Projected viscosity subgradient methods for variational inequalities with equilibrium problem constraints in Hilbert spaces

In this paper, we introduce and study some low computational cost numerical methods for finding a solution of a variational inequality problem over the solution set of an equilibrium problem in a real Hilbert space. The strong convergence of the iterative sequences generated by the proposed algorithms is obtained by combining viscosity-type approximations with projected subgradient techniques. First a general scheme is proposed, and afterwards two practical realizations of it are studied depending on the characteristics of the feasible set. When this set is described by convex inequalities, the projections onto the feasible set are replaced by projections onto half-spaces with the consequence that most iterates are outside the feasible domain. On the other hand, when the projections onto the feasible set can be easily computed, the method generates feasible points and can be considered as a generalization of Maingé’s method to equilibrium problem constraints. In both cases, the strong convergence of the sequences generated by the proposed algorithms is proven.     

Robustness of Bayesian D-optimal design for the logistic mixed model against misspecification of autocorrelation

In medicine and health sciences mixed effects models are often used to study time-structured data. Optimal designs for such studies have been shown useful to improve the precision of the estimators of the parameters. However, optimal designs for such studies are often derived under the assumption of a zero autocorrelation between the errors, especially for binary data. Ignoring or misspecifying the autocorrelation in the design stage can result in loss of efficiency. This paper addresses robustness of Bayesian D-optimal designs for the logistic mixed effects model for longitudinal data with a linear or quadratic time effect against incorrect specification of the autocorrelation. To find the Bayesian D-optimal allocations of time points for different values of the autocorrelation, under different priors for the fixed effects and different covariance structures of the random effects, a scalar function of the approximate variance–covariance matrix of the fixed effects is optimized. Two approximations are compared; one based on a first order penalized quasi likelihood (PQL1) and one based on an extended version of the generalized estimating equations (GEE). The results show that Bayesian D-optimal allocations of time points are robust against misspecification of the autocorrelation and are approximately equally spaced. Moreover, PQL1 and extended GEE give essentially the same Bayesian D-optimal allocation of time points for a given subject-to-measurement cost ratio. Furthermore, Bayesian optimal designs are hardly affected either by the choice of a covariance structure or by the choice of a prior distribution.     

Optimality and duality in nonsmooth multiobjective fractional programming problem with constraints

In this paper, we establish some quotient calculus rules in terms of contingent derivatives for the two extended-real-valued functions defined on a Banach space and study a nonsmooth multiobjective fractional programming problem with set, generalized inequality and equality constraints. We define a new parametric problem associated with these problem and introduce some concepts for the (local) weak minimizers to such problems. Some primal and dual necessary optimality conditions in terms of contingent derivatives for the local weak minimizers are provided. Under suitable assumptions, sufficient optimality conditions for the local weak minimizers which are very close to necessary optimality conditions are obtained. An application of the result for establishing three parametric, Mond–Weir and Wolfe dual problems and several various duality theorems for the same is presented. Some examples are also given for our findings.

     

Helium bubble and blister formation for Ni and an amorphous Fe-Ni-Mo-B alloy during 5 keV implantation at 300 K

Results are presented for helium bubble formation in Ni and amorphous Fe₄₀Ni₃₈Mo₄B_l8 during 5 keV He-implantation at 300 K. The formation of helium blisters on the surface is also reported.     

Analysis of benzophenone and 4-methylbenzophenone in breakfast cereals using ultrasonic extraction in combination with gas chromatography-tandem mass spectrometry (GC-MS)

Benzophenone (BP) and 4-methylbenzophenone (4MBP) are photo-initiators that are generally used to cure ink on carton boards.In this contribution, a fast and reliable method for the determination of BP and 4MBP in breakfast cereals is described. The sample was extracted ultrasonically using a mixture of dichloromethane and acetonitrile (1:1), followed by a clean-up of the extract using solid phase extraction with a silica cartridge. Finally, the extract was analysed by GC-MSⁿ. Benzophenone-d₁₀ was used as internal standard. The presented method is validated in terms of linearity, recovery, repeatability and intra-laboratory reproducibility, specificity, limit of detection and limit of quantification. In conclusion, this method is able to detect both BP and 4MBP at very low concentrations (LOD = 2 μg kg⁻¹) in breakfast cereals.     

Identification of Intermediates in Zeolite‐Catalyzed Reactions by In Situ UV/Vis Microspectroscopy and a Complementary Set of Molecular Simulations

The optical absorption properties of (poly)aromatic hydrocarbons occluded in a nanoporous environment were investigated by theoretical and experimental methods. The carbonaceous species are an essential part of a working catalyst for the methanol‐to‐olefins (MTO) process. In situ UV/Vis microscopy measurements on methanol conversion over the acidic solid catalysts H‐SAPO‐34 and H‐SSZ‐13 revealed the growth of various broad absorption bands around 400, 480, and 580 nm. The cationic nature of the involved species was determined by interaction of ammonia with the methanol‐treated samples. To determine which organic species contribute to the various bands, a systematic series of aromatics was analyzed by means of time‐dependent density functional theory (TDDFT) calculations. Static gas‐phase simulations revealed the influence of structurally different hydrocarbons on the absorption spectra, whereas the influence of the zeolitic framework was examined by using supramolecular models within a quantum mechanics/molecular mechanics framework. To fully understand the origin of the main absorption peaks, a molecular dynamics (MD) study on the organic species trapped in the inorganic host was essential. During such simulation the flexibility is fully taken into account and the effect on the UV/Vis spectra is determined by performing TDDFT calculations on various snapshots of the MD run. This procedure allows an energy absorption scale to be provided and the various absorption bands determined from in situ UV/Vis spectra to be assigned to structurally different species.     

Surface modification of an epoxy resin with polyamines via cyanuric chloride coupling

The presence of polyamine groups on the surface of dielectric resins potentially improves the adhesion with electrochemically deposited metals. In this article, first cyanuric chloride is covalently bound to the surface hydroxyl groups of the epoxy resin. The remaining reactive sites on the coupled cyanuric chloride molecule are then used to anchor polyamines. New data on the triazine coupling is presented. The surface reactions are monitored and characterized by means of ATR-IR, SEM-EDS, XPS and ToF-S-SIMS.