We show that thin film star-shaped macromolecules exhibit significant differences in their average vitrification behavior, in both magnitude and thickness dependence, from their linear analogs. This behavior is dictated by a combination of their functionality and arm length. Additionally, the glass transition temperature at the free surface of a star-shaped molecule film may be higher than that...

In this paper, the problem of pinning control for synchronization of complex dynamical networks is discussed. A cost function of the controlled network is defined by the feedback gain and the coupling strength of the network. An interesting result is that lower cost is achieved by the control scheme of pinning nodes with smaller degrees. Some rigorous mathematical analysis is presented for achi...

The equivalence between the inequalities of Babuška–Aziz and Friedrichs for sufficiently smooth bounded domains in the plane has been shown by Horgan and Payne 30 years ago. We prove that this equivalence, and the equality between the associated constants, is true without any regularity condition on the domain. For the Horgan–Payne inequality, which is an upper bound of the Friedrichs constant ...

In this paper, the problem of pinning control for synchronization of complex dynamical networks is discussed. A cost function of the controlled network is defined by the feedback gain and the coupling strength of the network. An interesting result is that lower cost is achieved by the control scheme of pinning nodes with smaller degrees. Some rigorous mathematical analysis is presented for achi...

This thesis studies transformation between geometric structures via geometric operations that act on some simplices of a geometric structure. Such a transformation is termed local transformation as an operation utilizes only information local to some neighboring simplices but nothing about other attributes or configurations global in nature to the structure. One famous algorithm of local transf...

We show that any compact subset of Rd which is the closure of a bounded star-shaped Lipschitz domain Ω, such that {Ω has positive reach in the sense of Federer, admits an optimal AM (admissible mesh), that is a sequence of polynomial norming sets with optimal cardinality. This extends a recent result of A. Kroó on C 2 star-shaped domains. Moreover, we prove constructively the existence of an op...

The possibility of releasing gold nanoparticles (GNP) into the environment has been 9 rapidly increasing with the wide spread and flourishing application of gold nanoparticles (GNPs) 10 in a wide range of areas. Consequently, environmental effects of GNP, especially toxicities to 11 living organisms have drawn great attention. However, their toxicological characteristics still 12 remain unclear...

Most star polymers with controlled molecular weight and low polydispersity are synthesized by living polymerization, in which only initiation and propagation reactions, but not chain transfer reaction, take place. Accordingly, the obtained star polymers are generally not contaminated with linear polymers. Recently, we have developed chain-growth condensation polymerization, a kind of living pol...

the hosoya index and the merrifield-simmons index are two types of graph invariants used in mathematical chemistry. in this paper, we give some formulas for computed these indices for some classes of corona product and link of two graphs. furthermore, we obtain exact formulas of hosoya and merrifield-simmons indices for the set of bicyclic graphs, caterpillars and dual star.