Ketu and the second invariant of a quadratic space

Using the Chern classes defined by Grothendieck, we map aK-theoretic invariant of invertible symmetric matrices defined by Giffen to the Clifford invariant.According to Herrmann Graßman'sWörterbuch zum Rig-veda, Ketu may not be connected with K₂ but es bezeichnet das, was sich sichtbar oder kenntlich macht ...     

Chemoselective Addition of Hydrazine to δ‐Keto Esters and Dimethylformamide‐Mediated Deesterification

The chemoselective reaction of hydrazine on the ketone rather than the ester in a gem diester system with a γ‐keto group by hydrazinium sulfate and a tandem deesterification of one of the esters in this system by N,N‐dimethylformamide are reported.     

Phase diagram study of CaBr2–CaHBr system

A study of binary, CaBr₂–CaHBr system was carried out by differential thermal analysis (DTA), covering the composition range from 100 % CaBr₂ to 100 % CaHBr between room temperature and 800 °C. From DTA results, the contour of solidus and liquidus temperatures with composition is plotted and the phase diagram of CaBr₂–CaHBr system is constructed. The system shows an eutectic reaction at 576 °C and the eutectic composition is 79.6 mol% CaBr₂. Co-existing phases in different phase fields are characterized by X-ray diffraction analysis.     

Phase diagram study of CaBr2–LiBr system using DTA

The phase diagram of binary LiBr–CaBr₂ system was investigated using differential thermal analysis (DTA) between room temperature and 800 °C. From the DTA results obtained over the entire range of composition from pure LiBr to pure CaBr₂ in steps of ~5 mol%, the phase diagram was constructed and is reported here. The results indicated the possible existence of a compound at 50 mol% LiBr, namely, LiCaBr₃. The compound undergoes peritectic decomposition at 552 °C. The system shows a eutectic reaction at 532 °C between this compound and LiBr phase, and the eutectic composition is close to 80 mol% LiBr. The compound LiCaBr₃ decomposes into CaBr₂ and LiBr phases below 272 °C. Co-existing phases in different phase fields are characterized by X-ray diffraction analysis.     

Three-component Heck–Diels–Alder cascade processes involving alkylallenes, aryl iodides and dienophiles

A wide variety of aryl/heteroaryl iodides undergo an intermolecular Heck reaction with alkylallenes to furnish 1,3-dienes. These subsequently react in situ with various dienophiles to give Diels–Alder adducts. The chemistry has been extended to incorporate cyclisation-anion capture methodology and the stereochemistry of the products has been determined.     

Chemo,stereo, and regioselective addition of α‐(2‐methoxyaryl)‐N‐aryl nitrones to diarylidineacetone: Synthesis of novel isoxazolidines

A new set of 2,3,4,5‐tetrasubstituted isoxazolidines with an α,β‐unsaturated carbonyl function at position 4 has been synthesized. The multicomponent approach and microwave irradiation protocol have also been investigated for the above synthesis.     

Synthesis and characterization of the aqueous solution chemistry of the food-derived carcinogen model N-acetoxy-N-(1-methyl-5H-pyrido[4,5-b]indol-3-yl)acetamide and its N-pivaloyloxy analogue

We report the synthesis of N-acetoxy-N-(1-methyl-5H-pyrido[4,5-b]indol-3-yl)acetamide, 7, its N-pivaloyloxy analogue, 9, and improved synthesis of indole-2-acetonitrile, 3 (70% in five steps from indole-2-carboxylic acid), the carcinogenic amine Trp-P-2, 4 (40% from 3), and the nitro compound, 5 (40% from 4 by oxidation with H₂O₂ using Mo(CO)₆ catalyst). In aqueous solution at neutral pH, 7 primarily undergoes C-O bond cleavage to yield the hydroxamic acid, 8, but under the same conditions the sterically hindered 9 decomposes predominately by N-O bond cleavage with a pH independent rate constant that is 7.5-fold smaller than that for 7. In the pH range 0.5-7.0 three different processes for the decomposition of 9 were detected by kinetics. Only the process that dominates at neutral pH generates a nitrenium species that can be trapped by N₃⁻.     

Sequential Pd/Ru-catalysed allenylation/olefin metathesis/1,3-dipolar cycloaddition route to novel heterocycles

A novel sequential palladium/ruthenium-catalysed four component process is described involving carbonylation of an aryl/heteroaryl iodide followed by allenylation to generate (π-allyl) palladium species which are intercepted by nitrogen nucleophiles to afford 1,6-dienes. Subsequent Ring-Closing Metathesis (RCM) affords C-acyl-N-heterocycles in good yield. These heterocycles proved to be active dipolarophiles in sequential and cascade 1,3-dipolar cycloaddition reactions (1,3-DC) as exemplified by reactions with nitrones and azomethine ylides.     

Palladium catalysed tandem cyclisation–anion capture. Part 8: Cascade hydrostannylation—cyclisation–anion capture and cascade hydroboration—cyclisation–anion capture on solid phase

Up to four bonds and five stereocentres are created, in five component processes (five point diversity), utilising resin bound aryl iodides by hydroboration or hydrostannylation of alkynes, followed by cyclisation–anion capture involving Suzuki or Stille reactions. Three small libraries were prepared to validate the chemistry.