On pointwise decay rates of time‐periodic solutions to the Navier–Stokes equation

We study the existence of a time‐periodic solution with pointwise decay properties to the Navier–Stokes equation in the whole space. We show that if the time‐periodic external force is sufficiently small in an appropriate sense, then there exists a time‐periodic solution $\{u,p\}$ of the Navier–Stokes equation such that $|{?}^j{u(t,x)|=O(|x|}^{1?n?j})$ and $|{?}^j{p(t,x)|=O(|x|}^{?n?j})(j=0,1,\dots )$ uniformly in $t\in \mathbb{R}$ as $|x|\to \infty$. Our solution decays faster than the time‐periodic Stokes fundamental solution and the faster decay of its spatial derivatives of higher order is also described.     

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.     

Total Synthesis of Zephycarinatines via Photocatalytic Reductive Radical ipso-Cyclization

We report herein a nonbiomimetic strategy for the total synthesis of the plicamine-type alkaloids zephycarinatines C and D. The key feature of the synthesis is a stereoselective reductive radical ipso-cyclization using visible-light-mediated photoredox catalysis. This cyclization enabled the construction of a 6,6-spirocyclic core structure through the addition of a carbon-centered radical onto the aromatic ring. Biological evaluation of zephycarinatines and their derivatives revealed that the synthetic derivative with a keto group displays moderate inhibitory activity against LPS-induced NO production. This approach could offer future opportunities to expand the chemical diversity of plicamine-type alkaloids as well as providing useful intermediates for their syntheses.     

On Default Priors for Robust Bayesian Estimation with Divergences

This paper presents objective priors for robust Bayesian estimation against outliers based on divergences. The minimum γ-divergence estimator is well-known to work well in estimation against heavy contamination. The robust Bayesian methods by using quasi-posterior distributions based on divergences have been also proposed in recent years. In the objective Bayesian framework, the selection of default prior distributions under such quasi-posterior distributions is an important problem. In this study, we provide some properties of reference and moment matching priors under the quasi-posterior distribution based on the γ-divergence. In particular, we show that the proposed priors are approximately robust under the condition on the contamination distribution without assuming any conditions on the contamination ratio. Some simulation studies are also presented.     

Defect-Free Synthesis of a Fully π-Conjugated Helical Ladder Polymer and Resolution into a Pair of Enantiomeric Helical Ladders**

Fully π-conjugated ladder polymers with a spiral geometry represent a new class of helical polymers with great potential for organic nanodevices, but there is no precedent for an optically active helical ladder polymer totally composed of achiral units. We now report the defect-free synthesis and resolution of a fully π-conjugated helical ladder polymer with a rigid helical cavity, which has been achieved by quantitative and chemoselective acid-promoted alkyne benzannulations of a rationally designed, random-coil achiral polymer followed by chromatographic enantioseparation. Because of a sufficiently high helix-inversion barrier, the isolated excess one-handed helical ladder polymer with a degree of polymerization of more than 15 showed a strong circular dichroism with a dissymmetry factor of up to 1.7×10⁻² and is thermally stable, maintaining its optical activity in solution even at 100 °C, as well-supported by molecular dynamics simulation.     

Unique Thermal Structural Phase Transitions Exhibited by Unsymmetrical Organometallic Gold(III)-Dithiolene Complexes with Pentylthio and Hexylthio Groups

Unsymmetrical gold(III)-dithiolene complexes are potential candidates for molecular materials that exhibit thermal structural phase transitions. In this study, unsymmetrical ppy-gold(III) (ppy⁻=C-deprotonated-2-phenylpyridine(−)) complexes [AuC5] and [AuC6] coordinated by dithiolene ligands containing tetrathiafulvalene (TTF) skeletons with pentylthio (2-{bis(pentylthio)-1,3-dithiol-2-ylidene}-1,3-dithiol-4,5-dithiolate(2−)) and hexylthio groups (2-{bis(hexylthio)-1,3-dithiol-2-ylidene}-1,3-dithiol-4,5-dithiolate(2−)) were synthesized. Both complexes exhibited a large absorption band at approximately 508 nm, owing to intramolecular ligand-to-ligand charge transfer. One-dimensional columnar structures with head-to-tail molecular arrangements around the metal ions were constructed in the crystals. The flexible alkylthio groups were intercalated into crystalline spaces between dithiolene ligands in the columns. [AuC5] exhibits a simple phase transition at 198 °C between crystalline and isotropic phases irreversibly. The crystalline phase of [AuC6] observed at 25 °C melted at 148 °C. Another crystalline phase grew above 148 °C with a very slow crystallization rate from the liquid phase and was completely transformed into an isotropic phase at 200 °C.     

Persistent Dialkylsilanone Generated by Dehydrobromination of Dialkylbromosilanol

A persistent dialkylsilanone was synthesized by the dehydrobromination of a dialkylbromosilanol with tris(trimethylsilyl)silyl potassium in solution at ?80 °C: It was characterized by NMR and IR spectroscopy, and was tested in several reactions. In ²⁹Si NMR spectrum in [D₈]toluene, the signal due to the unsaturated silicon nuclei was observed at 128.7 ppm. Reactions of the dialkylsilanone with water and mesitonitrile oxide gave a silanediol and a [2+3] cycloadduct, respectively. The silanone remains intact in [D₈]toluene below ?80 °C for at least two days, while it undergoes unprecedented isomerization to give a siloxysilene by means of 1,3‐silyl migration at higher temperatures.     

Solid‐Phase Combinatorial Synthesis and Biological Evaluation of Destruxin E Analogues

The solid‐phase combinatorial synthesis of cyclodepsipeptide destruxin E has been demonstrated. The combinatorial synthesis of cyclization precursors 8 was achieved by using a split and pool method on SynPhase Lanterns. The products were successfully macrolactonized in parallel in the solution phase by using 2‐methyl‐6‐nitrobenzoic anhydride and 4‐(dimethylamino)pyridine N‐oxide to afford macrolactones 9 , and the subsequent formation of an epoxide in the side chain gave 18 member destruxin E analogues 6 . Biological evaluation of analogues 6 indicated that the N‐MeAla residue was crucial to the induction of morphological changes in osteoclast‐like multinuclear cells (OCLs). Based on structure–activity relationships, azido‐containing analogues 15 were then designed for use as a molecular probe. The synthesis and biological evaluation of analogues 15 revealed that 15 b , in which the Ile residue was replaced with a Lys(N₃) residue, induced morphological changes in OCLs at a sufficient concentration, and modification around the Ile residue would be tolerated for attachment of a chemical tag toward the target identification of destruxin E ( 1 ).