The reaction of tetralones with nitriles: a simple approach to the synthesis of new substituted benzo[h]quinazolines, benzo[f]quinazolines and dibenzo[a,i]phenanthridines

The one-pot reaction of 1-tetralone with nitriles in the presence of triflic anhydride affords in good yields 2,4-disubstituted 5,6-dihydrobenzo[h]quinazolines, which oxidation with DDQ leads to the corresponding benzo[h]quinazolines. 2-Tetralone undergoes identical process forming 1,3-disubstituted 5,6-dihydrobenzo[f]quinazolines. However, when the reaction of 2-tetralone is carried out with methylthiocyanate as nitrile, 5-methylthiotetrahydrodibenzo[a,i]phenanthridines are isolated in good yields. Easy transformations of the methylthio group offer possible access to a variety of substituted dibenzo[a,i]phenanthridines.     

Benzylic cleavage and McLafferty rearrangement under electron ionization conditions in the fragmentation of 5,6-dialkyl-2, 4-diarylpyrimidines

Several 5,6-dialkyl-2,4-diarylpyrimidines were prepared and their electron ionization (EI) mass spectra reported. The benzylic cleavage takes place easily together with an important McLafferty rearrangement. The involvement of the nitrogen atom appears to be important in the fragmentation of 5-methyl-substituted pyrimidines. In contrast, the 6-methyl-substituted pyrimidines undergo benzylic cleavage without hydrogen transfer. Thus, the difference in the mass spectrometric behaviour allows the identification of these isomeric compounds which, in contrast, exhibit only small differences in their NMR spectra. Copyright 1999 John Wiley & Sons, Ltd.     

Counting and enumeration complexity with application to multicriteria scheduling

In this paper we tackle an important point of combinatorial optimisation: that of complexity theory when dealing with the counting or enumeration of optimal solutions. Complexity theory has been initially designed for decision problems and evolved over the years, for instance, to tackle particular features in optimisation problems. It has also evolved, more or less recently, towards the complexity of counting and enumeration problems and several complexity classes, which we review in this paper, have emerged in the literature. This kind of problems makes sense, notably, in the case of multicriteria optimisation where the aim is often to enumerate the set of the so-called Pareto optima. In the second part of this paper we review the complexity of multicriteria scheduling problems in the light of the previous complexity results.Received: November 2004 / Received version: March 2005MSC classification: 90B40, 90C29, 68Q15     

2,4-Bis(methylsulfanyl)pyrimidine o-quinodimethane: a versatile building block for functionalized fused pyrimidines

Two alternative methods for the preparation of new pyrimidine Diels-Alder cycloadducts from the readily available 2,4-bis(methylsulfanyl)-5,6-dihydrocyclobuta[d]pyrimidine are presented. In the first method, the in situ generated pyrimidine ortho-quinodimethane reacts with various dienophiles to form the respective cycloadducts bearing two methylthio groups, which can be easily replaced by other functional groups. In the second method, one or both of the methylsulfanyl groups of the starting pyrimidine are replaced first and the resulting functionalized pyrimidines are able to undergo Diels-Alder cyclization with different dienophiles to form pyrimidine cycloadducts. These alternative synthetic strategies provide access to a wide variety of pyrimidine cycloadducts with a different substitution pattern on the pyrimidine ring. Yield data indicate that the electronic nature of the functional groups strongly influence the efficiency of the cycloaddition reaction.     

Synthesis of 5‐Amino‐3,3‐dimethyl‐7‐phenyl‐3H‐[1,2]oxathiolo[4,3‐b]pyridine‐6‐carbonitrile 1,1‐Dioxides

The reaction of 4‐amino‐5,5‐dimethyl‐5H‐1,2‐oxathiole 2,2‐dioxide ( 1 ) with 2‐(arylidene)malononitriles 2 in ethanol, at reflux, using piperidine as catalyst, afforded 5‐amino‐3,3‐dimethyl‐7‐aryl‐3H‐[1,2]oxathiolo[4,3‐b]pyridine‐6‐carbonitrile 1,1‐dioxides ( 3 ) in moderate chemical yields.     

Acid promoted enantioselective oxygen-atom transfer from N-alkyl binaphthyl-derived oxaziridines onto sulfides

Acid-promoted asymmetric sulfoxidations of prochiral sulfides using binaphthyl-derived oxaziridines have been studied. The reactions of dialkyl or aryl-alkyl sulfides gave good yields of the corresponding sulfoxides with enantiopurities ranging from 20% to 80%. The influence of temperature and strength of the acid catalyst on enantioselectivity was studied. The absolute configuration of the resulting major enantiomer varied with the structure of the sulfide.     

Multiple Unbounded Positive Solutions for Three-Point BVPs with Sign-Changing Nonlinearities on the Positive Half-Line

This work is concerned with the existence of unbounded positive solutions for a second-order nonlinear three-point boundary value problem on the positive half-line. The interesting points of the results are that the nonlinearity depends on the solution and its derivative and may change sign. Moreover, it satisfies general polynomial growth conditions. New existence results of nontrivial single and multiple positive solutions are proved using recent fixed point theorems on cones in a special Banach space.     

Price competition and store competition: Store brands vs. national brand

This paper studies pricing strategies in a market channel composed of one national brand manufacturer and two retailers who, each, carry their own store brand and a national brand products. The model accounts for product competition between store brands and the national brand products, as well as for store competition between retailers.