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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: The paper presents a detailed study of a four component population dynamical model consisting of the biomasses of carbon of phytoplankton , nitrogen of phytoplankton , carbon of zooplankton and total free nutrient . In this model, both the influence of the internal (carbon) and external (nitrogen) nutrient on the growth of phytoplankton is included. This is usually termed a variable yield model in contrast to the constant yield model analyzed by J. Monod [Recherches sur la croissance des cultures bacteriennes, Herman, Paris, 1942. ]. The existence and stability of various steady states are discussed analytically and numerically using a computer simulation (AUTO) designed by Doedel [E.J. Doedel, AUTO: A program for the automatic bifurcation analysis of autonomous systems, Congr. Numer. 30 (1981) 265–284; E. Doedel, X. Wang, T. Fairgrieve, AUTO: Software for continuation and bifurcation problems in ordinary differential equations, in: Applied Mathematics Reports, California Institute of Technology, 1994]. Various bifurcation diagrams so obtained support the analytical results and identified complex behavior which cannot be obtained analytically. The purpose of this paper is as a preliminary step to determine the change in the richness of behavior as complexity, such as spatial compartments, is added, which in limiting form would be a continuous spatial dependence (as a partial differential equation model). [Copyright &y& Elsevier]

Abstract: In this paper we will investigate numerically gravity induced skeletal structure evolution during liquid phase sintering. Applying three-dimensional domain methodology, solid skeleton evolution will be introduced by the definition of skeleton units determined by the equilibrium dihedral angle and the formation of large solid skeletons arranged in a long chain of connected solid phase domains. The settling procedure will be simulated by using two general submodels: for free settling, in which solid phase domains fall under gravity over domains that have already settled, and for extended settling, in which settled domains continue their motion until they reach a position of local equilibrium. The same submodels will be applied for free settling and extended settling of solid skeletons. It will be assumed that under gravity conditions, Stokes’s law settling usually dominates microstructure formation, where the settling procedure will be simulated by computation of the settling time and average migration distance during a defined time interval. Thus gravity induced skeleton structure evolution will be simulated by simultaneous computation of the displacement of the center of mass. [Copyright &y& Elsevier]

Abstract: This paper deals with some developments of the mathematical kinetic theory for active particles to model large systems of interacting entities whose microscopic state includes not only geometric and mechanical variables but also peculiar functions or specific activities. The analysis is specifically focused on modelling living open systems in view of optimization, control problems, and derivation of macroscopic equations from the underlying microscopic description. [Copyright &y& Elsevier]

Abstract: In this paper, the existence of positive periodic solutions for a generalized delayed population model with stocking and feedback control is established by using the continuation theorem of coincidence degree theory. Then, by constructing a Lyapunov functional, the global attractivity of a positive periodic solution for the above model is established. [Copyright &y& Elsevier]

Abstract: A number of models involving reaction–diffusion equations have been developed by different authors to describe the changes in frequency of alleles in a population. Each of these models describes the case in which there are only two possible alleles at the locus in question. In the present paper, we are interested in the more realistic possibility of three alternative alleles. A system of reaction–diffusion equations can be developed to describe this situation. After transforming to the traveling wave coordinates, we introduce a nonlinear transformation which allows us to find exact solutions under certain conditions imposed on two of the parameters. [Copyright &y& Elsevier]

Abstract: This paper deals with the qualitative analysis of a model describing the competition between tumor and immune cells. Such competition is characterized by proliferation–destruction phenomena and the interacting entities are characterized by a microscopic state which is modified by interactions. The model also includes the description of the natural trend of immune cells to reach a healthy or sentinel level, even when they have been involved in the competition with the tumor cells. The model is developed in the mathematical framework of the kinetic theory for active particles. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the multipoint boundary value problem for one-dimensional -Laplacian subject to the boundary conditions: where . Applying the fixed point theorem due to Avery and Peterson, we study the existence of at least three symmetric positive solutions to the above boundary value problem. The interesting point is that the nonlinear term contains the first-order derivative explicitly and the boundary condition is of Sturm–Liouville type. [Copyright &y& Elsevier]

Abstract: In this paper, we give the solution of the inverse Sturm–Liouville problem on two partially coinciding spectra. In particular, in this case we obtain Hochstadt’s theorem concerning the structure of the difference for the singular Sturm Liouville problem defined on the finite interval having the singularity type at the points 0 and . [Copyright &y& Elsevier]

Abstract: This paper analyzes, on the basis of methods of the mathematical kinetic theory of active particles, some complexity problems related to the evolution of reciprocal feelings. Specifically, the analysis is focused on the complexity problems generated by triple interactions, with respect to simple binary encounters. Complexity refers not only to the structure of the equation, but also to the variable describing reciprocal feelings. [Copyright &y& Elsevier]

Abstract: Let be a sequence of i.i.d. random variables taking values in a real separable Hilbert space with mean zero and covariance and set . Let be the eigenvalues of arranged in non-increasing order and take into account the multiplicities. Let be the dimension of the corresponding eigenspace of largest eigenvalue . Let . This paper studies the precise rates for . We show that when and implies where is the Gamma function and . [Copyright &y& Elsevier]

Abstract: In this paper we have proven uniqueness theorems for estimation of the age-dependent parameter in the Gompertz survival model with a mortality deceleration rate, in the absence of age-specific mortality data. We obtained estimations dependent on and uniform in the population size . [Copyright &y& Elsevier]

Abstract: Upon demand realization in the newsvendor problem, it is often assumed that shortages result in lost sales penalties. However, in some practical situations, shortages are backlogged and the inventory manager is penalized based on the magnitude and duration of the shortage. In this paper, we investigate a variation of the newsvendor problem in which all shortages are backlogged and replenished through an emergency procurement process. Costs incurred during emergency procurement include a variable emergency ordering cost and a non-linear customer waiting cost. We derive closed form expressions for the optimal order quantity and emergency procurement rate for two special cases, and we propose a heuristic approximation for the general case. The effectiveness of the approximate solution is assessed through numerical experiments and sensitivity analysis. [Copyright &y& Elsevier]

Abstract: In this paper, we describe the mathematics and computer implementation of a robotic rat pup simulation. Our goal is to understand neurobehavioral principles in a mammalian model organism—the Norway rat pup (Rattus norvegicus). Our approach is unique in that animal, simulation, and robot studies occur in parallel and inform each other. Behavior is dependent on the nervous system, body morphology, physiology, environment, and the interactions among these elements. Autonomous robotics hardware models and their associated simulations allow the possibility of systematically manipulating variables in each of these elements in ways that would be impossible using live animals. Specifically, we describe the development and validation of a Newtonian-dynamics-based simulation of a robotic rat pup, including mathematical formulation and computer implementation. The computer simulation consists of three distinct components that interact to simulate robotic behavior: (1) dynamics of the robotic rat pup itself, including sensors and actuators, (2) environmental coupling dynamics of the robot arena with the robotic rat pup, and (3) the robot control algorithms as implemented on the physical robot. The mathematical formulation, software implementation, model identification, model validation, and an application example are all described. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to study a non-Kolmogrov type prey-predator system. First, we investigate the linear stability of the model by analyzing the associated characteristic equation of the linearized system. Second, we show that the system exhibits the Hopf bifurcation. The stability and direction of the Hopf bifurcation are determined by applying the norm form theory and center manifold theorem. Finally, numerical simulations are performed to illustrate the obtained results. [Copyright &y& Elsevier]

Abstract: Nonexponential evolution equations can be treated using a formalism involving the evolution operator method, which, unlike the ordinary case, is not expressed in terms of exponential operators. The use of this technique requires particular care associated with the operator ordering. In this paper, we will present a first systematic approach to this type of problems. [Copyright &y& Elsevier]