On the stability of self-adjointness of linear relations

This paper focuses on the stability of self-adjointness of linear relations under perturbations in Hilbert spaces. It is shown that a self-adjoint relation is still self-adjoint under bounded and relatively bounded perturbations. The results obtained in the present paper generalize the corresponding results for linear operators to linear relations, and some weaken the conditions of the related existing results

Catalytic polymeric nanoreactors : more than a solid supported catalyst

Polymeric nanostructures can be synthesized where the catalytic motif is covalently attached within the core domain and protected from the environment by a polymeric shell. Such nanoreactors can be easily recycled, and have shown unique properties when catalyzing reactions under pseudohomogeneous conditions. Many examples of how these catalytic nanostructures can act as nanosized reaction vessels have been reported in the literature. This prospective will focus on the exclusive features observed for these catalytic systems and highlight their potential as enzyme mimics, as well as the importance of further studies to unveil their full potential

Modelling the driving forces of Sydney's urban development (1971-96) in a cellular environment

[Abstract]: This paper demonstrates a flexible implementation of rules to control the simulation of urban development of Sydney from 1971 to 1996 using a cellular automata model. Five key factors, including the self propensity for development and neighbourhood support, slope constraint, transportation support, terrain and coastal proximity attractions and urban planning support are introduced into the model in a spatially explicit format, which generated a realistic estimation of the extent and timing of Sydney's urban development. With the flexibility of rule implementation within the model, more rules can be added as new 'If-Then' statements to fine-tune the model, provided that a good understanding of the rule is maintained and accurate data are collected