N. Sivakumar

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The present work considers the interpolation of the scattered data on the d-sphere by spherical polynomials. We prove bounds on the conditioning of the problem which rely only on the separation distance of the sampling nodes and on the degree of polynomials being used. To this end, we establish a packing argument for well separated sampling nodes and(More)
Let λ be a positive number, and let (x j : j ∈ Z) ⊂ R be a fixed Riesz-basis sequence, namely, (x j) is strictly increasing, and the set of functions {R ∋ t → e ix j t : j ∈ Z} is a Riesz basis (i.e., unconditional basis) for L 2 [−π, π]. Given a function f ∈ L 2 (R) whose Fourier transform is zero almost everywhere outside the interval [−π, π], there is a(More)
In the title compound, C33H23ClN4O3S·CHCl3, the thia-zole ring adopts an envelope conformation with the N atom as the flap, and the pyrrolidine ring adopts a half-chair conformation. The thia-zole ring mean plane makes a dihedral angle of 59.31 (1)° with the pyrrolidine ring mean plane, 71.67 (1)° with the chromene ring and 82.59 (1)° with the(More)
The title salt, 2C7H11N2 (+)·2C7H4NO4 (-)·3H2O, crystallized with two anions and two cations in the asymmetric unit, together with three water mol-ecules. Both 4-di-methyl-amino-pyridinium cations are protonated at their pyridine N atoms with the plane of the N(CH3)2 hetero atoms inclined to the pyridine ring by 4.5 (2) and 1.4 (2)°. In the 2-nitro-benzoate(More)
The asymmetric unit of the title compound 2C23H27N2O4 (+)·C8H4O4 (2-)·9H2O, contains a cation, an anionon a twofold axis and four and half mol-ecules of water, one of which is located on the twofold axis. In the cation, both fused pyrrolidine rings exhibit twisted conformations, while the piperidine rings adopt screw-boat and boat conformations. In the(More)
In the cation of the title salt, C23H27N2O4 (+)·C2HO4 (-)·2H2O, both fused pyrrolidine rings exhibit twisted conformations, while the piperidine rings adopt screw-boat and boat conformations. In the crystal, the three components are linked via O-H⋯O and N-H⋯O inter-actions, forming a tape along the b axis. The tapes are further linked by weak C-H⋯O hydrogen(More)