Game,set, and graph

In the twentieth century the theory of games was transformed. It began as an amusing pastime, and ended as a major branch of mathematical research and a key paradigm of economic theory. Here it will be argued that the transformation was the result of the work of mathematicians, such as Ernst Zermelo, John von Neumann and Dénes K?nig, who also contributed to two other areas of mathematics that were emerging at the same time: the theory of sets and the theory of graphs.     

Simulation of the Glass Transition of a Thin Aluminum Melt Layer at Ultrafast Cooling under Isobaric Conditions

JETP Letters - It is shown that a sharp increase in viscosity, a change in the decay rate of correlations, and the appearance of nonequilibrium and transverse sound in a thin film of aluminum melt...     

N-tert-Butoxycarbonyl (BOC) Deprotection Using Boron Trifluoride Etherate

A mild and efficient procedure is described for the removal of the tert-butoxycarbonyl (BOC) group using boron trifluoride etherate and molecular sieves in dichloromethane at room temperature. The scope of this procedure is explored for the deprotection of a variety of amines including amino acid derivatives.     

Novel Synthesis of (+/−)-cis-4-Amino-2-cyclopentene-1-methanol,a Key Intermediate in the Preparation of Carbocyclic 2′,3′-Didehydro-2′,3′-dideoxy Nucleosides

Abstract

Novel synthetic routes directed toward the preparation of (+/?)-cis -4-amino-2-cyclopentene-1-methanol are described. The routes investigated involve azide openings of chiral and non-chiral cyclopentyl epoxides.     

Cytotoxic and NF-κB inhibitory sesquiterpene lactones from Piptocoma rufescens

Six new (1-6) and eight known germacranolide-type sesquiterpene lactones, along with several known phenylpropanol coumarates and methylated flavonoids, were isolated from the leaves of Piptocoma rufescens, collected in the Dominican Republic. The new compounds were identified by analysis of their spectroscopic data, with the molecular structure of 3 being established by single-crystal X-ray diffraction. The absolute configurations of the sesquiterpene lactones isolated were determined from their CD and NOESY NMR spectra, together with the analysis of Mosher ester reactions. Bioassay screening results showed the majority of the sesquiterpene lactones isolated (1-13) to be highly cytotoxic toward the HT-29 human colon cancer cell line, with the most potent compound being 15-deoxygoyazensolide (10, IC(50), 0.26 μM). In addition, several of the sesquiterpene lactones exhibited NF-κB (p65) inhibitory activity.     

SILYL- AND GERMYL-DIAZADIPHOSPHETIDINES

Abstract

Reaction of the 1,3,2,4-diazadiphosphetidine, trans-[C₆H₅N(H)P(S)NC₆H₅]₂ with LiR (R = Me, n-Bu) followed by treatment of the resulting dianions with Me₃SiCl and Me₃GeBr produced trans-[C₆H₅N(R)P(S)NC₆H₅]₂(R = Me₃Si, 2; Me₃Ge, 3). Substitution occurs without cis-trans isomerization or significant cleavage of the 1,3,2,4-diazadiphosphetidine ring. 2 and 3 have been characterized by spectral (¹H and ³¹P NMR, IR, and MS) and elemental analytical data. Analogous reactions involving Me₃SnCl yield mixtures containing [C₆H₅N(SnMe₃)P(S)NC₆H₅]₂ which could not be isolated or completely characterized.     

Proposed Participation of Excited Monomer in the Free Radical-Catalyzed High Pressure,High Temperature Polymerization of Ethylene

The radiation-induced copolymerization of ethyl vinyl ether with dibutyl maleate was investigated over a wide range of comonomer compositions, dose rates, and in the temperature range from ?25 to 75° C. Both the rates of copolymerization and the molecular weights of the resulting copolymers were found to depend strongly on the initial comonomer composition, both reaching a maximum value at an equimolar comonomer composition. A copolymer was obtained in which the co-monomers alternate with regularity along the polymer chain over the entire range of comonomer compositions investigated. The monomer reactivity ratios were determined and found to be practically zero. The apparent activation energy was found to change at 35° C, the boiling point of the ethyl vinyl ether, from a value of 10.48 kJ/mole to a value of 18.86 kJ/mole above this temperature. This phase change also resulted in a marked decrease in the molecular weights of the copolymers formed above 35° C. The dose-rate dependence of the rate of copolymerization was found to be 0.70 over the dose-rate range     

Donor-Acceptor Complexes in Copolymerization. XXVI. Effect of Solvent,Temperature, and Complexing Agent on the Polymerization of Comonomer Charge Transfer Complexes

The copolymerization of styrene with methyl methacrylate (S/MMA = 4/1) or acrylonitrile (S/AN = 1/1) in the presence of ethylaluminum sesquichloride (EASC) yields 1/1 copolymer in toluene or chlorobenzene. In chloroform the S-MMA-EASC polymerization yields 60/40 copolymer while the S-AN-EASC polymerization yields 1/1 copolymer. In the presence of EASC, styrene-α-chloroacrylonitrile yields 1/1 copolymer (DMF or DMSO), S-AN yields 1/1 copolymer (DMSO) or radical copolymer (DMF), S-MMA yields radical copolymer (DMF or DMSO), α-methylstyrene-AN yields radical copolymer (DMSO) or traces of copolymer (DMF), and α-MS-methacrylo-nitrile yields traces of copolymer (DMSO) or no copolymer (DMF). When zinc chloride is used as complexing agent in DMF or DMSO, none of the monomer pairs undergoes polymerization. However, radical catalyzed polymerization of isoprene-AN-ZnCl₂ in DMF yields 1/1 alternating copolymer. The copolymerization of S/MMA in the presence of EASC yields 1/1 alternating copolymer up to 100°C, while the copolymerization of S/AN deviates from 1/1 alternating copolymer above 50°C. The copolymerization of S/MMA deviates from 1/1 copolymer at MMA/EASC mole ratios above 20 while the copolymerization of S/AN deviates from 1/1 copolymer at MMA/EASC ratios above 50.     

Donor-Acceptor Complexes in Copolymerization. XLIV. Copolymerization of Styrene and α-Methylstyrene with Acrylic and α-Substituted Acrylic Esters in the Presence of Aluminum Compounds

Abstract

The copolymerization of styrene (S) with methyl acrylate (MA) and with methyl methacrylate (MMA) in the presence of AlEt₃ yields equimolar, alternating copolymers while no polymer is formed in α-methylstyrene (MS)-MA and MS-MMA systems. In the presence of AlEt_1.5Cl_l,5 (EASC), S-MA and S-MMA yield alternating copolymers, S-methyl a-chloroacrylate (MCA), MS-MA and MS-MMA yield a mixture of alternating and cationic polymers, and MS-MCA yields cationic polymer only. In the presence of A1C1₃, S-MA and MS-MA yield a mixture of alternating and cationic polymers and S-MMA and MS-MMA yield cationic polymer only. The cotacticity distributions of the alternating S-MA and S-MMA copolymers prepared in the presence of AlEt₃, EASC, and A1C1, are the same; the coisotactic, co-heterotactic, and cosyndiotactic fractions being approximately in the ratio 1:2:1. The cosyndiotactic fractions of the alter-nating copolymers prepared in the presence of EASC are in the order MS-MMA > MS-MA > S-MCA > S-MMA=S-MA.