Affine scaling algorithm fails for semidefinite programming

In this paper, we introduce an affine scaling algorithm for semidefinite programming (SDP), and give an example of a semidefinite program such that the affine scaling algorithm converges to a non-optimal point. Both our program and its dual have interior feasible solutions and unique optimal solutions which satisfy strict complementarity, and they are non-degenerate everywhere.     

Second-order necessary optimality conditions for domain optimization problems of the Neumann type

In this paper, we treat a domain optimization problem in which the boundary-value problem is a Neumann problem. In the case where the domain is in a three-dimensional Euclidean space, the first-order and the second-order necessary conditions which the optimal domain must satisfy are derived under a constraint which is the generalization of the requisite of constant volume.Portions of this paper were presented at the 13th IFIP Conference on System Modelling and Optimization, Tokyo, Japan, 1987.     

Syntheses of fluorine-containing fused polycyclic compounds: photo-cycloaddition of indene to cyclic fluoro-olefins and some reactions concerning the adducts

Acetophenone photo-sensitized addition of indene to cyclic fluoro-olefins (1,2-dichlorohexafluorocyclopentene-1, 1,2-dichlorotetrafluorocyclobutene-1 and hexafluorocyclobutene) gave the corresponding cycloadducts in satisfactory yields. The cycloadducts obtained predominantly had exo configuration.Some reactions such as reduction, oxidation, dechlorination and halogenation, of the cycloadducts were also studied.     

Determination of the change of nuclear charge radius of the119Sn Mössbauer transition by internal conversion

Radioactive¹¹⁹Sb was implanted into six host matrices (CaSnO₃, Pt, Y, Au,-Sn, Pb) and internal conversion electrons of the 23.87 keV transition in¹¹⁹Sn were measured with an iron-free magnetic spectrometer as well as Mössbauer spectra. In the analysis of the conversion spectra of outermost electrons, the overlapping K-LM Auger lines were subtracted using the Auger spectrum of tin measured with another source of^117mSn, and the shake-off effect accompanying the conversion process was considered. From the correlation between the Mössbauer isomer shifts and the intensity ratios of O-shell to N₁-shell conversion electrons, the change of the nuclear charge radius of the 23.87 keV transition of¹¹⁹Sn was deduced to be R/R=(0.87 ± 0.25) × 10^–4 for a uniform charge distribution ofR= 1.2 ×A ^1/3 fm or, equivalently, r²>—=(3.6 ± 1.0) ×10^–3 fm².     

High n-value phases in the complex bismuth oxides with layered structure,Bi2CaNan−2NbnO3n+3

Complex bismuth oxides with layered structure are prepared with a series of compositions in the system Bi₂CaNb₂O₉-NaNbO₃. It is found by X-ray powder diffraction that each compound is composed of more than two phases, which are described by a formula Bi₂CaNa_n?2Nb_nO_3n+3, e.g., in the sample with the nominal composition Bi₂CaNb₂O₉ · 8NaNbO₃, the phases with n = 6 to 8 appear predominantly. These phases are closely intergrown to each other. Moreover, high-resolution electron microscopy reveals that microsyntactic intergrowth frequently occurs in the phases with n > 5. The occurrence of the latter intergrowth is explained in terms of the bond length obtained.     

Syntheses and reactions of functional polymers. XLII. Preparation and use of polymers having N-hydroxy-succinimide unit in the chain

Styrene-maleic anhydride alternating copolymer was converted to N-hydroxymaleimide-styrene copolymer by reaction with hydroxylamine in pyridine at room temperature. The conversion was more than 90%. From this copolymer, N-acetoxy- or N-benzoyloxymaleimide-styrene copolymers were derived by action of acetic anhydride or benzoyl chloride in dimethylformamide at room temperature. Acylation of several primary amines was carried out effectively by use of these N-acyloxyimide-styrene copolymers. The reaction of the acetylated copolymer with diethylamine at room temperature afforded N-hydroxyimide copolymer.     

An economical approach for peptide synthesis via regioselective C–N bond cleavage of lactams

An economical, solvent-free, and metal-free method for peptide synthesis via C–N bond cleavage using lactams has been developed. The method not only eliminates the need for condensation agents and their auxiliaries, which are essential for conventional peptide synthesis, but also exhibits high atom economy. The reaction is versatile because it can tolerate side chains bearing a range of functional groups, affording up to >99% yields of the corresponding peptides without racemisation or polymerisation. Moreover, the developed strategy enables peptide segment coupling, providing access to a hexapeptide that occurs as a repeat sequence in spider silk proteins.

An economical, solvent-free, and metal-free method for peptide synthesis via C–N bond cleavage using lactams has been developed.