Duality and the cosmological constant

A dynamical theory is studied in which a scalar field ϕ in Einstein-Minkowski space is coupled to the four-velocityN _μ of a preferred inertial observer in that space. As a consistent requirement on this coupling we study a principle of duality invariance of the dynamical mass term of ϕ at some universal length in the small-distance regime. In the large-distance regime duality breaking can be introduced by giving a background value to ϕ and a background direction toN _μ. It is shown that, in an appropriate approximation, duality breaking can be related to the emergence of a characteristic phase in which the condensation of the ground state allows massive excitations with a characteristic scale of squared mass which agrees with the present observational bound for the cosmological constant.     

A new approach based on the surrogating method in the project time compression problems

This paper develops a mathematical model for project time compression problems in CPM/PERT type networks. It is noted this formulation of the problem will be an adequate approximation for solving the time compression problem with any continuous and non-increasing time-cost curve. The kind of this model is Mixed Integer Linear Program (MILP) with zero-one variables, and the Benders' decomposition procedure for analyzing this model has been developed. Then this paper proposes a new approach based on the surrogating method for solving these problems. In addition, the required computer programs have been prepared by the author to execute the algorithm. An illustrative example solved by the new algorithm, and two methods are compared by several numerical examples. Computational experience with these data shows the superiority of the new approach.     

Syntheses of 5‐alkylthio‐1,3‐diaryl‐1,2,4‐triazoles

Arylation of the readily available 3‐alkythio‐5‐aryl‐1,2,4‐triazoles gave 5‐alkylthio‐1,3‐diaryl‐1,2,4‐triazoles in moderate yield. The structures of the latter were confirmed by NOE and ¹³C‐NMR.     

Microwave Assisted Conversion of Oximes and Semicarbazones to Carbonyl Compounds Using Benzyltriphenylphosphonium Peroxymonosulfate

Summary.  Benzyltriphenylphosphonium peroxymonosulfate in the presence of catalytic amounts of bismuth chloride was found to be an efficient and mild reagent for the oxidative cleavage of oximes and semicarbazones to the corresponding carbonyl compounds under microwave irradiation. Corresponding author. E-mail: haji@cc.iut.ac.ir Received March 4, 2002; accepted (revised) April 8, 2002     

Synthesis of 1,2,3-thiadiazolo[4,5-d] pyridazines,A new heterocyclic ring system

A method was developed for the synthesis of 5-carbethoxy-4-formyl-1,2,3-thiadiazole (I), its isomer (II); 5-benzoyl-4-formyl-1,2,3-thiadiazole (III), and its isomer (IV). It was demonstrated that although compounds I, III and IV with hydrazine gave 7H-1,2,3-thiadiazolo[4,5-d]-pyridazin-7-one (XXII), 7-phenyl-1,2,3-thiadiazolo[4,5-d]pyridazine (XXIII) and 4-phenyl-1,2,3-thiadiazolo[4,5-d]pyridazine (XXV), respectively; however, compound I gave its corresponding hydrazone (XXIV).     

Stereoselective synthesis of 4-hydroxy-2-phenylproline framework

Highly diastereoselective (>20:1) bromo-lactonization of N-sulfonyl-2-allyl-2-phenylglycine methyl ester (11) was observed. Successive treatment of the chiral lactone with MeONa gave the desired (2S,4R)-4-hydroxy-2-phenylproline derivative in high yield without erosion of the diastereoselectivity. The starting chiral non-racemic compound (5) was prepared from the racemic 2-phenylglycine using a classical kinetic resolution (crystallization), an asymmetric phase transfer alkylation, and an enzyme-catalyzed kinetic resolution.     

A convenient and regioselective oxidative bromination of electron-rich aromatic rings using potassium bromide and benzyltriphenylphosphonium peroxymonosulfate under nearly neutral reaction conditions

Regioselective oxidative bromination of electron-rich aromatic rings has been studied using potassium bromide as a bromine source in the presence of benzyltriphenylphosphonium peroxymonosulfate as oxidant under nearly neutral reaction conditions. In most cases we obtained monobrominated derivatives regioselectively and in good to high yields without the aid of strong acids.     

Selenium heterocycles. XXIX. Reaction of substituted 2-thioxo-1,3-thiaselenoles with ethyl diazoacetate,ethyl azidoformate and phenyl azide

Reaction of 5-substituted 2-thioxo-1,3-thiaselenoles with ethyl diazoacetate, phenyl azide and ethyl azidoformate afforded 2-substituted ω-carbethoxy-1,4-thiaselenafulvenes (II) , 5-substituted 2-phenylimino-1,3-thiaselenoles (IV) and 5-substituted 2-carbethoxyimino-1,3-thiaselenoles (V) , respectively. The structure of these compounds were confirmed by spectroscopic methods and chemical analysis.     

Syntheses of [1,2,3]selenadiazolo[4,5‐e]benzofuran or benzothiophene, [1,2,3]thiadiazolo[4,5‐e]benzofuran or benzothiophene,and 2‐benzofuranyl‐1,3,4‐oxodiazole derivatives

Dehydrogenation of ethyl 3‐methyl‐4‐oxo‐4,5,6,7‐tetrahydrobenzofuran‐2‐carboxylate 1 with 2,2′‐azobi‐sisobutyronitrile and N‐bromosuccinimide gave ethyl 4‐hydroxy‐3‐methylbenzofuran‐2‐carboxylate 3 . Reaction of compounds 3–4 with hydrazine hydrate afforded the corresponding hydrazides 5a‐b . The reaction of 5a‐b with aldehydes yielded substituted hydrazones 6a‐l . Compounds 7a‐d were prepared from compounds 6a‐d and bromine in acetic acid. Lead tetraacetate oxidation of compounds 6e‐l afforded substituted oxadiazoles 8e‐l . Selenium dioxide oxidation of 4‐oxo‐4,5,6,7‐tetrahydrobenzofuran semicarbazones 9, 14a and 4‐oxo‐4,5,6,7‐tetrahydrobenzothiophene 14b gave the tricyclic 1,2,3‐selenadiazoles 10, 15a and 15b respectively. Reaction of semicarbazones 9, 14a and 14b with thionyl chloride afforded the corresponding 1,2,3‐thiadiazoles 12, 16a and 16b respectively.