Furanverbindungen, 16. Mitt

Zusammenfassung Es wird die Synthese von 13-Oxo-4-methoxy-13H-benzo[i]-furo[2,3-a]xanthen beschrieben.

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Furano compounds XVI

The synthesis of 13-oxo-4-methoxy-13H-benzo[i]furo[2,3-a]-xanthene is recorded.

     

Statistical theory of parcticle size distributions in emulsions and suspensions

Summary The particle size distributions in emulsions and suspensions are mostly empirical. Here a rigorous statistical theory of the problem is given, leading to the logarithmic-normal distribution for the sizes of the particle. On the simple physical basis that the disruption of the interface and the evolution of the particle sizes during emulsification are random turbulent processes, the log-normal law is derived by considering the process as aMarkoff chain. An alternate simpler derivation is also presented. The nature of the simplifying assumption involved in the theory is clearly brought out. Some properties of the log-normal curve are given. The statistical analysis in fitting the log-normal distribution to the experimental data with special reference to the distortion of the fractile diagram and the advantages of a theoretical distribution over an empirical one are discussed in detail with suitable examples.

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Zusammenfassung Die Teilchenverteilungen von Emulsionen und Dispersionen sind meist empirisch. Hier wird eine strenge statistische Theorie des Problems gegeben, die zu der logarithmischen Normalverteilung der Teilchengr?\en führt. Auf der einfachen physikalischen Grundlage, da\ Zerbrechen der Oberfl?chen und die Entstehung der Teilchengr?\en w?hrend Emulgierung einem zuf?lligen turbulenten Proze\ zuzuschreiben sind, wird die log-Normalverteilung durch Analyse dieses Prozesses als eineMarkoffsche Kette abgeleitet. Eine einfache alternative Ableitung wird au\erdem gebracht. Die Natur der in die Theorie eingehenden Grundannahmen wird erkl?rt. Einige Eigenschaften der log-Normal-Kurve werden diskutiert. Die statistische Analyse zur Darstellung von Beobachtungsdaten mit Hilfe der log-Normalverteilung, speziell in Bezug auf die Ver?nderung der Kurven für H?ufigkeitsverteilungen sowie die Vorteile einer theoretischen Verteilung gegenüber einer empirischen Kurve, werden an geeigneten Beispielen in allen Einzelheiten dargelegt.

     

On an inhomogeneous deformation of a generalized Neo-Hookean material

We study the inhomogeneous deformation of a wedge of an incompressible generalized power-law Neo-Hookean material. We find solutions which have a boundary layer structure, in the sense that adjacent to the boundary the solution is inhomogeneous, while in the core region the solution is homogeneous. It is found that such solutions have an associated pressure field that is bounded. Inhomogeneous solutions are also possible when the pressure varies logarithmically with the radial coordinate. We also establish explicit exact solutions for specific values of the parameter. The results reduce to the Neo-Hookean solution when the power law exponent is set to unity.     

New universal relations for nonlinear isotropic elastic materials

A nonlinear isotropic elastic block is subjected to a homogeneous deformation consisting of simple shear superposed on triaxial extension. Two new relations are established for this deformation which are valid for all nonlinear elastic isotropic materials, and hence are universal relations. The first is a relation between the stretch ratios in the plane of shear and the amount of shear when the deformation is supported only by shear tractions. The second relation is established for a thin-walled cylinder under combined extension, inflation and torsion. Each material element of the cylinder undergoes the same local homogeneous deformation of shear superposed on triaxial extension. The properties of this deformation are used to establish a relation between pressure, twisting moment, angle of twist and current dimensions when no axial force is applied to the cylinder. It is shown that these relations also apply for a mixture of a nonlinear isotropic solid and a fluid.     

Highly charged ions in field evaporating 4d-transition metals

An energy-focused time-of-flight atom-probe has been employed in a search for high ionic charges obtained in field-evaporating Zr, Nb, Mo, Rh, Pd and Ag, the 4d-transition metals. Although no new higher charges than the already established ones are found for these metals the maximum abundance of the highest charge is determined in each case. An empirical rule predicting the limits of the charge of field-evaporating ions is proposed.     

Mass spring lattice modeling of the scanning laser source technique

The scanning laser source (SLS) technique is a promising new laser ultrasonic tool for the detection of small surface-breaking defects. The SLS approach is based on monitoring the changes in laser generated ultrasound as a laser source is scanned over a defect. Changes in amplitude and frequency content have been observed for ultrasound generated by the laser over uniform and defective areas. In this paper, the SLS technique is simulated numerically using the mass spring lattice model. Thermoelastic laser generation of ultrasound in an elastic material is modeled using a shear dipole distribution. The spatial and temporal energy distribution profiles of typical pulsed laser sources are used to model the laser source. The amplitude and spectral variations in the laser generated ultrasound as the SLS scans over a large aluminum block containing a small surface-breaking crack are observed. The experimentally observed SLS amplitude and spectral signatures are shown to be captured very well by the model. In addition, the possibility of utilizing the SLS technique to size surface-breaking cracks that are sub-wavelength in depth is explored.     

Vibrational spectra of Na4P2O7·10H2O

The IR and Raman spectra are measured and analysed for sodium pyrophosphate decahydrate. The spectra are interpreted on the basis of P₂O ₇ ⁴⁻ ion and water vibrations. The observed results fit with the features predicted for the factor goup model. The appearance of two sets of frequencies in the stretching and bending regions of water suggests the existence of two kinds of water molecules in the crystal. This is confirmed by deuterium substitution.     

Selektive Alkylierung chelatisierter Hydroxylgruppen in kondensierten Benzpyronen, 1. Mitt.

Zusammenfassung Da chelatisierte Hydroxylgruppen in kondensierten Polyhydroxypyronen einen Boracetatkomplex bilden, während andere Hydroxylgruppen im gleichen Molekül normale Acetylierung erleiden, und da aus diesem Komplex die Hydroxylgruppe leicht zurückgewonnen und mittels aktiven Silberoxids und Methyljodids alkyliert werden kann, war es möglich, 1,3-Dihydroxyxanthon selektiv zum 1-Methoxy-3-hydroxyxanthon zu alkylieren. Dessen Konstitution wurde durch Äthylierung zum 3-Äthoxyderivat bewiesen. Letzteres wurde unabhängig davon auch auf anderem Wege synthetisiert.Aus der Dissertation vonG. S. Puranik, Karnatak-Universität     

Theoretical study of the electronic spectrum of diimide by AB initio methods

A series of ab initio calculations is reported for the ground and low-lying valence and Rydberg states of diimide N₂H₂. Symmetric bending potential curves for both the cis and trans forms of this system have been obtained at the SCF level of treatment. In addition Cl calculations have been carried out for the trans-diimide ground state equilibrium nuclear conformation, using a configuration selection procedure described elsewhere; an associated energy extrapolation scheme is also employed which enables the effective solution of secular equations with orders of up to 40000. The ensuing Cl wavefunctions are interpreted in the discussion and the corresponding calculated energy differences between the various electronic states are compared with experimental transition energy results for both diimide and for related systems such as trans-azomethane. A more detailed analysis of the observed absorption bands in the ¹B_g-X¹A_g transition in N₂H₂ is also given, making use of calculated potential curve data as well as the pertinent Cl vertical energy difference. The dipole-forbiddenness of the excitation process is thereupon concluded to result in a distinct non-verticality for this electronic band system, causing its absorption maximum to occur at a position some 0.6 eV to the blue of the so-called vertical transition, i.e., that for which maximum vibrational overlap is obtained.     

An analysis of the complex molecular orbitals method

Numerical results for the ground state of the HN ₂ ⁺ and HCO⁺ molecular ions at their near equilibrium geometry, obtained by the complex molecular orbitals (CMO) method in the extended basis set, are reported. The CMO wavefunction of the HN ₂ ⁺ ion is compared with the CI wavefunction obtained in the same basis set. This reveals the nature of approximations inherent in the CMO method. A peculiar feature of the occupation numbers of the CMO natural orbitals is also explained.Alexander von Humboldt Fellow. On leave from the Institute Rudjer Bokovi, Zagreb, Croatia, Yugoslavia.