A New Route to 3-Phosphonylpyrazoles

The regioselective synthesis of 3-diethoxyphosphonopyrazoles has been accomplished through the addition of aryl or alkyl hydrazines to (3-ethoxyacryloyl)phosphonic acid diethyl ester. An example of hydrolysis of the pyrazolephosphonic ester to the corresponding acid is described.     

SO(2) Symmetry of a Maxwell p-Form Theory

We find a universal SO(2) symmetry of a p-form Maxwell theory for both odd and even p. For odd p, it corresponds to the duality rotations but for even p, it defines a new set of transformations which is not related to duality rotations. In both cases, a symmetry group defines a subgroup of the O(2,1) group of R-linear canonical transformations which has also a natural representation on the level of quantization condition for p-brane dyons.     

Diastereoselective synthesis of tetrahydrofurans via reaction of gamma,delta-epoxycarbanions with aldehydes

[reaction: see text] Hydroxymethyl-substituted tetrahydrofurans were prepared with high diastereoselectivity by reaction of the carbanion derived from 3,4-epoxybutyl phenyl sulfone with aldehydes in the presence of a mixture of lithium and potassium tert-butoxides. Initial formation of aldol-type adducts is a nondiastereoselective but reversible process; thus, subsequent formation of one main diastereoisomer is controlled by the relative rates of cyclization. The configuration of the carbon stereocenter at the oxirane ring is inverted in the course of the S(N)2 process, and two new centers are created diastereoselectively.     

Coordination modes of 2-mercapto-1,3-benzothiazolate in gallium and indium complexes

2-Mercapto-1,3-benzothiazole (mbztH) may act as a chelating or bridging ligand. In this study, reactions of mbztH with Me₃Ga and Me₃In were examined. The products were characterized by NMR spectroscopy, elemental analyses, melting point, and molecular weight determinations. Formation of mononuclear chelating complexes Me₂M(mbzt) (M = Ga, In) was observed in solutions. Crystallization of Me₂M(mbzt) yielded uncommon non-symmetrical dinuclear complexes Me₄M₂(mbzt)₂, in which one metal is bonded to two sulfurs and the other to two nitrogens.     

Crystal structure and magnetic properties of Ce7Ni5±xGe3±xIn6 and Pr7Ni5±xGe3±xIn6

The indides Ce₇Ni_5±xGe_3±xIn₆ and Pr₇Ni_5±xGe_3±xIn₆ were synthesized from the elements by arc-melting of the components. Single crystals were grown via special annealing sequences. Both structures were solved from X-ray single crystal diffraction data: new structure type, P6/m, Z=1, a=11.385(2), c=4.212(1) Å, wR₂=0.0640, 634F² values, 25 variables for Ce₇Ni_4.73Ge_3.27In₆ and a=11.355(6), c=4.183(2) Å, wR₂=0.0539, 563F² values, 25 variables for Pr₇Ni_4.96Ge_3.04In₆. Both indides show homogeneity ranges through Ni/Ge mixing (M sites). This new structure type can be derived from the AlB₂ structure type by a substitution of the Al and B atoms by CeM₁₂ and NiIn₆Ce₃ polyhedra (tricapped trigonal prism). Magnetic susceptibility measurements on a polycrystalline sample of Ce₇Ni₅Ge₃In₆ indicated Curie-Weiss like paramagnetic behavior down to 1.71 K with the effective magnetic moment slightly reduced in relation to the value expected for trivalent cerium ions. No magnetic ordering is evident.     

Bis(tetraethylammonium) tetrabromocobaltate(II) and bis(tetrabutylammonium) tetrabromomanganate(II): structure and magnetic properties

The crystal structures of tetrabromocobaltate(II) and tetrabromomanganate(II) salts of general formula [(C₂H₅)₄N]₂[CoBr₄] (1) and [(C₄H₉)₄N]₂[MnBr₄] (2) were determined. The manganese and cobalt cations are four-coordinated by bromide anions and they adopt a slightly distorted tetrahedral coordination. In the structure of both compounds there are neither hydrogen bonds nor any unusual short-range intermolecular interactions. Magnetic measurements of the powdered samples gave negative values of the Weiss constants equal to −4.9 and −1.1 K for (1) and (2), respectively, which suggest antiferromagnetic interactions to be transferred within the crystal lattice.     

On formal Laurent series

Several kinds of formal Laurent series have been introduced with some restrictions so far. This paper systematically sets up a natural definition and structure of formal Laurent series without those restrictions, including introducing a multiplication between formal Laurent series. This paper also provides some results on the algebraic structure of the space of formal Laurent series, denoted by \mathbbL\mathbb{L}. By means of the results of the generalized composition of formal power series, we define a composition of a Laurent series with a formal power series and provide a necessary and sufficient condition for the existence of such compositions. The calculus about formal Laurent series is also introduced.     

Ultrasonic system for accurate distance measurement in the air

This paper presents a system that accurately measures the distance travelled by ultrasound waves through the air. The simple design of the system and its obtained accuracy provide a tool for non-contact distance measurements required in the laser’s optical system that investigates the surface of the eyeball.