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.     

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.     

Variations on the theme of repeated distances

We give an asymptotically sharp estimate for the error term of the maximum number of unit distances determined byn points in ^{d, d}4. We also give asymptotically tight upper bounds on the total number of occurrences of the favourite distances fromn points in ^{d, d}4. Related results are proved for distances determined byn disjoint compact convex sets in ².At the time this paper was written, both authors were visiting the Technion — Israel Institute of Technology.     

On the infimum of the local time of a Wiener process

Let {W(t), t0} be a standard Wiener process, and let L(x, t) be its jointly continuous local time. Define

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.