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At the turn of this century Durand, and Lagarias and Pleasants established that key features of minimal subshifts (and their higher-dimensional analogues) to be studied are linearly repetitive, repulsive and power free. Since then, generalisations and extensions of these features, namely α-repetitive, α-repulsive and α-finite (α ≥ 1), have been introduced and studied.We establish the equivalence of α-repulsive and α-finite for general subshifts over finite alphabets. Further, we studied a family of aperiodic minimal subshifts stemming from Grigorchuk's infinite 2-group G. In particular, we show that these subshifts provide examples that demonstrate α-repulsive (and hence α-finite) is not equivalent to α-repetitive, for α > 1. We also give necessary and sufficient conditions for these subshifts to be α-repetitive, and α-repulsive (and hence α-finite). Moreover, we obtain an explicit formula for their complexity functions from which we deduce that they are uniquely ergodic. [ABSTRACT FROM AUTHOR]

At the turn of this century Durand, and Lagarias and Pleasants established that key features of minimal subshifts (and their higher-dimensional analogues) to be studied are linearly repetitive, repulsive and power free. Since then, generalisations and extensions of these features, namely α-repetitive, α-repulsive and α-finite (α≥1), have been introduced and studied. We establish the equivalence of α-repulsive and α-finite for general subshifts over finite alphabets. Further, we studied a family of aperiodic minimal subshifts stemming from Grigorchuk’s infinite 2-group G. In particular, we show that these subshifts provide examples that demonstrate α-repulsive (and hence α-finite) is not equivalent to α-repetitive, for α>1. We also give necessary and sufficient conditions for these subshifts to be α-repetitive, and α-repulsive (and hence α-finite). Moreover, we obtain an explicit formula for their complexity functions from which we deduce that they are uniquely ergodic. [ABSTRACT FROM AUTHOR]

The article reports that the Hausdorff-Alexandroff Theorem states that any compact metric space is the continuous image of Cantor's ternary set C. Restricting the cardinality leads to a sufficient condition. the cardinality of a space, which is the continuous image of C. The restriction on cardinality is a necessary and there are compact Hausdorff spaces with cardinality.

Investigating the processes that led to the end of the last interglacial period is relevant for understanding how our ongoing interglacial will end, which has been a matter of much debate (see, for example, refs 1, 2). A recent ice core from Greenland demonstrates climate cooling from 122,000 years ago driven by orbitally controlled insolation, with glacial inception at 118,000 years ago. Here we present an annually resolved, layer-counted record of varve thickness, quartz grain size and pollen assemblages from a maar lake in the Eifel (Germany), which documents a late Eemian aridity pulse lasting 468 years with dust storms, aridity, bushfire and a decline of thermophilous trees at the time of glacial inception. We interpret the decrease in both precipitation and temperature as an indication of a close link of this extreme climate event to a sudden southward shift of the position of the North Atlantic drift, the ocean current that brings warm surface waters to the northern European region. The late Eemian aridity pulse occurred at a 65° N July insolation of 416 W m-2, close to today's value of 428 W m-2 (ref. 9), and may therefore be relevant for the interpretation of present-day climate variability. [ABSTRACT FROM AUTHOR]

Examination of stratum corneum (SC) content with tape stripping and a colorimetric method is increasingly used. We examined the possible use of microplates in tandem with a colorimetric method to examine SC removed with tape stripping. As a corollary to this examination, the homogeneity of tape strips was examined.The commonly used Lowry assay was adapted for 96-well plates. Tapes were divided into four regions and sample disks of 5 mm diameter were taken from each and analyzed for SC mass using the adapted Lowry assay.Homogeneity of SC removal over different areas across a tape strip is limited.Quantification of SC by means of a 96-well microplate-based colorimetric method is feasible and shortens the time of analysis. However, when using D-Squame® tape disks, SC removal on a limited area of the tape is not predictive for SC removal on the entire tape as removal is inhomogenous. Therefore, SC protein extraction should be performed on a large enough area, eventually on the entire tape when quantifying SC mass removed by tape stripping. [ABSTRACT FROM AUTHOR]

Tape stripping is a common method for investigating stratum corneum (SC) physiology as well as bioavailability and bioequivalence of topical drugs.To investigate the influence of procedures (anatomical site, pressure, pressure duration, tape removal rate) inherent in each stripping protocol on changes in skin physiology.Tape stripping was performed using tapes on the forearm, forehead and back. On the forearm different pressures (165 and 330 g cm−2), durations of pressure (2 and 10 s), and removal rate (slow and rapid removal) were used. Changes in skin physiology were evaluated by measurement of transepidermal water loss (TEWL) and hydration.A significant influence of all parameters on the TEWL increase as a function of tape strip number was observed. The fastest increase was demonstrated on the forehead, followed by the back and, lastly, the forearm. Rapid removal produced a protracted increase in comparison with slow removal. Pressure for 10 s induced a faster increase in TEWL than 2 s pressure. Likewise, pressure at 330 g cm−2 induced an earlier increase than pressure at 165 g cm−2. Skin hydration was not influenced by the variables tested.Tape stripping results are influenced dramatically by all investigated parameters. A dynamic SC stress test to investigate SC cohesion more closely is proposed based on the present observations. [ABSTRACT FROM AUTHOR]

Exposure to ultraviolet radiation or ozone leads to skin damage including oxidation of skin biomolecules, as well as to depletion of constitutive antioxidants. The highly organized stratum corneum forming the main barrier against most xenobiotics is particularly susceptible to such damage and possible barrier perturbation may be the consequence. Whereas ample evidence exists for an increased permeability for different solutes including water after exposure to ultraviolet radiation, such an effect has not yet been reported for ozone. This study reports on the effect of such oxidative stressors using the hairless mouse as the skin model and measuring temperature-controlled transepidermal water loss (TEWL) as an indicator for skin barrier integrity. First, a strong dependency of the TEWL on skin temperature was observed, an effect that was clearly more pronounced than that found in man. Given this temperature dependency in untreated animals, we proceeded to determine the effects of both ultraviolet radiation and ozone on TEWL over a relevant physiological skin temperature range. Solar-simulated ultraviolet radiation (0.75-3 minimal erythemal dose) resulted in a delayed and dose-dependent skin barrier disruption over the entire temperature range investigated. Conversely, daily ozone exposure at 2 ppm for 1 week, however, did not significantly alter TEWL up to 72 h after the last exposure. The results demonstrate a differential response of the epidermis to two environmental stressors associated with oxidative damage; they suggest that chronic ozone exposure at relevant environmental levels does not lead to a detectable skin barrier defect, while solar UV exposure was demonstrated to increase epidermal water loss. Furthermore, experimental evidence clearly suggests that future studies applying TEWL measurements in animal models should be performed under carefully controlled skin temperature conditions. [ABSTRACT FROM AUTHOR]

Tape-stripping of the skin is a useful method for removing the stratum corneum and obtaining more information about the function of this skin layer as the main barrier for skin penetration. The amount of stratum corneum removed is of relevance in establishing the concentration profile of chemicals within the stratum corneum after topical application. Weighing is the preferred method for measuring the amount stripped, but because it is often subject to artifacts, alternative methods are sought. We present a simple, colorimetric method for determining the amount stratum corneum removed by sequential adhesive-tape-stripping of human skin in vivo. The method is based on quantification of the sodium hydroxide soluble protein fraction using a commercially available protein assay similar to the Lowry assay. The method is shown to be an accurate and reproducible alternative to weighing, also demonstrating uniform removal of stratum corneum layers following the very initial strips. [ABSTRACT FROM AUTHOR]