Approximation of Convex Bodies by ConvexBodies

For the affine distance d(C,D) between two convex bodies C, D(?) Rn, which reduces to the Banach-Mazur distance for symmetric convex bodies, the bounds of d(C, D) have been studied for many years. Some well known estimates for the upper-bounds are as follows: F. John proved d(C, D) < n1/2 if one is an ellipsoid and another is symmetric, d(C, D) < n if both are symmetric, and from F. John's result and d(C1,C2) < d(C1,C3)d(C2,C3) one has d(C,D) < n2 for general convex bodies; M. Lassak proved d(C, D) < (2n - 1) if one of them is symmetric. In this paper we get an estimate which includes all the results above as special cases and refines some of them in terms of measures of asymmetry for convex bodies.     

Electron microscope studies on a quenched FeMo alloy

An alloy of FeMo (50 atom%) quenched from the melt was studied using a high-resolution electron microscope. Three phases were frequently identified, viz, the σ-phase, the μ-phase, and the P-phase. The latter two were found to be rich in planar defects of intergrowth and twin type. The resolution obtained was better than 4 Å, as shown with calculated images. It was possible to derive the detailed atomic structure of the defects observed.     

Comparison of the fragmentations and reactivities of positive and negative ions. Thiocarboxylate ions

(1) Thiocarboxylate anions [RCOS]^? formed by dissociative secondary electron capture are either stable or fragment to yield [R]^?. (2) Thiocarboxylate cations [RCOS]⁺ formed by charge stripping from [RCOS]^?, fragment to form [R]⁺, [COS]^+. and [RCO]⁺ (not when R=CF₃). (3) Aryl hydrogen scrambling is observed in the case of the thiobenzoate cation. Aliphatic hydrogen scrambling is not detected for the thiopropionate cation.     

Proton polarization transfer in natural abundance 15N NMR studies of E- and Z-isomers of N-alkylformamides

Proton polarization transfer has been used for the convenient observation of proton coupled natural abundance ¹⁵N NMR spectra of the E- and Z-isomers of N-methylformamide at 10.14 MHz. Second-order spectral analysis is required to determine the ¹⁵N? H coupling constants, at least for the E-isomer of secondary formamides. An useful stereospecificity is observed for both the one- and two-bond ¹⁵N? H coupling constants.