Local torus actions modeled on the standard representation

We introduce the notion of a local torus action modeled on the standard representation (for simplicity, we call it a local torus action). It is a generalization of a locally standard torus action and also an underlying structure of a locally toric Lagrangian fibration. For a local torus action, we define two invariants called a characteristic pair and an Euler class of the orbit map, and prove that local torus actions are classified topologically by them. As a corollary, we obtain a topological classification of locally standard torus actions, which includes the topological classifications of quasi-toric manifolds by Davis and Januszkiewicz and of effective T²-actions on four-dimensional manifolds without nontrivial finite stabilizers by Orlik and Raymond. We discuss locally toric Lagrangian fibrations from the viewpoint of local torus actions. We also investigate the topology of a manifold equipped with a local torus action when the Euler class of the orbit map vanishes.     

Branching Random Walks in Space–Time Random Environment: Survival Probability,Global and Local Growth Rates

We study the survival probability and the growth rate for branching random walks in random environment (BRWRE). The particles perform simple symmetric random walks on the d-dimensional integer lattice, while at each time unit, they split into independent copies according to time–space i.i.d. offspring distributions. The BRWRE is naturally associated with the directed polymers in random environment (DPRE), for which the quantity called the free energy is well studied. We discuss the survival probability (both global and local) for BRWRE and give a criterion for its positivity in terms of the free energy of the associated DPRE. We also show that the global growth rate for the number of particles in BRWRE is given by the free energy of the associated DPRE, though the local growth rate is given by the directional free energy.     

Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes

Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and the lack of a general framework for classifications. While frustration-free Hamiltonians, which appear as fixed point Hamiltonians of renormalization group transformations, may serve as representatives of quantum phases, it is still difficult to analyze and classify quantum phases of arbitrary frustration-free Hamiltonians exhaustively. Here, we address these problems by sharpening our considerations to a certain subclass of frustration-free Hamiltonians, called stabilizer Hamiltonians, which have been actively studied in quantum information science. We propose a model of frustration-free Hamiltonians which covers a large class of physically realistic stabilizer Hamiltonians, constrained to only three physical conditions; the locality of interaction terms, translation symmetries and scale symmetries, meaning that the number of ground states does not grow with the system size. We show that quantum phases arising in two-dimensional models can be classified exactly through certain quantum coding theoretical operators, called logical operators, by proving that two models with topologically distinct shapes of logical operators are always separated by quantum phase transitions.     

Probing the Rotational Dynamics of meso‐(2‐Substituted)aryl Substituents in A2B‐Type Subporphyrins

A₂B‐type B‐methoxy subporphyrins 3 a – g and B‐phenyl subporphyrins 7 a – c , e , g bearing meso‐(2‐substituted)aryl substituents are synthesized, and their rotational dynamics are examined through variable‐temperature (VT) ¹H NMR spectroscopy. In these subporphyrins, the rotation of meso‐aryl substituents is hindered by a rationally installed 2‐substituent. The rotational barriers determined are considerably smaller than those reported previously for porphyrins. Comparison of the rotation activation parameters reveals a variable contribution of ΔH^≠ and ΔS^≠ in ΔG^≠. 2‐Methyl and 2‐ethyl groups of the meso‐aryl substituents in subporphyrins 3 e , 3 f , and 7 e induce larger rotational barriers than 2‐alkoxyl substituents. The rotational barriers of 3 g and 7 g are reduced by the presence of the 4‐dibenzylamino group owing to its ability to stabilize the coplanar rotation transition state electronically. The smaller rotational barriers found for B‐phenyl subporphyrins than for B‐methoxy subporphyrins indicate a negligible contribution of S_N1‐type heterolysis in the rotation of meso‐aryl substituents.     

Design and synthesis of 2-(1,3-dialkoxy-2-methylpropan-2-yl)-1,3-diarylpropanes as tethering units for folded H-stacking polymers

1,3-Diarylpropenes 9 having a 1,3-dialkoxy-2-methylpropan-2-yl group were designed as tethering monomers for folded H-stacking polymers, and were readily synthesized from 2-ethoxymethylidene malonate in four- or five-steps, including a facile sequential addition–elimination–addition reaction of benzyl zinc reagents. The preference for the closed (stacked) conformation in the resulting 2-substituted 1,3-diarylpropanes 9 was evaluated using MM2 calculations, ¹H NMR analyses, and fluorescence measurements. Copolymerization of the resulting monomers 9 with compounds containing π-units provided polymers with blue-shifted UV-absorptions both in solution and as films, compared with that of a model compound containing a single π-unit. This optical property is unique to H-aggregated π-units.     

Structure of tecophilin,a tri-caffeoylanthocyanin from the blue petals of Tecophilaea cyanocrocus, and the mechanism of blue color development

The pigment, tecophilin, in blue flowers of Tecophilaea cyanocrocus was isolated and the structure was determined to be 3-O-(6-O-α-l-rhamnopyranosyl-β-d-glucopyranosyl)-7-O-(6-O-(4-O-(2-O-(4-O-β-d-glucopyranosyl-(E)-caffeoyl)-6-O-(4-O-β-d-glucopyranosyl-(E)-caffeoyl)-β-d-glucopyranosyl)-(E)-caffeoyl)-β-d-glucopyranosyl)delphinidin. The reproduction experiment of the same color as petals according to the results of chemical analysis and measurement of vacuolar pH of blue cells clarified that the blue color solely develops by tecophilin without interaction of metal ions nor co-pigments. ¹H NMR analysis and CD spectrum indicate the co-existence of clockwise intermolecular self-association of the delphinidin nuclei and intramolecular π–π stacking between the chromophore and caffeoyl residues to derive bathochromic shift of the absorption spectrum and stabilize the color by preventing hydration reaction.     

Proposal for generation of high-intensity monochromatic Cherenkov radiation in THz range by femtosecond electron bunches in impurity-doped semiconductor tube

A novel method to generate high-power THz radiation is proposed. If a beam with a bunch length on the order of 100 fs is injected into an electron–hole plasma of a semiconductor with a plasma frequency on the order of THz, THz wake fields are coherently generated. If the beam moves on the axis of a hollow tube covered by a metal, the frequency spectrum of the radiation is composed of discrete components. Monochromatic radiation is obtained by making only the lowest frequency component coherent.     

Self-oscillating polymer gel as novel biomimetic materials exhibiting spatiotemporal structure

As a novel biomimetic polymer gel, we have been studying polymer gel with an autonomous self-oscillating function since it was firstly reported in 1996. For developing the polymer gels, we utilized an oscillating chemical reaction, called the Belousov?CZhabotinsky (BZ) reaction, which is recognized as a chemical model for understanding several autonomous phenomena in biological systems. The self-oscillating polymer gel is composed of a poly(N-isopropylacrylamide) network in which the metal catalyst for the BZ reaction is covalently immobilized. Under the coexistence of the reactants, the polymer undergoes spontaneous swelling?Cdeswelling changes (in the case of gel) or cyclic soluble?Cinsoluble changes (in the case of uncross-linked polymer) without any on?Coff switching of external stimuli. Several kinds of functional material systems utilizing the self-oscillating polymer and gel such as biomimetic actuators, mass transport surface, etc. are expected. Here, these recent progress on the self-oscillating polymer and gels and the design of functional material systems are summarized.     

Synthesis of 4-unsubstituted dihydropyrimidines. Nucleophilic substitution at position-2 of dihydropyrimidines

Synthesis of novel 4-unsubstituted dihydropyrimidines (DPs) was performed. Subsequently, a variety of 4-unsubstituted 1,4(3,4)-DPs with amino moieties at position-2 were obtained in excellent yields by activation of position-2 owing to regioselective alkoxycarbonylation at position-3 of the DP skeleton. 3-Oxo-2-phenyl-2,3,5,8-tetrahydro[1,2,4]triazolo[4,3-a]pyrimidine was obtained using phenylhydrazine instead of amines. Individual tautomers of 1,4(3,4)-DP were observed in the ¹H NMR spectra of one derivative depending on temperature and concentration. On the other hand, only 1,4-DP was found in the solid state by single-crystal X-ray crystallography.