A perturbation of ring derivations on Banach algebras

Suppose A is a Banach algebra and suppose is an approximate ring derivation in the sense of Hyers-Ulam-Rassias. This stability phenomenon was introduced for the first time in the subject of functional equations by Th.M. Rassias [Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297-300]. If A has an approximate identity, or if A is semisimple and commutative, then we prove that f is an exact ring derivation.     

Generalizations of spectrally multiplicative surjections between uniform algebras

Let $ A $ A and ℬ be unital semisimple commutative Banach algebras. It is shown that if surjections S,T: $ A $ A → ℬ with S(1)=T(1)= 1 and α ∈ ℂ \ {0} satisfy r(S(a)T(b) − α)= r(ab− α) for all a,b ∈ $ A $ A , then S=T and S is a real algebra isomorphism, where r(a) is the spectral radius of a. Let I be a nonempty set, A and B be uniform algebras. Let ρ, τ: I → A and S,T: I → B be maps satisfying σ _π (S(p)T(q)) ⊂ σ _π (ρ(p) τ(q)) for all p,q ∈ I, where σ _π (f) is the peripheral spectrum of f. Suppose that the ranges ρ(I), τ(I) ⊂ A and S(I),T(I) ⊂ B are closed under multiplication in a sense, and contain peaking functions “enough”. There exists a homeomorphism ϕ: Ch(B)→Ch(A) such that S(p)(y)= ρ(p)(ϕ(y)) and T(p)(y)= τ(p)(ϕ(y)) for every p ∈ I and y ∈ Ch(B), where Ch(A) is the Choquet boundary of A.     

Solvation of ions in hydrophilic layer of polyoxyethylated nonionic micelle. Cooperative approach by electrophoresis and ion-transfer voltammetry

Electrophoretic measurements of micellar mobility have revealed that polyoxyethylated nonionic surfactant micelles have negative zeta potential in various electrolytes, indicating that the partition of anions into the micelle dominates the entire electrolyte partition and the induced surface potential of the micelle. Although an excess of a negative charge is thus revealed in the micelle, it is uncertain whether anions are preferably solvated in the micelles or cations are expelled from the micelles. To determine the solvation energies of single ions in the hydrophilic layer of the micelle, we have performed ion transfer voltammetric measurements at microinterfaces between nitrobenzene and aqueous tetraethyleneglycol solution, which acts as a model for the palisade layer of the micelles. The cooperative utilization of these different methods has allowed us to determine the Gibbs free energy of transfer of a single ion without an extrathermodynamic assumption. On the basis of the resulting values, the partition of ions and the zeta potential induced by the imbalance of anionic and cationic partition have been quantitatively explained.     

Ecosystems perspective on financial networks: Diagnostic tools

The world economy consists of highly interconnected and interdependent commercial and financial networks. Here, we develop temporal and structural network tools to analyze the state of the economy and the financial markets. Our analysis indicates that a strong clustering can be a warning sign. Reduction in diversity, which was an essential aspect of the dynamics surrounding the financial markets crisis of 2008, is seen as a key emergent feature arising naturally from the evolutionary and adaptive dynamics inherent to the financial markets. Similarly, collusion amongst construction firms in a number of regions in Japan in the 2000s can be identified with the formation of clusters of anomalous highly connected companies. © 2013 Wiley Periodicals, Inc. Complexity 19: 22–36, 2013     

Ultracontractivity for Markov Semigroups and Quasi-Stationary Distributions

We prove the existence and uniqueness of quasi-stationary distributions for symmetric Markov processes. In particular, we show that if its Markov semigroup is intrinsic ultracontractive, then there exists a unique quasi-stationary distribution. We apply our results to one-dimensional diffusion processes.     

Nucleation of dynamic recrystallization and variant selection in copper bicrystals

Orientation-controlled copper bicrystals containing [001] symmetrical tilt boundaries aligned parallel to the loading axis were deformed in tension at 923?K and a strain rate of 4.2?×?10^?4?s^?1. The nucleation of dynamic recrystallization (DRX) was investigated along the grain boundary. For this purpose, both optical and orientation imaging microscopy methods were used. After grain-boundary migration (GBM) and bulging, nuclei appeared behind the most deeply indented grain boundary regions. The critical strain for nucleation was about one-quarter to one-half of the peak strain and depended on the misorientation angle. All the nuclei were twin-related (Σ3) to the matrices. Furthermore, all the primary twin traces were parallel to those of the inactive slip planes of the parent single crystals. Crystallographic analysis revealed the important role of the direction of GBM on twinning-plane variant selection. The characteristics of grain boundary nucleation depended sensitively on grain boundary character and on grain boundary mobility. The observed DRX nucleation mechanism is discussed in relation to the occurrence of GBM and twinning.     

Concise Synthesis of Potassium Acyltrifluoroborates from Aldehydes through Copper(I)‐Catalyzed Borylation/Oxidation

Potassium acyltrifluoroborates (KATs) were prepared through copper(I)‐catalyzed borylation of aldehydes and subsequent oxidation. This synthetic route is characterized by the wide range of aldehydes accessible, favorable step economy, mild reaction conditions, and tolerance of various functional groups, and it enables the facile generation of a range of KATs, for example, bearing halide, sulfide, acetal, or ester moieties. Moreover, this method was applied to the three‐step synthesis of various α‐amino acid analogues that bear a KAT moiety on the C‐terminus by using naturally occurring amino acids as the starting material.     

Chemical Bonding in Polarised Push–Pull Ethylenes

1,1‐Diamino‐2,2‐bis(triflyl)ethylenes with both twisted and planar structures around the partial “C=C” bond were synthesised. Bonding properties in these compounds were analysed by an experimental approach using high‐resolution X‐ray diffraction data treated with X‐ray wavefunction refinement (XWR). In the twisted compound, a dominant contribution of the charge‐separated resonance structure was revealed. On the contrary, the nearly planar compound still showed π‐bonding character, however, with a considerable contribution of the charge‐separated resonance structure.     

Local structural analysis of In-doped Bi2Se3 topological insulator using X-ray fluorescence holography

We performed X-ray fluorescence holography measurements on an In-doped Bi₂Se₃ topological insulator and obtained an in-plane atomic image in the vicinity of In. We found that atomic images at the positions of the first nearest neighbors (NNs) are very weak whereas those at the positions of the second and the third NNs are relatively strong. On the basis of the fact that In is half of the atomic number of Bi, we attributed the origin of this feature to the clustering of the In atoms in the Bi plane. We calculated the intensity of the atomic images and confirmed that the formation of In cluster results in a decrease by 30% in the first NN atomic image intensity. However, the decrease in the magnitude is not enough to explain the experimental results, suggesting another contribution such as the lattice distortions. The effect of the lattice distortion on the atomic image intensity is discussed on the basis of the simulation including the positional fluctuation of In atoms.