The Lifting Model for Reconfiguration

Given a pair of start and target configurations, each consisting of n pairwise disjoint disks in the plane, what is the minimum number of moves that suffice for transforming the start configuration into the target configuration? In one move a disk is lifted from the plane and placed back in the plane at another location, without intersecting any other disk. We discuss efficient algorithms for this task and estimate their number of moves under different assumptions on disk radii. We then extend our results for arbitrary disks to systems of pseudodisks, in particular to sets of homothetic copies of a convex object.     

State of various stereoregulating electron-donating compounds in titanium-magnesium catalysts for propylene polymerization: A diffuse reflectance IR spectroscopic study

Propylene polymerization on TiCl₄/donor/MgCl₂ (donor = ethyl benzoate, dibutyl phthalate, diisobutyl phthalate, diethyl 2,3-diisopropylsuccinate) supported catalysts is considered. The states of the donors in the catalysts have been investigated by diffuse reflectance IR spectroscopy. Data characterizing the distribution of the donors and the active component (TiCl₄) on the support surface have been obtained. Molecular weight distribution data for polypropylene are presented. The molecular weight distribution of polypropylene depends on the location of the donor and TiCl₄ molecules.     

Study of the viscoelastoplastic deformation of an element of a body with a three-branch loading path

Institute of Mechanics, Academy of Sciences of the Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 27, No. 12, pp. 26–33, December, 1991.     

On Intersection Problem for Perfect Binary Codes

The main result is that to any even integer q in the interval 0 ≤ q ≤ 2^{n+1-2log(n+1)}, there are two perfect codes C₁ and C₂ of length n = 2^m − 1, m ≥ 4, such that |C₁ ∩ C₂| = q.     

Synthesis of benzofurans via Pd-catalyzed oxidative cyclization of 2-allylphenols

Substituted 2-methylbenzofurans were obtained from 2-allylphenols via Pd²⁺-catalyzed oxidative cyclization using Cu(OAc)₂–LiCl as a reoxidant and wet DMF as a solvent.     

Five-membered-ring-substituted 1-methyl-1H-indeno[1,2-b]pyridines

1-Methyl-1H-indeno[1,2-b]pyridine and 1-methyl-1H-5-(, -dicarbomethoxyvinyl)-(formyl, acetyl)indeno[3,2-b]pyridines were obtained by treatment of N-methyl-4-azafluorenium iodide, as well as mixtures of it with acetylenedicarboxylic ester, dimethylformamide (DMF), and phosphorus oxychloride or acetic anhydride, with bases. 4-Azafluoronenone was used to synthesize 9-(p-methoxyphenyl)-4-azafluoren-9-ol, which was reduced to 9-(p-methoxyphenyl)-4-azafluorene, and 1-methyl-1H-5-(p-methoxyphenyl)indeno[3,2-b]pyridine was obtained from the methiodide of the latter.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1382–1386, October, 1981.     

Synthesis of 2-amino-5-cyano-1,3,4-oxadiazole and some of its derivatives

Preparative syntheses have been developed for 2-amino-5-cyano-1,3,4-oxadiazole from the semicarbazone of methyl glyoxylate and some of its transformations were studied. This product is an important intermediate in the preparation of its derivatives.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 1. 243–246, January, 1991.