Synthesis, structure and properties of pyrazole type tetrakis compounds

A series of pyrazole type tetrakis compounds has been synthesized by reaction of aromatic or heterocyclic dialdehydes and pyrazolone derivatives. Structure and tautomerism of the products were investigated by spectroscopic methods and X-ray analysis. Several tetrakis compounds form inclusion complexes with solvents like alcohols, ethers, and ketones in a definite ratio via hydrogen bonds.     

Calculated Auger emission spectrum of ammonia

Doubly ionized states of ammonia are calculated with Roothaan's symmetry-restricted open-shell SCF method. A GTO basis of double-ζ quality is used. Calculated energies compare well with previous calculations for the lowest doubly ionized states. Auger emission intensities are estimated using an analogy with the experimental Auger spectrum of neon.     

High-resolution transmission electron microscopy using negative spherical aberration.

A novel imaging mode for high-resolution transmission electron microscopy is described. It is based on the adjustment of a negative value of the spherical aberration C S of the objective lens of a transmission electron microscope equipped with a multipole aberration corrector system. Negative spherical aberration applied together with an overfocus yields high-resolution images with bright-atom contrast. Compared to all kinds of images taken in conventional transmission electron microscopes, where the then unavoidable positive spherical aberration is combined with an underfocus, the contrast is dramatically increased. This effect can only be understood on the basis of a full nonlinear imaging theory. Calculations show that the nonlinear contrast contributions diminish the image contrast relative to the linear image for a positive-C S setting whereas they reinforce the image contrast relative to the linear image for a negative-C S setting. The application of the new mode to the imaging of oxygen in SrTiO3 and YBa2Cu3O7 demonstrates the benefit to materials science investigations. It allows us to image directly, without further image processing, strongly scattering heavy-atom columns together with weakly scattering light-atom columns.     

On Proinov’s bound for the quadrature error of functions having a given modulus of continuity

Summary We discuss the question, under which conditions Proinovs upper bound for the quadrature error of functions having a given modulus of continuity is not improvable. Improvability usually holds if the quadrature formula is not a Riemannian sum. We derive a condition on the second Peano kernel yielding always the sharpness of Proinovs result. This condition is applicable to Gaussian quadrature.