On a special class of bicriterion path problems

In this paper we are concerned with a special class of bicriterion path problems. For the considered class of bicriterion problems at least one of the objectives is type MAXMIN. For the other one, besides an objective type MAXMIN also a MINSUM and a MINRATIO type objective are considered. Two algorithms are presented for the considered class of bicriterion path problems. The first one only determines the minimal complete set of nondominated paths and the second one determines the entire set of nondominated paths. Both algorithms can be used for any type of bicriterion path problems, since one of the objectives is type MAXMIN and an algorithm exists to determine the best path for the other objective. Computational statistics for the three types of considered bicriterion path problems are also presented.     

The gas-phase reaction of hydrazine and ozone: A nonphotolytic source of OH radicals for measurement of relative OH radical rate constants

The homogeneous gas-phase reaction of N₂H₄ with O₃ in air atmospheric pressure has been used to generate OH radicals in the dark, allowing the determination of relative OH radical rate constants for compounds which photolyze rapidly. This technique was first validated by determining the OH radical rate constant ratios for n-butane/cyclohexane and methanol/dimethyl ether, both of which are in excellent agreement with the literature values. The rate constant for the reaction of OH radicals with methyl nitrite at 300 ± 3 K was then determined relative to those for the reaction of OH radicals with n-hexane and dimethyl ether. The resulting rate constant of 1.8 × 10^?13 cm³/molecule·s is about seven times lower than those of previous measurements which employed a different nonphotolytic relative rate method.     

Stereochemistry of organic sulphur compounds: 12—Configurational assignment of 2-methylsulphinyl-1-phenylethanol and some O-derivatives

The conformational analysis of the diastereomeric 2-methylsulphinyl-1-phenylethanol and its O-methyl and O-acetyl derivatives has been performed by ¹H NMR spectroscopy. The study of the influence of dilution and solvent polarity changes on the coupling constants has permitted the configurational assignment of each diastereoisomer. The role played by hydrogen bonding in the hydroxysulphoxides has also been studied by IR spectroscopy.     

Remote stereocontrol in the Nazarov reaction: a new approach to the core of roseophilin

Three different procedures are compared to obtain properly substituted divinyl ketones in which one of the double bonds is embedded in a five-membered heterocyclic structure and therefore suitable to produce cyclopenta-fused pyrrole derivatives by the acid-catalyzed Nazarov reaction. These, on treatment with TFA, afforded 2,4-cis-disubstituted 2,3,4,5-tetrahydro-1H-cyclopenta[b]pyrrol-6-ones with high stereocontrol. One of these Nazarov products was oxidized to the corresponding 4,5-dihydro-1H-cyclopenta[b]pyrrol-6-one derivative, thus obtaining an enantiopure key intermediate in the total synthesis of roseophilin.     

Modular Group Algebras with Almost Maximal Lie Nilpotency Indices

Let be a field of positive characteristic and the group algebra of a group . It is known that, if is Lie nilpotent, then its upper (and lower) Lie nilpotency index is at most , where is the order of the commutator subgroup. The authors previously determined those groups for which this index is maximal and here they determine the groups for which it is `almost maximal', that is, it takes the next highest possible value, namely .Presented by V. Dl a b.Dedicated to Professor Vjacheslav Rudko on his 65th birthday.The research was supported by OTKA No. T 037202, No. T 038059 and Italian National Research Project “Group Theory and Application.”     

Additive decomposition of shear strength in cohesive granular media from grain-scale interactions

We study cemented granular media by introducing cohesive bonding (sliding or rolling friction and tensile strength) between grains in the framework of the contact dynamics method. We find that, for a wide range of bond parameters, the macroscopic angle of friction at the peak state can be split into three distinct terms of collisional, frictional and dilational origins. Remarkably, the macroscopic tensile strength depends only on the bond tensile strength, and the friction angle at the peak state is proportional to the dilatancy angle which varies linearly with sliding friction.