Syzygies of Cohen–Macaulay Modules over One Dimensional Cohen–Macaulay Local Rings

Algebras and Representation Theory - We study syzygies of (maximal) Cohen–Macaulay modules over one dimensional Cohen–Macaulay local rings. We assume that rings are generically...     

Concise Construction of the ACDE Ring System of Calyciphylline A Type Alkaloids by a [5+2] Cycloaddition

A concise route for construction of the ACDE ring skeleton in calyciphylline A type alkaloids was developed using an intramolecular [5+2] cycloaddition reaction of an oxidopyrylium species bearing a tetrasubstituted olefin. Key to the success of this reaction was the combination of acid and base, which accelerated the construction of this skeleton containing a spiro ring and vicinal quaternary carbon centers. The resultant tricyclic ADE ring compound was converted to an ACDE ring model through C−H oxidation and an aza-Wittig reaction.     

The Effect of Viscosity on the Diffusion and Termination Reaction of Organic Radical Pairs

The effect of viscosity on the diffusion efficiency (F_dif) of an organic radical pair in a solvent cage and the termination mechanism, that is, the selectivity of disproportionation (Disp) and combination (Comb) of the geminated caged radical pair and the diffused radicals encountered, were investigated quantitatively by following the photolysis of dimethyl 2,2′-azobis(2-methylpropionate) (V-601) in the absence and presence of PhSD. F_dif and Disp/Comb selectivity outside the cage [Disp_(dif)/Comb_(dif)] are highly sensitive to the viscosity. In contrast, the Disp/Comb selectivity inside the cage [Disp_(cage)/Comb_(cage)] is rather insensitive. The difference in viscosity dependence between Disp_(cage)/Comb_(cage) and Disp_(dif)/Comb_(dif) is explained by the spin state of the radical pair inside and outside the cage and the spin state dependent configurational changes of the radical pair upon their collision. Given that the configurational change of the radicals associates the displacement and reorganization of solvents around the radicals, the termination outside the cage, which requires larger change than that inside the cage, is highly viscosity dependent. Furthermore, while the bulk viscosity of each solvent shows good correlation with F_dif and Disp/Comb selectivity, microviscosity is the better parameter predicting F_dif and Disp_(dif)/Comb_(dif) selectivity regardless of the solvents.     

Generation of finite subgroups of the mapping class group of genus 2 surface by Dehn twists

In this note we give presentations, up to conjugacy, of all finite subgroups of the mapping class group of a closed surface of genus 2, using the Humphries generators. An application to homology representations is given.     

Synthesis,Structure, Optical,and Electrochemical Properties of Triple‐ and Quadruple‐Decker Co‐facial Tetrathiafulvalene Arrays

Understanding the details of the electronic structure in face‐to‐face arranged tetrathiafulvalenes (TTFs) is very important for the design of supramolecular functional materials and superior conductive organic materials. This article is a comprehensive study of the interactions among columnar stacked TTFs using trimeric (trimer) and tetrameric (tetramer) TTFs linked by alkylenedithio groups (‐S(CH₂)_nS‐, n=1–4) as models of triple‐ and quadruple‐decker TTF arrays. Single‐crystal X‐ray analyses of neutral trimeric TTFs revealed that the three TTF moieties are oriented in a zigzag arrangement. Cyclic voltammetry measurements (CV) reveal that the trimer and tetramer exhibited diverse reversible redox processes with multi‐electron transfers, depending on the length of the ‐S(CH₂)_nS‐ units and substituents. The electronic spectra of the radical cations, prepared by electrochemical oxidation, showed charge resonance (CR) bands in the NIR/IR region (1630–1850 nm), attributed to a mixed valence (MV) state of the triple‐ and quadruple‐decker TTF arrays. In the trimeric systems, the dicationic state (+2; 0.66 cation per TTF unit) was found to be a stable state, whereas the monocationic state (+1) was not observed in the electronic spectra. In the tetrameric system, substituent‐dependent redox processes were observed. Moreover, π‐trimers and π‐tetramers, which show a significant Davydov blueshift in the spectra, are formed in the tricationic (trimer) and tetracationic (tetramer) state. In addition, these attractive interactions are strongly dependent on the length of the linkage unit.     

Simultaneous Induction of Axial and Planar Chirality in Arene–Chromium Complexes by Molybdenum‐Catalyzed Enantioselective Ring‐Closing Metathesis

The molybdenum‐catalyzed asymmetric ring‐closing metathesis of the various C_s‐symmetric (π‐arene)chromium substrates provides the corresponding bridged planar‐chiral (π‐arene)chromium complexes in excellent yields with up to >99 % ee. With a bulky and unsymmetrical substituent, such as N‐indolyl or 1‐naphthyl, at the 2‐positions of the η⁶‐1,3‐diisopropenylbenzene ligands, both biaryl‐based axial chirality and π‐arene‐based planar chirality are simultaneously induced in the products. The axial chirality is retained even after the removal of the dicarbonylchromium fragment, and the chiral biaryl/heterobiaryl compounds are obtained with complete retention of the enantiopurity.     

A new aliphatic ester of hydroxysalicylic acid from fermented Carica papaya L. preparation with a potential hair growth stimulating activity

Abstract

An aliphatic ester of hydroxysalicylic acid (6), reported for the first time from a natural source in addition to five known compounds were isolated from the fermented Carica papaya L. preparation, a commercialized functional food. The known compounds were identified as 5-hydroxymethylfurfuraldehyde (1), trans-caffeic acid (2), butyl 4-hydroxybenzoate (butylparaben) (3), lycopene (4), benzyl isothiocyanate (5). Compounds 1 and 3 were reported for the first time from Papaya fruits through this study. The new compound showed a moderate antioxidant activity and a potent hair growth stimulating activity in vitro.     

Fiber-optic distributed measurement of polarization beat length using slope-assisted Brillouin optical correlation-domain reflectometry

Optical Review - We demonstrate distributed measurement of the polarization beat length along single-mode optical fibers (SMFs) using slope-assisted Brillouin optical correlation-domain...