Radiative kinks and fermionic zero modes in a (λφ6)1+1 model

We consider bidimensional scalar models including kink solutions _k (x). Using the hidden supersymmetric properties of the Dirac equation, we describe a general method to find normalizable fermionic zero modes. In particular, we apply the technique to a ( ⁶)₁₊₁ model. Going to the one-loop order of the effective potential, the emergence of a radiative kink provides an interesting scalar background in order to discuss the Dirac equation.     

Mössbauer and infrared spectroscopic studies of novel mixed valence states in cobaltous ferrocyanides and ferricyanides

Novel mixed valence states have been obtained by the treatment of cobaltous ferrocyanides (Co⁺²Fe^II) and ferricyanides (Co⁺²Fe^III) in an ozone flow. The CN stretching bands occur at 2085 cm^–1 for Co⁺²Fe^II and at 2160 cm^–1 for Co⁺²Fe^III. After the ozonization process of Co⁺²Fe^II, an intense band approximately at 2125 cm^–1 is detected. This intermediate band must correspond to a mixed valence state of the type: Fe^II–CN–Co²⁺–NC–Fe^III Mössbauer spectra recorded in situ during the ozonization of Co⁺²Fe^II show the presence of two components: a doublet with isomer shift and quadrupole splitting values close to the cobalti ferricyanide and a very broad line for the mixed valence state. From the Mössbauer and infrared spectra of the aged samples of the Co⁺²Fe^II after ozonization, a relaxation process to the initial state of the samples is observed but the mixed valence state is stable.     

Finite sphere packing and sphere covering

A basic problem of finite packing and covering is to determine, for a given number ofk unit balls in Euclideand-spaceE ^d , (1) the minimal volume of all convex bodies into which thek balls can be packed and (2) the maximal volume of all convex bodies which can be covered by thek balls. In the sausage conjectures by L. Fejes Tóth and J. M. Wills it is conjectured that, for alld5, linear arrangements of thek balls are best possible. In the paper several partial results are given to support both conjectures. Furthermore, some relations between finite and infinite (space) packing and covering are investigated.This paper was written while the first named author was visiting the Forschungsinstitut für Geistes- und Sozialwissenschaften at the University of Siegen.     

A connection between Fano configurations and Minkowski planes of odd order

It is shown in this paper that a pair of points contained in a Fano configuration in a projective plane of odd order cannot induce a Minkowski plane. From this result we derive that no pair of points in the Hughes plane of order 9 can induce a Minkowski plane.     

Interpolatory properties of best rationalL 1-approximations

In this paper the distribution of the zeros of the error function for bestL ₁-approximation by rational functions fromR _n,m is considered. It is shown that the maximal distance between such zeros isO(1/(n–m)), ifn > m.Communicated by Edward B. Saff.