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In this work, we develop a quasi-Newton-type method for equilibrium problems based on the proximal Newton-type structure given in Santos et al. (Optimization Letters 12(5), 997-1009, 2018). We consider a family of matrices verifying a bounded deterioration property. We prove that the sequence generated by the algorithm is well defined and under suitable assumptions we establish the linear convergence of the algorithm. Numerical experiments are reported.

The atypical hemolytic uremic syndrome (aHUS) in the newborn is a rare disease, with high morbidity. Eculizumab, considered a first-line drug in older children, is not approved in neonates and in children weighing less than 5 kg. We present a 5-day-old female newborn, born at 36 weeks' twin gestation, by emergency cesarean section due to cord prolapse, with birth weight of 2,035 g and Apgar score of 7/7/7, who develops microangiopathic hemolytic anemia, thrombocytopenia, and progressive acute renal failure. In day 5, after diagnosis of aHUS, a daily infusion of fresh frozen plasma begins, with improvement of thrombocytopenia and very slight improvement in renal function. The etiologic study (congenital infection, Shiga toxin, ADAMTS13 activity, directed metabolic study) was normal. C3c was slightly decreased. On day 16 for maintenance of anemia and severe renal failure, she started 300 mg/dose eculizumab. Anemia resolves in 10 weeks and creatinine has normal values after 13 weeks of treatment. The genetic study was normal. In this case, eculizumab is effective in controlling microangiopathy and in the recovery of renal function. Diagnosis of neonatal aHUS can be challenging because of phenotypic heterogeneity and potential overlap with other manifestations that may confound it, such as perinatal asphyxia or sepsis/disseminated intravascular coagulation.

In this paper, we propose and study the problem of solve non-linear inclusion problem in Banach spaces, where the involved operator can be written as sum of a Frechet differentiable function with a continuous perturbation. We use a specific technique introduced by Robinson (Numer. Math. 19, 341–347, 1972) to obtain Newton-Kantorovich theorem, which extends the results of Rokne (Numer. Math. 18, 401–412, 1971), for instance. In our main convergence result, we assume a kind of Holder condition. Thus, one of the major difficulties to obtain our main result is to show that the sequence of scalars associated with the Newton sequence is convergent. Numerical examples are given to justify the theoretical results.

Obtaining a realistic prediction of the corrosion rate of equipment employed in the oil and gas industry is vital for safe operations. During the last few years, several corrosion prediction models have been and are being developed by oil companies and research institutes. The corrosion prediction models are usually made to meet a specific type of corrosion scenario, such as corrosion in the presence of H2S, corrosion in the presence of organic acid, corrosion in the presence of CO2, among others. Because of the distinct philosophies of these models, different results can be obtained for the same cases. The corrosion rates predicted by different models have a great influence on the selection of materials, definition of inspection plans, among other important decisions; therefore, on the total cost of the project. Reliable predictions of the corrosion rate are vital to controlling the degradation, ensuring the integrity of the operation at an optimized cost. This paper presents partial results of a research project that aims to evaluate the variability of corrosion rate prediction obtained by applying different corrosion models. This information could support oil and gas companies in selecting the most suitable model for carrying out the expected corrosion rate in new installation projects, considering the expected operational condition. In this paper, a sensitivity analysis of the NORSOK corrosion prediction model, using Monte Carlo simulation, is presented. In order to perform the Sensitivity Analysis, a methodology composed of 4 phases was followed: Selection of parameters, Monte Carlo Simulations, Obtaining Corrosion Rates and Analysis. It was found that, for the analyzed cases, the parameters with the highest and lowest impact on the prediction of corrosion rates, respectively, were pH and total pressure.

An ab initio study of several hybrid improper ferroelectric (HIF) materials in the Ruddlesden–Popper phases and double perovskite structures is here presented. The focus is on the correlation between the electric field gradient at several nuclear sites (EFG) and the spontaneous electric polarization. As observed in some proper ferroelectrics, we found that the EFG tensor components, along possible switching paths to invert the polarization, are interchangeable between the ferroelectric and paraelectric phases in the HIF AA2'B2O7 and AA′B2O6 (A, A′ = Ca, Cd and B = Mn, Ti) compounds. The results indicate that the relationship between the main continuous component of the EFG tensor and the electric polarization, even at sites without inversion symmetry, is primarily quadratic. Moreover, the claimed linear correlation was not observed. These results open a route to analyze the local octahedral distortions that underline HIF materials' functional multiferroic properties.

Xylophagous organisms can cause damage both in forests and in felled wood. Bursaphelenchus xylophilus, which causes "Sudden Pine Wilting" in coniferous forest masses, and is currently considered a quarantine organism in the European Union. On the other hand, structural and carpentry wood is affected by subterranean termites (Reticulitermes spp.), that cause serious damage, both in buildings and furniture. Solutions for the control of both organisms have been evaluated, and mainly based on chemical or physical treatments. Lately more eco-sustainable biocontrol and/or bioprotection techniques are being investigated. Among these techniques, the modification of the associated microbiota is being studied, in nematode or entomopathogenic microorganisms, with metabolites that are capable of controlling both organisms. As these products are of biological origin they may minimize the environmental impact. The application of these latest techniques requires a deep understanding of the associated microbiota. Therefore, the objective of this work has been to identify the microbiota present in Bursaphelenchus xylophilus and Reticulitermes grassei, as well as their main enzymatic activities and how they may play important roles in the degradation of wood. The results have shown cellulase, chitinase and protease activities, enzymes that could serve as indicative parameters in the control of both organisms. This study opens future treatment techniques against both pests, within a sustainable bioeconomy.

One of the alternative treatments to avoid the application of biocides is thermal modification of wood, which increases the durability of wood against attack by wood decay organisms. The durability of Pinus sylvestris and Eucalyptus nitens thermotreated at 180 and 212 ºC, was studied. The results show that thermotreatment against wood decay fungi in P. sylvestris is slightly more effective than in E. nitens, especially against C. puteana. In the studied species of wood, both against P. placenta for pine, and T. versicolor for eucalyptus, the treatment at 212ºC makes the wood very durable. Against H. bajulus, both temperatures are effective, while these thermotreatments do not provide any durability against subterranean termites, neither in pine nor in eucalyptus.

The presence of aromatic compounds in rainwater is a matter of concern, mainly when the use of rainwater in buildings is intended. The present work aimed to assess the oxidation of a mixture of small aromatic compounds (benzoic, 3,5-dihydroxybenzoic and syringic acids) in rainwater by the UV/H

The effect of substituting Ca by Cd in several Ca3B2O7 Ruddlesden–Popper (RP) and double perovskite (DP) CaCdB2O6 systems, where B is Mn or Ti, is here deeply investigated through ab initio calculations. We show that these cation substitutions have a high impact on the ferroelectric properties in such perovskite-based ferroelectrics. Our results reveal the relations between octahedra rotations with the atomic displacements responsible for inducing large electrical polarization in hybrid improper ferroelectrics. We show that these chemical substitutions tailor ferroelectric properties and can be used to engineer RP and DP systems, increasing their applicability range as ferroelectric or piezoelectric materials.

In this paper, we propose a Bregman regularized proximal point method for solving monotone equilibrium problems. Existence and uniqueness results as well as convergence of the sequence to a solution of an equilibrium problem is analyzed. We assume a coercivity condition on the Bregman function weaker than the one considered in the literature on equilibrium problems with Bregman regularization. Numerical experiments illustrate the efficiency of the method.

This paper presents ab initio calculations on stability properties and phase diagrams of Ca- and Cd-related hybrid improper ferroelectric materials, with the Ruddlesden–Popper (RP) and double perovskite (DP) structures. The results show that enthalpy relations favor the decomposition of Cd-based RP compounds, indicating that experimental synthesis may be nontrivial. Thus, pure Cd-related RP compounds are not stable. The RP Ca3B2O7 (B = Ti, Mn) systems, however, admit the incorporation of certain percentages of Cd replacing Ca, providing a possible route for tuning ferroelectric properties through chemical substitution. In addition, the stability results indicate that the Ca2TiO4 RP is not stable, in agreement with previous investigations. Searching for alternative stable phases, we found that the forsterite structure might be stable at room temperature and a new structure for this material. Moreover, the results reveal that the Cd-based DP CaCdTi2O6 is dynamically stable, therefore, a possible new hybrid improper ferroelectric.

The oxygen octahedral rotations in ${\mathrm{Ca}}_{2}\mathrm{Mn}{\mathrm{O}}_{4}$, the first member of the $\mathrm{Ca}\mathrm{O}{({\mathrm{CaMnO}}_{3})}_{n}$ Ruddlesden-Popper family, is probed through a set of complementary techniques, including temperature-dependent neutron and x-ray diffraction, combined with local probe studies and ab initio calculations. Here we demonstrate the enhancement of the uniaxial negative thermal expansion coefficient from $\ensuremath{-}1.26\ifmmode\pm\else\textpm\fi{}0.25$ to $\ensuremath{-}21\ifmmode\pm\else\textpm\fi{}1.8$ ppm/K at the second order $I{4}_{1}/acd$ to $I4/mmm$ structural phase transition, providing direct evidence for the corkscrew atomic mechanism. We establish, also, that the predicted $I4/mmm$ high symmetry is attained around 1050 K. At lower temperatures, within the 10--1000 K temperature range, our first-principles calculations and detailed analysis of the Ca local environment reveals that the reported $Aba2$ structural phase, coexisting with the $I{4}_{1}/acd$ one, cannot describe correctly this compound. On the other hand, our data allow for the coexistence of the locally identical $I{4}_{1}/acd$ and $Acam$ structural phases.

We present an interior proximal method for solving constrained nonconvex optimization problems where the objective function is given by the difference of two convex function (DC function). ...

In this paper, we consider the problem of finding solutions of nonlinear inclusion problems in Banach space. Using convex optimization techniques introduced by Robinson (Numer Math 19:341–347, 1972), a convergence theorem for Kantorovich-like methods is given, which improves the results of Yamamoto (Jpn J Appl Math 3(2):295–313, 1986; Numer Math 51(5):545–557, 1987) and Robinson (Numer Math 19:341–347, 1972). The result is compared with previously known results. Numerical examples further justify the theoretical results.

In this work we extend the method considered by von Heusinger et al. (Math Program 132(1):99–123, 2012) to the setting of equilibrium problems. Moreover, we introduce a family of auxiliary bifunctions containing that one used by them. We prove that the method is locally convergent and we establish the superlinear/quadratic convergence of the algorithm to a solution of the problem under suitable assumptions. An application of the proposed method to multiobjective optimization problems is considered. Some preliminary numerical results are reported showing the performance of our algorithm.

We propose a weighting subgradient algorithm for solving multiobjective minimization problems on a nonempty closed convex subset of an Euclidean space. This method combines weighting technique and the classical projected subgradient method, using a divergent series steplength rule. Under the assumption of convexity, we show that the sequence generated by this method converges to a Pareto optimal point of the problem. Some numerical results are presented.

The structural phase transition path from the low-temperature polar structure up to the highest symmetric phase in the hybrid improper ferroelectric ${\mathrm{Ca}}_{3}{\mathrm{Mn}}_{2}{\mathrm{O}}_{7}$ compound is here investigated at atomic scale. Measurements using the perturbed angular correlation local probe technique are combined with ab initio electronic structure calculations to observe the evolution of the electric field gradient parameters at the $\mathrm{Ca}$ site within the 10--1200 K temperature range. The results show that polar-phase clusters persist at temperatures as high as 500 K. In addition, evidence is given for a structural phase transition occurring above 1150 K. The high-temperature symmetry is here confirmed to be $I4/mmm$.

In this paper, we propose an algorithm for solving multiobjective minimization problems on nonempty closed convex subsets of the Euclidean space. The proposed method combines a reflection technique for obtaining a feasible point with a projected subgradient method. Under suitable assumptions, we show that the sequence generated using this method converges to a Pareto optimal point of the problem. We also present some numerical results.

Based on the constrained variational inequality problem considered by Censor, Gibali and Reich (Numerical Algorithms, 2012), we propose, the constrained equilibrium problem (CEP), which consists in finding a point in the intersection of two nonempty, closed and convex subsets of an Euclidean space, C and D, such that is a solution of an equilibrium problem on C. In this work, an algorithm using projections is proposed to solve (CEP). Convergence properties of the algorithm are established under mild assumptions. Some numerical results are reported.

In this paper, we propose a penalized gradient projection algorithm for solving the continuous convex separable knapsack problem, which is simpler than existing methods and competitive in practice. The algorithm only performs function and gradient evaluations, sums, and updates of parameters. The relatively complex task of the algorithm, which consists in minimizing a function in a compact set, is given by a closed formula. The convergence of the algorithm is presented. Moreover, to demonstrate its efficiency, illustrative computational results are presented for medium-sized problems.