Reactions of alkyl (z)‐2‐[(E)‐2‐ethoxycarbonyl‐2‐(2‐pyridinyl)‐ethenyl]amino‐3‐dimethylaminopropenoates with C‐ and N‐nucleophiles. the synthesis of fused pyranones,pyridinones and pyrimidinones

Alkyl 2‐[2‐ethoxycarbonyl‐2‐(2‐pyridinyl)ethenyl]amino‐3‐dimethylaminopropenoates 3 and 4 were transformed with C‐and N‐nucleophiles into β‐heteroaryl‐α,β‐didehydro‐α‐amino acid derivatives 13 ‐ 16 , substituted 3‐amino‐4H‐quinolizin‐4‐one 17, 2H,5H‐benzo[b]pyran‐2,5‐dione 18 and 19 , 2H,5H‐pyrano[4,3‐b]pyran‐2,5‐dione 20 , 2H,5H‐pyrano[3,2‐c]benzo[b]pyran‐2,5‐dione 21 , 2H‐1‐benzopyran‐2‐one 22 and 24 , pyrido[l,2‐a]pyrimidin‐4‐one 31–34 and 39 derivatives, and N‐heteroaryl‐1H‐imidazole‐4‐carboxylates 37 and 38 .     

Pulsed field-ionization photoelectron-photoion coincidence study of the process N2+hnu-->N++N+e-: bond dissociation energies of N2 and N2+

We have examined the dissociative photoionization reaction N2+hnu-->N++N+e- near its threshold using the pulsed field-ionization photoelectron-photoion coincidence (PFI-PEPICO) time-of-flight (TOF) method. By examining the kinetic-energy release based on the simulation of the N+ PFI-PEPICO TOF peak profile as a function of vacuum ultraviolet photon energy and by analyzing the breakdown curves of N+ and N2+, we have determined the 0-K threshold or appearance energy (AE) of this reaction to be 24.2884+/-0.0010 eV. Using this 0-K AE, together with known ionization energies of N and N2, results in more precise values for the 0-K bond dissociation energies of N-N (9.7543+/-0.0010 eV) and N-N+ (8.7076+/-0.0010 eV) and the 0-K heats of formation for N (112.469+/-0.012 kcal/mol) and N+ (447.634+/-0.012 kcal/mol).     

Barbituric acid initiated rearrangement of 2,2'-pyridil into 5,5'-(2-pyrilidine)bisbarbituric acid

[reaction: see text] In the study of the barbituric acid initiated 2,2'-pyridil rearrangement, a very efficient synthetic procedure (isolated yield 80-90%) for the preparation of useful 2-pyrilidenes 3 was developed.     

Small Triangle-Free Configurations of Points and Lines

In the paper we show that all combinatorial triangle-free configurations for v ≤ 18 are geometrically realizable. We also show that there is a unique smallest astral (18₃) triangle-free configuration and its Levi graph is the generalized Petersen graph G(18,5). In addition, we present geometric realizations of the unique flag transitive triangle-free configuration (20₃) and the unique point transitive triangle-free configuration (21₃).     

Invariance in adelic quantum mechanics

Adelic quantum mechanics is form-invariant under an interchange of real andp-adic number fields as well as rings ofp-adic integers. We also show that in adelic quantum mechanics Feynman’s path integrals for quadratic actions with rational coefficients are invariant under changes of their entries within nonzero rational numbers.     

Strictly antipodal sets

A subsetA ofE ³ is called strictly antipodal provided that for every pairX ₁,X ₂ of points ofA there is a pairH ₁,H ₂ of parallel supporting planes ofA such thatH _i ∩A={X _i}. The main result asserts that a strictly antipodal set has at most five points. This strengthens a recent result of Croft [2]. This research was supported in part by the United States Air Force under Grant No. AF-EOAR 63-63 and monitored by the European Office, Office of Aerospace Research.     

Hartree-Fock and density functional complete basis-set (CBS) predicted nuclear shielding anisotropy and shielding tensor components

The nuclear shielding anisotropy and shielding tensor components calculated using the hybrid density functional B3PW91 are reported for a model set of compounds comprised of N2, NH3, CH4, C2H4, HCN and CH3CN. An estimation of density functional theory (DFT) and Hartree-Fock complete basis-set limit (CBS) parameters from a 2 (3) point exact fit vs. least-squares fit was obtained with the cc-pVxZ and aug-cc-pVxZ basis sets (x=D, T, Q, 5, 6). Both Hartree-Fock- and DFT-predicted CBS shielding anisotropies and shielding tensor components of the model molecules were in reasonable agreement with available experimental data. The utility of using a limited CBS approach for calculating accurate anisotropic shielding parameters of larger molecules as complementary methods to solid-state NMR is proposed.