Simplex pivots on the set packing polytope

This paper considers the set packing problem max{wx: Ax b, x 0 and integral}, whereA is anm × n 0–1 matrix,w is a 1 ×n weight vector of real numbers andb is anm × 1 vector of ones. In equality form, its linear programming relaxation is max{wx: (x, y) P(A)} whereP(A) = {(x, y):Ax +I _m y =b, x0,y0}. Letx ¹ be any feasible solution to the set packing problem that is not optimal and lety ¹ =b – Ax ¹; then (x ¹,y ¹) is an integral extreme point ofP(A). We show that there exists a sequence of simplex pivots from (x ¹,y ¹) to (x*,y*), wherex* is an optimal solution to the set packing problem andy* =b – Ax*, that satisfies the following properties. Each pivot column has positive reduced weight and each pivot element equals plus one. The number of pivots equals the number of components ofx* that are nonbasic in (x ¹,y ¹).This research was supported by NSF Grants ECS-8005360 and ECS-8307473 to Cornell University.     

Modification of poly(vinyl chloride). XXXI. Crosslinking of poly(vinyl chloride) with 2-R-4,6-dithiol-s-triazine and metal activators

Crosslinking of poly(vinyl chloride) (PVC) with 2-R-4,6-dithiol-s-triazine (R-DT) and metal activators has been studied to determine crosslinking rate constants, induction periods, and apparent activation energy and the final efficiency of crosslinking agents. The rate constants were about 1.4–7.5 min^?1 and the induction periods were about 6.8–24.3 min for various kinds of R-DT at 180°C. The activation energy was about 16.6–33 kcal/mol over the temperature range 160–195°C. The rate constants were strongly influenced by 2-substituted groups (R) in R-DT and increased in the order R′O-? R′NH-< (R′)₂N, where R′ is an alkyl or aryl group. Further, the rate constants increased in the order of: metal carboxylates < metal carboxylates < metal oxides for the activators and in the order of: Pb < Mg < Ca < Ba < Na for metal atoms. The final efficiency was about 75–80% for the activators such as MgO, MgCO₃, PbO, and SnO. The activators containing Na, Ca, and Ba atoms, however, gave final efficiency of more than 100%.     

Synthesis of fluorinated pyridines by the balz-schiemann reaction. An alternative route to enoxacin,a new antibacterial pyridonecarboxylic acid

Fluorination of the 2,6-disubstituted 3-aminopyridines 5 and 12 by the Balz-Schiemann reaction is described. 2,6-Dichloro-3-pyridinediazonium tetrafluoroborate ( 6 ) and 2-substituted 6-acetylamino-3-pyridinediazonium tetrafluoroborates 13 were heated with or without a solvent to give the corresponding fluorinated pyridines 7 and 14 , respectively, in good yields. 2-Substituted 6-acetylamino-3-fluoropyridines ( 14 ) were converted by a known method into a series of 7-substituted 1-ethyl-6-fluoro-1,4-dihydro-4-oxo-1,8-naphthyridine-3-carboxylic acids 21 including enoxacin [1-ethyl-6-fluoro-1,4-dihydro-4-oxo-7-(1-piperazinyl)-1,8-naphthyridine-3-carboxylic acid [( 2 )], a new potential antibacterial agent.     

Quantification of end groups in polystyrenes by pyrolysis–gas chromatography

The determination of end groups in polystyrenes (PSts) polymerized anionically with n-butyllithium as the initiator was carried out by pyrolysis-gas chromatography (Py-GC). The relative proportions of the end groups decrease with increasing molecular weight (MW). Consequently, the peaks which reflect the structure of the end groups can be distinguished by comparing pyrograms of samples with different MW. By comparing the intensities of these peaks relative to total intensities of all the peaks in the pyrogram, the numberaverage molecular weight (M_n) of the polymer can be estimated. The observed M_n values of PSts estimated by this method are compared with those determined by size exclusion chromatography (SEC). By this method it was possible to make direct determination of M_n values of PSts with MWs between 1000 and ca. 1 million. Furthermore, the calibration curve produced by the relative intensity of one of the most characteristic peaks (2-phenyl-1-heptene; C₄H₉? CH₂C (Ph) = CH₂) for the end group to total intensity of all the peaks in the pyrogram, gave rapid and highly reproducible M_n values. © 1994 John Wiley & Sons, Inc.     

n-type organic field-effect transistors with very high electron mobility based on thiazole oligomers with trifluoromethylphenyl groups

Novel thiazole oligomers and thiazole/thiophene co-oligomers with trifluoromethylphenyl groups were developed as n-type semiconductors for OFETs. They showed excellent n-type performances with high electron mobilities. A 5,5'-bithiazole with trifluoromethylphenyl groups forms a closely packed two-dimensional columnar structure leading to a high performance n-type FET. The electron mobility was enhanced to 1.83 cm2/Vs on the OTS-treated substrate.     

Intermolecular Anionic Rearrangement of the Trimethylgerml Group in Trimethylgermylacetonitrile Anions

Intermolecular anionic rearrangement of the trimethylgermyl group in trimethylgermylacetonitrile, bis(trimethylgermyl)acetonitrile, and tris(trimethylgermyl)acetonitrile is described.     

Synthetic study for two 2H‐chromenic acids, 8‐chlorocannabiorcichromenic acid and mycochromenic acid

Two 2H‐chromenes having a fully substituted benzene ring, 8‐chlorocannabiorcichromene ( 1 ) and mycochromenic acid ( 2 ), were synthesized by a condensation of salicylaldehydes with isopropylidenemalonate or the thermal cyclization of corresponding propargyl ethers.     

Chemoselectivity in molybdenum catalyzed alcohol and aldehyde oxidations

Hydrogen peroxide in the presence of (NH₄)₆Mo₇O₂₄ · 4H₂O and potassium carbonate is a chemoselective method to oxidize secondary alcohols to ketones and to oxidize aldehydes to acids, the latter also accelerated by cerium chloride.