Classifying resolving subcategories over a Cohen–Macaulay local ring

Let R be a Cohen–Macaulay local ring. Denote by mod R the category of finitely generated R-modules. In this paper, we consider the classification problem of resolving subcategories of mod R in terms of specialization-closed subsets of Spec R. We give a classification of the resolving subcategories closed under tensor products and transposes. Under restrictive hypotheses, we also give better classification results.     

Enhancement of Higgs to diphoton decay width in non-perturbative Higgs model

We investigate a possibility if a loop diagram via Higgsino can enhance the Higgs to diphoton decay width in supersymmetric models with an extension of Higgs sector. A model with an additional non-renormalizable term of Higgs fields is firstly analyzed where the higher order term can introduce the Higgs coupling to Higgsinos as well as charged Higgs bosons. We point out that a choice of the Higgs coupling to obtain a significant size of enhancement of diphoton decay width reduces the Higgs mass and/or a size of non-renormalizable term needs to be large and a cutoff scale is around the weak scale. Another model in which the Higgsino mass term is generated by a non-perturbative instanton effect via a strong dynamics in a context of SUSY QCD is also suggested. It is shown that the sign of the Higgs coupling to fermions is opposite from perturbative models due to an operator including bosonic fields in the denominator and a constructive contribution to the diphoton decay amplitude can be easily obtained in this kind of model.     

A Model of Competition Among More than Two Languages

We extend the Abrams–Strogatz model for competition between two languages (Abrams and Strogatz in Nature 424:900, 2003) to the case of n (≥2) competing states (i.e., languages). Although the Abrams–Strogatz model for n=2 can be interpreted as modeling either majority preference or minority aversion, the two mechanisms are distinct when n≥3. We find that the condition for the coexistence of different states is independent of n under the pure majority preference, whereas it depends on n under the pure minority aversion. We also show that the stable coexistence equilibrium and stable monopoly equilibria can be multistable under the minority aversion and not under the majority preference. Furthermore, we obtain the phase diagram of the model when the effects of the majority preference and minority aversion are mixed, under the condition that different states have the same attractiveness. We show that the multistability is a generic property of the model facilitated by large n.     

Synthetic study of a moss-produced oxylipin and its structural revision

The proposed structure for a moss-produced acetylenic oxylipin (10-keto-type structure) was synthesized from a known glycidol derivative by an 11-step sequence involving epoxide ring opening with a terminal acetylene and enzymatic hydrolysis of a methyl ester intermediate. The NMR spectra of the proposed structure was, however, different from those of the natural oxylipin, which prompted us to synthesize its 9-epi-isomer and two diastereomeric 12-keto-type positional isomers. Comparison of the NMR spectra of the three isomers with those of the natural oxylipin indicated that the natural oxylipin was actually a mixture of the two diastereomeric positional isomers.     

Recent topics of gold catalyst featuring Z-type ligands

In the long history regarding the development of the transition metal-catalyzed reactions, almost all ligands in metals are classified as the covalent X-type and/or dative L-type ligands. Therefore, exploring the reactivity of the metal complexes bearing the σ-acceptor, i.e., the Z-ligand, is required. This digest briefly describes our recent results regarding 1) the syntheses of gold complexes featuring the Z-type ligand, and 2) their catalytic reactions, which would be speculated that the electron-withdrawing effect of the Z-ligand on the neighboring gold activated the catalytic reactivity due to the increase in the Lewis acidity.     

High‐Pressure Synthesis of A2NiO2Ag2Se2 (A=Sr,Ba) with a High‐Spin Ni2+ in Square‐Planar Coordination

Square‐planar coordinate Ni²⁺ ions in oxides are exclusively limited to a low‐spin state (S=0) owing to extensive crystal field splitting. Layered oxychalcogenides A₂Ni^IIO₂Ag₂Se₂ (A=Sr, Ba) with the S=1 NiO₂ square lattice are now reported. The structural analysis revealed that the Ni²⁺ ion is under‐bonded by a significant tensile strain from neighboring Ag₂Se₂ layers, leading to the reduction in crystal field splitting. Ba₂NiO₂Ag₂Se₂ exhibits a G‐type spin order at 130 K, indicating fairly strong in‐plane interactions. The high‐pressure synthesis employed here possibly assists the expansion of NiO₂ square lattice by taking the advantage of the difference in compressibility in oxide and selenide layers.     

Control of the Dynamic Motion of a Gel Actuator Driven by the Belousov‐Zhabotinsky Reaction

A novel self‐oscillating gel actuator with gradient structure, which generates a pendulum motion by fixing one edge of the gel without external stimuli was achieved. The gel was synthesized by copolymerizing the ruthenium catalyst for the Belousov‐Zhabotinsky reaction with N‐isopropylacrylamide and 2‐acrylamido‐2‐methylpropane sulfonic acid. Furthermore, we clarified that the period and amplitude for the self‐oscillating behavior of the gel actuator are controllable by changing the composition, temperature, and size of the gel. The maximum amplitude of the novel gel actuator is about a 100 times larger than that of the conventional self‐oscillating gel system.

     

Rhodium‐Catalyzed Stitching Polymerization of 1,5‐Hexadiynes and Related Oligoalkynes

A new mode of polymerization, rhodium‐catalyzed stitching polymerization, has been developed for the synthesis of π‐conjugated polymers with bridged repeating units from nonconjugated 1,5‐hexadiynes containing both terminal and internal alkyne moieties as monomers. The polymerization proceeded smoothly with a high degree of stitching efficiency under mild conditions, and 1,5,9‐decatriyne and 1,5,9,13‐tetradecatetrayne monomers could also be employed. The present polymerization strategy would be particularly beneficial for the synthesis of polymers consisting of a repeating unit that is difficult to prepare as a stable monomer because it does not require the use of a preformed bridged π‐conjugated monomer.     

Single-pixel camera with hole-array disk

Optical Review - A single-pixel camera is composed of optical coding masks, a photo detector, and a computational decoder as the important feature that it requires no image sensor for imaging, and...