Microwave assisted synthesis of 3-aminoindole-2-carbonitriles from anthranilonitriles via N-unprotected 2-(cyanomethylamino)benzonitriles

Anthranilonitrile 3a, 4,5-dimethoxyanthranilonitrile 3b and 5-nitroanthranilonitrile 3c, react with paraformaldehyde, KCN and ZnCl₂ in acetic acid under acid catalysis (H₂SO₄) in a sealed tube at ca. 55 °C to give the corresponding 2-(cyanomethylamino)benzonitriles 4a-c in 96, 86 and 57% yields, respectively. Thorpe-Ziegler cyclisation of the N-unprotected 2-(cyanomethylamino)benzonitriles 4a-c with K₂CO₃ in EtOH at elevated temperatures and pressures using either microwave heating or conventional heating in a sealed tube gives 3-amino, 3-amino-5,6-dimethoxy, and 3-amino-5-nitroindole-2-carbonitriles 2a-c in moderate to good yields. All new compounds are fully characterised.     

Role of rigidity on the activity of proteinase inhibitors and their peptide mimics

The Bowman-Birk inhibitors (BBIs) are a family of proteins that share a canonical loop structure whose presence in a conserved conformation is linked to their inhibitory activity. We study the conformational properties of the canonical loop using a graph theoretical approach as implemented in the floppy inclusions and rigid substructure topography (FIRST). We find that the canonical loop is an independent rigid cluster in the natural inhibitors. We have further used this technique to identify residues that play an important role in the structural rigidity of the protein by quantifying their contribution to the overall rigidity of the inhibitor. We find that the conserved elements among the natural and synthetic peptides are the ones that contribute the most to rigidity, even if they are located far from the active site, as rigidity effects are nonlinear and hence nonlocal. The results help to elucidate why certain mutations in the loop of the BBI produce peptides that fail to have the designed inhibitory activity.     

Observation of the enhancement in enantioselectivity with conversion for the aziridination of styrene using copper bis(oxazoline) complexes

During the aziridination of styrene using copper bis(oxazoline) complexes the ee increases with conversion due to further reactions of the product.     

Clathrate solvates of tetra­kis(4‐methoxy­carbonyl­phenyl)porphyrin and its zinc(II)–pyridine complex,in which the porphyrin host structures are stabilized by porphyrin–porphyrin stacking and C—H⋯O attractions

Tetra­kis(4‐methoxy­carbonyl­phenyl)porphyrin, or tetra­methyl 4,4′,4′′,4′′′‐porphyrin‐5,10,15,20‐tetra­benzoate, crystallizes as a nitro­benzene 1.9‐solvate, C₅₂H₃₈N₄O₈·1.9C₆H₅NO₂, (I). The solvent mol­ecules are contained in extended channels which propagate through the host lattice between parallel screw/glide‐related columns of offset‐stacked porphyrin entities. Side packing of these columns involves π–π inter­actions between the methoxy­carbonyl­phenyl residues. Mol­ecules of the porphyrin host lie on crystallographic inversion centres. The zinc(II)–pyridine derivative pyridine­(tetra­methyl 4,4′,4′′,4′′′‐porphyrin‐5,10,15,20‐tetra­benzoato)zinc(II), [Zn(C₅₂H₃₆N₄O₈)(C₅H₅N)], (II), is a square‐pyramidal five‐coordinate complex with pyridine as an apical ligand, which crystallizes as a chloro­form–pyridine solvate. The metallo­porphyrin–pyridine units form an open layered arrangement, occluding the non‐coordinated solvent moieties within the intra­layer inter­porphyrin voids. Within such arrays, the host porphyrin mol­ecules are in contact with one another through the peripheral methoxy­carbonyl substituents. The crystal packing consists of a bilayered arrangement of inversion‐related porphyrin layers, with the axial ligands mutually penetrating into the voids of neighbouring arrays and tight offset stacking of these bilayers.     

Semiglobal results for on a complex space with arbitrary singularities

We obtain some -results for the operator on forms that vanish to high order on the singular set of a complex space.

     

Pairs of positive solutions for nonlinear elliptic equations with the <Emphasis Type="Italic">p</Emphasis>-Laplacian and a nonsmooth potential

In this paper we examine a nonlinear elliptic problem driven by the p-Laplacian differential operator and with a potential function which is only locally Lipschitz, not necessarily C¹ (hemivariational inequality). Using the nonsmooth critical point theory of Chang, we obtain two strictly positive solutions. One solution is obtained by minimization of a suitable modification of the energy functional. The second solution is obtained by generalizing a result of Brezis-Nirenberg about the local C¹₀-minimizers versus the local H¹₀-minimizers of a C¹-functional. Mathematics Subject Classification (2000) 35J50, 35J85, 35R70     

Multiple solutions of constant sign for nonlinear nonsmooth eigenvalue problems near resonance

In this paper we study a class of nonlinear elliptic eigenvalue problems driven by the p-Laplacian and having a nonsmooth locally Lipschitz potential. We show that as the parameter approaches (= the principal eigenvalue of ) from the right, the problem has three nontrivial solutions of constant sign. Our approach is variational based on the nonsmooth critical point theory for locally Lipschitz functions. In the process of the proof we also establish a generalization of a recent result of Brezis and Nirenberg for C₀¹ versus W₀^1,p minimizers of a locally Lipschitz functional. In addition we prove a result of independent interest on the existence of an additional critical point in the presence of a local minimizer of constant sign. Finally by restricting further the asymptotic behavior of the potential at infinity, we show that for all the problem has two solutions one strictly positive and the other strictly negative.Received: 7 January 2003, Accepted: 12 May 2003, Published online: 4 September 2003Mathematics Subject Classification (2000): 35J20, 35J85, 35R70     

Variational Approach to Uniform Rigid Rotation of Ginzburg—Landau Vortices

Time periodic solutions for the hyperbolic gauged Ginzburg–Landau system, with spatial domain the unit disc, are shown to exist. Time periodic solutions representing bound states of vortices rotating about one another have been previously obtained in the near self-dual limit, using perturbative techniques. In contrast, we here take a variational approach, the solutions being obtained as critical points of an indefinite functional. We consider a special class of solutions which map out, uniformly in time, an orbit of the rotation group SO(2). It is shown that in the limit of large coupling constant the solutions have nontrivial time dependence or, as is shown to be equivalent, are not radially symmetric in any gauge.     

Construction of entropy solutions for one dimensional elastodynamics via time discretisation

It is shown that the variational approximation scheme for one-dimensional elastodynamics given by time discretisation converges, subsequentially, weakly and a.e. to a weak solution which satisfies the entropy inequalities. We also prove convergence under the restriction of positive spatial derivative (for longitudinal motions).