On the split property for inclusions of -algebras

A characterization of the quasi-split property for an inclusion of -algebras in terms of the metrically nuclear maps is established. This result extends the known characterization relative to inclusions of -factors. An application to type von Neumann algebras is also presented.

     

En">Characters and Composition Factor Multiplicities for the Lie Superalgebra $${\mathfrak{g}}{\mathfrak{l}}$$ ( m / n )

The multiplicities a of simple modules L in the composition series of Kac modules V lambda for the Lie superalgebra (m/n ) were described by Serganova, leading to her solution of the character problem for (m/n ). In Serganova's algorithm all with nonzero a are determined for a given this algorithm, turns out to be rather complicated. In this Letter, a simple rule is conjectured to find all nonzero a for any given weight . In particular, we claim that for an r-fold atypical weight there are 2r distinct weights such that a = 1, and a = 0 for all other weights . Some related properties on the multiplicities a are proved, and arguments in favour of our main conjecture are given. Finally, an extension of the conjecture describing the inverse of the matrix of Kazhdan–Lusztig polynomials is discussed.     

Microemulsions: Effect of alkyl chain length of alcohol and alkane

In microemulsions consisting of four components, i.e. detergent — water — oil — cosurfactant, the free energy of transfer from the continuous oil phase to the interfacial region for the cosurfactant is reported. From the effect of temperature on the free energy, the entropy and the enthalpy values are also reported. The effect of chain length of the alcohol (cosurfactant) is also described. It is further shown, that if the oil phase consists of hexadecane, then the free energy changes as a linear function of the number of carbon atoms in the cosurfactant. On the other hand, if the oil phase is benzene, the cosurfactant chain length has very little effect. These data are analyzed with respect to the microemulsion structure and stability.     

The overload phenomenon in gas chromatography

The usual concepts of the dynamics of an overloaded solute band fail to explain several phenomena such as the typical “leading-tail” shape and retention deviations exhibited by overloaded peaks, and why these defects are more commonly observed in short columns. These and other related deviations from theory can be rationalized by a non-classical approach to the overloading phenomenon.     

The crystal and molecular structure of cyclopentadienyltin(II) chloride. The bonding of the cyclopentadienyl group in tin(II) compounds

The crystal and molecular structure of cyclopentadienyltin(II) chloride has been determined from three-dimensional X-ray data. The crystals are orthorhombic, space group Pc2₁n. The unit cell, of dimensions a = 5.711(5), b = 6.225(5), c = 17.24(2) Å, contains four molecules. The structure has been refined by full matrix least squares techniques to a final R value of 0.083 for 717 independent reflections. In the crystal unsymmetrical tin-chlorine bridges are present between the units of C₅H₅SnCl.It is suggested that in cyclopentadienyltin(II) compounds the cyclopentadienyl group occupies more than one coordination site as a result of the donation of π electron density from the cyclopentadienyl ring into an empty acceptor orbital of the tin atom having π symmetry.     

Analysis of two neutron (proton) transfer reaction data in the Zr-region

The spectroscopic amplitudes, form factors, angular distributions and total cross-sections for two nucleon transfer reactions in Zr-region in the zero range distorted wave Born approximation are calculated using consistent set of shell model wave functions. A single normalisation factor gives a good fit to all the two neutron transfer reaction data whereas the corresponding fit for the two-proton transfer reaction data is less satisfactory.     

Measurement of the electric form factor of the neutron at Q2 = 0.3-0.8 (GeV/ c) 2 ⋆

The electric form factor of the neutron, G_E,n, has been measured at the Mainz Microtron by recoil polarimetry in the quasielastic D(¯e, e¯n)p reaction. Three data points have been extracted at squared four-momentum transfers Q ² = 0.3, 0.6 and 0.8 (GeV/c)². Corrections for nuclear binding effects have been applied.This revised version was published online in March 2005. In the previous version, the email address of one author was inadvertently assigned to multiple authors.     

Nucleon electromagnetic form factors and polarization observables in space-like and time-like regions

We perform a global analysis of the experimental data of the electromagnetic nucleon form factors, in space-like and time-like regions. We give the expressions of the observables in annihilation processes, such as p + ¯↦ℓ⁺ + ℓ^-, ℓ = e or μ, in terms of form factors. We discuss some of the phenomenological models proposed in the literature for the space-like region, and consider their analytical continuation to the time-like region. After determining the parameters through a fit on the available data, we give predictions for the observables which will be experimentally accessible with large statistics, polarized annihilation reactions