On optimal estimates for the solutions of linear difference equations on the circle

A linear difference equation arising in the proof of Moser's twist mapping theorem is solved and optimal estimates for the solution are established.     

The Purpose and Age of Underwater Walls in the Bay of Elaia of Western Turkey: A Multidisciplinary Approach

Pergamum (modern: Bergama) was operating an important harbour used by military forces and merchants at the city of Elaia during Hellenistic and Roman Imperial times. Harbour‐related facilities such as warehouses, breakwaters and wharfs document the importance of this harbour site not only for the Pergamenians. This paper focuses on the purpose and age of six submerged wall structures situated approximately 1 km south of the ancient closed harbour basin of Elaia. Geoelectric cross‐sections and semi‐aquatic coring near these walls failed to detect any solid basement under the walls which excludes their possible use as breakwaters or wharfs. Instead, the walls were most likely delineating and separating evaporation ponds of salt works, which compares well with similar structures from other periods and places around the Mediterranean. Combined OSL and ¹⁴C‐dating determined the construction age of the installation between the 4th and 6th centuries A.D. Subsequent (re‐)uses are likely and are in agreement with findings from archaeological surveys.     

Evolution of the Paleocene-Early Eocene larger benthic foraminifera in the Tethyan Himalaya of Tibet, China

The Paleocene-Early Eocene larger benthic foraminifera (LBF) in the far eastern Neo-Tethyan Ocean of Tibet still remain poorly known. Here, we present a novel, high-resolution larger foraminiferal biozonation from the shallow-water limestones in Tibet, which will improve our current understanding of the larger foraminiferal evolution in the eastern Neo-Tethyan Ocean. Based on one continuous section at Tingri and three separate sections at Gamba, ten Shallow Benthic Zones (SBZ 1–10) have been designated in Tibet by following the principle of Oppel Zone. In contrast to those in Europe, the Paleocene LBFs in Tibet are characterized by high diversification of Lockhartia, Kathina, Daviesina, Miscellanea, Ranikothalia, and Operculina and show progressively increasing diversity of genera and species during SBZ 2–5. Adult dimorphism and large shell size of some LBFs as well as differentiation of the diversity between genera and species initiated as early as SBZ 3. It suggests that the occurrence of the Larger Foraminifera Turnover (LFT) was probably not synchronous in the entire Neo-Tethyan Ocean, because in Europe, the LFT was generally thought to occur at the beginning of SBZ 5. During the Early Eocene, the LBFs in Tibet decreased markedly on the generic level and increased on the species level, and some new genera (Alveolina, Orbitolites, Nummulites, Assilina, Discocyclina) have gained predominance in Tibet. It is nearly identical to the evolution of the LBFs in Europe and indicates a high-degree homogenization of the LBFs in the entire Neo-Tethyan Ocean. Furthermore, the Paleocene-Eocene (P-E) boundary in shallow-water environments has been clearly identified by us, and it is situated in the upper part of SBZ 5 and associated with no evident biotic turnover of shallow benthic foraminiferal communities. The possible diachroneity of the LFT in the Neo-Tethyan Ocean and the evident lagging of the Paleocene-Eocene Thermal Maximum (PETM) behind the LFT imply that the LFT could only be the result of a natural evolutionary process and has no linkage with the PETM. Notably, a transient but distinct larger foraminiferal extinction and origination (LFEO) event has been found in Tibet, which is characterized by a sudden disappearance of all Paleocene lamellar-perforate LBFs, such as Lockhartia, Kathina, Daviesina, Miscellanea, Ranikothalia, and Operculina, and the initial dominance of the Early Eocene porcellaneous-walled Alveolina. The LFEO marks the boundary between SBZ 5 and 6, and might only occur in the low-latitude areas of the Neo-Tethyan Ocean. Surprisingly, the LFEO coincides with the initial recovery of the Carbon Isotope Excursion (CIE), and their synchronicity implies that some possible mechanisms causing the rapid recovery of the CIE probably had also led to the LFEO in the shallow-water environments.     

The causes of land-use and land-cover change: moving beyond the myths

Common understanding of the causes of land-use and land-cover change is dominated by simplifications which, in turn, underlie many environment-development policies. This article tracks some of the major myths on driving forces of land-cover change and proposes alternative pathways of change that are better supported by case study evidence. Cases reviewed support the conclusion that neither population nor poverty alone constitute the sole and major underlying causes of land-cover change worldwide. Rather, peoples’ responses to economic opportunities, as mediated by institutional factors, drive land-cover changes. Opportunities and constraints for new land uses are created by local as well as national markets and policies. Global forces become the main determinants of land-use change, as they amplify or attenuate local factors.     

Dynamics of decametric radio-sources and standing Alfvén waves in jovian magnetosphere

Short (S-) bursts and narrow-band events (NB) of jovian decametric emission (DAM) form oscillating bands near certain frequencies in dynamical spectra. This paper is focused on the S/NB-structure with time-scales longer than 0.03 s. It is shown that there is a clear resemblance between S/NB spectral features and trajectories of electrons in the parallel electric field of the standing Alfvén wave.     

Comparison of Mathematical Methods of Potential Modeling

Various attempts are known to turn the “catalogue” of mineral deposit models compiled by Cox and Singer (1986) operational, and have initiated activities called “potential mapping”, “potential modeling”, or “targeting”. The common ultimate objective is to estimate the probability for a given location that a mineralization of a given type occurred. The mathematics range from “weights of evidence” and others featuring a Bayesian approach to logistic regression by maximum likelihood, and include other realizations by means of fuzzy methods, genetic programming, and artificial neural nets. Once developed and coded, applications are not restricted to mineral prospection and exploration but include any kind of occurrences and their estimated probabilities, e.g., risk assessment of land slides and many others.