Weak density of smooth maps for the Dirichlet energy between manifolds

We prove that given a simply connected compact manifold M and a closed manifold N, any map in the Sobolev space W ^1,2(M,N) can be approximated weakly by smooth maps between M and N. Submitted: September 2002, Final version: November 2002.     

Magnetic and transport properties of double distorted perovskites CaCuMn6O12 and CaCu2Mn5O12

Magnetic and transport properties of double distorted perovskites CaCuMn₆O₁₂ and CaCu₂Mn₅O₁₂ are studied in a range 2–300 K. The leading role in magnetism of these compounds belongs to antiferromagnetic exchange interaction of Cu²⁺ in square coordination with Mn³⁺/Mn⁴⁺ in octahedral coordination. The values of saturation magnetization indicate that Mn³⁺ ions in square coordination are coupled ferromagnetically with Mn³⁺/Mn⁴⁺ in octahedral coordination. The colossal magnetoresistance in the pellet samples is due assumingly to intergranular spin-polarized tunneling of current carriers.     

Endomorphism valued cohomology and gauge-neutral matter

For several physically interesting Calabi-Yau manifolds, we count and parametrize gauge-neutral matter particles occurring in corresponding superstring compactifications. To this end, we use the technique of exact and spectral sequences and then describe and discuss our results in the more familiar tensor notation.Supported by the Robert A. Welch Foundation and the NSF Grant: PHY 8605978. On leave of absence from the Ruder Bokovi Institute, Bijenika 54, YU-41000 Zagreb, Croatia, Yugoslavia     

Solvent extraction and lanthanide complexation studies with new terdentate ligands containing two 1,3,5-triazine moieties

The extracting agent 2,6-bis(4,6-di-pivaloylamino-1,3,5-triazin-2-yl)-pyridine (L(5)) in n-octanol was found, in synergy with 2-bromodecanoic acid, to give D(Am)/D(Eu) separation factors (SFs) between 2.4 and 3.7 when used to extract the metal ions from 0.02-0.12 M HNO(3). Slightly higher SFs (4-6) were obtained in the absence of the synergist when the ligand was used to extract Am(III) and Eu(III) from 0.98 M HNO(3). In order to investigate the possible nature of the extracted species crystal structures of L(5) and the complex formed between Yb(III) with 2,6-bis(4,6-di-amino-1,3,5-triazin-2-yl)-pyridine (L(4)) were also determined. The structure of L(5) shows 3 methanol solvent molecules all of which form 2 or 3 hydrogen bonds with triazine nitrogen atoms, amide nitrogen or oxygen atoms, or pyridine nitrogen atoms. However, L(5) is relatively unstable in metal complexation reactions and loses amide groups to form the parent tetramine L(4). The crystal structure of Yb(L(4))(NO(3))(3) shows ytterbium in a 9-coordinate environment being bonded to three donor atoms of the ligand and three bidentate nitrate ions. The solvent extraction properties of L(4) and L(5) are far inferior to those found for the 2,6-bis-(1,2,4-triazin-3-yl)-pyridines (L(1)) which have SF values of ca. 140 and theoretical calculations have been made to compare the electronic properties of the ligands. The electronic charge distribution in L(4) and L(5) is similar to that found in other terdentate ligands such as terpyridine which have equally poor extraction properties and suggests that the unique properties of L(1) evolve from the presence of two adjacent nitrogen atoms in the triazine rings.     

The complete matter sector in a three-generation compactification

We consider a Calabi-Yau compactification paradigm with three light generations and anR-symmetry. From a special form of the Tian-Yau manifold, we also construct a new three-generation model with markedly different phenomenology. Thecomplete spectrum of all light matter fields is obtained in a universal way and moreover in a physically suitable basis, allowing a straightforward analysis of all their couplings. Here we discuss all the renormalizable Yukawa couplings. This computation can equally well be repeated for all compactification models based on Calabi-Yau complete intersections in products of homogeneous spaces.     

Behavior of the magnetic subsystems in Nd2BaNiO5

The temperature dependences of the heat capacity, the magnetic susceptibility, and the splitting of the ground Kramers doublet of the Nd³⁺ ion in the chain magnet Nd₂BaNiO₅ are studied. An antiferromagnetic phase transition manifests itself as anomalies in all these dependences. The parameters of the Nd-Ni and Nd-Nd interactions are estimated. The field dependence of the magnetization has two anomalies. A strong magnetic anisotropy prevents the magnetic moments of the Nd³⁺ ion from deviating from axis c in the crystal even in an external magnetic field. The processes of magnetization and the internal specific features of a chain of spins S = 1 are discussed.     

Indentation-induced deformations of GaAs(011) at a high temperature

Indentation tests were performed at a high temperature on GaAs(011). This orientation allowed the activation of normal and inclined slip systems. Samples with two different thicknesses were prepared and a large range of loads was used. Observations on decreasing scales were carried out using different microscopies and more particularly transmission electron microscopy on thin foils prepared by the focused-ion-beam technique. The back side of the thinnest samples could be deformed using the highest loads. The deformation was observed to be anisotropic on the back side as well as at the indented surface. On one side of the indentation, an anisotropic climb of matter was revealed and associated with microtwinning development. Convergent-beam electron diffraction as well as chemical etching allowed us to determine rigorously the polarity of the samples and the character of dislocations ( for g) generated by the indenter. The dislocations extending deeper into the samples were determined to be fdislocations. This result was discussed in view of the difference between the core reconstructions and mobilities of fand gdislocations.     

Space-Time Dynamics of?Gazeau-Klauder Coherent States in?Power-Law Potentials

Gazeau-Klauder coherent states are developed for power-law potentials and their evolution in space and time is analyzed. We show that these states follow classical dynamics as long as the underlying energy spectrum is linear, otherwise they follow a classical-like evolution upto a few classical periods and disperse thereafter, despite its special construction. Auto-correlation function and probability density as a function of space and time explain the spatio-temporal behavior of these states.