Mueller matrices in fluorescence scattering

A reappraisal of the 1929 analysis of luminescence by Soleillet reveals the form of the Mueller matrix for fluorescence scattering whose parameters are directly defined in terms of the now-familiar fluorescence anisotropy parameter. If the scattering analyte is optically active, it is further shown how fluorescence detected circular dichroism and circularly polarized luminescence can be recovered, simultaneously and free of artifacts.     

Structural and magnetic studies on RPtIn deuterides (R=Tb,Er, Tm)

In this communication, structural and magnetic properties of RPtInD_1.3 (R=Tb, Er, Tm) deuterides are reported. For the first time deuterium-rich compounds were synthesized for the RPtIn family. The investigated deuterides crystallize with the hexagonal ZrNiAl-type crystal structure, with slightly different lattice constants with respect to the basic compounds. In general, the a-lattice constant exhibit contraction, while the c-lattice constant tends to increase upon introducing deuterium. The compounds with Tb and Er shows magnetic ordering at 95 K and 15.5 K, respectively. On the other hand, for Tm based sample no magnetic ordering was evidenced down to 2 K.     

Fast atom diffraction during grazing scattering from a MgO(001) surface

Fast neutral atoms and molecules with energies from 0.4 up to 3 keV are scattered under a grazing angle of incidence from a clean and flat MgO(001) surface. For “axial surface channeling” conditions, we observe defined diffraction patterns in the angular intensity distributions for scattered ³He and ⁴He atoms as well as H₂ molecules. The diffraction patterns are analyzed in terms of semiclassical trajectory calculations making use of projectile surface interaction potentials derived from density functional theory and from pair potentials calculated from Hartree–Fock wave functions. From comparison of measured and calculated diffraction patterns we deduced the rumpling of the topmost surface layer of MgO(001), i.e. an inward shift of Mg²⁺ ions with respect to O^2? ions, of (0.03±0.03) Å.     

Separately harmonic and subharmonic functions

Let u(x, y) be defined in B ₁×B ₂ where B ₁ ^m and B ₂ ⁿ , and assume that u(x, ·) harmonic for every fixed x and u(·, y) is subharmonic for every fixed y. We show that if u(·, y) is, in addition, C ² for each y then u is subharmonic in B ₁×B ₂ in both variables jointly.     

Prime ideals and radicals of centred extensions and tensor products

In this paper, we study prime ideals and radicals of centred extensions of rings. Obtained results are applied to tensor products of algebras over commutative rings. This research was partially supported by Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Brazil. The second-named author was also supported by KBN grant 2 P301 035 06.     

A new heuristic algorithm solving the linear ordering problem

The linear ordering problem is an NP-hard combinatorial problem with a large number of applications. Contrary to another very popular problem from the same category, the traveling salesman problem, relatively little space in the literature has been devoted to the linear ordering problem so far. This is particularly true for the question of developing good heuristic algorithms solving this problem.In the paper we propose a new heuristic algorithm solving the linear ordering problem. In this algorithm we made use of the sorting through insertion pattern as well as of the operation of permutation reversal. The surprisingly positive effect of the reversal operation, justified in part theoretically and confirmed in computational examples, seems to be the result of a unique property of the problem, called in the paper the symmetry of the linear ordering problem. This property consists in the fact that if a given permutation is an optimal solution of the problem with the criterion function being maximized, then the reversed permutation is a solution of the problem with the same criterion function being minimized.