copyright &y& Elsevier]

Abstract: This is a continuation of our paper [M. Liu, K. Wang, Asymptotic properties and simulations of a stochastic logistic model under regime switching, Math. Comput. Modelling 54 (2011) 2139–2154]. First, we establish the sufficient conditions for stochastic permanence which are much weaker than those in our previous paper. Then we study some new asymptotic properties of this model. The lower-growth rate and the upper-growth rate of the positive solution are investigated. The superior limit of the average in time of the sample path of the solution is also estimated. Finally, some simulation figures are introduced to illustrate the main results. Some recent investigations are improved and generalized. [Copyright &y& Elsevier]

Abstract: This paper investigates the optimal length of lease period and maintenance policy for leased equipment. In order to have steady revenue, the lessor (owner) of equipment may provide a discount to encourage the lessee (user) to sign a contract with a longer lease period. However, as the lease period increases, the maintenance cost also increases due to the deterioration or usage of the equipment. Therefore, there is a need to determine an appropriate length of lease period and a corresponding maintenance policy for the leased equipment from the viewpoint of the lessor such that the expected total profit is maximized. In this paper, the following maintenance scheme is considered. When the leased equipment fails, a minimal repair is conducted to bring the equipment back to an operating condition. Furthermore, when the age of the equipment reaches a specified level (called as a control-limit), an imperfect preventive maintenance (PM) is carried out to avoid possible failures. Under this maintenance scheme, the mathematical model of the expected total profit is developed and the optimal length of lease period and the corresponding optimal maintenance policy are derived. Finally, some numerical examples are given to illustrate the effects of the length of lease period and the maintenance policy on the expected total profit. [Copyright &y& Elsevier]

Abstract: The 2004 Basel Committee on Banking Supervision Accord (known as Basel II) provides a common framework for banks to determine their minimum capital requirements for solvency purposes. For credit risk (the most important one for banking) Basel II uses an asymptotic single risk factor (ASRF) model and, as we demonstrate in the paper, assumes two fundamental hypotheses: Firstly, that there is only one risk factor common to all banks; and secondly, that the number of debtors in bank portfolios is high enough to ensure that no single debtor’s behaviour can have a significant impact on the portfolio value as a whole. This allows capital requirements to be estimated by using a model based on the percentage of defaulting borrowers . The model only requires values for two variables: the probability of default and loss if default occurs. Using a 99% likelihood and assuming that all sectors are equally correlated, the model estimates through the cumulative distribution function for the Gaussian distribution. But many bank portfolios do not fit these hypotheses, and therefore the ASRF model underestimates actual capital requirements. Thus, a surcharge for concentration risk is required. There are two kinds of concentration risk (sector and name concentration risk), each one corresponding to the violation of one of the above mentioned hypotheses. Supervisory authorities are currently developing models to incorporate this surcharge into banking solvency rules. In Spain, the Spanish Central Bank bases its surcharge proposal for sectorial concentration on the Herfindahl–Hirschman Index (HHI). In this paper we show that HHI treats all sectors as equally risky and propose an alternative index (CI) in which sectors are weighted according to risk. Moreover, our index also incorporates the relations between each pair of sectors (in the HHI framework no sectorial relationship is considered). Our proposal is based on an adjusted variance–covariance matrix, in which negative covariances have been equalled to 0. We demonstrate the HHI is a particular case of our proposed index, by means of simplifying hypotheses. As we will show, the proposed index has two fundamental properties: it is lower and upper bounded; and it decreases as concentration and/or risk decreases. These properties allow the index to be incorporated into bank risk management models. In this way bank estimations can improve upon those based on the supervisory model and, according to banking rules, can also be used for determining the capital surcharge for sectorial concentration. [Copyright &y& Elsevier]

Abstract: Snow cover is a common and relatively stable land cover condition in winter for cold north regions in China. Snow cover has significant effects on water and heat transfers in frozen soil; it needs to be considered in the study of frozen soil water–heat coupled movements. On the basis of previous research results and physical process analysis of water and heat movements in snow cover and soil, a snow cover–soil union water–heat coupled movements model is established in this paper. The numerical simulation was conducted by using a finite difference method. The results indicate that the simulated values have a similar trend to the measured values and the numerical simulation had big relative errors. However, the average absolute errors of the total and liquid moisture content in frozen soil were all less than 4%, and that of the frozen soil temperature was 1.37 °C. The errors of the numerical simulation were still within the acceptable range. Thus, the snow cover–soil union water–heat coupled movement model constructed in this paper is rational. [Copyright &y& Elsevier]

Abstract: The criteria in multiple criteria decision-making (MCDM) problems often have independent and dependent characteristics simultaneously, so they cannot be evaluated by conventional additive or non-additive measures in real-life environments. This paper proposes a new hybrid MCDM model to solve location selection problems, and the results of solving MCDM problems tallied with real-life circumstances due to the use of two concepts in the new hybrid model. The concepts comprise a new structural model and a new evaluation method. The new structural modeling technique is used to draw the hierarchical/network framework, and the MCDM problem is solved using the proposed evaluation method. Here, the fuzzy ANP (analytic network process) is used to construct fuzzy weights of all criteria. Linguistic terms characterized by triangular fuzzy numbers are then used to denote the evaluation values of all alternatives versus various criteria. Finally, the aggregation fuzzy assessments of different alternatives are ranked to determine the best selection. Furthermore, this paper uses a numerical example for selecting the location of an international distribution center in Pacific Asia to illustrate the proposed method. Through this example, this paper demonstrates the applicability of the proposed method, and the results show that this method is an effective means for tackling MCDM problems. [Copyright &y& Elsevier]

Abstract: This paper presents the analysis of delay-dependent bounded input bounded output (BIBO) stability for a class of switched uncertain neutral systems. The uncertainty is assumed to be of structured linear fractional form which includes the norm-bounded uncertainty as a special case. First, by introducing the general variation-of-constants formula of neutral systems with perturbation, the BIBO stability property of general linear switched neutral systems with perturbation is established. Next, combining the general variation-of-constants formula with the state-dependent switching rule, new approaches are presented to design the feedback controller and the switching rules. Furthermore, the BIBO stability criteria are obtained in terms of the so-called Lyapunov–Metzler linear matrix inequalities (LMIs). Finally, simulation examples are given to demonstrate the effectiveness and the potential of the proposed techniques in this paper. [Copyright &y& Elsevier]

Abstract: This paper proposes a new concept of a semi-canonical process. As an uncertain process, it is mainly proved that the total variation of a semi-canonical process is bounded almost surely, and the quadratic variation is almost surely. Some other conclusions of variation are also given in this paper. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the Bass model, which is widely used as a first-purchase diffusion model in marketing research. Estimation of its parameters has been approached in the literature by various techniques. In this paper, we consider the nonlinear weighted total least squares (TLS) fitting approach. We show that it is possible that the TLS estimate does not exist. As a main result, two theorems on the existence of the total least squares estimate are obtained, as well as their generalization in the total norm (). Several illustrative numerical examples are given to illustrate the efficiency of our approach. [Copyright &y& Elsevier]

Abstract: In this paper, we show that the main results in a recent paper by Zhang and Yan [X. Zhang and G. Yan, Machine scheduling problems with a general learning effect, Mathematical and Computer Modelling 51 (2010) 84–90] are incorrect as an important reason is missing, that is, the processing time of a job is variable according to a general learning effect. Here we point out these wrong results by a counter-example. In addition, we give a revised model with a general learning effect. We show that some single machine scheduling problems are still polynomially solvable under the revised model. We also show that some special cases of the flowshop scheduling problems can be solved in polynomial time under the revised model. [ABSTRACT FROM AUTHOR]

Abstract: This note points out some technical problems in the proofs of some lemmas in the above-mentioned paper, and presents their corresponding corrections. Nevertheless, the main results of that paper are still true. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we give the details of the numerical solution of a three-dimensional multispecies diffuse interface model of tumor growth, which was derived in [S.M. Wise, J.S. Lowengrub, H.B. Frieboes, V. Cristini, Three-dimensional multispecies nonlinear tumor growth–I: model and numerical method, J. Theoret. Biol. 253 (2008) 524–543] and used to study the development of glioma in [H.B. Frieboes, J.S. Lowengrub, S.M. Wise, X. Zheng, P. Macklin, E.L. Bearer, V. Cristini, Computer simulation of glioma growth and morphology, NeuroImage 37 (2007) S59–S70] and tumor invasion in [E.L. Bearer, J.S. Lowengrub, Y.L. Chuang, H.B. Frieboes, F. Jin, S.M. Wise, M. Ferrari, D.B. Agus, V. Cristini, Multiparameter computational modeling of tumor invasion, Cancer Res. 69 (2009) 4493–4501; H.B. Frieboes, F. Jin, Y.L. Chuang, S.M. Wise, J.S. Lowengrub, V. Cristini, Three-dimensional multispecies nonlinear tumor growth—II: tissue invasion and angiogenesis, J. Theoret. Biol. 264 (2010) 1254–1278]. The model has a thermodynamic basis, is related to recently developed mixture models, and is capable of providing a detailed description of tumor progression. It utilizes a diffuse interface approach, whereby sharp tumor boundaries are replaced by narrow transition layers that arise due to differential adhesive forces among the cell-species. The model consists of fourth-order nonlinear advection–reaction–diffusion equations (of Cahn–Hilliard-type) for the cell-species coupled with reaction–diffusion equations for the substrate components. Computing numerical solutions of the model is challenging because the equations are coupled, highly nonlinear, and numerically stiff. In this paper we describe a fully adaptive, nonlinear multigrid/finite difference method for efficiently solving the equations. We demonstrate the convergence of the algorithm and we present simulations of tumor growth in 2D and 3D that demonstrate the capabilities of the algorithm in accurately and efficiently simulating the progression of tumors with complex morphologies. [Copyright &y& Elsevier]

Abstract: This paper deals with the modelling of aggregation and/or fragmentation physical phenomena for large systems of interacting living entities in the framework of the mathematical kinetic theory for active particles. After introducing various mathematical structures in terms of systems of nonlinear integro-differential equations with quadratic type nonlinearities and variable number of equations, the relative qualitative analysis of the initial value problem is presented. Finally, the paper deals with the derivation of macroscopic equations based on the underlying description at the microscopic scale delivered by the kinetic theory models. [Copyright &y& Elsevier]

Abstract: Different persons often choose different contents in multi-document as summary. To optimize summarization, we will focus on the selection of content and seeking their valuable features. Statistical methods for automatic summarization are very important. In this paper, we research the correlation between the eigenvalue of content unit in the original document cluster and the probability of the content unit to be selected as a human summary based on a statistical method. When a Basic Element and word are considered as a content unit, we draw conclusions, in user-focus summarization. It is excellent that the BE is regarded as content unit granularity, and it is proved that the frequency eigenvalue of the BE is more suitable to embody content units’ weightiness than the TFIDF value. Moreover, the paper reveals that the given topic on user-focus summarization is helpful for the selection of content unit and quality of summarization. They often choose those content units as a summary in which the emerging frequency is relatively high in the sentences including the content unit of a given topic and neighboring sentences. Through researching potential behavioural modes about manual summary, we will put these effect factors of summarization quality into the process of content unit selection and summary generation to optimize automatic summarization. [Copyright &y& Elsevier]

Abstract: Hardware/software (HW/SW) partitioning is one of the crucial steps of co-design systems. It determines which components of the systems are implemented in hardware and which ones are in software. In this paper the computing model is extended to cater for the path-based HW/SW partitioning with the fine granularity in which communication penalties between system components must be considered. On the new computing model an efficient heuristic algorithm is developed, in which both speedup in hardware and communication penalty are taken into account. In addition, an efficient tabu search algorithm is also customized in this paper to refine the approximate solutions produced by the heuristic algorithm. Simulation results show that the heuristic algorithm runs fast and is able to produce high-quality approximate solutions. Moreover, the tabu search algorithm can further refine them to nearly optimal solutions within an acceptable runtime. The difference between the approximate solutions and the optimal ones is bounded by 0.5%, and it hardly increases with the increase of the problem size. [Copyright &y& Elsevier]

Abstract: Hub location selection problems have become one of the most popular and important issues not only in the truck transportation and the air transportation, but also in the marine transportation. The main focus of this paper is on container transshipment hub locations in southeastern Asia. Transshipment is the fastest growing segment of the containerport market, resulting in significant scope to develop new transshipment terminal capacity to cater for future expected traffic flows. A shipping carrier not only calculates transport distances and operation costs, but also evaluates some qualitative conditions for existing hub locations and then selects an optimal container transshipment hub location in the region. In this paper, a fuzzy multiple criteria decision-making (FMCDM) model is proposed for evaluating and selecting the container transshipment hub port. Finally, the utilization of the proposed FMCDM model is demonstrated with a case study of hub locations in southeastern Asia. The results show that the FMCDM model proposed in this paper can be used to explain the evaluation and decision-making procedures of hub location selection well. In addition, the preferences are calculated for existing hub locations and these are then compared with a new proposed container transshipment hub location in the region, in this instance the Port of Shanghai. Furthermore, a sensitivity analysis is performed. [Copyright &y& Elsevier]

Abstract: In this paper we review some mathematical modelling of organ reparative processes (wound healing) for both the physiological and pathological case. The natural process of healing consists in a series of overlapping phases involving cells, chemicals, extracellular matrix (ECM) and the environment surrounding the wound site. Sometimes the healing process fails and the reparative mechanism produces pathological conditions which are commonly termed fibrosis or fibroproliferative disorders. Biological insight into the pathogenesis, progression and possible regression of fibrosis is lacking and many issues are still open. Mathematical modelling can surely play its part in this field and this paper is aimed at showing what has been done so far and what has still to be done to achieve a unified framework for studying these kinds of problems. Due to the high complexity of this phenomenon, multi-scale modelling is certainly the appropriate approach that should be used for studying these kinds of problems. Unfortunately most of the mathematical literature on this topic consists of macroscopic continuous models which fail to investigate processes occurring at smaller length scales (cellular, sub-cellular). We present a review of some of the mathematical literature, showing the widely used approaches, focusing on the interpretation of results and indicating possible developments in the study of these highly complex systems. [Copyright &y& Elsevier]

Abstract: Part 1 of this paper proposed a methodology for the efficient determination of gradient information, when optimising a vehicle’s suspension characteristics for ride comfort and handling. The non-linear full vehicle model, and simplified models for gradient information has been discussed, and validated. In this paper, the simplified models presented in Part 1 are used for gradient information simulations. The convergence histories of the optimisation are compared to those obtained when only the full, computationally expensive, vehicle model is used. For illustration of the proposed gradient-based optimisation methodology, up to four design variables are considered in modelling the suspension characteristics. The proposed methodology is found to be an efficient alternative for the optimisation of the vehicle’s suspension characteristics. The undesirable effects associated with noise in the gradient information is effectively reduced, using the simplified models. Substantial benefits are achieved in terms of computational time needed to reach a solution. [Copyright &y& Elsevier]

Abstract: This paper addresses the short-term capacity planning problem in a make-to-order (MTO) operation environment. A mathematical model is presented to aid an operations manager in an MTO environment to select a set of potential customer orders to maximize the operational profit such that all the selected orders are fulfilled by their deadline. With a given capacity limit on each source for each resource type, solving this model leads to an optimal capacity plan as required for the selected orders over a given (finite) planning horizon. The proposed model considers regular time, overtime, and outsourcing as the sources for each resource type. By applying this model to a small MTO operation, this paper demonstrates a contrast between maximal capacity utilization and optimal operational profit. [Copyright &y& Elsevier]

Abstract: In this paper, six univariate forecasting models for the container throughput volumes in Taiwan’s three major ports are presented. The six univariate models include the classical decomposition model, the trigonometric regression model, the regression model with seasonal dummy variables, the grey model, the hybrid grey model, and the SARIMA model. The purpose of this paper is to search for a model that can provide the most accurate prediction of container throughput. By applying monthly data to these models and comparing the prediction results based on mean absolute error, mean absolute percent error and root mean squared error, we find that in general the classical decomposition model appears to be the best model for forecasting container throughput with seasonal variations. The result of this study may be helpful for predicting the short-term variation in demand for the container throughput of other international ports. [Copyright &y& Elsevier]

Abstract: In this paper, we consider a plate–beam system in which the Reissner–Mindlin plate model is combined with the Timoshenko beam model. Natural frequencies and vibration modes for the system are calculated using the finite element method. The interface conditions at the contact between the plate and beams are discussed in some detail. The impact of regularity on the enforcement of certain interface conditions is an important feature of the paper. [Copyright &y& Elsevier]

Abstract: In this paper, we explore the inventory replenishment policy for the kind of items in which the demand is sensitive to stock and selling price. As a matter of fact, the inventory system discussed by this paper is the same as that of Peng-Sheng You et al. [Peng-Sheng You, Yi-Chih Hsieh, An EOQ model with stock and price sensitive demand, Mathematical and Computer Modelling 45(2007)933-942]. However, they only gave the optimal decision rules without price change, with a single price change and with two price changes. Here, for any given , the times of price changes, we give a sufficient condition for optimal decision rules and develop the closed form of the optimal prices. Finally, several numerical examples are given to illustrate the theoretical results. [Copyright &y& Elsevier]

Abstract: The effectiveness of the first entry of the original series by GM(1, 1) is researched in this paper. The results show that the modelling values and forecasts are independent of the first entry of the original series. The grey prediction model presented in this paper is called first-entry GM(1, 1), abbreviated as FGM(1, 1), which is based on the existing GM(1, 1) but modelled with data including the first-entry’s messages of the original series. A proof concerning this subject has been presented by other authors. However, the algorithm of their direct proof is too complicated. A more compact algorithm is presented in this paper to prove the first entry of the original series ineffective to the modelling values and forecasts by GM(1, 1). Then, an arbitrary number can be inserted in the front of the original series to extract the messages from its first entry. Only a few data (usually fewer than ten) are used for model building. This paper deals with the effectiveness of the first entry of the original series by GM(1, 1). [Copyright &y& Elsevier]

Abstract: In this paper, we propose an algebraic method based on solving some inequalities of polynomial type to control the error value of interpolation formulas whose residue depends on a monic polynomial. This method then leads to construct some piecewise approximations (splines) of statistical type, which are based on a specific partition of the main interval. In other words, in this model of spline, approximate criteria are considered fixed and sub-intervals corresponding to criteria are derived as accurately as possible. In this sense, some statistical concepts such as expected value, variance measure, skewness and kurtosis coefficients are also inserted into the definition of statistical splines. Finally, a numerical results section is separately given to confirm all results in the paper. [Copyright &y& Elsevier]

Abstract: The growth of avascular tumors has been studied by many authors. In this paper we study a special kind of cancer, ductal carcinoma in situ (DCIS) in order to investigate possible procedures to connect free boundary model of DCIS with clinical data. This paper is to present some results of our research on mathematical modeling, analysis, and numerical simulations of ductal carcinoma in situ. In particular, we formulate a number of inverse problems for the well-posed free boundary valued problem related to clinical diagnose of cancer. [Copyright &y& Elsevier]

Abstract: In this paper we suggest solutions to the actuaries, facing the problem of estimating future mortality tables, especially in cases where there is a lack of relevant data and where the tendencies are not easy to estimate directly. We propose the utilization of external sources of information in the form of other, published mortality tables and use formal statistical tests to decide among these possible candidates. The procedure can also be applied for checking e.g. the goodness of mortality selection factors. We suggest the use of parametric families in modelling; for example the simple 2-parameter Azbel model. We conclude the paper by a simulation study which allows for the quantification of the possible risks related to unforeseen changes in the mortality tables in the future. To calibrate the variances of these models, initial estimates are needed, which we get by the Lee–Carter method. [Copyright &y& Elsevier]

Abstract: Recent research in computer systems security has evolved into trust issues, which are now becoming an important topic. The majority of approaches for trust modeling addressed trust by actually focusing on security, and some of them addressed also trust as such. This paper presents a formal apparatus that concentrates on trust as such. It is flexible enough to accommodate the driving factors behind trust and consequently different trust-focused methodologies and technologies. The basic goal of the work presented in this paper is the definition of qualitative trust modeling methodology for trust management in contemporary computing environments that efficiently complements existing quantitative methodologies. Further, an open conceptual model for trust management is presented that accommodates various qualitative and quantitative trust management methodologies. This model has also been implemented in the web services environment, and this is discussed in this paper as well. [Copyright &y& Elsevier]

Abstract: This paper reveals the latency errors in the manufacturing and assembly of the toroidal drive and integrates these errors in the coordinate systems and the mathematical models of the meshing equations for the conjugate surfaces between the planet worm-gear and the sun-worm and between the planet worm-gear and the stationary internal toroidal gear. The paper further develops the tooth profile model and the contact curves with the latency errors and examines the error effect on the helix model and the helix lead angle model. In addition, two kinds of limit curve model and the induced normal curvature models are further derived. This provides a comprehensive study of error effect on the meshing characteristics of the novel drive. [Copyright &y& Elsevier]

Abstract: The main object of the present paper is to introduce certain novel classes of meromorphic multivalent functions , and . In this paper, we obtain coefficient estimates, distortion theorems, radii of convexity and closure theorems for the class . Several interesting results involving the Hadamard product of functions belonging to the classes and are also derived. Also integral transforms of functions in the classes and are studied. [Copyright &y& Elsevier]

Abstract: This paper proposes two new distance-constrained capacitated vehicle routing problems (DCVRPs) to investigate for the first time, and study potential benefits in flexibly assigning start and end depots. The first problem, DCVRP_Fix is an extension of the traditional symmetric DCVRP, with additional service and travel time constraints, minimization of the number of vehicles and flexible application to both symmetric and asymmetric problems. The second problem, DCVRP_Flex is a relaxation of DCVRP_Fix to enable the flexible assignment of start and end depots. This allows vehicles the freedom to start and end their tour at different depots, while allowing for intermediate visits to any depot (for reloading) during the tour. Network models, integer programming formulations and solution algorithms for both problems are developed and presented in this paper. An analytical comparison of both problems is carried out with Singapore as a case study, considering the impact of depot locations and problem symmetry using four cases. Results show a generation of cost savings up to 49.1% by DCVRP_Flex across all the four cases. A significant portion of this stems from the flexibility to reload at any depot while the rest of it is derived from the flexibility to return to any depot. DCVRP_Flex’s adaptability and superior performance over DCVRP_Fix provides strong motivation for further research on improved exact algorithms and heuristics for this problem. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate bidirectional associative memory Cohen–Grossberg neural networks with time delays. By applying the Young inequality technique, Dini derivative, and introducing many real parameters, a series of new and useful criteria on the existence and uniqueness of an equilibrium point and its global asymptotical stability are established. It is shown that in some special cases of the results, the stability criteria can be easily checked. Finally, an example is given to illustrate the result obtained in this paper. [Copyright &y& Elsevier]

Abstract: A mathematical model is developed for the rate of healing of a circular or elliptic wound. In this paper the regeneration, decay and transport of a generic ‘growth factor’, which induces the healing of the wound, is taken into account. Further, an equation of motion is derived for radial healing of a circular wound. The expressions for the equation of motion and the distribution of the growth factor are related in such a way that no healing occurs if the growth factor concentration at the wound edge is below a threshold value. In this paper we investigate the influence of the behaviour of the thickness of the active layer, in which the growth factor is produced, on the healing process. Also a correction is made to a result in earlier work. [Copyright &y& Elsevier]

Abstract: This paper deals with the modelling and development of computational schemes to simulate pultrusion processes. Two different computational methods, finite differences and elements, are properly developed and critically analyzed. The methods are applied to a model, implemented with suitable boundary conditions, proposed in this paper. Simulations, compared with experimental data available in the literature, show a good agreement between theory and experiments. [Copyright &y& Elsevier]

Abstract: The main object of the present paper is a preliminary discussion of a way to describe any three-dimensional structure of a folded protein by means of a suitable three-dimensional matrix, as well as of its possible use for the forecast of the natural spatial structure of a protein of which only the amino acid sequence is known. The contents of this paper are confined to the introduction of the language and to its application to some particularly simple (and short) proteins as samples of this kind of description and as a start-point to draw the mathematical tools to be added in this context to express the geometric information in such a way as to apply the methods of inference of computational statistics. As a matter of fact, we hope to be able to show in future papers that such representation, when suitably completed by the introduction of a suitable discrete version of the notion of “deformation field” and of other geometric notions, allows the reconstruction of the folded configuration of a protein by a suitable “abstract” version of some recent and powerful statistical methods usually applied to image recognition, in turn suitably extended from the two-dimensional to the three-dimensional case (cf. [D. Geman, S. Geman, Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images, IEEE Trans. Pattern Anal. Mach. Intell. 6 (1984)]). [Copyright &y& Elsevier]

Abstract: The paper presents the specific framework and a set of simulations computed on the basis of a kinetic model of interest in the field of the Social Sciences. The model is a reduced version of a comprehensive more general one, and it relates to the specific case of a competing bipartisan political system. The model structure contains terms with localized interactions and mean field terms. In the first part of the paper the mathematical details of the model are recalled. In the second part the simulations are presented with reference to the various scenarios examined. Finally a discussion on research perspectives is formulated. [Copyright &y& Elsevier]

Abstract: This paper deals with the modeling of the thermal field during machining processes by laser beam local heating. The analysis refers to the identification of mathematical models suitable to describe the large variety of complex phenomena which occur during the machining process. Specifically, this paper provides the modelling assessment to deal with the solution of mathematical problems toward simulation and with specific engineering applications related to the above technological system. [Copyright &y& Elsevier]

Abstract: The purpose of the paper is to investigate a possibility of application of Plücker''s conoid in engineering geometry of surfaces. The research reveals that Plücker''s conoid itself is a complex 3D characteristic image. On the premises of Plücker''s conoid, the 2D characteristic curves of novel kind are introduced. We refer to these characteristic curves as to the An R (P)-indicatrix and An k (P)-indicatrix of the surface P. The characteristic curves An R (P) and An k (P) in many cases are similar to the corresponding Dupin''s indicatrices Dup R (P) and Dup k (P). For two interacting surfaces the developed approach yields introducing of the Plücker''s relative indicatrices Pl R (P/T) and Pl k (P/T). Finally, the 3D characteristic curves Pl R (P/T) and Pl k (P/T) reduced to the planar characteristic curves An R (P/T) and An k (P/T), i.e., to the so-called An R (P/T)- and An k (P/T)-relative indicatrices. The characteristic curves An R (P/T) and An k (P/T) could be employed. [(a)] for analytical description of local topology of composite surfaces along the linkage curve; [(b)] for developing of the optimal tool-paths for sculptured surface machining on multiaxis NC machine, as well as for analytical description of conditions of proper sculptured surface machining; [(c)] for improving accuracy of solution to the problem of contact of two elastic bodies, etc. These characteristic curves reported in the paper in many cases are similar to the indicatrices of conformity Cnf R (P/T) and Cnf k (P/T) of two smooth rugular surfaces earlier developed by the author. The obtained results perfectly correlate with the results obtained by other researchers, as well as with the results earlier developed by the author. [Copyright &y& Elsevier]

Abstract: Theoretical studies of biological populations via analysis and/or simulation of deterministic and stochastic systems sometimes end up drawing conflicting conclusions. Papers purporting to investigate the same dynamics, albeit through different methods, often cannot agree on essential properties of the system being modeled. This problem often arises when trying to compare results that were obtained from different kinds of mathematical models, say those based on differential equations and individual-based stochastic models. While such models can successfully represent or characterize different views of the same phenomena, it is important to know when two different approaches are comparable, as well as any limitations that may be inherent in such a comparison. This survey paper is directed primarily to mathematical biologists whose primary mode of operation is partial differential equations. More generally, we seek to illuminate connections between the two main realms of spatial modeling. We begin by presenting a quick introduction to a class of stochastic spatial models, known as interacting particle systems, which are readily applicable to biological (and many other) systems. We then give examples of how various scaled limits of these models give rise to reaction-diffusion equations and integrodifferential equations. The first case falls under the heading of hydrodynamic limits and the second case is an example of a mean-field limit theorem. [Copyright &y& Elsevier]

The topic of the paper is in the area of mathematical modeling of the contact of two smooth regular surfaces in the first order of tangency. The paper is aiming to develop an approach for the mathematical description of the geometry of tangency of two smooth regular surfaces, which share a common point, and in such way to describe geometry of contact of two surfaces not only qualitatively, but quantitatively as well. Various approaches of the first-, second-, and higher-order approximation are discussed. To resolve the problem under consideration, a characteristic curve of new kind is introduced. We refer to this characteristic curve as the so-called indicatrix of conformity of two surfaces, which are tangent to each other at a point. Application of the indicatrix of conformity enables one developing an appropriate quantitative and qualitative description of the geometry of contact of two smooth regular surfaces in the first order of tangency. The results presented in the paper will have many practical applications in science and engineering: . [Copyright &y& Elsevier]

It is a very well-known fact that calculations necessary to analyze transient conditions in hydraulic systems are very time-consuming and difficult to organize, especially in complex systems. Nevertheless, such calculations are necessary to achieve efficiency and economy in the design and operation, as well as safety in these systems, since those objectives need precise calculations of pressures and flowrates. Suitable mathematical modeling of the different elements in a hydraulic system is necessary to get useful results, which help fulfill those objectives. In this paper, the mathematical model described in [1] is generalized to complex pressurized hydraulic systems. To model the behavior of the fluid within the ducts, use is made of the so-called elastic model, which is numerically solved by the methods of characteristics. Nevertheless, the main objective of this paper hinges on the treatment of the boundary conditions that allow developing a general model virtually representing every combination of elements at a given location of the system. The final objective is to provide the users with a powerful tool to devise the potential risks to which an installation may be exposed and to develop suitable protection strategies. [Copyright &y& Elsevier]

This paper considers a statistical method of estimating mean shift for a fraction defective of population. One traditional method for this estimation problem has been known as the CUSUM (cumulative sum) method, and it provides a method of estimating the occurrence of a shift in the mean from the observed data. We consider this estimation problem of shift occurrence in a production process. It is assumed that the process has two states, one is good (fraction defective low) and the other bad (fraction defective high), and starts in good state with probability one. We are interested in judging when the state has moved to the bad state by analyzing the observed data.In this paper, we model such a phenomenon as a hidden-Markov model. The states which are unobservable in a hidden-Markov model can be analyzed from the sequence of observed results. Hence, the advantage of this modeling technique is that the unknown parameters which are included in the hidden states can be estimated. We compare the performance of this hidden-Markov model with the CUSUM method based on several simulation data sets. [Copyright &y& Elsevier]

This paper considers a duopolistic inventory model with reallocation. Customers move according to the rectilinear distance over a plane market and choose a player whom they first visit with a probability dependent on their positions. This model can be interpreted as one of the unit-square games with pure strategies of continuous cardinary. We consider the optimal strategies for two players from a viewpoint of pure strategies. The purpose of this paper is concretely to find an equilibrium point with respect to the optimal ordering quantities which minimize the total costs by using a payoff bimatrix in the deterministic model and to find the optimal solution in the stochastic model. As can be seen in this paper, there is a unique equilibrium point. [Copyright &y& Elsevier]

Abstract: In this paper, we will employ some dynamic inequalities of Opial’s type on time scales to prove several results related to the spacing between consecutive zeros of a solution of a second order dynamic equation with a damping term. We also obtain several results related to the spacing between a zero of the solution and/or a zero of its derivative. As a special case, we will establish some new results for differential and difference equations with damping terms. For illustration, we will derive some well-known results obtained for differential equations without damping terms. The results yield conditions for disfocality and disconjugacy for dynamic equations with damping terms on time scales. [Copyright &y& Elsevier]