Synthesis of 5-aza-analogues of angucyclines: manipulation of the 2-deoxy-C-glycoside subunit

Based on a heterocyclic Diels-Alder strategy, a concise synthesis of 5-aza-analogues of angucyclines bearing a 2-deoxy-C-glycoside subunit is reported. Starting from a common intermediate, a peracetylated D-2-deoxyglucose could be linked to carbons C9 or C10 of the tetracyclic framework. Further manipulations of the sugar residue allowed the installation of bromo and azido substituents at carbon C6′.     

Interfacial tension of liquids from the height and contact angle of a single sessile drop

The height of a sessile drop of liquid when placed on a smooth solid surface increases as the drop volume increases, until it reaches a limiting value for a very large drop. The magnitude of the height and the contact angle depends on the different physical properties of the system. A large value for the contact angle is often associated with a large value for height and vice versa. From the data of measured limiting height, Z _Θ ^∞ and contact angle,Θ, the surface or interfacial tension,γ, can be estimated using the following equation: $$\gamma = \Delta \rho \cdot g \cdot (Z_\Theta ^\infty )^2 /2(1 - \cos (\Theta ))$$ whereΔ? is the density difference between the sessile drop and that of its surrounding medium,g is the gravitational force of acceleration. In this study, the magnitude ofγ of water for various systems is estimated. These values agree with the literature values. Furthermore, the values ofγ for various liquid₁/ solid/liquid₂ systems agree with data from other methods. Thus, the above equation is valid for different liquid-solid systems. It is further shown that very accurate measurements of contact angle,Θ, can be carried out for systems in which Z _Θ Δ _? andγ are known. The variation ofΘ with the height and volume of the sessile drop is analyzed for different systems.     

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.     

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.