On fuzzy subgroups and fuzzy ideals under triangular norms

In this communication, we explicitly point out that the principal results of Liu 1982 basically deduced from the definition of binary operation ° on the set F(X) of all fuzzy subsets of X, also hold if one uses the weaker definition of product under triangular norm °_t. Fuzzy ideals with respect to the triangular norms are also defined.     

13C NMR examination of some N-thioaroylmorpholine–bromine adducts

The ¹³C NMR chemical shifts of three N-thioaroylmorpholine–bromine adducts, previously used as synthetic intermediates, are compared and discussed in the light of the corresponding shifts of the parent thioamides and suitable model compounds. Chemical shift changes are interpreted in terms of the electronic perturbation resulting from bromine coordination at sulphur.     

A simulation model for aircraft sequencing in the near terminal area

The objective of this study is the development of a simulation model to assist in aircraft sequencing operations in the terminal area. After the definition of the main characteristics of the model, a general structure of a terminal area is considered with a variable number of feeder fixes and alternative paths from the fixes to the runways. The model is designed so as to evaluate different operating policies. A discrete events simulation philosophy, using Fortran as simulation language, is employed. Finally a model application to the Rome terminal area is illustrated. The results obtained show that the model, here presented, is general enough to simulate the terminal area behaviour of any airport.     

Enhancement of shake-up structure in alkali-metal-ion exchanged forms of α-Zr(HPO4)2 by sputtering

Mg Kα ESCA spectra of several α-Zr(PO₄)₂M₂ compounds (M = Li⁺, Na⁺, K⁺, Cs⁺) have been obtained. Satellite structure is observed at ～7–8 eV from the main P 2s peak (corresponding to ～15–16 eV from the main Zr 3d_{$\text{5}\text{2}$} peak). The intensity of the satellite depends on the counter-ion intercalated. For a given counter-ion it is strongly increased by sputtering, the rate of increase being also dependent on the counter-ion. This observation is interpreted mainly in terms of electron-defect formation similar to that involved in the formation of colour centres by radiation damage, and subsequent charge-transfer shake-up of the trapped electrons to the electron-deficient phosphorus or Zr(IV) centres.     

Studies on the synthesis of heterocyclic compounds. III. Synthesis of 1,3,2-benzodioxa- and 1,3,2-benzoxathiarsole derivatives

The preparation and reaction of 1,3,2-benzodioxa- and 1,3,2-benzoxathiarsoles (IIa-b) are described. Spiran derivatives Va-c are obtained by treating IIa-b with Ia-b and triethylamine, while the reaction of IIa-b with sodium hydroxide, ethoxide and p-cresolate gives the compounds VIa-b, VIIa-b and VIIIa-b, that can evolve to Xa-b. Reaction of IIa-b with sodium p-toluenethio-late and n-butyllithium gave the compounds IXa-b and XIa-b respectively. The structure of the prepared compounds has been determined by elemental analysis and spectroscopic data.     

The electrostatics of Einstein’s unified field theory

When sources are added at their right-hand sides, and g_(ik) is a priori assumed to be the metric, the equations of Einstein’s Hermitian theory of relativity were shown to allow for an exact solution that describes the general electrostatic field of n point charges. Moreover, the injunction of spherical symmetry of g_(ik) in the infinitesimal neighbourhood of each of the charges was proved to yield the equilibrium conditions of the n charges in keeping with ordinary electrostatics. The tensor g_(ik), however, cannot be the metric of the theory, since it enters neither the eikonal equation nor the equation of motion of uncharged test particles. A physically correct metric that rules both the behaviour of wave fronts and of uncharged matter is the one indicated by Hély.In the present paper it is shown how the electrostatic solution predicts the structure of the n charged particles and their mutual positions of electrostatic equilibrium when Hély’s physically correct metric is adopted.     

Unexpected density fluctuations in jammed disordered sphere packings

We computationally study jammed disordered hard-sphere packings as large as a million particles. We show that the packings are saturated and hyperuniform, i.e., that local density fluctuations grow only as a logarithmically augmented surface area rather than the volume of the window. The structure factor shows an unusual nonanalytic linear dependence near the origin, S(k) approximately |k|. In addition to exponentially damped oscillations seen in liquids, this implies a weak power-law tail in the total correlation function, h(r) approximately -r(-4), and a long-ranged direct correlation function c(r).     

A novel and highly efficient synthetic route to unsymmetrical organoselenides using cesium bases

A new and convenient one-pot method for the preparation of unsymmetrical selenides has been developed. In the presence of cesium hydroxide, molecular sieves, and DMF, benzeneselenol undergoes direct alkylation with various alkyl halides for the synthesis of alkyl phenyl selenides in moderate to excellent yields. Another method to prepare unsymmetrical organoselenides was also completed by coupling terminal alkynes with benzeneselenyl bromide. As an application, the synthesis of a selenopeptide was also accomplished. Furthermore, this methodology was extended to the synthesis of an organoselenide on solid support.