Remarks on a Noncanonical Representation for a Stationary Gaussian Process

For a stationary centered Gaussian process, we construct a noncanonical representation which has an infinite-dimensional orthogonal complement that is nontrivial. The authors have already proposed a systematic method for the construction of noncanonical representation having a finite-dimensional orthogonal complement.     

Coupled-Mode Analysis of an NRD-Guide Coupler Based on Singular Perturbation Technique

A coupled-mode formulation for an NRD-guide coupler is presented using the singular perturbation technique. The first-order and second-order perturbations are taken into account in the analysis and the coupled-mode equations based on the eigenmodes of each waveguide in isolation are derived. The propagation constants obtained by these equations are compared with those by the exact theory, conventional coupled-mode theory, and improved coupled-mode theory. The numerical results of present formulation are in good agreement with the exact theory and superior to those of the other formulations.     

Synthesis and functionalities of poly(N‐vinylalkylamide). XII. Synthesis and thermosensitive property of poly(vinylamine) copolymer prepared from poly(N‐vinylformamide‐co‐N‐vinylisobutyramide)

The differences in the polymerization abilities of N‐vinylformamide (NVF) and N‐vinylisobutyramide (NVIBA) and the synthesis of their copolymers were studied. The polymerization abilities were fairly good and quite similar to those of N‐vinyl‐ acetamide (NVA), a monomer in the same class as N‐vinylalkylamides. Since the monomer reactivity ratios were r₁ = 1.08 and r₂ = 0.92 (M₁ = NVF, M₂ = NVIBA), respectively, it is clear that the comonomers definitely were converted to random copolymers. The resulting copolymers poly(NVF‐co‐NVIBA) exhibited the cloud points sharply. The light transmittance profiles were the same as those for poly(NVIBA) although they increased from 39 °C for poly(NVIBA), with an increase in the corresponding hydrophilic NVF component. Our final objective was to produce a cloud point controlled polymer material with primary amino groups. To achieve this, we examined the hydrolysis of poly(NVF), poly(NVA), poly(NVIBA), and poly(NVF‐co‐NVIBA) to obtain poly(vinylamine) [poly(VAm)]. The hydrolytic cleavage of poly(NVF) and poly(NVA) was promoted by an increase in temperature. However, poly(NVIBA) was not cleaved appreciably. The hydrolysis of poly(NVF‐co‐NVIBA) was done under controlled conditions, and amino groups selectively were introduced to only one of two components of the copolymer. The cloud point of the hydrolyzed copolymer shifted to a higher temperature than that of the copolymer. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3674–3681, 2000     

Rotaxane Synthesis by an End-Capping Strategy via Swelling Axle-Phenols

A method for rotaxane synthesis by enlargement of the size of the terminal phenol group of the axle component by aromatic bromination has been developed. This method may be regarded as an end-capping strategy involving the swelling of the phenol group at the axle terminal. The advantages of the present strategy include: ready availability of axle components with a variety of swelling precursors, wide product scope (19 examples given including a [3]rotaxane), mild conditions for the swelling process, rich potential for the derivatization of the brominated rotaxanes, and possible release of the axle component by degradative dethreading of the thermally stable brominated rotaxanes under the basic conditions.     

Akaike's Information Criterion for Stoichiometry Inference of Supramolecular Complexes

“How do we decide the stoichiometry of host–guest complexes?” This question has long been answered by the Job plot since its first report in 1928. However, as the Job plot was claimed to be misleading in 2016, the question became an open question again and called for renewed investigations. An information-theoretic approach, called Akaike's information criterion, is introduced in this study to select the best model of host–guest complexes, which can rank the models with weight of evidence. A few test cases with unique cylindrical hosts were examined to demonstrate the applicability of the information-theoretic method. Consequently, reasonable views over the thermodynamic behaviors of dumbbell-and-cylinder complexes were obtained. Akaike's information criterion can be a useful and superior alternative to statistical null hypothesis testing, which was proposed as a remedy in place of the Job plot.     

Does Chiral Sensitivity of a Structure Depend on the Metal Core? Alkali Ion Complexes of Cyclo(Tyr-Tyr)

Alkali metal complexes of cyclic dipeptide cyclo Tyr-Tyr have been studied under cryogenic ion trap conditions. Their structure was obtained by combining Infra-Red Photo-Dissociation (IRPD) and quantum chemical calculations. The structural motif strongly depends on the relative chirality of the tyrosine residues. For residues of identical chirality, the cation interacts with one amide oxygen and one of the aromatic rings only; the distance between the aromatic rings does not change with the nature of the metal. In contrast, for residues of opposite chirality, the metal cation is located in between the two aromatic rings and interacts with both of them. The distance between the two aromatic rings strongly depends on the metal. Electronic spectra obtained by Ultra Violet Photodissociation (UVPD) spectroscopy and analysis of the UV photo-fragments shed light on the excited state deactivation processes, which depend on both the chirality of the residue and that of the metal ion core. Na⁺ stands out by the presence of low-lying charge transfer states resulting in the broadening of the electronic spectrum.