Synthesis,Properties, and Redox Behavior of 1,1,4,4‐Tetracyano‐2‐ferrocenyl‐1,3‐butadienes Connected by Aryl,Biaryl, and Teraryl Spacers

Aryl‐substituted 1,1,4,4‐tetracyano‐1,3‐butadienes (FcTCBDs) and bis(1,1,4,4‐tetracyanobutadiene)s (bis‐FcTCBDs), possessing a ferrocenyl group on each terminal, were prepared by the reaction of a variety of alkynes with tetracyanoethylene (TCNE) in a [2+2] cycloaddition reaction, followed by retro‐electrocyclization of the initially formed [2+2] cycloadducts (i.e., cyclobutene derivatives). The characteristic intramolecular charge transfer (ICT) between the donor (ferrocene) and acceptor (TCBD) moieties were investigated by using UV/Vis spectroscopy. The redox behaviors of FcTCBDs and bis‐FcTCBDs were examined by cyclic voltammetry (CV) and differential pulse voltammetry (DPV), which revealed their properties of multi‐electron transfer depending on the number of ferrocene and TCBD moieties. Moreover, significant color changes were observed by visible spectroscopy under the electrochemical reduction conditions.     

Structural modeling of beams on elastic foundations with elasticity couplings

A new simplified structural model and its governing equations for beams on elastic foundations with elastic coupling are proposed. This modeling system is simple but appropriate for the initial structural design of large-scale submerged floating-beam structures moored by tension legs spaced at uniform interval along the beam. The model is actually for beam on discrete elastic supports rather than on continuous elastic foundations. Therefore, the governing equations are based on finite difference calculus and solutions for beams on discrete elastic supports with elasticity coupling are also proposed. To clarify the applicability limit of the proposed model, the equivalence between a beam on discrete elastic supports and that on continuous elastic foundation is investigated by comparisons of characteristic solutions.     

On square roots of the Haar state on compact quantum groups

The paper is concerned with the extension of the classical study of probability measures on a compact group which are square roots of the Haar measure, due to Diaconis and Shahshahani, to the context of compact quantum groups. We provide a simple characterisation for compact quantum groups which admit no non-trivial square roots of the Haar state in terms of their corepresentation theory. In particular it is shown that such compact quantum groups are necessarily of Kac type and their subalgebras generated by the coefficients of a fixed two-dimensional irreducible corepresentation are isomorphic (as finite quantum groups) to the algebra of functions on the group of unit quaternions. An example of a quantum group whose Haar state admits no nontrivial square root and which is neither commutative nor cocommutative is given.     

Microfluidic chip electrophoresis for biochemical analysis

Microfluidic chip electrophoresis has been widely employed for separation of various biochemical species owing to its advantages of low sample consumption, low cost, fast analysis, high throughput, and integration capability. In this article, we reviewed the development of four different modes of microfluidics‐based electrophoresis technologies including capillary electrophoresis, gel electrophoresis, dielectrophoresis, and field (electric) flow fractionation. Coupling detection schemes on microfluidic electrophoresis platform were also reviewed such as optical, electrochemical, and mass spectrometry method. We further discussed the innovative applications of microfluidic electrophoresis for biomacromolecules (nucleic acids and proteins), biochemical small molecules (amino acids, metabolites, ions, etc.), and bioparticles (cells and pathogens) analysis. The future direction of microfluidic chip electrophoresis was predicted.     

Comprehensive characterisation of the E phase of 6-octyl-2-phenylazulene

Molecular dynamics in the soft crystal, E phase of 6-octyl-2-phenylazulene was studied by X-ray diffraction, and dielectric and Fourier transform infrared spectroscopies. Clear dielectric dispersion is observed due to the head-to-tail disordering in a kHz range around 400 K. The CH stretching frequencies exhibit more pronounced shifts at the phase transition point from the high-temperature ordered crystal to the E phase than that at the melting from the E phase to the isotropic liquid. The results are discussed in comparison with a typical E series, 4-n-alkyl-4′-isothiocyanatobiphenyl (n being the number of carbon atoms in the alkyl group).     

Electron-boson coupling and oxygen-isotope effect in the optical conductivity of high-Tc superconductors

We have investigated electron-boson coupling in the optical conductivity of high-T_c superconductors through the optical self-energy. The real part of the self-energy (ReΣ^op(ω)) of YBa₂Cu₃O_y (YBCO) shows a characteristic doping dependence. In the optimally doped YBCO, ReΣ^op(ω) has a single peak around 65 meV, which corresponds to the kink structure of the band dispersion. On the other hand, in the under-doped YBCO, the peak structure of ReΣ^op(ω) splits into two parts. To evaluate contribution from the phonons in electron-boson coupling, we have measured oxygen-isotope effects by substituting ¹⁶O→¹⁸O for the optimally doped and under-doped YBCO.     

Mathematical analogy of a beam on elastic supports as a beam on elastic foundation

This paper presents the mathematical hypothesis that a beam on equidistant elastic supports (BOES) can be considered as a beam on an elastic foundation (BOEF) in static and free vibration problems. This modeling of BOES as BOEF is presumed to be applicable to a limited range of support stiffness, spacing and flexural rigidity of the beam. The authors investigate the applicability of the modeling of BOEF from the property of characteristic solutions obtained from governing equations of both BOES and BOEF. In this study, the formulation of BOES leads to governing difference equations, and the motions of BOEF are expressed by differential equations. This is because exact solutions must be employed in order to verify their analogy accurately. The characteristic solutions obtained from these two governing equations are compared to each other in order to investigate the relationship between them.