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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.
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 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.
Problems for elliptic partial differential equations on manifolds M with singularities M' (here with piece-wise smooth geometry)are studied in terms of pseudo-differential algebras with hierarchies of symbols that consist of scalar and operator-valued components. Classical boundary value problems (with or without the transmission property) belong to the examples. They are a model for operator algebras on manifolds M with higher "polyhedral" singularities. The operators are block matrices that have upper left corners containing the pseudo-differential operators on the regular M\M' (plus certain Mellin and Green summands) and are degenerate (in streched coordinates) in a typical way near M'. By definition M' is again a manifold with singularities. The same is true of M'', and so on. The block matrices consist of trace, potential and Mellin and Green operators, acting between weighted Sobolev spaces on M(j) and M(k), with 0 ≤ j, k ≤ ord M; here M(0) denotes M, M(1) denotes M', etc. We generate these algebras, including their symbol hierarchies, by iterating so-called "edgifications" and "conifications" os algebras that have already been constructed, and we study ellipicity, parametrics and Fredholm property within these algebras.
We construct an algebra of pseudo-differential boundary value problems that contains the classical Shapiro-Lopatinskij elliptic problems as well as all differential elliptic problems of Dirac type with APS boundary conditions, together with their parametrices. Global pseudo-differential projections on the boundary are used to define ellipticity and to show the Fredholm property in suitable scales of spaces.
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.
Kapital und Menschenrechte
(1999)
In socialist economies firms have provided various social benefits, like child care, health care, food subsidies, housing etc. Using panel data from Bulgarian and Polish firms, this paper attempts to explain firm-specific provision of social benefits in the process of transition. We investigate empirically with the help of qualitative response models, how ownership type and structure, firm size, profitability, change in management, foreign direct investment, wage and employment policies, union involvement and employee power have impacted the state of non-wage benefits provision.
Inhalt: Teil A - Exkursionsberichte 1 Auckland 2 Hamilton 3 Rotorua 4 Tongariro 5 Wellington 6 Abel Tasman National Park 7 Punakaiki 8 Franz Josef Glacier 9 Wanaka 10 Christchurch Teil B - Referate 11 Neuseelands Bevölkerung (KK) 12 Die Maori (AF) 13 Einwanderung in Neuseeland (MB, AS, BW) 14 Die frühe europäische Besiedlung (LE) 15 Das politische System und die Auslandspolitik (TM) 16 Das Sozialsystem in Neuseeland (CH) 17 Die Wohnungspolitik Neuseelands (CL) 18 Infrastruktur und Bildung in Neuseeland (AH) 19 Die Landwirtschaft (TH) 20 Nachhaltigkeit und der Resource Management Act (MK, MG) 21 Die Restrukturierung des Energiesektors (MW) 22 Restructuring - ein lokales Beispiel (JP) 23 Die Perspektiven der sozialen Marktwirtschaft am Beispiel Neuseelands (TG) 24 Literaturverzeichnis
Inhaltsübersicht I. Einführung II. Rechtliche Grundlagen für das Verbot der Kinderarbeit a) Die Kinderrechtskonvention b) Die Internationale Arbeitsorganisation und ihre Regelungen c) Die Konferenz über Kinderarbeit in Amsterdam und Oslo 1997 d) Aktivitäten der Vereinten Nationen und von UNICEF e) Resümee III. Sozialklauseln zur Bekämpfung von Kinderarbeit a) Allgemeines b) Vereinbarkeit von Sozialklauseln mit dem Prinzip des freien Welthandels? c) Interessenlage der Akteure zum Einsatz von Sozialklauseln- die Gewerkschaften IV.Bewertung
Inhalt: Edzard Schmidt-Jortzig Menschenrechtliche Entwicklung in Deutschland im Lichte des internationalen Vertragsrechts Thomas Buergenthal Die Bedeutung der Allgemeinen Erklärung der Menschenrechte für den internationalen Menschenrechtsschutz Hans Christian Krüger Der europäische Menschenrechtsschutz in einem veränderten Europa Norman Weiß 50 Jahre Allgemeine: Erklärung der Menschenrechte — Zusammenfassender Bericht über die übrigen Veranstaltungen Eckart Klein Zur Eröffnung der Ausstellung „Menschenrechte für alle" — 50 Jahre Allgemeine Erklärung der Menschenrechte am 28. August 1998
Industrial policy and social strategy at the corporate level in Poland : questionnaire results
(1999)
This paper presents results from a survey of industrial policy of the state and the social security system at the corporate level in Poland. Previous reports in this area indicated preferable directions of research to be taken in order to prove various hypotheses of the purposefulness of an integral approach to industrial policy and social security in the analysis of economic processes in transition (see Weikard 1997). This paper summarises the results and draws conclusions from a questionnaire study on subsidies, social benefits and economic policy in Polish firms during the process of transformation. Our results and conclusions show the scope and character of the processes in the area of industrial and social policy in the period 1994 to 1997. The paper is divided into five parts. The first part concerns the aims and methodology of the questionnaire; it also gives a brief description of the sample. The second part shows how enterprises dealt with the issues of employment and wages in this period. The third part characterises industrial policy at the corporate level, while the next presents results from the survey of various social schemes pursued. The final part aims at an integral approach in the analysis of various processes taking place in Polish enterprises. The survey was conducted in the period April to June 1998. Its aim was to observe certain phenomena occurring at the corporate level. The questionnaire was distributed among the managers, directors and presidents of large-size enterprises, which had been selected to satisfy the following three criteria. Firstly, the number of employees had to be considerable (over 300 workers). This criterion was applied following the consideration that certain social phenomena are more conspicuous in enterprises with large manpower. Secondly, only operating enterprises were selected, the enterprises which closed down were disregarded. Finally, for the purposes of the survey the units differed as regards their legal situation and form of ownership. Out of over 1800 enterprises 370 units were drawn where we sent the questionnaire. Unfortunately, as many as 51.9% of the respondents refused co-operation, questions to a certain extent puts the representativeness of the sample in question. Finally, 178 questionnaires were subsequently completed and returned for analysis. However, not all of these questionnaires included full answers to all of the 75 questions; therefore, while discussing the results of the survey we have indicated the number of relevant answers we have received.
The aim of the work was to present the results of the analyses economic standing of the partnership companies which lease agricultural real estate from Agricultural Property Agency of State Treasury (APA) in 1996 and 1997. The analyses proved poor economic condition of the firms under investigation and especially their low level of stabilisation (the index of total debt was in 1996 equal to 0.88 and in 1997 to 0.96) and the low level of their solvency.
The economy in Poland has changed tremendously in recent years. Agricultural enterprises can defend their market share only if they are able to adjust quickly and efficiently to new circumstances. The most effective strategy to cope with changing operating conditions is a strategy of permanent development of human resources. This strategy must embrace a constant improvement of professional entrepreneurial skills and of management structures within organizations. Only such a strategy will allow businesses to hold on to or to increase their market standing despite strong competition. It will also allow them to meet, for instance, the newly introduced standardisation procedures for goods produced and supplied. This challenge holds especially true for agricultural enterprises that operate in highly competitive markets; markets which are currently characterised by a permanent surplus of supply over demand and a great number of businesses, mainly of small or medium size. Demand in the agricultural market is exerted by millions of consumers, all of different consumption habits with idiosyncratic consumption preferences. Agricultural producers as a group are extremely sensitive to any kind of change in their environment. This is especially true in the current transition period when a worsening of economic conditions can be observed: an economic downturn caused by the price of inputs increasing at a faster rate than agricultural product prices and an ineffective agricultural policy. One of the agricultural production factors which allows for quick adjustment to change and which can thus be used to improve one’s market position is the human factor. It is a wellknown fact that a good level of professional skills in combination with ongoing means of furthering and updating professional qualifications of workers can help to facilitate coping with market challenges. The aim of this study is first to determine specific quality and quantity features of human resources in agricultural production, looking, inter alia, at changes in employment, specific employment structures and the number of recruitments and dismissals in a given period. A further aim was to undertake an efficiency analysis of limited partnerships which leased their agricultural real estate from the Agricultural Property Agency (APA) in the Voivodeship of Gorzów between 1995 and 1997. The first analysis was carried out using data which were collected from surveys amongst the owners of 36 privately owned farms and the managers of 14 limited partnerships. The data cover the period between 1994 and 1997. The incentive to conduct research on large farms in the Gorzów Voivodeship using the Data Envelopment Analysis method (DEA) lay in the outcome of various earlier studies on the financial standing of limited partnerships leasing real estate from APA in the Gorzów Voivodeship in 1996 and 1997. Apart from general adjustment processes, these inquiries proved that, in 1997, the economic condition of the farms analysed was worse when compared to the situation in 1996; the following ratios worsened: the financial support ratio, the liquidity ratio, the turnover ratio, the profitability ratio and the cost level ratio (see Świtłyk, 1998, 1999). These results determined the focus of our research, namely input efficiency in particular limited partnerships. The base of our calculations was a research model which consisted of efficiency measures focusing on firms’ inputs The analysis was carried out on a sample of 90 firms in the years between 1995 and 1997 (30 firms every year). Other data material was collected from national statistical office reports on incomes, costs and financial results (F-O1) and statistics about land usage, crop area and yields (R-O5). In the next section we briefly discuss privatisation in agriculture. Sections 3 and 4 present results from our survey. Section 5 concludes.
- Ott Heinrich Fugger 1592-1644 (Stephanie Haberer) - Die Militarisierung der Habsburgermonarchie 1740-1790 (Michael Hochedlinger) - Das preußische Kantonsystem in brandenburgischen Städten (Martin Winter) - Söldnerleben am Vorabend des Dreißigjährigen Krieges (Holger Th. Gräf) - Desertion in der Armee Friedrichs des Großen (Jörg Muth) - Sozialstruktur u. politische Wirksamkeit des brandenburgischen Adels (Frank Göse) - Eigensinnige Bauern, ehrgeizige Amtmänner, fürstliche Gutsherren (Heinrich Kaak) - Männlicher Muth und Teutsche Ehre (Karen Hagemann) - Formular für Beitrittserklärung