Thee + e −→¯nn cross section predicted remarkably larger than thee + e −→¯pp one

It is shown that all global analyses of nucleon electromagnetic form factor data predict the electron-positron annihilation into neutron-antineutron cross section (for which there are no data till now) to be in a finite energy region substantially larger than the electron-positron annihilation into the proton-antiproton one.Dedicated to the memory of M. Gmitro.     

Aldo Cossu’s Work in Finite Geometry

A survey of the contributions of Aldo Cossu in finite geometry is given. Dedicated to the memory of Professor Aldo Cossu     

On the Behavior of Some Second Order Nonlinear Differential Equations

Qualitative behavior of second order nonlinear differential equations of type y″+p(t)y+q(t)f(y)=0, is studied. It includes properties such as positivity, number of zeros, oscillating nature, boundedness and monotonicity of the solutions.     

Mappings of finite distortion: Hausdorff measure of zero sets

We prove that a for a mapping f of finite distortion , the -Hausdorff measure of any point preimage is zero provided is integrable, with , and the multiplicity function of f is essentially bounded. As a consequence for we obtain that the mapping is then open and discrete. Received: 18 June 2001 / Revised version: 31 January 2002 / Published online: 27 June 2002     

Fejér means of functions on noncommutative Vilenkin groups with respect to the character system

Summary It is known that the Fejér means - with respect to the character system of the Walsh, and bounded Vilenkin groups - of an integrable function converge to the function a.e. In this work we discuss analogous problems on the complete product of finite, not necessarily Abelian groups with respect to the character system for functions that are constant on the conjugacy classes. We find that the nonabelian case differs from the commutative case. We prove the a.e. convergence of the (C,1) means of the Fourier series of square integrable functions. We also prove the existence of a function f∊L^q for some q >1 such that sup |σ_n f | = + ∞ a.e. This is a sharp contrast between the Abelian and the nonabelian cases.     

Order Embeddings with Irrational Codomain: Debreu Properties of Real Subsets

The objective of this paper is to investigate the role of the set of irrational numbers as the codomain of order-preserving functions defined on topological totally preordered sets. We will show that although the set of irrational numbers does not satisfy the Debreu property it is still nonetheless true that any lower (respectively, upper) semicontinuous total preorder representable by a real-valued strictly isotone function (semicontinuous or not) also admits a representation by means of a lower (respectively, upper) semicontinuous strictly isotone function that takes values in the set of irrational numbers. These results are obtained by means of a direct construction. Moreover, they can be related to Cantor’s characterization of the real line to obtain much more general results on the semicontinuous Debreu properties of a wide family of subsets of the real line.      

Flat Information Geometries in Black Hole Thermodynamics

The Hessian of either the entropy or the energy function can be regarded as a metric on a Gibbs surface. For two parameter families of asymptotically flat black holes in arbitrary dimension one or the other of these metrics are flat, and the state space is a flat wedge. The mathematical reason for this is traced back to the scale invariance of the Einstein–Maxwell equations. The picture of state space that we obtain makes some properties such as the occurence of divergent specific heats transparent.Supported by VR.     

A simple proof of Sanov’s theorem*

A simple self-contained proof of Sanov's theorem in τ-topology is given, well suited for a first course on large deviations. *This work was supported by the Hungarian National Foundation for Scientific Research under Grant T046376