Reducible Connections in Massless Topological QCD and 4-manifolds

A role of reducible connections in Non-Abelian Seiberg-Witten invariants is analyzed with massless Topological QCD where monopole is extended to non-Abelian groups version. By giving small external fields, we found that vacuum expectation value can be separated into a part from Donaldson theory, a part from Abelian Monopole theory and a part from non-Abelian monopole theory. As a by-product, we find identities of U(1) topological invariants. In our proof, the duality relation and Higgs mechanism are not necessary.Comment: 23 pages, Latex, Some mistakes and typographical errors are revised in it. Especially, results written in section 4 are change

Tandem aza-Claisen rearrangement and ring closing metathesis reactions: the stereoselective synthesis of functionalised carbocyclic amides

A one-pot, tandem process has been developed for the efficient synthesis of functionalised carbocyclic amides. A substituted cyclopentenyl trichloroacetamide was synthesised using a tandem thermal aza-Claisen rearrangement and RCM process, while an analogous cyclohexenyl trichloroacetamide was generated with high diastereoselectivity using a tandem MOM-ether directed metal-catalysed aza-Claisen rearrangement and RCM process

Reactivity of (Bicyclo[5.1.0]octadienyl)iron(1+) Cations: Application to the Synthesis of cis-2-(2’-carboxycyclopropyl)glycines

The addition of carbon and heteroatom nucleophiles to (bicyclo[5.1.0]octadienyl)Fe(CO)2L+ cations 5 or 8 (L = CO, PPh3) generally proceeds via attack at the dienyl terminus on the face of the ligand opposite to iron to generate 6-substituted (bicyclo[5.1.0]octa-2,4-diene)iron complexes (11 or 13). In certain cases, these products are unstable with respect to elimination of a proton and the nucleophilic substituent to afford (cyclooctatetraene)Fe(CO)2L (4 or 7). Decomplexation of 13f, arising from addition of phthalimide to 8, gave N-(bicyclo[5.1.0]octa-3,5-dien-2-yl)phthalimide (19). Oxidative cleavage of 19 (RuCl3/NaIO4) followed by esterification gave the cyclopropane diester 22, which upon hydrolysis gave cis-2-(2‘-carboxycyclopropyl)glycine (CCG-III, 18) (eight steps from 4, 43% overall yield). This methodology was also utilized for preparation of stereospecifically deuterated CCG-III (d-18) and optically enriched (−)-18. Deprotonation of 22 resulted in cyclopropane ring opening to afford the benzoindolizidine (23)

A template-based approach for the generation of abstractable and reducible models of featured networks

We investigate the relationship between symmetry reduction and inductive reasoning when applied to model checking networks of featured components. Popular reduction techniques for combatting state space explosion in model checking, like abstraction and symmetry reduction, can only be applied effectively when the natural symmetry of a system is not destroyed during specification. We introduce a property which ensures this is preserved, open symmetry. We describe a template-based approach for the construction of open symmetric Promela specifications of featured systems. For certain systems (safely featured parameterised systems) our generated specifications are suitable for conversion to abstract specifications representing any size of network. This enables feature interaction analysis to be carried out, via model checking and induction, for systems of any number of featured components. In addition, we show how, for any balanced network of components, by using a graphical representation of the features and the process communication structure, a group of permutations of the underlying state space of the generated specification can be determined easily. Due to the open symmetry of our Promela specifications, this group of permutations can be used directly for symmetry reduced model checking. The main contributions of this paper are an automatic method for developing open symmetric specifications which can be used for generic feature interaction analysis, and the novel application of symmetry detection and reduction in the context of model checking featured networks. We apply our techniques to a well known example of a featured network – an email system

Reactivity of (3-Methylpentadienyl)iron(1+) Cation: Late-stage Introduction of a (3-Methyl-2Z,4-pentadien-1-yl) Side Chain

The 3-methyl-2Z,4-pentadien-1-yl sidechain is found in various sesquiterpenes and diterpenes. A route for the late stage introduction of this functionality was developed which relies on nucleophilic attack on the (3-methylpentadienyl)iron(1+) cation, followed by oxidative decomplexation. This methodology was applied to the synthesis of the proposed structure of heteroscyphic acid A methyl ester. Realization of this synthesis led to a correction of the proposed structure

Regio- and Stereoselective Ruthenium Catalyzed Hydrovinylation of 1,3-Dienes: Application to the Generation of a 20S-Steroidal Sidechain

The addition of ethylene to 1,3-dienes and 1-vinylcycloalkenes, catalyzed by two ruthenium complexes, proceeds in a regioselective fashion to afford 3-methyl-1,4-dienes as products. For a steroidal-based 1-vinylcycloalkene, the addition is stereospecific, giving a product with a 20(S) configuration