ON THE RELATION BETWEEN GLOBAL PROPERTIES OF LINEAR DIFFERENCE AND DIFFERENTIAL-EQUATIONS WITH POLYNOMIAL COEFFICIENTS .1.

AbstractThis paper is concerned with applications of the Mellin transformation in the study of homogeneous linear differential and difference equations with polynomial coefficients. We begin by considering a differential equation (D) with regular singularities at O and ∞ and arbitrary singularities in the rest of the complex plane, and the difference equation (Δ′) obtained from (D) by a variant of the formal Mellin transformation. We define fundamental systems of solutions of (Δ′), analytic in either a right or a left half plane. by the use of Mellin transforms of microsolutions of (D). The relations between these fundamental systems are expressed in terms of central connection matrices of (D). Second, we study the differential equation (D1) obtained from (D) by means of a formal Laplace transformation and the difference equation (Δ1) obtained from (D1) by a formal Mellin transformation. We use Mellin transforms of "ordinary" solutions of (D1) with moderate growth at ∞ to construct fundamental systems of solutions of (Δ1). The relation between these fundamental systems involves certain Stokes multipliers and a formal monodromy matrix of (D1)

Tussen secularisering en religiositeit: De dynamiek van protestantse theologiebeoefening

In Protestantism the notion of faith is a core category. It expresses a specific and dynamic relationship between God and the human world. In the development of modern Protestant theology, processes of subjectivism and secularization, especially in the West-European context, have shaped the concept of faith. Since Protestant theology is increasingly influenced by globalization, the urgent task is to maintain a dialectical balance between: (1) the appreciation of personal involvement and human subjectivity in the life of faith, (2) the emphasis on the divine priority and initiative in the salvation process. The Protestant identity is at stake. HTS Theological Studies Vol. 63 (3) 2007: pp. 853-86

Welfare of farmed fish : towards a sustainable development of European aquaculture

The European project FASTFISH has developed a fish behaviour monitoring system for aquaculture to ensure that fish production continues to be legitimised by society and remains competitive in production performance. Adoption of the monitoring system in society is a political process of choices and strategies, requiring experience and capacity from all stakeholders. The main challenge of FASTFISH is to combine learning processes as well as accountability for retailers and non-governmental organisations by establishing a platform facilitating stakeholder arrangement

Tussen secularisering en religiositeit: De dynamiek van protestantse theologiebeoefening

Between secularization and religiosity: The dynamics of Protestant theologyIn Protestantism the notion of faith is a core category. It expresses a specific and dynamic relationship between God and the human world. In the development of modern Protestant theology, processes of subjectivism and secularization, especially in theWest-European context, have shaped the concept of faith. Since Protestant theology is increasingly influenced by globalization, the urgent task is to maintain a dialectical balance between: (1) the appreciation of personal involvement and human subjectivity in the life of faith, (2) the emphasis on the divine priority and initiative in the salvation process. The Protestant identity is at stake

In planta localisation patterns of MADS domain proteins during floral development in Arabidopsis thaliana

Background: MADS domain transcription factors play important roles in various developmental processes in flowering plants. Members of this family play a prominent role in the transition to flowering and the specification of floral organ identity. Several studies reported mRNA expression patterns of the genes encoding these MADS domain proteins, however, these studies do not provide the necessary information on the temporal and spatial localisation of the proteins. We have made GREEN FLUORESCENT PROTEIN (GFP) translational fusions with the four MADS domain proteins SEPALLATA3, AGAMOUS, FRUITFULL and APETALA1 from the model plant Arabidopsis thaliana and analysed the protein localisation patterns in living plant tissues by confocal laser scanning microscopy (CLSM). Results: We unravelled the protein localisation patterns of the four MADS domain proteins at a cellular and subcellular level in inflorescence and floral meristems, during development of the early flower bud stages, and during further differentiation of the floral organs. The protein localisation patterns revealed a few deviations from known mRNA expression patterns, suggesting a non-cell autonomous action of these factors or alternative control mechanisms. In addition, we observed a change in the subcellular localisation of SEPALLATA3 from a predominantly nuclear localisation to a more cytoplasmic localisation, occurring specifically during petal and stamen development. Furthermore, we show that the down-regulation of the homeodomain transcription factor WUSCHEL in ovular tissues is preceded by the occurrence of both AGAMOUS and SEPALLATA3 proteins, supporting the hypothesis that both proteins together suppress WUSCHEL expression in the ovule. Conclusion: This approach provides a highly detailed in situ map of MADS domain protein presence during early and later stages of floral development. The subcellular localisation of the transcription factors in the cytoplasm, as observed at certain stages during development, points to mechanisms other than transcriptional control. Together this information is essential to understand the role of these proteins in the regulatory processes that drive floral development and leads to new hypotheses

A general construction of constrained parity-check codes for optical recording

This paper proposes a general and systematic code design method to efficiently combine constrained codes with parity-check (PC) codes for optical recording. The proposed constrained PC code includes two component codes: the normal constrained (NC) code and the parity-related constrained (PRC) code. They are designed based on the same finite state machine (FSM). The rates of the designed codes are only a few tenths below the theoretical maximum. The PC constraint is defined by the generator matrix (or generator polynomial) of a linear binary PC code, which can detect any type of dominant error events or error event combinations of the system. Error propagation due to parity bits is avoided, since both component codes are protected by PCs. Two approaches are proposed to design the code in the non-return-to-zero-inverse (NRZI) format and the non-return-to-zero (NRZ) format, respectively. Designing the codes in NRZ format may reduce the number of parity bits required for error detection and simplify post-processing for error correction. Examples of several newly designed codes are illustrated. Simulation results with the Blu-Ray disc (BD) systems show that the new d = 1 constrained 4-bit PC code significantly outperforms the rate 2/3 code without parity, at both nominal density and high density