Absolute values and real parts for functions in the smirnov class

Let N₊ denote the Smirnov class on the open unit disc D. It is easy to see that for any outer function g in N₊, there exists a function G in N₊ such that |g|; ≤ ReG on δ. We describe such a G. In general, G may not be outer. In this paper, a necessary and sufficient condition on g is given for the existence of an outer function G such that |;g|; < ReG. When g belongs to the Hardy space H¹, G is trivially given as the Herglotz integral of |;g|;.     

Finite dimensional semisimple Q-algebras

A Q-algebra can be represented as an operator algebra on an infinite dimensional Hilbert space. However we don’t know whether a finite n-dimensional Q-algebra can be represented on a Hilbert space of dimension n except n = 1, 2. It is known that a two dimensional Q-algebra is just a two dimensional commutative operator algebra on a two dimensional Hilbert space. In this paper we study a finite n-dimensional semisimple Q-algebra on a finite n-dimensional Hilbert space. In particular we describe a three dimensional Q-algebra of the disc algebra on a three dimensional Hilbert space. Our studies are related to the Pick interpolation problem for a uniform algebra.     

Breakage of λ-DNA by inorganic tin and organotin compounds as environmental pollutants

In proportion to the environmental pollution problems caused by organotin compounds, the genotoxicities of tin compounds in the environments have become of interest so as to estimate their safety in recent years. In this work, isolated λ-DNA (double-strand DNA) was incubated with inorganic tin(II) and tin(IV) and five organotin compounds [n-butyltin trichloride, di(n-butyltin) dichloride, methyltin trichloride, dimethyltin dichloride and trimethyltin chloride] in reaction systems both with and without hydrogen peroxide (H₂O₂) content. The tin compounds tested in this study did not induce DNA breakage in the absence of hydrogen peroxide. Divalent inorganic tin (SnCl₂) and tetravalent inorganic tin (SnCl₄) caused DNA breakage in the presence of hydrogen peroxide (10 mM), and the DNA damage activity of inorganic tin was much more potent in divalent inorganic tin (SnCl₂) than in tetravalent inorganic tin (SnCl₄). Divalent inorganic tin (SnCl₂) induced DNA breakage in a concentration-dependent fashion at concentrations greater than 0.1 mM of SnCl₂ in the presence of hydrogen peroxide (10 mM). DNA breakage was not caused by n-butyltin compounds and methyltin compounds either in the presence or in the absence of hydrogen peroxide.     

Highly regio- and stereocontrolled SN2′ reactions of gem-difluorinated vinyloxiranes with monoalkylcopper reagents

Reaction of gem-difluorinated vinyloxiranes with RCu(X)Li allowed us to introduce the R group regioselectively at the fluorine-attached terminal carbon atom in an S_N2′ manner to afford (E)-allylic alcohols exclusively, while homoallylic alcohols with anti stereochemical relationship were found to be obtained selectively from higher-ordered cuprates derived from CuCl and RMgBr in a ratio of 1:3.     

Stereoselective synthesis of CF3-substituted aziridines by Lewis acid-mediated aziridination of aldimines with diazoacetates

Treatment of trifluoroacetaldehyde N,O-acetal with diazoacetate in the presence of a Lewis acid furnished CF₃-substituted aziridinecarboxylates in good yields. Both cis and trans isomers were obtained stereoselectively by the proper choice of the ester substituents. Use of a chiral diazoacetate derived from (R)-pantolactone led to highly diastereoselective aziridination (94% de).     

Vanadate-stimulated release of hepatic lipase activity from liver.

Vanadate stimulated the release of rat hepatic lipase activity from liver slices into an incubation medium in a time- and dose-dependent manner. Insulin, however, failed to have this stimulatory action, and the release by heparin was recognized, but was not additive to that by vanadate. Amiloride, an inhibitor of tyrosine kinase in some receptors and of the Na+/H+ exchange system suppressed the vanadate-stimulated release. Biochanin A, a different type of tyrosine kinase inhibitor than amiloride, also suppressed the effect of vanadate. The stimulation by vanadate was clearly preserved in Na(+)-, K(+)-, or Ca(2+)-free medium, suggesting that neither the Na+/H+ exchange system, Na+, K(+)-adenosine triphosphatase, nor Ca(2+)-influx into cells is involved in the action of this substance. These results suggest that vanadate-stimulated release of the enzyme activity is associated with the activation of the tyrosine kinase activity.     

Total synthesis of (+)-tubelactomicin A. 2. Synthesis of the upper-half segment and completion of the total synthesis

[reaction: see text]. We have completed the total synthesis of natural (+)-tubelactomicin A (1), a 16-membered macrolide antibiotic. This Letter presents a highly efficient synthesis of the upper-half segment (C14-C24) and the completion of the total synthesis featuring a high-yielding Stille coupling for the connection of the upper-half and lower-half segments and Mukaiyama macrolactonization for the construction of the entire structure of 1.     

Formation and stabilization model of the 42-mer Abeta radical: implications for the long-lasting oxidative stress in Alzheimer's disease

Amyloid fibrils mainly consist of 40-mer and 42-mer peptides (Abeta40, Abeta42). Abeta42 is believed to play a crucial role in the pathogenesis of Alzheimer's disease because its aggregative ability and neurotoxicity are considerably greater than those of Abeta40. The neurotoxicity of Abeta peptides involving the generation of free radicals is closely related to the S-oxidized radical cation of Met-35. However, the cation's origin and mechanism of stabilization remain unclear. Recently, structural models of fibrillar Abeta42 and Abeta40 based on systematic proline replacement have been proposed by our group [Morimoto, A.; et al. J. Biol. Chem. 2004, 279, 52781] and Wetzel's group [Williams, A. D.; et al. J. Mol. Biol. 2004, 335, 833], respectively. A major difference between these models is that our model of Abeta42 has a C-terminal beta-sheet region. Our biophysical study on Abeta42 using electron spin resonance (ESR) suggests that the S-oxidized radical cation of Met-35 could be generated by the reduction of the tyrosyl radical at Tyr-10 through a turn structure at positions 22 and 23, and stabilized by a C-terminal carboxylate anion through an intramolecular beta-sheet at positions 35-37 and 40-42 to form a C-terminal core that would lead to aggregation. A time-course analysis of the generation of radicals using ESR suggests that stabilization of the radicals by aggregation might be a main reason for the long-lasting oxidative stress of Abeta42. In contrast, the S-oxidized radical cation of Abeta40 is too short-lived to induce potent neurotoxicity because no such stabilization of radicals occurs in Abeta40.