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Projection methods are a popular class of methods for solving equilibrium problems. In this paper, we propose approximate one projection methods for solving a class of equilibrium problems, where the cost bifunctions are paramonotone, the feasible sets are defined by a continuous convex function inequality and not necessarily differentiable in the Euclidean space Rs. At each main iteration step in our algorithms, the usual projections onto the feasible set are replaced by computing inexact subgradients and one projection onto the intersection of two halfspaces containing the solution set of the equilibrium problems. Then, by choosing suitable parameters, we prove convergence of the whole generated sequence to a solution of the problems, under only the assumptions of continuity and paramonotonicity of the bifunctions. Finally, we present some computational examples to illustrate the assumptions of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Background/aims: To compare treatment outcomes with and without silicone oil tamponade in patients undergoing pars plana vitrectomy (PPV) for severe endogenous bacterial endophthalmitis (BEE). Methods: One hundred and eight consecutive patients with severe BEE (defined by the absence of pupil red reflex at presentation and/or dense vitreous opacity on ultrasound and no improvement after 24-36 hours of medical treatment) were randomly assigned to two treatment groups: Group 1, standard PPV with intravitreal antibiotics; and Group 2, PPV with intravitreal antibiotics and silicone tamponade. Overall success was defined as: a visual acuity ⩾ count fingers at 1 meter, with an attached retina, and no intraocular oil. Results: Fifty three patients were randomized to Group 1 and 55 patients to Group 2. The mean age of study subjects was 32 years and baseline clinical characteristics were similar in both groups. At the final follow-up visit at 9 months, the overall success rate of Group 2 (67.3%) was significantly better than Group 1 (43.4%; P=0.01). There were also fewer devastating complications (such as inoperable retinal detachment, phthisis bulbi) in Group 2 compared with Group 1 (21.8% versus 43.4%; P=0.01). Conclusion: The outcome at 9 months of patients with BEE treated by vitrectomy with silicone oil was better than those treated by vitrectomy alone. [ABSTRACT FROM AUTHOR]

We theoretically address the electronic structure of mono- and simple bi-layer armchair graphene nanoribbons (AGNRs) when they are infected by extrinsic charged dilute impurity. This is done with the aid of the modified tight-binding method considering the edge effects and the Green's function approach. Also, the interplay of host and guest electrons are studied within the full self-consistent Born approximation. Given that the main basic electronic features can be captured from the electronic density of states (DOS), we focus on the perturbed DOS of lattices corresponding to the different widths. The modified model says that there is no metallic phase due to the edge states. We found that the impurity effects lead to the emergence of midgap states in DOS of both systems so that a semiconductor-to-semimetal phase transition occurs at strong enough impurity concentrations and/or impurity scattering potentials. The intensity of semiconductor-to-semimetal phase transition in monolayer (bilayer) ultra-narrow (realistic) ribbons is sharper than bilayers (monolayers). In both lattices, electron-hole symmetry breaks down as a result of induced-impurity states. The findings of this research would provide a base for future experimental studies and improve the applications of AGNRs in logic semiconductor devices in industry. [ABSTRACT FROM AUTHOR]