A study of the influence of center conditions on the domain of parameters of Newton’s method by using recurrence relations

This paper focuses on the importance of center conditions on the first derivative of the operator involved in the solution of nonlinear equations by Newton’s method when the semilocal convergence of the method is established from the technique of recurrence relations.     

A heuristic approach for the stochastic optimization of mine production schedules

Traditionally, mining engineers plan an open pit mine considering pre-established conditions of operation of the plant(s) derived from a previous plant optimization. By contrast, mineral processing engineers optimize the processing plants by considering a regular feed from the mine, with respect to quantity and quality of the materials. The methods implemented to optimize mine and metallurgical plans simultaneously are known in the mining industry as global or simultaneous optimizers. The development of these methods has been of major concern for the mining industry over the last decade. Some algorithms are available in commercial mining software packages however, these algorithms ignore the inherent geological uncertainty associated with the deposit being considered, which leads to shortfalls in production, quality, and expected cashflows. This paper presents a heuristic method to generate life-of-mine production schedules that consider operating alternatives for processing plants and incorporate geological uncertainty. The method uses iterative improvement by swapping periods and destinations of the mining blocks to generate the final solution. The implementation of the method at a copper deposit shows its ability to control mine and processing capacities while increasing the expected net present value by 30% when compared with a solution generated using a standard industry practice.     

Scatter search for minimizing weighted tardiness in a single machine scheduling with setups

Single machine scheduling problems have many real-life applications and may be hard to solve due to the particular characteristics of some production environments. In this paper, we tackle the single machine scheduling problem with sequence-dependent setup times with the objective of minimizing the weighted tardiness. To solve this problem, we propose a scatter search algorithm which uses path relinking in its core. This algorithm is enhanced with some procedures to speed-up the neighbors’ evaluation and with some diversification and intensification techniques, the latter taking some elements from iterated local search. We conducted an experimental study across a well-known set of instances to analyze the contribution of each component to the overall performance of the algorithm, as well as to compare our proposal with the state-of-the-art metaheuristics, obtaining competitive results. We also propose a new benchmark with larger and more challenging instances and provide the first results for them.     

Application of chitosan matrix for delivery of rutin

Chitosan matrices are an alternative material to the food industry, due to its ability to release bioactive compounds through interconnected cavities. Chitosan is a biomaterial of excellence, because it shows unique features, such as biocompatibility, non-toxicity, bactericidal action and the ability to associate with other compounds. Thus, this study aimed the development of chitosan matrices incorporated with rutin, as well as the evaluation of rutin release. Chitosan matrices with rutin were prepared by the coacervation method in alkaline solution and subsequently characterized through FT-IR, TG-DSC, X-ray diffraction, SEM and further submitted to rutin release assay. Results show the effectiveness in the incorporation of rutin into the polymeric matrix. The polymeric matrix with rutin can quickly release it, which provides a wide range of applications, such as carrier of rutin as a micronutrient food additive.     

A Safety Strategy for Producing Poly(Acrylic Acid) of Low Molar Mass

The synthesis of poly(acrylic acid) (PAA) of low molar mass under safe conditions is difficult due to the high polymerization rate of acrylic acid (AA) and the fast heat generation. The aqueous‐solution “semibatch” polymerization of non‐ionized AA in almost starved conditions involves high initiator loads when low molar masses are required. This article proposes the simultaneous feeding of AA and nonconventional chain transfer agents (CTA) as a strategy aimed at controlling both the molar masses and the generated heat rate. Three CTAs are investigated: 2‐mercaptoethanol, thioglycolic acid, and isopropyl alcohol. Even when PAA of relatively low molar mass can be produced by adequately selecting the flow rates and concentrations of both AA and CTA, it is found that the nature of CTA can have a significant effect on the polymerizations kinetics. The mechanisms responsible for these effects are discussed with the help of a representative mathematical model.

     

A multi-objective capacitated rural school bus routing problem with heterogeneous fleet and mixed loads

Four multi-objective meta-heuristic algorithms are presented to solve a multi-objective capacitated rural school bus routing problem with a heterogeneous fleet and mixed loads. Three objectives are considered: the total weighted traveling time of the students, the balance of routes among drivers, and the routing costs. The proposed methods were compared with one from the literature, and their performance assessed observing three multi-objective metrics: cardinality, coverage, and hyper-volume. All four devised methods outperformed the one from the literature. The algorithm with a path relinking procedure embedded during the crowding distance selection scheme had the best overall performance.     

Nonuniform exponential dichotomies and Lyapunov functions

For the nonautonomous dynamics defined by a sequence of bounded linear operators acting on an arbitrary Hilbert space, we obtain a characterization of the notion of a nonuniform exponential dichotomy in terms of quadratic Lyapunov sequences. We emphasize that, in sharp contrast with previous results, we consider the general case of possibly noninvertible linear operators, thus requiring only the invertibility along the unstable direction. As an application, we give a simple proof of the robustness of a nonuniform exponential dichotomy under sufficiently small linear perturbations.     

On the Pseudolinear Crossing Number

A drawing of a graph is pseudolinear if there is a pseudoline arrangement such that each pseudoline contains exactly one edge of the drawing. The pseudolinear crossing number of a graph G is the minimum number of pairwise crossings of edges in a pseudolinear drawing of G. We establish several facts on the pseudolinear crossing number, including its computational complexity and its relationship to the usual crossing number and to the rectilinear crossing number. This investigation was motivated by open questions and issues raised by Marcus Schaefer in his comprehensive survey of the many variants of the crossing number of a graph.