On the Positive Mass Theorem for Manifolds with Corners

We study the positive mass theorem for certain non-smooth metrics following P. Miao’s work. Our approach is to smooth the metric using the Ricci flow. As well as improving some previous results on the behaviour of the ADM mass under the Ricci flow, we extend the analysis of the zero mass case to higher dimensions.     

Best Partial Covering of a Convex Domain by Congruent Circles of a Given Total Area

Generalizing results of L. Fejes Toth [3], [5], we prove the following theorem. Let R be a convex domain of area |R| and let S be a finite family of at least two congruent circles of total area t. Then for the area |F| of the part of R covered by the circles of S, the inequality |F|< tf(|R|/t) holds, where f(x) is the area of the intersection of a circle of unit area and a regular hexagon of area x concentric with the circle.     

Determination of mitoxantrone with a fiber-optic device

A major problem in therapeutic use of the cytostatic agent mitoxantrone is the occurrence of side effects. Estimation of the drug concentration in or next to the tumor can lead to a reduction of the toxicity through accurate dose adjustment. In this paper a method for the determination of mitoxantrone by a fibre-optic device is described. The advantage of the system is the possibility of remote sensing at the working site of the cytostatic agent by a method that is simple in handling and sufficient in sensitivity. The measuring principle is based on the blue colour of mitoxantrone. The function of the device was tested byin vitro assays; linear calibration curves in a concentration range between 2 and 10g of mitoxantrone per ml of sample solution were obtained.     

Pyridazines with heteroatom substituents in positions 3 and 5. 6. SN reactions in position 5 of 2-aryl-5-hydroxypyridazin-3(2H)-ones

The nucleophilic introduction of chloro- ( 2 ), azido- ( 4 ), (substituted) amino ( 3, 6 ), mercapto ( 10 ) and hydrazino-groups ( 13 ) into 2-aryl-5-hydroxypyridazin-3(2H)-ones [3] is described. The 5-aminopyridazin-3(2H)-one ( 6 ) also reacts with activated malonates 8 [4] to give pyrido[2,3-d]pyridazines 9 . Hydrazino compounds 13 can be treated with aldehydes to yield compounds 14 . Iodine can be introduced into position 4 of 5 -amino -(15 ) and 5-hydroxypyridazin-3(2H)-ones ( 17 ) by electrophilic substitution to afford compounds 18 .     

The role of oxoammonium cation in the SOD-mimic activity of cyclic nitroxides

Cyclic nitroxides (RNO(*)) mimic the activity of superoxide dismutase (SOD) and demonstrate antioxidant properties in numerous in vitro and in vivo models. Their broad antioxidant activity may involve the participation of their reduced and oxidized forms, that is, hydroxylamine (RNO-H) and oxoammonium cation (RNO(+)). To examine this possibility we studied the reactions of RNO(*) and RNO(+) with HO(2)(*)/O(2)(*)(-) and with several reductants by pulse radiolysis and rapid-mixing stopped-flow techniques. The oxoammonium cations were generated by electrochemical and radiolytic oxidation of 2,2,6,6-tetramethylpiperidinoxyl (TPO) and 3-carbamoyl-2,2,5,5-tetramethylpyrrolidinoxyl (3-CP). The rate constant for the reaction of RNO(*) with HO(2)(*) to form RNO(+) was determined to be (1.2 +/- 0.1) x 10(8) for TPO and (1.3 +/- 0.1) x 10(6) M(-)(1) s(-)(1) for 3-CP. The kinetics results demonstrate that the reaction of RNO(*) with HO(2)(*) proceeds via an inner-sphere electron-transfer mechanism. The rate constant for the reaction of RNO(*) with O(2)(*)(-) is lower than 1 x 10(3) M(-)(1) s(-)(1). The rate constant for the reaction of RNO(+) with O(2)(*)(-) was determined to be (3.4 +/- 0.2) x 10(9) for TPO(+) and (5.0 +/- 0.2) x 10(9) M(-)(1) s(-)(1) for 3-CP(+). Hence, both nitroxides catalyze the dismutation of superoxide through the RNO(*)/RNO(+) redox couple, and the dependence of the catalytic rate constant, k(cat), on pH displayed a bell-shaped curve having a maximum around pH 4. The oxoammonium cation oxidized ferrocyanide and HO(2)(-) by a one-electron transfer, whereas the oxidation of methanol, formate, and NADH proceeded through a two-electron-transfer reaction. The redox potential of RNO(*)/RNO(+) couple was calculated to be 0.75 and 0.89 V for 3-CP and TPO, respectively. The elucidated mechanism provides a clearer insight into the biological antioxidant properties of cyclic nitroxides that should permit design of even more effective antioxidants.     

Synthesis of 8-amino-9-β-D-ribofuranosylpurin-6-thione and related 6-substituted-8-aminopurine nucleosides

Acetylation of 8-amino-9-β-D-ribofuranosylpurin-6-one (III), followed by chlorination of the tetraacetyl derivative 8-acetamido-9-(2,3,5-tri-O-aeetyl-β-D-ribofuranosyl)purin-6-one (IV) with phosphorus oxychloride yielded 8-aeetamido-6-ehloro-9-(2,3,5-tri-O-acetyl-β-D-ribofuranosyl)-purine (V). The 6-chloro substitutent of V was readily displaced with thiourea to give, after treatment with sodium methoxide 8-acetamido-9-β-D-ribofuranosylpurine-6-thione (VIII). Chlorination of 8-bromo-9-(2,3,5-tri-O-acetyl-β-D-ribofuranosyl)purin-6-one (IX) yielded 6,8-dichloro-9-(2,3,5-tri-O-acetyl-β-D-ribofuranosyl)purine (X), which underwent nucleophilic displacement with ethanolic ammonia selectively in the 8 position. The resulting 8-amino-6-chloro-9-β-D-ribofuranosylpurine (VII) was converted to 8-amino-9-β-D-ribofuranosylpurine-6-thione (I), 8-amino-6-methylthio-9-β-D-ribofuranosylpurine (II), and to 8-amino-6-hydrazino-9-β-D-ribofuranosylpurine (XI).     

Continuous hot electron generation in Pt/TiO2, Pd/TiO2, and Pt/GaN catalytic nanodiodes from oxidation of carbon monoxide

Thin films (<10 nm) of platinum or palladium were deposited on TiO2 or GaN to form Schottky diodes. We detected and monitored the continuous electron flow across the metal-oxide interfaces of Pt/TiO2, Pd/TiO2, and Pt/GaN during the catalytic oxidation of carbon monoxide. The electron excitation and flow in the metals were due to conversion of energy released by the oxidation of carbon monoxide into the kinetic energy of free electrons in platinum and palladium. The best conversion of three electrons per four CO2 molecules was observed from 5 nm Pt/TiO2.     

Methane dissociative adsorption on the Pt(111) surface over the 300-500 K temperature and 1-10 Torr pressure ranges

The dissociative adsorption of methane on the Pt(111) surface has been investigated and characterized over the 1-10 Torr pressure and 300-500 K temperature ranges using sum frequency generation (SFG) vibrational spectroscopy and Auger electron spectroscopy (AES). At a reaction temperature of 300 K and a pressure of 1 Torr, C-H bond dissociation occurs in methane on the Pt(111) surface to produce adsorbed methyl (CH(3)) groups, carbon, and hydrogen. SFG results suggest that C-C coupling occurs at higher reaction temperatures and pressures. At 400 K, methyl groups react with adsorbed C to form ethylidyne (C(2)H(3)), which dehydrogenates at 500 K to form ethynyl (C(2)H) and methylidyne (CH) species, as shown by SFG. By 600 K, all of the ethylidyne has reacted to form the dissociation products ethynyl and methylidyne. Calculated C-H bond dissociation probabilities for methane, determined by carbon deposition measured by AES, are in the 10(-8) range and increase with increasing reaction temperature. A mechanism has been developed and is compared with conclusions from other experimental and theoretical studies using single crystals.