A kinetic method for the determination of nanogram amounts of cadmium (II) by its catalytic effect on the complex formation of manganese(II) withα,β,γ,δ-tetra-(p-sulf onatophenyl) porphine

Summary Cadmium(II) accelerates the complex formation reaction of manganese (II) with, , , -tetra(p-sulfonatophenyl)porphine (H₂TPPS₄). Cadmium(II) concentration as low as 10^–7 mol dm^–3 can be determined from the decrease in absorbance at 413 nm (_max of H₂TPPS₄) at a fixed time after the start of the reaction of manganese(II) with H₂TPPS₄. After the separation of lead(II) by coprecipitation of manganese(IV) oxide, the method is highly selective and is free from interference of most substances usually encountered. Sandell's sensitivity calculated from the calibration curve at 30 min after the start of the reaction is 1.43×10^–1 ng cm^–2.

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Eine kinetische Methode zur Bestimmung von Nanogrammengen von Cadmium(II) mit Hilfe seines katalytischen Effekts bei der Komplexbildung von Mangan(II) mit , , , -Tetra-(p-sulfonatophenyl)-porphin

Zusammenfassung Cadmium (II) beschleunigt die Komplexbildung von Mangan (II) mit, , , -Tetra-(p-sulfonatophenyl)-porphin (H₂TPPS₄). Konzentrationen bis zu 10^–7 Mol/l können durch Messung des Rückganges der Absorbanz bei 413 nm (_max von H₂TPPS₄) nach einer bestimmten Zeit gemessen werden. Nach Abtrennung von Blei(II) durch Mitfällung mit Mangan (IV)oxid ist die Methode sehr selektiv und frei von Störungen durch die meisten üblicherweise vorliegenden Substanzen. Die Empfindlichkeit nach Sandell, ermittelt aus der Eichkurve 30 min nach dem Start der Reaktion, beträgt 1,43×10^–1 ng/cm².

     

Partialsynthesen und Reaktionen von Abietanderivaten (Lanugonen) aus Plectranthus lanuginosus und verwandten Verbindungen

Partial Syntheses and Reactions of Abietanoid Derivatives (Lanugones) from Plectranthus lanuginosus and of Related Compounds Interconversions by partial syntheses of several lanugones establish their absolute configuration at C(15). Unexpected reactions exemplify the unique reactivity of these abietanoic diterpenes, - Lanugone O ( 4 ) was prepared in several steps from (15S)-coleon C ( 8a ; Scheme 2) thus establishing its (15S)-configuration. One of the intermediates, the 12-O-acetyl-6-oxoroyleanone 12 , through acetyl-migration sets up an equilibrium with the vinylogous quinone 13 (Scheme 3). - The chirality at C(15) in the dihydrofuran moiety of lanugone Q ( 16 ) was proven by acid-catalyzed conversion of lanugone O ( 4 ) to 16 . - Instead of the usual nucleophilic attack shown by quinomethanes, lanugone L (1 ) is electrophilically substituted at C(7) by acetic anhydride/pyridine (Scheme 1). - In a homosigmatropic [1,5]-H-shift, lanugone G ( 17 ) in solution is converted to the corresponding allyl substituted royleanone 18 (Scheme 4). - Methanolysis of lanugone J ( 19 ) leads to the expected royleanone 20 having the 2-methoxypropyl side chain ( Scheme 5 ). Similar reactions were found in acetolytic reactions. However, treatment-of spirocoleons with SOCl₂/DMF produces mainly 12-deoxyroyleanones with allyl- and 2-chloropropyl groups, i. e. 19 → 26 and 27 ; 28 → 29 . The possible natural occurrence of these compounds is emphasized.     

A challenge to novel fluoropolymers

Perfluoro(vinyl ether) derivatives are extremely versatile monomers in preparing a variety of functional fluoropolymers. In this paper, two challenging topics in the development of novel fluoropolymers will be introduced. Carboxylated perfluoro(vinyl ether) can be copolymerized with tetrafluoroethylene to afford perfluorinated ion-exchange membranes, which realize the innovative process for pollution-free and energy-saving chlor-alkali production. Another topic includes the discovery of selective cyclo-polymerization of specially designed difunctional perfluoromonomers such as perfluoro(allyl vinyl ether) which is readily derived from the carboxylated perfluoro(vinyl ether). The novel perfluoropolymer with a cyclic structure in the main chain is characterized by an exceptional transparency, and has been commercialized with expectation of major applications in electronics industries.     

Conservative numerical schemes for the Ostrovsky equation

The Ostrovsky equation describes gravity waves under the influence of Coriolis force. It is known that solutions of this equation conserve the L² norm and an energy function that is determined non-locally. In this paper we propose four conservative numerical schemes for this equation: a finite difference scheme and a pseudospectral scheme that conserve the norm, and the same types of schemes that conserve the energy. A numerical comparison of these schemes is also provided, which indicates that the energy conservative schemes perform better than the norm conservative schemes.     

Singularities of Blaschke normal maps of convex surfaces

We prove that the difference between the numbers of positive swallowtails and negative swallowtails of the Blaschke normal map for a given convex surface in affine space is equal to the Euler number of the subset where the affine shape operator has negative determinant.     

Mutually disjoint designs and new 5‐designs derived from groups and codes

The article gives constructions of disjoint 5‐designs obtained from permutation groups and extremal self‐dual codes. Several new simple 5‐designs are found with parameters that were left open in the table of 5‐designs given in (G. B. Khosrovshahi and R. Laue, t‐Designs with t⩾3, in “Handbook of Combinatorial Designs”, 2nd edn, C. J. Colbourn and J. H. Dinitz (Editors), Chapman & Hall/CRC, Boca Raton, FL, 2007, pp. 79–101), namely, 5−(v, k, λ) designs with (v, k, λ)=(18, 8, 2m) (m=6, 9), (19, 9, 7m) (m=6, 9), (24, 9, 6m) (m=3, 4, 5), (25, 9, 30), (25, 10, 24m) (m=4, 5), (26, 10, 126), (30, 12, 440), (32, 6, 3m) (m=2, 3, 4), (33, 7, 84), and (36, 12, 45n) for 2⩽n⩽17. These results imply that a simple 5−(v, k, λ) design with (v, k)=(24, 9), (25, 9), (26, 10), (32, 6), or (33, 7) exists for all admissible values of λ. © 2010 Wiley Periodicals, Inc. J Combin Designs 18: 305–317, 2010     

Central limit theorems for realized volatility under hitting times of an irregular grid

We consider a continuous semi-martingale sampled at hitting times of an irregular grid. The goal of this work is to analyze the asymptotic behavior of the realized volatility under this rather natural observation scheme. This framework strongly differs from the well understood situations when the sampling times are deterministic or when the grid is regular. Indeed, neither Gaussian approximations nor symmetry properties can be used. In this setting, as the distance between two consecutive barriers tends to zero, we establish central limit theorems for the normalized error of the realized volatility. In particular, we show that there is no bias in the limiting process.     

On the classification of weighing matrices and self‐orthogonal codes

We provide a classification method of weighing matrices based on a classification of self‐orthogonal codes. Using this method, we classify weighing matrices of orders up to 15 and order 17, by revising some known classification. In addition, we give a revised classification of weighing matrices of weight 5. A revised classification of ternary maximal self‐orthogonal codes of lengths 18 and 19 is also presented. © 2011 Wiley Periodicals, Inc. J Combin Designs 20:40–57, 2012     

The Two-Point Codes with the Designed Distance on a Hermitian Curve in Even Characteristic

In Homma M and Kim SJ [2], the authors considered two-point codes on a Hermitian curve defined over fields of odd characteristic. In this paper, we study the geometry of a Hermitian curve over fields of even characteristic and classify the two-point codes whose minimum distances agree with the designed ones.     

Self-Orthogonal 3-(56,12,65) Designs and Extremal Doubly-Even Self-Dual Codes of Length 56

In this paper, we show that the code generated by the rows of a block-point incidence matrix of a self-orthogonal 3-(56,12,65) design is a doubly-even self-dual code of length 56. As a consequence, it is shown that an extremal doubly-even self-dual code of length 56 is generated by the codewords of minimum weight. We also demonstrate that there are more than one thousand inequivalent extremal doubly-even self-dual [56,28,12] codes. This result shows that there are more than one thousand non-isomorphic self-orthogonal 3-(56,12,65) designs. AMS Classification: 94B05, 05B05