Persistent oscillations in a threshold adjustment model

In this paper we present a simple time-continuous behavioural model of habit formation. Addictive behaviour is damped by a threshold which adapts itself to the habit. This adaptive behaviour of the threshold may lead to periodic fluctuations of the consumption rate, the habit and the threshold. It turns out that both a low adjustment rate of the threshold as well as a steep consumption function favour oscillatory patterns.     

General admissibility for linear estimators in a general multivariate linear model under balanced loss function

A generalization of Zellner’s balanced loss function is proposed. General admissibility in a general multivariate linear model is investigated under the generalized balanced loss function. And the sufficient and necessary conditions for linear estimators to be generally admissible in classes of homogeneous and nonhomogeneous linear estimators are given, respectively.     

Functional Carbazole-Fullerene Complexes: A New Perspective of Carbazoles Acting as Nano-Octopus to Capture Globular Fullerenes

Fullerene host-guest constructs have attracted increasing attention owing to their molecular-level hybrid arrangements. However, the usage of simple carbazolic derivatives to bind with fullerenes is rare. In this research, three novel carbazolic derivatives, containing a tunable bridging linker and carbazole units for the capturing of fullerenes, are rationally designed. Unlike the general concave-convex interactions, fullerenes could interact with the planar carbazole subunits to form 2-dimensional hexagonal/quadrilateral cocrystals with alternating stacking patterns of 1 : 1 or 1 : 2 stoichiometry, as well as the controllable fullerene packing modes. At the meanwhile, good electron-transporting performances and significant photovoltaic effects were realized when a continuous C_60⋅⋅⋅C₆₀ interaction channel existed. The results indicate that the introduction of such carbazolic system into fullerene receptor would provide new insights into novel fullerene host-guest architectures for versatile applications.     

Benzene Induced 1H NMR Shifts of Chromeno-Compounds: An Aid to Differentiate Linear and Angular Chromenoflavones

Benzene-induced shifts (BIS) in the ¹H NMR spectra of nine chromeno-compounds have been studied. It provides a simple non-destructive technique for distinguishing linear isomers of chromenoflavones from their angular counterparts. BIS also assists in the assignment of chromene proton signals in chromeno-compounds.     

Electron Transfer around a Molecular Corner

The distance dependence of electron transfer (ET) is commonly investigated in linear rigid rod‐like compounds, but studies of molecular wires with integrated corners imposing 90° angles are very rare. By using spirobifluorene as a key bridging element and by substituting it at different positions, two isomeric series of donor‐bridge‐acceptor compounds with either nearly linear or angled geometries were obtained. Photoinduced ET in both series is dominated by rapid through‐bond hole hopping across oligofluorene bridges over distances of up to 70 Å. Despite considerable conformational flexibility, direct through‐space and through‐solvent ET is negligible even in the angled series. The independence of the ET rate constant on the total number of fluorene units in the angled series is attributed to a rate‐limiting tunneling step through the spirobifluorene corner. This finding is relevant for multidimensional ET systems and grids in which individual molecular wires are interlinked at 90° angles.     

LIOUVILLIAN AND ANALYTIC FIRST INTEGRALS FOR THE BRUSSELATOR SYSTEM

We characterize the Liouvillian and analytic first integrals for the polynomial differential systems of the form x′ = a - (b + 1)x + x²y, y′ = bx - x²y, with a, b ∈ ?, called the Brusselator differential systems.     

Smoothing properties of transition semigroups in hilbert spaces

The paper gives conditions under which the transition semigroup corresponding to a large class of semilinear equations on a Hilbert space transforms Borel functions onto Frechet differentia hies ones.     

Electron-phonon coupling in cuprate and iron-based superconductors revealed by Raman scattering

Electron-phonon coupling （EPC） in cuprate and iron-based superconducting systems, as revealed by Raman scat- tering, is briefly reviewed. We introduce how to extract the coupling information through phonon lineshape. Then we discuss the strength of EPC in different high-temperature superconductor （HTSC） systems and possible factors affecting the strength. A comparative study between Raman phonon theories and experiments allows us to gain insight into some crucial electronic properties, especially superconductivity. Finally, we summarize and compare EPC in the two existing HTSC systems, and discuss what role it may play in the HTSC.