Conformally flat null electromagnetic field

A class of conformally flat solutions for null electromagnetic field is presented. Explicit forms of the field tensors are also given. The null field is characterized by shear-free, twist-free, expansion-free, and geodetic null congruences.     

Haloacetylated enol ethers. 6 [5]. Synthesis of 4,5-trimethylene-4,5-dihydroisoxazoles

The investigation of the effect of the cyclopentane ring on the regiochemistry of the reactions of 2-acetylcyclopentanones 1a-d and β-methoxyvinyl trifluoromethyl ketone derivative 2a with hydroxylamine hydrochloride is reported. The reactions give regiospecifically the 4,5-trimethylene-4,5-dihydroisoxazoles 3a-d in good yields.     

Au and Cu Atoms on NaCl(001): a single-atom based memory device prototype?

We present a first-principle study of gold and copper atoms adsorbed in NaCl(001) surfaces. Motivated by a recent STM experiment on this subject, the electronic and magnetic properties of Au and Cu atoms are investigated, as well as the modifications in these properties under charge injection. Similarities of these systems and the corresponding isolated atom are exploited. A discussion about the possibility of applying the studied systems on high-density memory devices is addressed.     

Rhenium complexes of tris(pyrazolyl)methanes and sulfonate derivative

The trioxo [ReO(3){SO(3)C(pz)(3)}] (1) (pz = pyrazolyl) and oxo [ReOCl{SO(3)C(pz)(3)}(PPh(3))]Cl (2) compounds with tris(pyrazolyl)methanesulfonate were obtained by treatment of Re(2)O(7) or [ReOCl(3)(PPh(3))(2)], respectively, with Li[SO(3)C(pz)(3)], whereas [ReCl(3){HC(pz)(3)}] (3), [ReCl(3){HC(3,5-Me(2)pz)(3)}] (4) and [ReCl(4){eta(2)-HC(pz)(3)}] (5) were prepared by reaction of [ReOCl(3)(PPh(3))(2)] (3,4) or [ReCl(4)(NCMe)(2)] (5) with hydrotris(pyrazolyl)methane HC(pz)(3) (3,5) or hydrotris(3,5-dimethyl-1-pyrazolyl)methane HC(3,5-Me(2)pz)(3) (4). [ReO{SO(3)C(pz)(3)}{OC(CH(3))(2)pz}][ReO(4)] 6, with a chelated pyrazolyl-alkoxide, was derived from an unprecedented ketone-pyrazolyl coupling on reaction of crude 1 with acetone. The compounds have been characterized by elemental analyses, IR and NMR spectroscopies, FAB-MS spectrometry and cyclic voltammetry and, in the case of 5 and 6, also by single-crystal X-ray diffraction. The electrochemical E(L) Lever parameter has been estimated, for the first time, for the SO(3)C(pz)(3)(-) and oxo ligands allowing the measurement of their electron-donor character and comparison with other ligands. Compounds 1, 2 and 6 appear to be the first tris(pyrazolyl)methanesulfonate complexes of rhenium to be reported.     

Transport properties of strongly correlated electrons in quantum dots studied with a simple circuit model

Numerical calculations are shown to reproduce the main results of recent experiments involving nonlocal spin control in quantum dots [Craig, Science 304, 565 (2004).]. In particular, the experimentally reported zero-bias-peak splitting is clearly observed in our studies. To understand these results, a simple "circuit model" is introduced and shown to qualitatively describe the experiments. The main idea is that the splitting originates in a Fano antiresonance, which is caused by having one quantum dot side connected in relation to the current's path. This scenario provides an explanation of the results of Craig et al. that is an alternative to the RKKY proposal, also addressed here.     

Singular rational curves with points of nearly-maximal weight

In this article we study rational curves with a unique unibranch genus-g singularity, which is of κ-hyperelliptic type in the sense of [27]; we focus on the cases $\kappa =0$ and $\kappa =1$, in which the semigroup associated to the singularity is of (sub)maximal weight. We obtain a partial classification of these curves according to the linear series they support, the scrolls on which they lie, and their gonality.     

Homomorphisms and congruences on regular semigroups with associate inverse subsemigroups

An associate inverse subsemigroup of a regular semigroup S is a subsemigroup T of S containing a least associate x* of each x ∈ S, in relation to the natural partial order ≤. In [1] the authors describe the structure of regular semigroups with an associate inverse subsemigroup, satisfying two natural conditions. In this paper we describe all *-homomorphisms and all *-congruences on such semigroups.