Desoxyzucker, 4. Mitt.: Verbesserung der Darstellung von 3-Desoxy-d-ribohexose (3-Desoxy-d-glucose) und ihres 3-Mercaptoderivats aus 1,2-5,6-Di-O-isopropyliden-α-d-glucofuranose

Zusammenfassung Das 3-O-(S-Methyl-dithiocarbonat) der 1,2-5,6-Di-O-isopropyliden--d-glucofuranose wurde bei einer Temperatur von 490–510° und im Vakuum 20–30 mm Hg in einer Ausbeute von 60% in das 3-S-(S-Methyl-dithiocarbonat) der 1,2-5,6-Di-O-isopropyliden-3-mercapto-3-desoxy--d-ribohexofuranose umgelagert, wodurch die angeführte Verbindung zur Darstellung von 3-Desoxy-d-ribohexose (3-Desoxy-d-glucose) und ihrer Isopropylidenderivate, ggf. zur Darstellung von 3-Mercapto-3-desoxy-d-glucose und ihrer Derivate sehr geeignet wird.Mit 1 Abbildung3. Mitt.: Coll. Czechoslov. Chem. Comm.27, 94 (1962).     

The effect of X-ray coherence on crystalline diffraction

The importance of respecting the coherent properties of X-rays in the physical interpretation of the profiles of the X-ray diffraction patterns is pointed out. Drawing the analogy between Young's experiment and two-atom X-ray scattering, the author applies the elementary theory of coherence, developed for light optics, to X-ray diffraction by a linear atomic lattice. As his considerations concerning the effect of coherence on diffraction by such a lattice are impossible to verify experimentallly, he tests their correctness by spectrographical measurements of the width of an optical grating diffraction line under different coherence and experimental conditions. The paper is dedicated to the memory of Dr. A. Vaíek, Professor of the J. E. Purkyn University in Brno, who died on November 16, 1966.     

Gamma-ray spectrum of192Au

The gamma-ray spectrum of 5 h¹⁹²Au has been measured by means of the germanium detector. A number of about 200 new transitions were found in addition to the transitions known from the conversion electron measurement of Nyman et al. (Arkiv f. fysik29 (1965), 321) and 82 internal conversion coefficients were determined from the relations between conversion lineand gamma-ray intensities. From energies, intensities and multipolarities of transitions the existence of 20 new levels is very probable, in many cases with spin-parity assignments too.     

Interpolating polynomial wavelets on [−1,1]

The present paper gives a contribution of wavelet aspects to classical algebraic polynomial approximation theory. As is so often the case in classical approximation, the authors follow the pattern provided by the trigonometric polynomial case. Algebraic polynomial interpolating scaling functions and wavelets are constructed by using the interpolation properties of de la Vallée Poussin kernels with respect to the four kinds of Chebyshev weights. For the decomposition and reconstruction of a given function the structure of the involved matrices is studied in order to reduce the computational effort by means of fast discrete cosine and sine transforms. Dedicated to Prof. Guiseppe Mastroianni on the occasion of his 65th birthday.AMS subject classification 65D05, 65T60     

An abinitio study of protonation and alkylation of aminopyridine

STO-3G abinitio calculations show that the first site of protonation in 2-, 3- and 4-aminopyridines is the cyclic nitrogen, whatever the position of the amino group. There is an excellent linear relationship between the calculated proton affinities and the experimental pK_a values (r = 0.995). The protonation site is also confirmed by π→π* transition energy variations as a function of position of the amino-group due to protonation; these effects are connected with the MO structures. Basicity and reactivity in alkylation reveal lone pair localization.     

Unbalanced optimal transport: Dynamic and Kantorovich formulations

This article presents a new class of distances between arbitrary nonnegative Radon measures inspired by optimal transport. These distances are defined by two equivalent alternative formulations: (i) a dynamic formulation defining the distance as a geodesic distance over the space of measures (ii) a static “Kantorovich” formulation where the distance is the minimum of an optimization problem over pairs of couplings describing the transfer (transport, creation and destruction) of mass between two measures. Both formulations are convex optimization problems, and the ability to switch from one to the other depending on the targeted application is a crucial property of our models. Of particular interest is the Wasserstein–Fisher–Rao metric recently introduced independently by name="bbr0070" href="#br0070" class="workspace-trigger">[7], name="bbr0150" href="#br0150" class="workspace-trigger">[15]. Defined initially through a dynamic formulation, it belongs to this class of metrics and hence automatically benefits from a static Kantorovich formulation.     

Stability of Hereditary Graph Classes Under Closure Operations

If is a subclass of the class of claw‐free graphs, then is said to be stable if, for any , the local completion of G at any vertex is also in . If is a closure operation that turns a claw‐free graph into a line graph by a series of local completions and is stable, then for any . In this article, we study stability of hereditary classes of claw‐free graphs defined in terms of a family of connected closed forbidden subgraphs. We characterize line graph preimages of graphs in families that yield stable classes, we identify minimal families that yield stable classes in the finite case, and we also give a general background for techniques for handling unstable classes by proving that their closure may be included into another (possibly stable) class.