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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: 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: This paper considers the Liénard-type systems with continuously distributed delays. Some sufficient conditions for the existence and exponential stability of the almost periodic solutions are established, which are new and complement previously known results. [Copyright &y& Elsevier]

Abstract: In this paper, a Markovian queue with two heterogeneous servers and multiple vacations has been studied. For this system, the stationary queue length distribution and mean system size have been obtained by using matrix geometric method. The busy period analysis of the system and mean waiting time distribution are discussed. Extensive numerical illustrations are provided. [Copyright &y& Elsevier]