Axially chiral dicarboxylic acid catalyzed asymmetric semipinacol rearrangement of cyclic β-hydroxy-α-diazo esters

The development of axially chiral dicarboxylic acid catalyzed desymmetrizing asymmetric semipinacol rearrangement of symmetrically substituted six-membered cyclic β-hydroxy-α-diazo esters is reported as a means to give chiral cycloheptanones with good enantioselectivities.     

Accurate and sensitive high-performance liquid chromatographic method for geometrical and structural photoisomers of bilirubin IX alpha using the relative molar absorptivity values.

It has been reported that considerable differences exist between the relative molar absorptivity values of the geometrical and structural photoisomers of bilirubin. We have devised an accurate HPLC method for photoisomer quantification based on the following principle: the sum of both the integrated peak areas corrected by each factor for each photoisomer, and the integrated peak area of unchanged (ZZ)-bilirubin [(ZZ)-B] after an anaerobic photoirradiation, should be constant and equal to the integrated peak area of initial (ZZ)-bilirubin [(ZZ)-Bi] before photoirradiation. On this basis, the following equation can be used to determine each factor. [equation: see text] alpha, beta, gamma and delta represent the factors used to correct the integrated peak areas of individual bilirubin photoisomers, and they are arranged in the order of the formula. It was demonstrated that the relative 455 nm molar absorptivity values for (ZZ)-bilirubin and all its geometrical and structural photoisomers, i.e., (ZZ)-bilirubin, (ZE)-bilirubin (EZ)-bilirubin, (EZ)-cyclobilirubin (= lumirubin) and (EE)-cyclobilirubin in the HPLC eluent, are, respectively, 1.0, 0.81 (= alpha), 0.54 (= beta), 0.47 (= gamma) and 0.39 (= delta).     

The effects of the homogeneity of non-crystalline Pb---Ti---O gels on the complex thermal processes leading to PbTiO3 formation

The effects of the homogeneity of precursor non-crystalline Pb---Ti---O gels on their transformation to crystalline PbTiO₃ were studied. Hydrous gels were prepared via two different routes, i.e., (i) mixing two unitary sols (MS), and (ii) co-precipitation (CP). Mechanical pretreatment was also carried out, primarily for the purpose of homogenization. The local homogeneity was evaluated by elementary microanalysis using a transmission electron microscope. The process of ball-milling the MS gel for 3 h improved its homogeneity only slightly. However, the homogeneity of the ball-milled MS gel suddenly increased to that of the CP gel on subsequent heating to a temperature as low as 483 K. This type of thermal homogenization was not observed for the unground MS gel. The evaporation of lead monoxide on further heating to 1023 K was also suppressed by preliminary ball-milling. All these results suggest that the ionic migration and the formation of Pb---O---Ti bonds in the gels take place during the mechanical activation with the aid of OH groups.     

Belt‐Shaped Cyclonaphthylenes

The recent development of cyclo‐para‐phenylenes has demonstrated the feasibility of radial π systems in nanohoop structures, especially in the crystalline state. However, in contrast to macrocyclic molecules with benzene units, which have a several‐decades‐long history, macrocycles composed solely of naphthylene units (the smallest acene) have been much less explored. Although two examples of cyclonaphthylenes have been reported to date, neither possesses a radial π system. We herein report the first example of belt‐shaped cyclonaphthylenes with curved π systems. The molecule, [8]cyclo‐amphi‐naphthylene, is linked at the 2,6‐positions of the naphthylene units, thus affording belt‐shaped molecules. Although the molecular structures are flexible, which allows for rotation of the naphthylene units in solution, they can be rigidified with the aid of methylene bridges to afford persistent molecular structures in solution.     

Total synthesis of polygalolide A

The total synthesis of polygalolide A was accomplished through intramolecular C-glycosylation of glucal modified with siloxyfuran. The siloxyfuran group and siloxy substituent at the C-3 position played crucial roles in allowing direct access to the highly substituted oxabicyclo[3.2.1] core skeleton with correct quaternary stereogenic centers.     

Total Colorings Of Degenerate Graphs

A total coloring of a graph G is a coloring of all elements of G, i.e. vertices and edges, such that no two adjacent or incident elements receive the same color. A graph G is s-degenerate for a positive integer s if G can be reduced to a trivial graph by successive removal of vertices with degree ≤s. We prove that an s-degenerate graph G has a total coloring with Δ+1 colors if the maximum degree Δ of G is sufficiently large, say Δ≥4s+3. Our proof yields an efficient algorithm to find such a total coloring. We also give a lineartime algorithm to find a total coloring of a graph G with the minimum number of colors if G is a partial k-tree, that is, the tree-width of G is bounded by a fixed integer k.     

On topologically distinct solutions of the Dirichlet problem for Yang-Mills connections

We prove that for generic Dirichlet boundary data there exist infinitely many topologically distinct solutions to the Dirichlet problem for -Yang-Mills equations over . These are absolute Yang-Mills minimizers in topologically distinct connected components of the space of connections considered. There is a special case for which only finitely many topologically distinct solutions can be found by our method. This corresponds to the simultaneous existence of self dual and anti-self dual solutions, for the given boundary data. If the boundary data is non-flat there exists always more than one solution. This paper generalizes to Yang-Mills fields an important result by Brezis and Coron, who show existence of more than one minimizing harmonic map for non-constant Dirichlet data in two dimensions. Received February 1, 1996 / Accepted March 15, 1996