Let Σ be a σ-algebra of subsets of a set Ω and $B(\Sigma)$ be the Banach space of all bounded Σ-measurable scalar functions on Ω. Let $\tau(B(\Sigma),ca(\Sigma))$ denote the natural Mackey topology on $B(\Sigma)$. It is shown that a linear operator T from $B(\Sigma)$ to a Banach space E is Bochner representable if and only if T is a nuclear operator between the locally convex space $(B(\Sigma),\tau(B(\Sigma),ca(\Sigma)))$ and the Banach space E. We derive a formula for the trace of a Bochner representable operator $T:B({\cal B} o)\rightarrow B({\cal B} o)$ generated by a function $f\in L^1({\cal B} o, C(\Omega))$, where Ω is a compact Hausdorff space.

This article discusses the objectives of the Stone Age Man in Caves of the Tatra Mountains project, which aims to explain the mysterious absence of evidence for the Palaeolithic in the Tatra Mountains of Eastern Europe. We present preliminary work from Hučivá Cave, which demonstrates clear traces of Magdalenian settlement within this region.

The photoelectromagnetic (PEM) investigations are proposed for determination of diffusion length of carriers in graphene. The presented measurements are performed in Corbino configuration using noncontact technique. The circular PEM currents are detected in an outer coil by induction if illumination intensity is periodically varied. The theoretical dependence of PEM response on magnetic field induction, intensity and spatial distribution of illumination as well as on frequency of illumination chopping is presented. Experimental PEM data are presented for graphene films grown by CVD processing on a cooper foil and transferred onto a glass substrate. The presented method of investigations should be essential for development of graphene electronic and optoelectronic devices.