Characterization of $$H^1$$ H 1 Sobolev Spaces by Square Functions of Marcinkiewicz Type

We establish characterization of \(H^1\) Sobolev spaces by certain square functions of Marcinkiewicz type. The square functions are related to the Lusin area integrals. Also, in the one dimensional case, the non-periodic version of the function of Marcinkiewicz is applied to characterize weighted \(H^1\) Sobolev spaces.

     

Synthesis and Polymerization of (S)-4-Methyl-2-N,N-dimethylaminopentyl Methacrylate

(S)-4-Methyl-2-N,N-dimethylaminopentyl methacrylate (DMAPM) was synthesized from the reaction of N,N-dimethyl-L-leucinol with methacryl chloride, and its radical polymerization was investigated. It was found that DMAPM readily polymerized by α,α¹-azobisisobutyronitrile (AIBN) as an initiator to give poly-DMAPM. The copolymerization of DMAPM(M₁) with styrene(Mz) was also studied in various solvents with AIBN as an initiator at 60°C. From the result obtained in benzene, Q and e values of DMAPM were determined to be 0.64 and -0.04, respectively. Specific rotations of the copolymers of DMAPM with styrene were not proportional to the weight percent of the DMAPM unit incorporated, but the observed relation gave a downward curve. The copolymerizations DMAPM with α, β-disubstituted monomers such as maleic acid, maleimide, and N-phenylmaleimide were carried out in order to induce asymmetric center in the polymer chain. After hydrolysis of the copolymers obtained, the hydrolyzed polymers were found to be optically active, suggesting an induction of asymmetric center into the polymer chain.     

Polymerization of 5-Substituted Cyclooctenes with Tungsten and Molybdenum Catalysts

Polymerizations of cyclooctene, 5-methyl, 5-chloro-, and 5-methoxycyclooctenes were studied. Cyclooctene (CO) and 5-methylcyclooctene (MCO) provided high polymers in 80% yield with the use of WCl₆/AlEti._B Cl_u5 or WCl₆/AlEtCl₂ catalyst. 5-Chlorocyclooctene gave oligomer in 50% yield with WCl₆/AlEt₂Cl catalyst. Neither polymer nor oligomer was produced from 5-methoxycyclooctene. These polymers were found to be produced through a ring-opening mechanism. The ratio of cis to trans structure in poly(CO) and poly(MCO) was determined by measurements of the decoupled ′H-NMR spectrum. Poly(CO) containing more than 50% trans structure was a crystalline solid at room temperature, while the polymer containing 30% of trans structure did not crystallize at room temperature. Poly(MCO) was amorphous, regardless of the content of trans structure. Poly(CO) and poly(MCO) obtained with MoCU/AlEtaCl or MoCU/AlEtCb catalyst contained no carbon-carbon double bond, and a vinyl polymerization mechanism was expected for this system.     

Ni-catalyzed α-arylation of secondary α-bromo-α-fluoro-β-lactam: cross-coupling of a secondary fluorine-containing electrophile

A highly diastereoselective cross-coupling reaction of an α-bromo-α-fluoro-β-lactam with a wide range of aryl Grignard reagents was catalyzed by Ni/bis(oxazoline) in yields of up to 98%. The product was obtained diastereoselectively as an anti-isomer. This is the first successful α-arylation of an α-fluoro-β-lactam to produce diverse α-aryl-α-fluoro-β-lactams.     

Enzymatic syntheses of unnatural head-to-tail pentacyclic triterpenes by tetraprenyl-β-curcumene cyclase

Little is known of the biosynthesis of sesquarterpenes and the synthesis of unnatural terpenoids by sesquarterpene biosynthetic enzymes has not yet been reported. In this study, the enzymatic cyclization of head-to-tail acyclic triterpene β-hexaprene—a natural product isolated from Bacillus clausii—using tetraprenyl-β-curcumene cyclase (TC) from Bacillus subtilis resulted in the formation of two unnatural pentacyclic triterpenes. It was revealed that B. subtilis TC, which forms tetracyclic terpenoid scaffold from tetraprenyl-β-curcumene in vivo, could be used to construct the 6/6/6/6/6-fused pentacyclic scaffold in vitro, suggesting that the active site cavity of TC has sufficient space to accommodate this unnatural pentacyclic scaffold. This is the first report demonstrating the utility of a sesquarterpene cyclase toward the synthesis of unnatural terpenoids.     

CRYSTALLIZATION PHENOMENA IN FATS AND LIPIDS

This article reviews recent studies of crystallization behavior of polymorphic modifications of principal saturated and mono-cis-un-saturated fatty acids, and of mixed-acid triacylglycerols; stearic acid, oleic acid, erucic acid and SOS (symmetric l,3-di-stearoyl-2-oleoyl glycerol). Thermodynamic and kinetic aspects of the polymorphic crystallization are discussed in relation to molecular structures and thermal properties, which have newly been elucidated with X-ray diffractometry and vibrational spectroscopy.     

Polymer colloids formed by polyelectrolyte complexation of vinyl polymers and polysaccharides in aqueous solution

The polyelectrolyte complex formed from the polyanion and polycation was studied by turbidimetry, static and electrophoretic light scattering, and elementary analysis. Sodium salts of polyacrylate (PA) and heparin (Hep) were chosen as the polyanion, and hydrochloric salts of poly(vinyl amine) (PVA) and chitosan (Chts) as the polycation. Although these vinyl polymers and polysaccharides have remarkably different backbone chemical structures and linear charge densities, all the four combinations PA-PVA, PA-Chts, Hep-PVA, and Hep-Chts provide almost stoichiometric polyelectrolyte complexes which are slightly charged owing to the adsorption of the excess polyelectrolyte component onto the neutral complex. The charges stabilize the complex colloids in aqueous solution of a non-stoichiometric mixture, and the aggregation number of the complex colloids increases with approaching to the stoichiometric mixing ratio. The mixing ratio dependence of the aggregation number for the four complexes is explained by the model proposed in the previous study.     

Thermotropic semi-rigid copoly(imide-carbonate)s composed of 3,4,3",4"-p-terphenyltetracarboxdi-imide and 3,4,3',4'-biphenyltetracarboxdi-imide rings

New semi-rigid copoly(imide-carbonate)s composed of 3,4,3",4"-p-terphenyltetracarboxdi-imide and 3,4,3',4'-biphenyltetracarboxdi-imide units and neighbouring homologous penta- and hexa-methylene spacer chains were prepared by melt polycondensation; the relationships between polymer structure and liquid crystalline (LC) properties are discussed. Differential scanning calorimetry measurements, polarizing microscope observations, miscibility tests and variable temperature X-ray analyses suggest that the 3,4,3",4"-p-terphenyltetracarboxdi-imide-rich copolymers form thermotropic LC nematic and smectic phases, but the 3,4,3',4'-biphenyltetracarboxdi-imide-rich copolymers are amorphous and have no LC melts. Therefore, the presence of 3,4,3",4"-p-terphenyltetracarboxdi-imide units confers good mesogenic properties.     

Synthesis of Methyl (Methyl D-and L-Idopyranosid)Uronates from myo-Inositol

Abstract

Methyl (methyl α-D-(9a), α-(9b), β-D-(10a), and β-L-(10b) idopyranosid)uronates were synthesized from myo-inositol. Baeyer-Villiger oxidation of the optically resolved inosose derivatives (3a and 3b) proceeded regioselectively to afford 4a and 4b in high yields, respectively. Ring-opening of the 7-membered hemiacetal-lactones (4a and 4b) with acid and subsequent deprotection gave the title compounds.     

Heterodinuclear Lanthanoid‐Containing Polyoxometalates: Stepwise Synthesis and Single‐Molecule Magnet Behavior

Polyoxometalates (POMs) with heterodinuclear lanthanoid cores, TBA₈H₄[{Ln(μ₂‐OH)₂Ln′}(γ‐SiW₁₀O₃₆)₂] ( LnLn′ ; Ln=Gd, Dy; Ln′=Eu, Yb, Lu; TBA=tetra‐n‐butylammonium), were successfully synthesized through the stepwise incorporation of two types of lanthanoid cations into the vacant sites of lacunary [γ‐SiW₁₀O₃₆]^8? units without the use of templating cations. The incorporation of a Ln³⁺ ion into the vacant site between two [γ‐SiW₁₀O₃₆]^8? units afforded mononuclear Ln³⁺‐containing sandwich‐type POMs with vacant sites ( Ln1 ; TBA₈H₅[{Ln(H₂O)₄}(γ‐SiW₁₀O₃₆)₂]; Ln=Dy, Gd, La). The vacant sites in Ln1 were surrounded by coordinating W? O and Ln? O oxygen atoms. On the addition of one equivalent of [Ln′(acac)₃] to solutions of Dy1 or Gd1 in 1,2‐dichloroethane (DCE), heterodinuclear lanthanoid cores with bis(μ₂‐OH) bridging ligands, [Dy(μ₂‐OH)₂Ln′]⁴⁺, were selectively synthesized ( LnLn′ ; Ln=Dy, Gd; Ln′=Eu, Yb, Lu). On the other hand, La1 , which contained the largest lanthanoid cation, could not accommodate a second Ln′³⁺ ion. DyLn′ showed single‐molecule magnet behavior and their energy barriers for magnetization reversal (ΔE/k_B) could be manipulated by adjusting the coordination geometry and anisotropy of the Dy³⁺ ion by tuning the adjacent Ln′³⁺ ion in the heterodinuclear [Dy(μ₂‐OH)₂Ln′]⁴⁺ cores. The energy barriers increased in the order: DyLu (ΔE/k_B=48 K)< DyYb (53 K)< DyDy (66 K)< DyEu (73 K), with an increase in the ionic radii of Ln′³⁺; DyEu showed the highest energy barrier.