Cover Picture: Toroidal Micelles of Uniform Size from Diblock Copolymers (Angew. Chem. Int. Ed. 25/2009)

Pure toroidal micelles of highly uniform shape and size are presented by T. Chang et al. in their Communication on page 4594 ff. The donut‐shaped micelles are prepared by spontaneous self‐assembly of a polyisoprene‐block‐poly(2‐vinylpyridine) copolymer, and are stable enough to act as a template for the growth of gold nanoparticles along the ring surface.

     

Exciton Binding Energies in Conjugated Polyelectrolyte Films

Molecular design: The electronic structure of conjugated polyelectrolytes as a function of ionization potential (IP) and electron affinity (EA) is determined using X‐ray absorption and emission spectroscopy (see figure). Different functional groups give rise to dissimilar transport gaps and exciton binding energies.

     

An approximation property of exponential functions

We solve the inhomogeneous linear first order differential equations of the form y′(x) ? λy(x) = Σ _m=0 ^∞ a _m (x ? c) ^m , and prove an approximation property of exponential functions. More precisely, we prove the local Hyers-Ulam stability of linear first order differential equations of the form y′(x) = λy(x) in a special class of analytic functions.     

Convergence theorems based on hybrid methods for generalized equilibrium problems and fixed point problems

The purpose of this work is to introduce a hybrid projection method for finding a common element of the set of a generalized equilibrium problem, the set of solutions to a variational inequality and the set of fixed points of a strict pseudo-contraction in a real Hilbert space.     

Strong convergence of composite iterative methods for equilibrium problems and fixed point problems

We introduce a new composite iterative scheme by viscosity approximation method for finding a common point of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping. Our results substantially improve the corresponding results of Takahashi and Takahashi [A. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506-515]. Essentially a new approach for finding solutions of equilibrium problems and the fixed points of nonexpansive mappings is provided.     

A characterization of isometries on an open convex set,II

Let E ⁿ be an n-dimensional Euclidean space with n ≥ 2. In this paper, we generalize a classical theorem of Beckman and Quarles by proving that if a mapping, from an open convex subset Co of E ⁿ into E ⁿ , preserves a distance ρ, then the restriction of f to an open convex subset C _∞ of C ₀ is an isometry. This work was supported by 2007 Hongik University Research Fund.     

Self-induced 1-D molecular chain growth of thiophene on Ge(100)

The adsorption of thiophene on Ge(100) has been studied using scanning tunneling microscopy (STM), high-resolution core-level photoemission spectroscopy (HRPES), and density functional theory (DFT) calculations. Until now, thiophene is known to react with the Ge(100) dimer through a [4 + 2] cycloaddition reaction at room temperature, similar to the case of thiophene on Si(100). However, we found that thiophene has two adsorption geometries on Ge(100) at room temperature, such as a kinetically favorable Ge-S dative bonding configuration and a thermodynamically stable [4 + 2] cycloaddition adduct. Moreover, our STM results show that under 0.25 ML thiophene molecules preferentially produce one-dimensional molecular chain structures on Ge(100) via the Ge-S dative bonding configuration.     

Ab initio quantum chemistry calculations on the electronic structure of heavier alkyne congeners: diradical character and reactivity

The electronic structure of the heavier congeners of alkynes has been studied with emphasis on characterizing their extent of diradical character. Four orbitals play a crucial role in determining the electronic structure in planar trans-bent geometries. Two are associated with an out-of-plane pi interaction, pi and pi, and two are associated with in-plane interactions and/or in-plane lone pairs, LP(n-) and LP(n+). The ordering of these orbitals can change depending upon geometry. One extreme, corresponding to the local minimum for Si-Si and Ge-Ge, is a diradicaloid multiple-bonding configuration where LP and pi are nominally occupied. Another extreme, corresponding to a local minimum for Sn-Sn, is a relatively closed-shell single-bond configuration where LP and LP are nominally occupied. This ordering leads to predicted bond shortening upon excitation from singlet to triplet state. For the heavier elements, there appears to be very little energy penalty for large geometric distortions that convert from one ordering to the other on the singlet surface. The implications of these results with respect to experimental observations are discussed.