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     

On Non-Continuous Dirichlet Processes

We introduce here some Itô calculus for non-continuous Dirichlet processes. Such calculus extends what was known for continuous Dirichlet processes or for semimartingales. In particular we prove that non-continuous Dirichlet processes are stable under C ¹ transformation.     

Large Deviations of Empirical Measures Under Symmetric Interaction

We prove the large deviation principle for the joint empirical measure of pairs of random variables which are coupled by a totally symmetric interaction. The rate function is given by an explicit bilinear expression, which is finite only on product measures and hence is non-convex.     

Plasma-driven inflation

The possibility of inflation without any genuine scalar is discussed. It is suggested that drops of primordial plasma may drive inflation. The model, although naive, is consistent with observational data.     

Two-point Padé approximants for formal Stieltjes series

We prove that certain two-point Padé approximants occupying the diagonal of the Padé table form monotone sequences of lower and upper bounds uniformly converging to a Stieltjes function. The results can be applied to the theory of inhomogeneous media for the calculation of the bounds on the effective transport coefficients of heterogeneous materials.     

A Goal Programming model of the reference point method

Real-life decision problems are usually so complex they cannot be modeled with a single objective function, thus creating a need for clear and efficient techniques of handling multiple criteria to support the decision process. The most commonly used technique is Goal Programming. It is clear and appealing, but in the case of multiobjective optimization problems strongly criticized due to its noncompliance with the efficiency (Pareto-optimality) principle. On the other hand, the reference point method, although using similar control parameters as Goal Programming, always generates efficient solutions. In this paper, we show how the reference point method can be modeled within the Goal Programming methodology. It allows us to simplify implementations of the reference point method as well as shows how Goal Programming with relaxation of some traditional assumptions can be extended to a multiobjective optimization technique meeting the efficiency principle.     

Some remarks on the theorem of Möbius

H.S.M. Coxeter in his book Introduction to Geometry quotes a theorem of Möbius. In the paper two counterexamples are given. A corrected version of the theorem is stated and proved.     

Diffractive proteon fragmentation in 16, 32, and 110 GeV/cK − p interactions and the diffractive production of heavy quarks(s\bar s,c\bar c)

The inclusive proton diffraction dissociation cross sections in 16, 32, and 110 GeV/cK ^? p interactions are determined from the spike nearx=1 in the inclusive negative particle spectra and are compared to those obtained inK?p interactions using other selection methods at various energies. The same procedure is applied to events containing aV ⁰ in order to obtain the cross section for diffractive \(s\bar s\) production. While the total cross section for proton diffraction is found to be approximately constant in the energy range studied here, proton diffraction yielding an \(s\bar s - pair\) is found to increase significantly. In particular it is almost constant at 85 μb forΛ ⁰ and Σ production but for \(NK\bar K\) it rises from zero at 16 GeV.c to about 200 μb at 110 GeV/c. From the result for \(s\bar s\) diffractive production an estimate for the \(c\bar c\) diffractive production cross section of approximately 1–10 μb at 110 GeV/c is obtained.     

Experimental upper limits for hadronic and axion decays of the γ(1S)

A search for the decays γ→ρπ, γ→J/ψX and γ→γa (whereX is undetermined and a is an axion) has been completed using the LENA detector at the DORIS storage ring. No evidence for any of these processes was found. For these decay modes we set branching fraction upper limits (90% C.L.) of 2.1×10^?3, 2.0×10^?2 and 9.1×10^?4, respectively.     

Neutron diffraction study of RECo2Si2 intermetallics

A neutron diffraction study of polycrystalline RECo₂Si₂ intermetallics (RE = Pr, Nd, Tb, Ho, Er) carried out at liquid helium temperature shows the presence of a collinear antiferromagnetic ordering of +?+? type. Magnetic moment is localized on RE ions only and amounts to the RE³⁺ free ion value. In ErCo₂Si₂ the magnetic moment is normal to the tetragonal unique axis, whereas in the remaining compounds the magnetic moment is aligned along it. Néel points were determined from the temperature dependence of magnetic peak heights.