Three Electrons in a Two-Dimensional Parabolic Trap: The Relative Motion Solution

In agreement with the Kohn theorem the relative motion (rel) of three electrons in a two-dimensional parabolic trap separates from the centre-of-mass (CM) motion. By introducing new coordinates the Hamiltonian for relative motion in the approximation of non-interacting electrons can be taken to the normal form. The eigenstates of the normalized Hamiltonian are products of the Fock-Darwin states for normal modes. The energy levels for relative motion are obtained by diagonalizing the exact Hamiltonian in the eigenbasis for the non-interacting case. In this basis the interaction matrix elements can be obtained in the analytical form. Since the rank of the Hamiltonian matrix is significantly reduced, the calculations are faster and more accurate than those for the full (CM + rel) motion. This advantage is especially important for the calculations of excited states and the analysis of energy spectra.     

Lattice valued intuitionistic fuzzy sets

In this paper a new definition of a lattice valued intuitionistic fuzzy set (LIFS) is introduced, in an attempt to overcome the disadvantages of earlier definitions. Some properties of this kind of fuzzy sets and their basic operations are given. The theorem of synthesis is proved: For every two families of subsets of a set satisfying certain conditions, there is an lattice valued intuitionistic fuzzy set for which these are families of level sets. The research supported by Serbian Ministry of Science and Technology, Grant No. 1227.     

Lanthanum nitrate decomposition by both temperature programmed heating and citrate gel combustion

Thermal decomposition of lanthanum nitrate to lanthanum oxide was carried out by both temperature programmed heating (TPH) and citrate-gel combustion. The temperature programmed heating was carried out under flow of oxidizing (air), neutral (nitrogen) and reducing (25 vol.% hydrogen+argone mixture) gases, and the processes were controlled by simultaneous thermogravimetry and differential thermal analysis. It was shown that hydrogen atmosphere helps to reduce temperatures of all decomposition steps. The results of TPH were utilized to check the nature of residues in the products of lanthanum nitrate-to-oxide conversion performed via citrate-gel combustion technique.     

Inherited LU-factorizations of matrices

Various types of LU-factorizations for nonsingular matrices, where L is a lower triangular matrix and U is an upper triangular matrix, are defined and characterized. These types of LU-factorizations are extended to the general m × n case. The more general conditions are considered in the light of the structures of [C.R. Johnson, D.D. Olesky, P. Van den Driessche, Inherited matrix entries: LU factorizations, SIAM J. Matrix Anal. Appl. 10 (1989) 99-104]. Applications to graphs and adjacency matrices are investigated. Conditions for the product of a lower and an upper triangular matrix to be the zero matrix are also obtained.     

Synthesis and thermal crosslinking of oxazolidine‐functionalized polyurethanes

A new oxazolidine derivative was obtained from phenol, 2‐amino‐2‐methylpropane‐1,3‐diol and paraformaldehyde. The reaction of this novel oxazolidine diol with phenylisocyanate lead to a urethane model compound which can be polymerized thermally by oxazolidine ring opening to give a Mannich bridge structure. Linear segmented polyurethanes were prepared by reaction of different ratios of oxazolidine diol and commercial polyethylenglycol (M_w ～ 400) with 4,4′‐methylenbis (cyclohexylisocyanate) (HMDI, 90% isomers mixture). The polyurethanes were thermally characterized and crosslinked by oxazolidine ring opening to obtain materials which showed improved thermal stability. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4965–4973, 2007     

AFM, SEM and GIXRD studies of thin films of red polycarbazolyldiacetylenes

In this paper we report the results of a morphological and structural investigation on film properties of a soluble polydiacetylene, the poly[1,6-bis(3,6-dihexadecyl-N-carbazolyl)-2,4-hexadiyne] (polyDCHD-HS). The red films of this polymer, prepared by standard spin-coating techniques, revealed absence of linear dichroism and birefringence in contrast with the ordered mesophases detected by powder X-ray studies. In order to interpret the optical behavior of this polymer, we performed AFM and SEM studies of polyDCHD-HS films spun on hydrophylic and hydrophobic glass substrates. We found the presence of surfaces organized in rod-like particles, more regularly oriented on the hydrophylic substrate. GIXRD studies, carried out on films sufficiently thick to allow the observation of the diffraction pattern, reveled the presence of a lamellar structure with a spacing of 3.22 nm. The low intensity of the diffraction peaks and the isotropic linear optical properties of the films show that the lamellar mesophases are not extended over large areas. These findings were compared with the data obtained from AFM and SEM studies on films of two other polydiacetylenes, the poly[1-(3,6-dihexadexyl-N-carbazolyl)-6-(N-carbazolyl)-2,4-hexadyine] (polya-DCHD) and the poly[1,6-bis(3,6-dipalmitoyl-N-carbazolyl)-2,4-hexadyine] (polyDPCHD), spun on hydrophylic glass substrate. The results confirmed the presence of nodular morphologies which seem to be a general characteristic of this class of materials. The particles organization appears instead related to the chemical nature of the substituents on the carbazolyl rings.     

Cinnamic acid amides and lignanamides from Aptenia cordifolia

Examination of the hydroalcoholic extract of the leaves of Aptenia cordifolia has afforded three cinnamic acid amides and two lignanamides. Structures were established on the basis of spectroscopic data, including 2D-NMR analyses.