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.     

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.     

Stationary axisymmetric solutions in the vacuum Jordan-Brans-Dicke theory

It is shown that any stationary axisymmetric solution to the vacuum field equations of the Jordan-Brans-Dicke (JBD) theory may be obtained from a composition of any stationary axisymmetric vacuum Einstein spacetime with the Weyl class of metrics. Thus, generating solution techniques can be used to obtain any stationary axisymmetric JBD vacuum solution. In this manner, C. B. G. McIntosh's results concerning this topic are improved upon.     

Effect of Xe ion irration of Fe/Sn bilayers

Films of Fe (20 nm) and Sn (40 nm) have been deposited by PVD onto Al supports and irradiated with 100 keV Xe ions at a dose of 5×10¹⁵ ions/cm². Scanning electron microscopy (SEM) shows that the irregular morphology of deposited Sn is considerably flattened by irradiation, which produces also a noticeable sputtering of Sn. Conversion electron Mössbauer spectroscopy (CEMS) reveals the formation at the interface of a variety of intermetallic phases which is enhanced by irradiation. These phases, seem to be insensible to prolonged (several months) room temperature aging. Their thermal stability under annealing at temperature up to 523 K has also been investigated.