A note on price and quality competition between asymmetric firms

This paper analyzes the impact of asymmetry between firms on the outcome of price and quality competition from a microeconomic viewpoint. Consumers purchase a product based on not only its price but also its quality level; therefore, two firms compete in determining their prices and quality levels to maximize their profits. The asymmetry arises from the difference in consumers’ loyalty to each firm; that asymmetry then determines a character of differentiation between firms. Our purpose is to show how asymmetry influences competition under varying consumers’ price- and quality-sensitivity. In doing so, we extend earlier work in the area of price and quality competition. We show that in both the moderately quality-sensitive and price-sensitive markets, higher consumers’ sensitivity as well as lower consumers’ loyalty to any firm leads to intense competition, resulting in a decrease of both firms’ equilibrium profits. On the other hand, in highly quality-sensitive market, asymmetry compels the smaller firm to change its competitive strategy. In general, this is more beneficial to the larger firm, as the smaller firm’s profit tends to decline. In the worst case, the smaller firm is driven out of business under equilibrium.     

Fisher information metric and Poisson kernels

A complete Riemannian manifold X with negative curvature satisfying −b²?KX?−a²<0 for some constants a,b, is naturally mapped in the space of probability measures on the ideal boundary ∂X by assigning the Poisson kernels. We show that this map is embedding and the pull-back metric of the Fisher information metric by this embedding coincides with the original metric of X up to constant provided X is a rank one symmetric space of non-compact type. Furthermore, we give a geometric meaning of the embedding.     

One-step syntheses of alkyl glycosides and alkyl-substituted DNA oligomers by chemoselective glycosidations using DNA bases

The simple and practical synthesis of alkyl glycosides by novel chemoselective glycosidations using natural resources, DNA and RNA nucleosides, was realized, and the one-step synthesis of chemoselectively modified DNA oligomers using the glycosidation method was also demonstrated.     

Rhodium–Iodide Complex on a Catalytically Active SiO2 Surface for One-Pot Hydrosilylation–CO2 Cycloaddition

In this study, a novel Rh–iodide complex was synthesized through a surface reaction between an immobilized Rh cyclooctadiene complex and alkylammonium iodide (N⁺I⁻) on SiO₂. In the presence of ammonium cations, the SiO₂-supported Rh–iodide complex could be effectively used for the one-pot synthesis of various silylcarbonate derivatives starting from epoxy olefins, hydrosilanes, and CO₂. The maximum turnover numbers (TONs) for the hydrosilylation reaction and the CO₂ cycloaddition were 7600 (Rh) and 130 (N⁺I⁻), respectively. The catalyst exhibited much higher performance for hydrosilylation than solely the Rh complex on SiO₂. The mechanism of the Rh-catalyzed hydrosilylation reaction and the local structure of Rh, which is affected by the co-immobilized N⁺I⁻, were investigated by using Rh and I K-edge XAFS and XPS. Analysis of the XAFS profiles indicated the presence of a Rh−I bond. The Rh unit was in its electron-rich state. Curve-fitting analysis of the Rh K-edge EXAFS profiles suggests dissociation of the cycloocta-1,5-diene (COD) ligand from the Rh center. Results from spectroscopic and kinetic analyses revealed that the high activity of the catalyst (during hydrosilylation) could be attributed to a decrease in steric hindrance and the electron-rich state of the Rh. The decrease in the steric hindrance could be attributed to the absence of COD, and the electron-rich state promoted the oxidative addition of Si−H. To the best of our knowledge, this is the first example of a one-pot silylcarbonate synthesis as well as a determination of a novel surface Rh–iodide complex and its catalysis.     

Overcoming Steric Hindrance in Aryl-Aryl Homocoupling via On-Surface Copolymerization

On-surface synthesis is a unique tool for growing low-dimensional carbon nanomaterials with precise structural control down to the atomic level. This novel approach relies on carefully designed precursor molecules, which are deposited on suitable substrates and activated to ultimately form the desired nanostructures. One of the most applied reactions to covalently interlink molecular precursors is dehalogenative aryl-aryl coupling. Despite the versatility of this approach, many unsuccessful attempts are also known, most of them associated to the poor capability of the activated precursors to couple to each other. Such failure is often related to the steric hindrance between reactants, which may arise due to their coplanarity upon adsorption on a surface. Here, we propose a copolymerization approach to overcome the limitations that prevent intermolecular homocoupling. We apply the strategy of using suitable linkers as additional reactants to the formation of fully conjugated polycyclic nanowires incorporating non-benzenoid rings.     

Chiral Supramolecular Nanoarchitectures from Macroscopic Mechanical Rotations: Effects on Enantioselective Aggregation Behavior of Phthalocyanines

Fluid dynamics, resulting from the macroscopic mechanical rotation of either a rotary evaporator or a magnetic stirrer, has been shown to selectively induce one of two enantiomers (mirror‐image structures) in certain nanoscale supramolecules. As an alternative to giving a chiral twist to synthesized supramolecules or polymers, it is a challenge to reproducibly prepare chiral species by only using macroscopic mechanical rotations. Demonstrated here is a highly reproducible method for rotary‐evaporation‐induced enantioselective H‐aggregation of achiral phthalocyanines. Chiral induction mechanisms are proposed by using the chiroptical‐sign‐based absolute structures. These results will provide insight to the origin of the homochirality of life, and serves as a pioneering study in a novel scientific field in terms of admixing nanoscale molecular chemistry and macroscopic fluid dynamics.     

Push–Pull Bisnaphthyridylamine Supramolecular Nanoparticles: Polarity-Induced Aggregation and Crystallization-Induced Emission Enhancement and Fluorescence Resonance Energy Transfer

Emissive push–pull-type bisnaphthyridylamine derivatives ( BNA-X : X=Me, Et, Bzl, Ph, BuBr, and BuTEMPO) aggregate in aqueous methanol. Furthermore, a two-step emission and aggregation process is controllable by varying the methanol-to-water ratio. At 2:3 MeOH/H₂O, crystallization-induced emission enhancement (CIEE) occurs via formation of an emissive crystal phase, whereas, at 1:9 MeOH/H₂O, aggregation-induced emission enhancement (AIEE) occurs, induced by emissive supramolecular nanoparticles (NPs). For BNA-Ph , the emission quantum yield was 25 times higher in aqueous methanol than that in pure methanol. Despite the high hydrophobicity of BNA-X (C log P=6.1–8.0), the spherical NPs were monodisperse (polydispersity indices <0.2). Moreover, the emissive NPs exhibited fluorescence resonance energy transfer (FRET) with pyrene; however, for BNA-X bearing the TEMPO radical ( BNA-BuTEMPO ), no FRET was observed because of quenching. In particular, the BNA-BuTEMPO NPs have a slow rotational correlation time (1.3 ns), suggesting applications as magnetic resonance imaging contrast agents with large relaxivity.     

TEMPO-substituted polyacrylamide for an aqueous electrolyte-typed and organic-based rechargeable device

A hydrophilic radical polymer, poly(2,2,6,6-teteramethylpiperidinyloxyl-4-yl acrylamide) (PTAm), was synthesized via oxidation of the corresponding precursor polymer, poly(2,2,6,6-teteramethylpiperidine-4-yl acrylamide). Electrochemical properties of the PTAm layer were characterized in three aqueous electrolytes of sodium chloride (NaCl), sodium tetrafluoroborate (NaBF4), and sodium hexafluorophosphate (NaPF6) to optimize its activity as an organic cathode. The counter anion species significantly affected the capacity and the cycle performance of the PTAm layer. The PTAm layer in the presence of BF4? displayed quantitative redox capacity beyond 1 μm layer thickness and maintained the discharging capacity of 110 mAh g-1 (97% vs. the calculated capacity) even after 1000 cycle charging/discharging, which could be ascribed to its appropriate affinity to the aqueous electrolyte without any dissolution into the electrolyte. A totally organic-based rechargeable cell was fabricated using PTAm and poly(N-4,4’-bipyridinium-N-decamethylene dibromide) as the cathode and the anode, respectively, and the aqueous electrolyte of NaBF4. The cell gave a plateau voltage at 1.2 V both on charging and discharging and an excellent charging/discharging cyclability of >2000 with high coulombic efficiency of >95%.