Einmal ist keinmal. Peculiar burial practices of prehistoric communities settling the Lublin-Volhynia Upland in the Early Iron Age

The study addresses remains of two peculiar graves unearthed at the site Mikulin 9 in the Dobużek Scarp (Pol. Skarpa Dobużańska) area in Western Volhynia. Unique character of the burials under consideration consists in the peculiarity of funeral ritual performed, scenario of which was basically divided into two acts of burning of the deceased – once on cremation pyres, and then in the eventual places of their interment (grave pits). Both the graves under consideration as well as analogical finds from the western part of the Lublin-Volhynian Upland and its northern foreland can be connected with an impact form the Pontic area and dated back to the Early Scythian Period. Historically, their presence is commonly considered as a result of westward migrations of forest-steppe people form the area of nowadays Ukraine triggered by the appearance of Indo-Iranian Scythian tribes. In the case of the presented burials no less significant from the peculiar eastern burial rite performed seem their localization. When discussing the Dobużek Scarp area as a destiny point of one of such migrations, clearly Pontic character of the escarpment’s physiography should be taken into consideration. The local conditions of the already unsettled loess paha of Dobużek escarpment must have peculiarly attracted pastoral communities arriving from the east. Moreover, the graves were placed in a very exposed point within the preexisting prehistoric landscape, to wit – they were dug into today non-existent but then dominating the area long barrows of the Funnel Beaker Culture. It seems likely that by the act of burying their kinsman into the exposed Eneolithic mounds the incomers tried to create an ancestral tie with the area and thereby justify their presence “here and now”.

Gateaux Differentiability of Convex Functions and Weak Dentable Set in Nonseparable Banach Spaces

In this paper, we prove that if C⁎⁎ is a ε-separable bounded subset of X⁎⁎, then every convex function g≤σC is Ga^teaux differentiable at a dense Gδ subset G of X⁎ if and only if every subset of ∂σC(0)∩X is weakly dentable. Moreover, we also prove that if C is a closed convex set, then dσC(x⁎)=x if and only if x is a weakly exposed point of C exposed by x⁎. Finally, we prove that X is an Asplund space if and only if, for every bounded closed convex set C⁎ of X⁎, there exists a dense subset G of X⁎⁎ such that σC⁎ is Ga^teaux differentiable on G and dσC⁎(G)⊂C⁎. We also prove that X is an Asplund space if and only if, for every w⁎-lower semicontinuous convex function f, there exists a dense subset G of X⁎⁎ such that f is Ga^teaux differentiable on G and df(G)⊂X⁎.

Entropy and rotation sets: A toy model approach

Given a continuous dynamical system [Formula: see text] on a compact metric space [Formula: see text] and a continuous potential [Formula: see text], the generalized rotation set is the subset of [Formula: see text] consisting of all integrals of [Formula: see text] with respect to all invariant probability measures. The localized entropy at a point in the rotation set is defined as the supremum of the measure-theoretic entropies over all invariant measures whose integrals produce that point. In this paper, we provide an introduction to the theory of rotation sets and localized entropies. Moreover, we consider a shift map and construct a Lipschitz continuous potential, for which we are able to explicitly compute the geometric shape of the rotation set and its boundary measures. We show that at a particular exposed point on the boundary there are exactly two ergodic localized measures of maximal entropy.

Sum of two inner functions and exposed points in H1

If h is an outer function in H1 then it is shown that h = (q1 + q2)g where both q1 and q2 are inner functions with Im almost everywhere, and g is a strong outer function (equivalently, g/∥g∥1 is an exposed point of the unit ball of H1). If q1 + q2 is nonconstant then such an h is not strongly outer. Moreover a sum of two inner functions is studied.

Report on Archives of the Popular and Revolutionary Republic of Guinea in Conakry

Before I came to Conakry I had been warned that the archives were in poor condition, had suffered damage from the elements and from the termites, and were not well maintained. One scholar who worked here in the 1960s spoke not only of termite damage but of chickens and goats wandering through. To my pleasant surprise I have found that the archives are fairly extensive, that they are in relatively good condition, and that they are being maintained as well as can be expected. The locale is not an ideal one, though its location on an exposed point of land near the sea makes for pleasant breezes and good cross-ventilation. There is no control of either temperature or humidity in the building. While some dossiers are partially damaged, I have not seen one that is not usable. My biggest problem has been the handwriting of the clerks and administrators who made copies of correspondence in local registers.The original work of organizing the archives was done by Madeira Keita, the R.D.A. leader, who worked here during the early 1950s. The classification system he set up was maintained by Damien d'Almeida, who published a repertoire in 1962. The repertoire is fairly detailed and it notes when a dossier or a register is in poor condition. The classification system is sound, though occasionally one finds documents, reports, and correspondance grouped together in a haphazard manner. The problem was more the sloppy recordkeeping of the colonial administration than the work of the undermanned archivists. In general, I have been to find what I have wanted and the organization has been very useful. The present archivist, Moctar Ba, is competent and seems conscientious.

On strongly exposing functionals

Let X be a real Banach space and let K be a bounded closed convex subset of X. We prove that the set of strongly exposing functions K^ of K is a (norm) dense G8 in X* if and only if for any bounded closed convex subset C such that K⊄C, there exists a point x in K which is a strongly exposed point of conv (C ∪ K). As an application, we show that if X* is weakly compact generated, then for any weakly compact subset K in X, the set K^ is a dense G8 in X*.

The Perception of Briefly Exposed Point-Sources of Light

Point-sources of light (dots) were exposed for 10 to 50 msec, before five dark-adapted subjects in a dimly illuminated room. During voluntary fixation with one eye, the target was exposed some 10° on the nasal side of the optic axis. The intensity X duration of all targets was 2 X threshold and they consisted of either a single dot, or a pair of dots separated by a distance that was less than that required for two-point discrimination. In two-thirds of trials both the single-dot and the two-dot targets were perceived as short thin lines of various orientation. Although individual percepts were unpredictable, there was a preferred or most likely orientation for responses to the single-dot target; this was near to the horizontal for all five subjects. There was no significant difference between the preferred orientations for single-dot targets tested at sites more than 1° apart in the visual field. When two single-dot targets, separated by about 1°, were exposed simultaneously, the orientations of the perceived lines sometimes differed by as much as 80°; occasionally, one target was reported as a dot while the other was seen as a thin line. If the single-dot was briefly exposed between two continuously visible and parallel straight lines, the target usually appeared as a thin line, parallel to the framing lines. Some of these results appear to be consistent with the hypothesis that the human visual cortex, like that of the cat and monkey, contains neurones that are orientation specific.