Measurement of an arbitrary parallel displacement of a rigid body by using polychromatic speckle patterns

A novel speckle method for measuring the parallel displacement of a rigid body in an arbitrary direction is presented. The amount of displacement as well as its angle made with the optical axis is to be measured from the Fourier transform patterns of a doubly exposed photographic plate.     

Phonon diffraction gratings

A two-dimensional diffraction grating for phonons is described. It scatters thermal phonons strongly when their dominant wavelength is equal to the grating's lattice constant. Through measurements of the Kapitza resistance between the silicon crystal carrying the grating and liquid helium, it is shown that the scattering by the grating is predominantly coherent, as expected for phonon diffraction.     

Certain integral transforms with the Macdonald function Kν(z) in the kernels

Four integral transforms are considered with the Macdonald function in their kernels. Existence and inversion theorems are proved and Parseval equalities are established in a Hilbert space, in a Wiener normed ring, and in the space of generalized Gelfand-Shilov functions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 990–993, July, 1990.     

Boundary value problem for a parabolic system in a domain with a conical point on the boundary

We study the first initial-boundary value problem for strongly parabolic systems in cylinders whose bases have conical points. An illustrating example for the heat equation is presented.     

The chemistry of vicinal tricarbonyls : A synthesis of (±)-slaframine and (±)-6-epi-slaframine

A synthesis of (±)-slaframine and (±)-6-epi-slaframine is described. The approach makes use of the intramolecular alkylation of an N-substituted 3-hydroxypyrrole-2-carboxylate ester.     

Stabilité des carboxylates de terres,III. Maléates,méthylsuccinates et malates

The stability constants of maleates, methylsuccinates and malates of rare earths have been determined at 25.0 °C and at ionic strength 0,100 (NaClO₄) by a potentiometric method. Each ligand forms 1 : 1 and 1 : 2 complexes in aqueous solution, the malates being the most stable. The first and the second dissociation constants of the ligand acids were also measured. The 1 : 2 maleates of La, Pr, Nd, Sm, and Eu have been isolated.     

On a Question of Gowers

We show that any subset of density \frac100log_*^1/4 n \frac{100}{log_*^{1/4} n} of an n by n square in \mathbbZ² \mathbb{Z}^2 contains an isoceles right-angle triangle with a fixed orientation whose sides are parallel to the axes, for all sufficiently large n.