Josef Meixner: his life and his orthogonal polynomials

This paper starts with a biographical sketch of the life of Josef Meixner. Then his motivations to work on orthogonal polynomials and special functions are reviewed. Meixner's 1934 paper introducing the Meixner and Meixner-Pollaczek polynomials is discussed in detail. Truksa's forgotten 1931 paper, which already contains the Meixner polynomials, is mentioned. The paper ends with a survey of the reception of Meixner's 1934 paper.Comment: v4: 18 pages, generating function for Krawtchouk polynomials on p.10 correcte

Signal and System Approximation from General Measurements

In this paper we analyze the behavior of system approximation processes for stable linear time-invariant (LTI) systems and signals in the Paley-Wiener space PW_\pi^1. We consider approximation processes, where the input signal is not directly used to generate the system output, but instead a sequence of numbers is used that is generated from the input signal by measurement functionals. We consider classical sampling which corresponds to a pointwise evaluation of the signal, as well as several more general measurement functionals. We show that a stable system approximation is not possible for pointwise sampling, because there exist signals and systems such that the approximation process diverges. This remains true even with oversampling. However, if more general measurement functionals are considered, a stable approximation is possible if oversampling is used. Further, we show that without oversampling we have divergence for a large class of practically relevant measurement procedures.Comment: This paper will be published as part of the book "New Perspectives on Approximation and Sampling Theory - Festschrift in honor of Paul Butzer's 85th birthday" in the Applied and Numerical Harmonic Analysis Series, Birkhauser (Springer-Verlag). Parts of this work have been presented at the IEEE International Conference on Acoustics, Speech, and Signal Processing 2014 (ICASSP 2014

The Zero-Removing Property and Lagrange-Type Interpolation Series

The classical Kramer sampling theorem, which provides a method for obtaining orthogonal sampling formulas, can be formulated in a more general nonorthogonal setting. In this setting, a challenging problem is to characterize the situations when the obtained nonorthogonal sampling formulas can be expressed as Lagrange-type interpolation series. In this article a necessary and sufficient condition is given in terms of the zero removing property. Roughly speaking, this property concerns the stability of the sampled functions on removing a finite number of their zeros

A note on maximal estimates for stochastic convolutions

In stochastic partial differential equations it is important to have pathwise regularity properties of stochastic convolutions. In this note we present a new sufficient condition for the pathwise continuity of stochastic convolutions in Banach spaces.Comment: Minor correction

The Red Sea, Coastal Landscapes, and Hominin Dispersals

This chapter provides a critical assessment of environment, landscape and resources in the Red Sea region over the past five million years in relation to archaeological evidence of hominin settlement, and of current hypotheses about the role of the region as a pathway or obstacle to population dispersals between Africa and Asia and the possible significance of coastal colonization. The discussion assesses the impact of factors such as topography and the distribution of resources on land and on the seacoast, taking account of geographical variation and changes in geology, sea levels and palaeoclimate. The merits of northern and southern routes of movement at either end of the Red Sea are compared. All the evidence indicates that there has been no land connection at the southern end since the beginning of the Pliocene period, but that short sea crossings would have been possible at lowest sea-level stands with little or no technical aids. More important than the possibilities of crossing the southern channel is the nature of the resources available in the adjacent coastal zones. There were many climatic episodes wetter than today, and during these periods water draining from the Arabian escarpment provided productive conditions for large mammals and human populations in coastal regions and eastwards into the desert. During drier episodes the coastal region would have provided important refugia both in upland areas and on the emerged shelves exposed by lowered sea level, especially in the southern sector and on both sides of the Red Sea. Marine resources may have offered an added advantage in coastal areas, but evidence for their exploitation is very limited, and their role has been over-exaggerated in hypotheses of coastal colonization

Landscape science: a Russian geographical tradition

The Russian geographical tradition of landscape science (landshaftovedenie) is analyzed with particular reference to its initiator, Lev Semenovich Berg (1876-1950). The differences between prevailing Russian and Western concepts of landscape in geography are discussed, and their common origins in German geographical thought in the late nineteenth and early twentieth centuries are delineated. It is argued that the principal differences are accounted for by a number of factors, of which Russia's own distinctive tradition in environmental science deriving from the work of V. V. Dokuchaev (1846-1903), the activities of certain key individuals (such as Berg and C. O. Sauer), and the very different social and political circumstances in different parts of the world appear to be the most significant. At the same time it is noted that neither in Russia nor in the West have geographers succeeded in specifying an agreed and unproblematic understanding of landscape, or more broadly in promoting a common geographical conception of human-environment relationships. In light of such uncertainties, the latter part of the article argues for closer international links between the variant landscape traditions in geography as an important contribution to the quest for sustainability

Carbon stable isotope analysis of cereal remains as a way to reconstruct water availability: preliminary results

Reconstructing past water availability, both as rainfall and irrigation, is important to answer questions about the way society reacts to climate and its changes and the role of irrigation in the development of social complexity. Carbon stable isotope analysis of archaeobotanical remains is a potentially valuable method for reconstructing water availability. To further define the relationship between water availability and plant carbon isotope composition and to set up baseline values for the Southern Levant, grains of experimentally grown barley and sorghum were studied. The cereal crops were grown at three stations under five different irrigation regimes in Jordan. Results indicate that a positive but weak relationship exists between irrigation regime and total water input of barley grains, but no relationship was found for sorghum. The relationship for barley is site-specific and inter-annual variation was present at Deir ‘Alla, but not at Ramtha and Khirbet as-Samra

Recent progress on univariate and multivariate polynomial and spline quasi-interpolants

Polynomial and spline quasi-interpolants (QIs) are practical and effective approximation operators. Among their remarkable properties, let us cite for example: good shape properties, easy computation and evaluation (no linear system to solve), uniform boundedness independently of the degree (polynomials) or of the partition (splines), good approximation order. We shall emphasize new results on various types of univariate and multivariate polynomial or spline QIs, depending on the nature of coefficient functionals, which can be differential, discrete or integral. We shall also present some applications of QIs to numerical methods