Strongly countable dimensional compacta form the Hurewicz set

The hyperspaces of strongly countable dimensional compacta of positive dimension and of strongly countable dimensional continua of dimension greater than 1 in the Hilbert cube are homeomorphic to the Hurewicz set of all nonempty countable closed subsets of the unit interval [0,1]. These facts hold true, in particular, for covering dimension dim and cohomological dimension dimG, where G is any Abelian group.     

Effect of Ga doping on magneto-transport properties in colossal magnetoresistive La0.7Ca0.3Mn1−xGaxO3 (0<x<0.1)

Samples of La_0.7Ca_0.3Mn_1−xGa_xO₃ with x=0, 0.025, 0.05 and 0.10 were prepared by standard solid-state reaction. They were first characterized chemically, including the microstructure. The magnetic properties and various transport properties, i.e. the electrical resistivity, magnetoresistivity (for a field below 8 T), thermoelectric power and thermal conductivity measured each time on the same sample, are reported. The markedly different behaviour of the x=0.1 sample from those with a smaller Ga content, is discussed. The dilution of the Mn³⁺/Mn⁴⁺ interactions with Ga doping considerably reduces the ferromagnetic double exchange interaction within the manganese lattice leading to a decrease of the Curie temperature. The polaron binding energy varies from 224 to 243 meV with increased Ga doping.     

Multinuclear magnetic resonance study of some mesoionic oxatriazoles containing nitrogenous exocyclic groups

¹H,¹³C,¹⁴N and¹⁵N NMR measurements are reported for four mesoionic 1-oxa-2, 3, 4-triazoles containing exocyclic nitrogenous groups. The NMR signal assignments are discussed and compared with those previously published for some corresponding oxatriazoles. The results obtained support the proposed cyclic mesoionic structures for the compounds studied. The questions of possible charge delocalization and valence tautomerism are addressed. Compound with N^– H as a exocyclic group (Fig. 1) is found to be relatively unstable, this is attributed to proton migration in the corresponding non-cyclic form of this molecule.Published in Khimiya Geterotsikiicheskikh Soedinenii, No. 9, pp. 1260–1263, September, 1995.     

On quartics with three-divisible sets of cusps

 We study the geometry and codes of quartic surfaces with many cusps. We apply Gr?bner bases to find examples of various configurations of cusps on quartics. Received: 10 May 2002 / Revised version: 11 November 2002 Published online: 3 March 2003 Permanent address: Institute of Mathematics, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland. e-mail: rams@mi.uni-erlangen.de, rams@im.uj.edu.pl Research partially supported by the Schwerpunktprogramm ``Global methods in complex geometry' of the Deutsche Forschungsgemeinschaft, and by EAGER. Mathematics Subject Classification (2000): 14J25, 14J17     

Leggett-Williams norm-type theorems for coincidences

We study the existence of positive solutions to the operator equation Lx = Nx, where L is a linear Fredholm mapping of index zero and N is a nonlinear operator. Using the properties of cones in Banach spaces and Leray-Schauder degree for completely continuous operators, k-set contractions and condensing mappings, we obtain some refinements of the results established in [3] and [14]. Received: 9 July 2005; revised: 12 January 2006     

On automorphisms of n-dimensional Laguerre space

We examine some properties of two types of inversions in the isotropical model of n-dimensional Laguerre space. Moreover we establish an isomorphism between the isotropical and the cylinder models of the n-dimensional Laguerre space. We prove also that every automorphism of the n-dimensional Laguerre space is a composition of a pseudodilatation and some involutive maps.     

The measure of a translated ball in uniformly convex spaces

Let (E, ¦·¦) be a uniformly convex Banach space with the modulus of uniform convexity of power type. Let be the convolution of the distribution of a random series inE with independent one-dimensional components and an arbitrary probability measure onE. Under some assumptions about the components and the smoothness of the norm we show that there exists a constant such that |{·<t}–{·+r<t}|r ^q , whereq depends on the properties of the norm. We specify it in the case ofL spaces, >1.     

Crystal structure of m-nitrobenzoic anhydride

The title compound (C₁₄H₈N₂O₇,M _r =306.2) crystallizes in the orthorhombic space group Pbca witha=6.962(1).b=24.688(1), andc=15.890(1)Å,V=2731.0 ų,D _x =1.489 g·cm^–3 forZ=8,=0.98 mm^–1,F(000)=1296,T=293 K. FinalR=0.053 for 1873 observed reflections. The structure was solved by direct methods. Approximately planar molecules lie perpendicular to the [100] direction and show partial stacking. The structure is the first example of a symmetric anhydride which does not retain the symmetry in the crystal state. The two independent nitro groups twist out of the ring planes by 10.5 and 14.8°, respectively.     

Structure of 18-cyanoprogesterone,C22H29O2N

The crystal structure of 18-cyanoprogesterone was determined by X-ray diffraction methods:P2₁2₁2₁ a=7.436(2),b=11.322(2),c=22.642(2) Å. The structure was solved usingShelx-86. Final conventionalR=0.054.R _w =0.051 for 1841 reflections. TheA ring has an intermediate sofa-half-chair conformation with asymmetry parameters C _s ^/1 =11.0, C ₂ ^3,4 =14.9. The steroid skeleton exhibits a flattening of theA ring relative to the rest of the molecule. The progesterone side chain has a typical conformation, and the C16-C17-C20-O20 torsion angle is –19.0(6)°.     

In-trees and plane embeddings of outerplanar graphs

A notion of anin-tree is introduced. It is then used to characterize and count plane embeddings of outerplanar graphs. In-trees have also been applied in the study of independent vertex covers of faces in outerplanar graphs.This research was partially supported by the grant RP.I.09, from the Institute of Informatics, University of Warsaw. Hospitality of the Institute of Datalogy, University of Copenhagen where this research has been completed is gratefully acknowledged.