q-transformation theory

We obtain the complete set of states of theq-oscillator in both configuration space and momentum space as well as the transformation between these spaces. The states as well as the matrix elements lie in the SU _q (2) algebra. To obtain transition probabilities, one must take the Woronowicz square.     

On stable geometries

Within the concept of projective lattice geometry we are considering the class of stable geometries which have also been introduced in [14]. The investigation of their basic properties will result in fundamental structure theorems which especially give a lattice-geometric characterization of free left modules of rank 6 over proper right Bezout rings of stable rank 2. This yields a proper generalization of previous results of ours.     

Jupiter's Great Red Spot and zonal winds as a self-consistent,one-layer,quasigeostrophic flow

We present the point of view that both the vortices and the east-west zonal winds of Jupiter are confined to the planet's shallow weather layer and that their dynamics is completely described by the weakly dissipated, weakly forced quasigeostrophic (QG) equation. The weather layer is the region just below the tropopause and contains the visible clouds. The forcing mimics the overshoot of fluid from an underlying convection zone. The late-time solutions of the weakly forced and dissipated QG equations appear to be a small subset of the unforced and undissipated equations and are robust attractors. We illustrate QG vortex dynamics and attempt to explain the important features of Jupiter's Great Red Spot and other vortices: their shapes, locations with respect to the extrema of the east-west winds, stagnation points, numbers as a function of latitude, mergers, break-ups, cloud morphologies, internal distributions of vorticity, and signs of rotation with respect to both the planet's rotation and the shear of their surrounding east-west winds. Initial-value calculations in which the weather layer starts at rest produce oscillatory east-west winds. Like the Jovian winds, the winds are east-west asymmetric and have Karman vortex streets located only at the west-going jets. From numerical calculations we present an empirically derived energy criterion that determines whether QG vortices survive in oscillatory zonal flows with nonzero potential vorticity gradients. We show that a recent proof that claims that all QG vortices decay when embedded in oscillatory zonal flows is too restrictive in its assumptions. We show that the asymmetries in the cloud morphologies and numbers of cyclones and anticyclones can be accounted for by a QG model of the Jovian atmosphere, and we compare the QG model with competing models.     

Theoretical study of some heterocyclic amines with applications to the chemistry of 9-amino-1,2,3,4-tetrahydroacridine

9-Amino-1,2,3,4-tetrahydroacridine (THA ), a potent cholinesterase inhibitor, was recently used in the treatment of Alzheimer's disease. On attempting to prepare a dihydropyridine ? pyridinium salt-based redox chemical delivery system (CDS ) to enhance brain delivery of THA , several of the practical synthetic challenges were examined by using a theoretical MO approach. The structures, reactivities and stability of THA , derivatives of THA and a model compound, 4-aminopyridine, a simple dibasic heterocyclic amine, were studied in the framework of the AM -1 approximation. The study included the possible protonated forms of THA and 4-aminopyridine. The calculated heats of formation showed that ring nitrogen protonated forms are more stable for both THA and 4-aminopyridine. The calculated heats of formation showed that ring nitrogen protonated forms are more stable for both THA and 4-aminopyridine, consistent with experimental results. Electron delocalization is responsible for the remarkable stability of these molecules and for the observed lack of reactivity of the amino group, both in the basic and protonated forms. The site of N-alkylation of the 9-nicotinamide derivative of THA (an intermediate in the synthesis of THA -CDS ) is controlled by electronic, thermodynamic, and steric factors.     

5-Pyrimidylboronic acid and 2-methoxy-5-pyrimidylboronic acid: new heteroarylpyrimidine derivatives via Suzuki cross-coupling reactions

5-Pyrimidylboronic acid and 2-methoxy-5-pyrimidylboronic acid 4 have been synthesised by lithium-halogen exchange reactions on 5-bromopyrimidine and 2-methoxy-5-bromopyrimidine, respectively, followed by reaction with triisopropylborate. Suzuki cross-coupling reactions of 2 and 4 with heteroaryl halides [Na(2)CO(3), Pd(PPh(3))(2)Cl(2), 1,4-dioxane, 95 degrees C] yield heteroarylpyrimidines (heteroaryl = thienyl, quinolyl and pyrimidyl). Two-fold reaction of 2 with 4,6-dichloropyrimidine 12 gave 4,6-bis(5-pyrimidyl)pyrimidine 8(56% yield). Reaction of 4,6-dichloropyrimidine with 2-methoxy-5-pyridylboronic acid gave 4,6-bis(2-methoxy-5-pyridyl)pyrimidine 14 (84% yield). Conversion of into 4,6-bis(2-chloro-5-pyridyl)pyrimidine 15 (63% yield) followed by two-fold Suzuki reaction with 4-tert-butylbenzeneboronic acid gave the penta-arylene derivative 4,6-bis[2-(4-tert-butyl)phenyl-5-pyridyl]pyrimidine 16 (16% yield). Analogous reaction of 12 with 2-methoxy-3-pyridylboronic acid 17 gave 4,6-bis(2-methoxy-3-pyridyl)pyrimidine 18 (64% yield). The X-ray crystal structures of compound 2.0.5H(2)O and compound 18 are reported. The two hydroxyl H atoms in 2 have the usual exo-endo orientation. However, unlike most arylboronic acids, molecule 2 does not form a centrosymmetric hydrogen-bonded dimer. In molecule 18, the pyridine rings form dihedral angles of 39.9 degrees and 22.8 degrees with the central pyrimidine ring.