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In 1914 Bohr proved that there is an r ∈ (0, 1) such that if a power series converges in the unit disk and its sum has modulus less than 1 then, for |z| < r, the sum of absolute values of its terms is again less than 1. Recently analogous results were obtained for functions of several variables. The aim of this paper is to comprehend the theorem of Bohr in the context of solutions to second order elliptic equations meeting the maximum principle.
The end of the cold war division of the Baltic Sea in 1989, and the three Baltic states’ return to independence in 1991 created new opportunities for the decision-makers of the area, as well as new possibilities for fashioning security in the region. This article will examine the security debate affecting the Baltic Sea region in the post-cold war period, and in particular, the relevance of the European Union to that debate. The following section will examine various concepts of security relevant to the Baltic region; the third section looks at the EU and the Baltic area; and the last part deals with the implications that EU membership by the Baltic Sea states may have for the security of the Baltic Sea zone.
Local Orders, Global Chaos
(1999)
The ill-posed inversion of multiwavelength lidar data by a hybrid method of variable projection
(1999)
The ill-posed problem of aerosol distribution determination from a small number of backscatter and extinction lidar measurements was solved successfully via a hybrid method by a variable dimension of projection with B-Splines. Numerical simulation results with noisy data at different measurement situations show that it is possible to derive a reconstruction of the aerosol distribution only with 4 measurements.
The Green formula is proved for boundary value problems (BVPs), when "basic" operator is arbitrary partial differential operator with variable matrix coefficients and "boundary" operators are quasi-normal with vector-coeficients. If the system possesses the fundamental solution, representation formula for a solution is derived and boundedness properties of participating layer potentials from function spaces on the boundary (Besov, Zygmund spaces) into appropriate weighted function spaces on the inner and the outer domains are established. Some related problems are discussed in conclusion: traces of functions from weighted spaces, traces of potential-type functions, Plemelji formulae,Calderón projections, restricted smoothness of the underlying surface and coefficients. The results have essential applications in investigations of BVPs by the potential method, in apriori estimates and in asymptotics of solutions.
Using the Riemannian connection on a compact manifold X, we show that the algebra of classical pseudo-differential operators on X generates a canonical deformation quantization on the cotangent manifold T*X. The corresponding Abelian connection is calculated explicitly in terms of the of the exponential mapping. We prove also that the index theorem for elliptic operators may be obtained as a consequence of the index theorem for deformation quantization.
This paper focuses on some of the factors explaining recent trends in decentralisation, and some areas where decentralisation has had a positive impact, including bringing citizens into public affairs, improving sub-national public administration, and stimulating local economic development. It concludes by exploring the dangers and the implications for governments of differing capabilities starting out on the decentralisation path. More specifically, the paper stresses the underlying incentive structures within states in reform. It suggests a country-specific discussion of both vertical and horizontal incentive structures in decentralisation, as well as clear-cut accountability within a public sector in change. While vertical incentive structures mean defined rules for intergovernmental relationships, horizontal incentive structures mean defined rules between local governments, their citizens and the local private sector. Both sets of incentives need to be reformed jointly to stimulate better results from decentralisation and for better performance of local government. Neglecting one of them, could harm development. Above all, politics and processes are key to understanding, and eventually, managing decentralisation effectively.
The article mobilises the concept of strategic culture in order to identify the impact of history upon contemporary security policy. The article will first look at the "wholesale construction" of a strategic culture after the Second World War in West Germany before exploring its impact upon security policy since the end of the Cold War in two areas: the Bundeswehr's out-of-area role and conscription. The central argument presented here is that the strategic culture of the former Federal Republic now writ large on to the new united Germany sets the context within which security policies are designed. This strategic culture, as will be argued, acts as both a facilitating and a restraining variable on behaviour, making certain policy options possible and others impossible.
BACKGROUND. Although there is a wealth of empirical studies examining the effects and the correlates of student gender in school, teacher gender has rarely been a research focus. Since Greece is one of the few Western countries with an about equal percentage of male and female teachers at primary and secondary levels of public education, it offers itself as a well-suited context for exploring teacher gender-related influences. AIMS. The aim of the study was to examine gender-related differences in Greek classrooms focusing on teacher gender. It was hypothesised that due to the societal context clear gender effects could be detected. It was also assumed that teacher-student interaction patterns would be influenced by teacher gender not so much as a main effect but as interaction effects involving variables such as student gender, student achievement, grade, and teacher specialisation. Samples. The samples consisted of 1041 elementary school (mean age = 11.4 years) and 862 secondary school (mean age = 14.3 years) students in public schools in Greece. METHODS. A multi-informant and multiperspective approach to academic and psychosocial competence was used, involving teacher, peer, and self-ratings. Achievement data were also obtained. RESULTS. Several significant teacher gender differences were found in teachers' assessment of students' competence at both age groups. Furthermore, various domains of children's self-concept were found to be different in classes of female and male teachers. CONCLUSIONS. The findings indicate the need to use teacher gender as a relevant variable in future research.
We prove a theorem on analytic representation of integrable CR functions on hypersurfaces with singular points. Moreover, the behaviour of representing analytic functions near singular points is investigated. We are aimed at explaining the new effect caused by the presence of a singularity rather than at treating the problem in full generality.
Pseudodifferential analysis on manifolds with boundary - a comparison of b-calculus and cone algebra
(1999)
We establish a relation between two different approaches to a complete pseudodifferential analysis of totally characteristic or Fuchs type operators on compact manifolds with boundary respectively conical singularities: Melrose's (overblown) b-calculus and Schulze's cone algebra. Though quite different in their definition, we show that these two pseudodifferential calculi basically contain the same operators.
Quantization methods in differential equations : Chapter 2: Quantization of Lagrangian modules
(1999)
In this chapter we use the wave packet transform described in Chapter 1 to quantize extended classical states represented by so-called Lagrangian sumbanifolds of the phase space. Functions on a Lagrangian manifold form a module over the ring of classical Hamiltonian functions on the phase space (with respect to pointwise multiplication). The quantization procedure intertwines this multiplication with the action of the corresponding quantum Hamiltonians; hence we speak of quantization of Lagrangian modules. The semiclassical states obtained by this quantization procedure provide asymptotic solutions to differential equations with a small parameter. Locally, such solutions can be represented by WKB elements. Global solutions are given by Maslov's canonical operator [2]; also see, e.g., [3] and the references therein. Here the canonical operator is obtained in the framework of the universal quantization procedure provided by the wave packet transform. This procedure was suggested in [4] (see also the references there) and further developed in [5]; our exposition is in the spirit of these papers. Some further bibliographical remarks can be found in the beginning of Chapter 1.
We prove a general theorem on the local property of the relative index for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions) this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities as well as for elliptic boundary value problems with a symmetry condition for the conormal symbol.
We study the approach to the theory of hypergeometric functions in several variables via a generalization of the Horn system of differential equations. A formula for the dimension of its solution space is given. Using this formula we construct an explicit basis in the space of holomorphic solutions to the generalized Horn system under some assumptions on its parameters. These results are applied to the problem of describing the complement of the amoeba of a rational function, which was posed in [12].
An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems. A connection with Gilkey's theory of η-invariants is established.
An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems. A connection with Gilkey's theory of η-invariants is established.