Descriptions of operators in quantum mechanics

The problem of expressing a general dynamical variable in quantum mechanics as a function of a primitive set of operators is studied from several points of view. In the context of the Heisenberg commutation relation, the Weyl representation for operators and a new Fourier-Mellin representation are related to the Heisenberg group and the groupSL(2,R) respectively. The description of unitary transformations via generating functions is analysed in detail. The relation between functions and ordered functions of noncommuting operators is discussed, and results closely paralleling classical results are obtained.

Self accomodation morphology of martensite variants in Zr---2.5wt%Nb alloy

The role of self accomodation of the different mertensite variants controlling the morphologies of the Zr---2.5wt%Nb alloy martensite has been examined. Three distinct types of grouping of martensite variants have been found to be predominantly present. Crystallographic descriptions of these groups have been provided and the degrees of self accomodation for these have been estimated and compared with those corresponding to other possible variant groupings around the symmetry axes of the parent phase. The frequently observed 3-variant group, which shows an “indentation mark” morphology when viewed along left angle bracket111right-pointing angle bracketβ directions in the transmission electron microscope, has been seen to have the highest degree of self accomodation amongst the cases considered. Based on the observations made, a growth sequence leading to the formation of the final martensitic structure has been proposed.

A Case Study in Matching Service Descriptions to Implementations in an Existing System

A number of companies are trying to migrate large monolithic software systems to Service Oriented Architectures. A common approach to do this is to first identify and describe desired services (i.e., create a model), and then to locate portions of code within the existing system that implement the described services. In this paper we describe a detailed case study we undertook to match a model to an open-source business application. We describe the systematic methodology we used, the results of the exercise, as well as several observations that throw light on the nature of this problem. We also suggest and validate heuristics that are likely to be useful in partially automating the process of matching service descriptions to implementations.

Reactivity of some tetra substituted furans and thiophenes towards BF3-Et(2)O catalysed Diels-Alder reaction

Some tetra substituted furans and thiophenes were reacted with methyl acrylate under BF3-etherate catalysed Diels-Alder conditions. While the derivatives of furan underwent Diels-Alder reaction in a facile manner, an observation of 2,5-dimethyl-3,4-dianisylthiophene undergoing Diels-Alder reaction with methyl acrylate is remarkable. (C) 1997, Elsevier Science Ltd.

Phalangopsidae crickets from the Indian Region (Orthoptera, Grylloidea), with the descriptions of new taxa, diagnoses for genera, and a key to Indian genera

The Indian region is presently the second region after the Neotropics in terms of diversity of phalangopsid crickets. Yet their study is impeded by the lack of necessary taxonomic tools for taxon identification. In the present paper, all generic diagnoses are clarified, using morphological and genitalic characters; female genitalia are described and illustrated for all genera with known females. New taxa are described from southern India: Kempiola flavipunctatus Desutter-Grandcolas n. sp., Opiliosina meridionalis Desutter-Grandcolas n. gen., n. sp., Phalangopsina bolivari Desutter-Grandcolas n. sp., P. chopardi Desutter-Grandcolas n. sp., P. gravelyi Desutter-Grandcolas n. sp., and Speluncasina Desutter-Grandcolas n. gen. The list of phalangopsid crickets from the Indian Region is updated, and a key to phalangopsid genera proposed. A lectotype and a paralectotype are designated to fix the name of Phalangopsina dubia (Bolivar, 1900). Opilionacris annandalei Chopard, 1928, previously transferred to the African genus Phaeophilacris Walker, 1871, is transferred to the genus Speluncasina Desutter-Grandcolas n. gen., while Larandopsis jharnae Bhowmik, 1981 and L. newguineae Bhowmik, 1981 described from New Guinea are transferred to the eneopterine genus Lebinthus Stal, 1877. Finally Luzaropsis confusa Chopard, 1969 is removed from its synonymy with L. ferruginea Walker, 1871.

Insertion Reactions of Six-Membered Cyclopalladated N,N `,N `'-Triarylguanidine, Pd{kappa(2)(C,N)-C6H3Me-3(NHC(NHAr)(=NAr))-2)(mu-Br)](2) (Ar=2-MeC6H4) with PhCC C-C(O)OR (R = Me and Et): A Gateway to Second Orthopalladation through Novel Rearrangements

The reaction of Pd{kappa(2)(C,N)-C6H3Me-3-(NHC(NHAr)(=NAr))-2}(mu-Br)](2) (Ar = 2-MeC6H4; 1) with 4 equiv of PhC C-C(O)OMe in CH2Cl2 afforded Pd{kappa(2)(C,N)-C(Ph)=C(C(O)OMe)C(Ph)=C(C(O)-OMe)C6H3Me-3(N=C(NH Ar)(2))-2}Br] (Ar = 2-MeC6H4; 2) in 70% yield, and the aforementioned reaction carried out with 10 equiv of PhC C-C(O)OR (R = Me, and Et) afforded an admixture of two regioisomers of Pd{kappa(3)(N,C,O)-O=C(OR)-C5Ph3(C(O)OR)C(C(O)OR)C6H3Me-3(N=C(NHAr)( 2))- 2}Br] (Ar = 2-MeC6H4; R = Me (3a/3b), Et (4a/4b)) in 80 and 87% yields, respectively. In one attempt, the minor regioisomer, 4b, was isolated from the mixture in 6% yield by fractional crystallization. Palladacycles 3a/3b and 4a/4b, upon stirring in CH2Cl2/MeCN (1/1, v/v) mixture at ambient condition for S days, afforded Pd{eta(3)-allyl,(KN)-N-1)-C-5(C(O)OR)(2)Ph3C-(C(O)OR)C6H3Me-3(N=C(NH Ar)(2))(-2)}Br] (Ar = 2-MeC6H4; R = Me (5a/5b), Et (6a/6b)) in 94 and 93% yields, respectively. Palladacycles 3a/3b and 4a/4b, upon reaction with AgOTf in CH2CH2/Me2C(O) (1/1, v/v) mixture at ambient temperature for 15 min, afforded Pd{kappa(3)(N,C,O)-O=C(OR)C5Ph3(C(O)OR)C(C(O)OR)C6H3Me-3(N=C(NHAr)(2 ))-2}(OTf)] (Ar = 2-MeC6H4; R = Me (7a/7b), Et (8a/8b)) in 79 and 77% yields, respectively. Palladacycles 7a/7b and 8a/ 8b, upon reflux in PhC1 separately for 6 h, or palladacycles 5a/5b and 6a/6b, upon treatment with AgOTf in CH2Cl2/Me2C(O) (7/3, v/v) mixture for 15 min, afforded Pd{(eta(2)-Ph)C5Ph2(C(O)OR)kappa(2)(C,N)-C(C(O)OR)C6H3Me-3(N=C(NHAr) (2))-2}(OTf)] (Ar = 2-MeC6H4; R = Me (9a/9h), Et (10a/10b)) in >= 87% yields. Palladacycles 9a/9b, upon stirring in MeCN in the presence of excess NaOAc followed by crystallization of the reaction mixture in the same solvent, afforded Pd{kappa(3)(N,C,C)-(C6H4)C5Ph2(C(O)OMe)(2)C(C(O)OMe)(2)C6H3Me-3(N=C( NHAr)(2))-2}(NCMe)] (Ar = 2-MeC6H4; 11a/11b) in 82% yield. The new palladacycles were characterized by analytical, IR, and NMR (H-1 and C-13) spectroscopic techniques, and the molecular structures of 2, 3a, 4a, 4b, 5a, 6a, 7a, 9a, 10a, and 11a-d(3) were determined by single crystal X-ray diffraction. The frameworks in the aforementioned palladacycles, except that present in 2, are unprecedented. Plausible pathways for the formation of new palladacycles and the influence of the guanidine unit in 1, substituents in alkynes, reaction conditions, and electrophilicity of the bromide and the triflate upon the frameworks of the insertion products have been discussed.