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  • 1990-1994  (23,754)
  • 1980-1984
  • 1994  (23,754)
  • Mathematics  (16,026)
  • Geography  (7,728)
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  • Books  (9)
  • Articles  (23,754)
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  • 1990-1994  (23,754)
  • 1980-1984
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  • 1
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: The construction of a composite index is described to rank U.S. metropolitan areas for educational attainment. The suggested methodology departs from traditional rank sum methods in that this approach utilizes data resulting in a continuous scale, whereas in the rank sum method, no use is made of the actual values of the data, but merely their rankings. The proposed index circumvents several practical problems because the numbers generated are metric measures allowing the use of arithmetic and statistical operations. Data used are pupil/teacher ratio, an effort index, and academic options in higher education. Comparisons are made across areas by population size and by geographic region.
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  • 2
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: Using data from the National Conference of State Legislatures, this paper examines the state budget stabilization funds of Indiana, Iowa, Missouri, Michigan, Minnesota, Ohio, and Wisconsin. Unlike previous research, this paper examines the movement of the fund balances over time (between 1983 and 1991), to see how the fund balances move in relation to a number of indicators of state fiscal health. The results of this research show that the use of these funds varies significantly among the states as does the level of funding and therefore the ability of the funds to serve as an effective tool for counter-cyclical state fiscal policy.
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  • 3
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: Book reviewed in this article:Agriculture, Environment, and Health: Sustainable Development in the 21st Century. Vernon W. Ruttan, Editor.Managing Water as an Economic Resource. James Winpenny.Trials of Transition: Economic Reform in the Former Communist Bloc. Michael Keren and Gur Ofer, Editors.Tower Block: Modern Public Houslng in England, Scotland, Wales and Northern Ireland. Miles Glendinning and Stefan Muthesius.Capital and Communities in Black and White: The Intersections of Race, Class, and Uneven Development. Gregory S.Restructuring for Innovation: The Remaking of the U.S. Semiconductor Industry. David P. Angel.Technopolis: High-Technology Industry and Regional Development in Southern California. Allen J. Scott.
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  • 4
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: The results of this study confirm the expected positive relationship between economic development agency spending and employment growth among the states. Furthermore, it is concluded that past studies, by failing to control for state economic development agency spending in estimated regression equations, have underestimated the negative impact of personal taxes on employment growth.
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  • 5
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: This paper explores the impact of new technology adoption upon the market performance of small industrial firms. Survey data from a six-sector sample of Western New York manufacturers are presented. The results suggest a positive relationship between new technology adoption and growth of exports, value-added, and total sales. A central finding of the study is that flexible manufacturing systems (FMS) confer different types of technical and commercial advantages across sectors. Two broad groups of process innovators are identified: (1) those that adopt new technology primarily to cut unit costs; and (2) those that aspire toward greater production flexibility. The paper concludes with a brief discussion of the regional development implications that flow from the empirical results.
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  • 6
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: This paper presents results of a hierarchical, fixed-question survey that sought responses about flexible machining cells, flexible labor cells, and concurrent changes in plant operations among nonelectrical machinery manufacturers in Illinois, Indiana, Michigan, Ohio, and Wisconsin. General results indicate that the majority of firms in the American Midwest do not possess flexible manufacturing capability. Of those that do possess this capability, most adopted flexible labor cells prior to adopting flexible machining cells. These cells are small, employing relatively few workers and producing a limited line of products. While the adoption process has been plagued with training, scheduling, and integration problems, most plant managers are pleased with the performance of their flexible manufacturing cells. Management has been reluctant to break out of traditional relationships with suppliers, to trim levels of management and to explore strategic alliances with competitors. Survey results are disaggregated by year, size, positon-in-organization, and by union affiliation.
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  • 7
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: Book Review in This Article:POSTMODERN CONTENTIONS: EPOCHS, POLITICS, SPACE. Edited by John Paul Jones III, Wolfgang Natter, and Theodore Schatzki.RESTRUCTURING HEGEMONY IN THE GLOBAL POLITICAL ECONOMY: THE RISE OF TRANSNATIONAL NEW-LIBERALISM IN THE 1980s. Edited by Henk Overbeek.THE DEVELOPMENT PROCESS IN SMALL ISLAND STATES. Edited by Douglas G. Lockhart, David Drakakis-Smith, and John Schembri.DEFENSE SPENDING AND ECONOMIC GROWTH. Edited by James E. Payne and Anandi Sahu.URBAN FINANCE UNDER SIEGE. Edited by Thomas R. Swartz and Frank J. Bonello.STATE & RESERVATION: NEW PERSPECTIVES ON FEDERAL INDIAN POLICY. Edited by George Pierre Castile and Robert L. Bee.
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  • 8
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: Despite the fact that nonemployment income makes up approximately one-third of all personal income, its impact on local area economies has not been closely examined. This study uses Michigan county data to examine the impact of nonemployment income on nonbasic income over a twenty-seven-year period. This impact is compared to the impact of basic income by employing regression analysis to estimate comparative multiplier effects for both types of income. Nonemployment income is found to have a significant impact on nonbasic income, particularly in metropolitan and nonmetropolitan urban counties, where its impact appears to be stronger than that of basic income.
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  • 9
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
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  • 10
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: This paper examines spatial-temporal trends in the international system of corporate banking centers. It is evident that the largest corporations locate their headquarters in a formal national decision-making hierarchy and that national and regional nodes within this hierarchy house the headquarters of major banks. Initially these banks link clients internally. However, as domestic corporations evolve into transnationals, banks follow their customers overseas and establish foreign headquarters. The results of the study indicate that, until 1975, American banking corporations and their financial centers dominated global banking. Since then other countries, most notably Japan and Germany, have successfully challenged this hegemony, while others like the United Kingdom and Canada have been in relative decline. The 1980s witnessed a new era of international coordination of the world's largest industrial countries. Canada, for example, opened its doors to international banking, joined the G-7, and presently is linked to the world's major banking centers.
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  • 11
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: Over the past fifteen years, legislative, regulatory, and technological changes have occurred which have redefined the concept of a “local” bank deposit market. This study employs an interest rate covariability model to evaluate the geographic extent of bank retail CD markets. Classifying deposits according to both size and maturity, a total of four markets are analyzed using yield data for six major state banking areas. The evidence presented for all four cases supports the view that significant, though not perfect, integration exists. The principal finding is that the geographic scope of retail CD markets is inversely related to both size and maturity.
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  • 12
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: The success of economic development initiatives in achieving a significant and sustained improvement for a target area is strongly influenced by the size of the local multiplier. New economic activity is generally site specific and the proportion of spending and re-spending that generates local multiplier effect will vary with the hierarchical level of community in which the activity is located. Leakages in the form of outshopping by community residents and expenditures in the community that constitute payments to agents outside the home community are estimated for communities in six functional levels that, combined, represent the complete trade center hierarchy in Saskatchewan. The resulting multipliers are found to vary with functional level, with the smallest communities having the smallest multipliers. When rural areas are being targeted for economic development, more rural economic activity can be generated by focusing on relatively large rural communities.
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  • 13
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: Hong Kong, Singapore, Korea, and Taiwan (the Asian newly industrialized economies [NIEs]) were the economic success stories of the 1970s and 1980s. While there are a number of competing explanations for their rapid growth, some focusing upon the process of export-led development, the Asian NIEs face a more hostile global competitive environment than heretofore acknowledged. Their competitiveness in labor-intensive and traded-goods manufactured industries has been undermined by new competitors including the ASEAN countries of Indonesia, Malaysia, Thailand, and the Philippines, as well as China. With new competitors, the rise of trading blocs, and the shrinkage of export surpluses (over imports) it is doubtful if the NIEs will be able to sustain past rates of growth over the coming years. The capacity to adjust efficiently to changing circumstances has become a vital determinate of long-term growth of the NIEs. Whatever the virtues of past state-based industrial policies, restructuring is now a very important part of the life of firms in the NIEs’labor-intensive industries. Moreover, the significance of these industries in each of the NIEs has been undercut by the growing importance of the global finance industry and its attendant political economy.
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  • 14
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: The paper presents a model of worktrip length for rural nonmetropolitan resident women. We find that some factors important in constraining the length of urban women's commute, such as linking worktrips with household-related trips. are less relevant in a rural setting. We also find that women working in non-feminized occupations, women receiving employer-provided health benefits, and women with better transportation resources, tend to have longer worktrips.
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  • 15
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
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  • 16
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: This paper presents a historical perspective of growth of the Mexican automobile industry, focusing on the changing position of Third-World producers within the global motor vehicle industry. Both the impact of Mexican government policies directed toward increasing international competitiveness and that of adjustments made by transnational corporations to changes in technology and production methods are reviewed. Finally, a demand function that relates the proportion of the industry output that is exported to relative producer prices, Mexican and U.S. income, and government policy variables is estimated. The results of that analysis are consistent with the hypotheses that Mexican automotive sector exports are significantly related to (1) relative Mexico/U.S. producer prices, (2) income in the United States, and (3) changes in Mexican government export promotion policies initiated in 1983. These specific results, coupled with the global changes taking place in the industry, lead to the conclusion that Mexico can be expected to continue on its course toward fuller integration into the world motor vehicle industry as a producer of both finished vehicles and parts. While this would be a probable scenario even in the absence of the North American Free Trade Agreement, the Agreement is likely to accelerate the growth of internationally competitive automotive sector production in Mexico.
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  • 17
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: Existing studies of convergence across jurisdictions of a nation have focused on developed economies. A key assumption underlying regional convergence is geographical factor mobility, and in a developed economy, mobility is facilitated by low transportation costs. By the same token, convergence in a less-developed economy may be impeded by the absence of a well-developed transportation infrastructure. We examine the rate and industrial composition of economic convergence in a neighboring less-developed country (LDC), Mexico, to examine how it might have differed from the U.S. experience.We find evidence of stronger convergence in Gross State Product per capita in Mexico relative to existing estimates of U.S. convergence. Further, while manufacturing activity has been found to be a primary source of convergence in the U.S., we find weaker evidence of convergence of manufacturing activity in Mexico. On the other hand, industries such as hotels and transportation were found to be significantly influential in regional convergence in the Mexican economy.
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  • 18
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
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  • 19
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: Book reviewed in this article:Institutional Incentives and Sustainable Development: Infrastructure Policies in Perspective. Elinor Ostrom, Larry Schroeder, and Susan Wynne.The Colonizer's Model OF THE World: Geographical Diffusionism AND Eurocentric History. James Blaut.The Age OF Migration: International Population Movements IN The Modern World. Stephen Castles and Mark J. Miller.Environmental Problems In Eastern Europe. F.W. Carter and D. Turnock, Editors.China's Economic Reform: Administering The Introduction Of The Market Mechanism. George Totten and Zhou Shulian.Regional Advantage: Culture and Competition in Silicon Valley And Route 128. AnnaLee Saxenian.
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  • 20
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: This paper establishes the concept of production system as an analytical framework to embrace recent industrial changes. Five dimensions of production system changes are posited. A case study of the Korean consumer electronics sector shows that the companies have experienced diverse patterns of changes, but these changes are generally related to plant location, ownership, export orientation, and company size.
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  • 21
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: This paper focuses on restructuring in eleven first-tier suppliers in the South Wales motor components sector and examines the influence of production politics, including plant-local labor market relations, on the implementation of flexible manufacaturing during the 1980s. Although industrial geographers have recognized the role of recruitment and training in the restructuring of the spatial division of labor they have tended to focus primarily on the role of new firms operating at “green field” sites and view this process as functional to the needs of capital. However, the argument of this paper will be that while new forms of work organization are influenced by the technical and commercial possibilities of new technology and markets, the form of work organization cannot simply be “read off” from the macro-economic level, but will be partially determined by existing spatiallyuneven social relations of production.
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  • 22
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: Institutions matter to economic development—particularly to the process of economic transformation. New technologies and new ways of organizing economic activity do not emerge in a vacuum, but bear the imprint of institutional arrangements. Economic transformation thus entails institutional adaptation as well as technological change—the emergence of new ways of organizing production or production systems and new sets of social and economic relationships which provide the institutional context for economic growth and development. Just as importantly, new institutional arrangements do not emerge tabula rasa, but reflect the legacy of old social and institutional forms. Given particular social and institutional legacies, different societies adapt differently to economic transformation. This article employs a theoretically-informed comparative examination of postwar Japanese capitalism to explore the critical role played by institutions in the process of economic transformation.
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  • 23
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: This paper presents a contemporary survey and synthesis of research on the regional dimensions of technology and competitiveness and explores ways in which technological change has influenced industrial restructuring in U.S. regions. Neoclassical models of regional growth are judged to be seriously wanting in their treatment of technological change. Industrial organization theories such as product/profit cycles, best-practice firms, and flexible specialization have proven to be more illuminating. However, the task remains to integrate technology as a core element in a geography of production and regional economic change that includes both global strategic decision-making of companies and the viability of plants in particular regional settings. Although the federal government as sponsor and procurer of technology has contributed significantly to regional industrial restructuring, the prospects for state and local governments to facilitate technological change appear to be very limited.
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  • 24
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: A case study of the Hong Kong watch industry demonstrates the adaptive flexibility of labor-intensive industrial clusters. The study describes the evolution of industry in Hong Kong, and highlights the unique attributes of the country's economic history which have influenced the structure of production systems in the country. Focusing on the role of global competition, the case study identifies the constraints posed by a labor-intensive flexible production system in the face of continuous technological change in the industry.
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  • 25
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: There is little consensus in the development literature on whether it is supply explanations such as competitiveness levels, or, the external demand structure which drive the link between exports and economic growth. This paper attempts to reconcile the polarization of the aforementioned viewpoints by examining the effects of both world demand and a country's competitiveness in exports on the relationship between export growth and economic growth. The results indicate that only developing countries which are highly competitive and which also face relatively favorable external demand for their exports experience above-average growth. Weak external demand reduces the positive effects of exports on growth substantially but may be offset by high levels of competitiveness in trade. The results imply that both regional and Third World growth studies on the link between exports and economic growth would profit more from integrating both supply as well as external demand explanations rather than succumb to one of the two viewpoints.
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  • 26
    Electronic Resource
    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: Input-output models are frequently used to estimate impacts, benefits or damages from some event. These analytic models and the questions they are designed to answer are usually based on political definitions of regions. However the true impacts propagate according to the actual spatial pattern of the regional economy. Because of the divergence between the political regions used for analysis and the economic regions on the ground, the economic impacts which spill over political boundaries can sometimes become analytically important. This paper applies these concepts to a case study of allocating irrigation water from the Pecos River in Texas and New Mexico. The U.S. Supreme Court has ruled that New Mexico used water belonging to Texas. Our analysis suggests that the spillover benefits to Texas from New Mexico's use of the water might equal or exceed the benefits which Texas would have gotten from using the water itself. Texas might be better off because New Mexico took its water.
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  • 27
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    Electronic Resource
    Oxford, UK : Blackwell Publishing Ltd
    Growth and change 25 (1994), S. 0 
    ISSN: 1468-2257
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Geography , Economics
    Notes: Book reviewed in this article:The Structure of a Modern Economy: The United States, 1929–89. by Kenneth E. Boulding.Inequality Reexamined. Amartya Sen.Work in the Fast Lane: Flexibility, Divisions of Labor, and Inequality in High-Tech Industries. Glenna Colclough and Charles M. Tolbert II.Persistent Poverty in Rural America. Rural Sociological Society Task Force on Persistent Rural Poverty.Deep Disagreement in U.S. Agriculture: Making Sense of Policy Conflict. by Christopher Hamlin and Philip T. Shepard.Dividing the Waters: Governing Groundwater in Southern California. William Blomquist.Trading Industries: Trading Regions. Helzi Noponen, Julie Graham and Ann Markusen, editors.Trading in a New World Order: The Impact of Telecommunications and Data Services on International Trade in Services by Bruno Lanvin, editor.Exports and Local Development: Mexico's New Maquiladoras. Patricia A. Wilson.Latin America's Turnaround: Privatization, Foreign Investment, and Growth. Paul H. Boeker, editor.The Dynamics of Liberalization: Tanzania and the IMF by Horace Campbell and Howard Stein, editors.Keynes General Theory of Interest: A Reconsideration. Fiona C. Maclachlan.Microcomputer-Based Input-Output Modeling: Applications to Economic Development. Daniel M. Otto and Thomas G. Johnson, editors.
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  • 28
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3866-3880 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Two-point and four-point graphs appearing in a three-loop approximation in the field theory renormalization group scheme are calculated in general dimensions. Combining Feynman parameterization and direct integration loop integrals are represented in the form of the expressions, depending on the space dimension d as a parameter. The expressions obtained enables one to consider renormalization group functions directly at noninteger d.
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  • 29
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4505-4516 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is observed that the existence of an attracting set in the class of solutions to the stochastic Lagrangian variational principle leads to a natural problem of convergence of diffusions in the Carlen class. It is then shown how dynamical properties enable one to prove some convergence results in the two-dimensional Gaussian case.
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  • 30
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4568-4593 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A complete classification of natural transformations of finite order of Lagrangians into energies over n-dimensional manifolds, where n≥2, is given herein. The classification of natural transformations of finite order of vector fields and Lagrangians into energies and constants of the motion is also obtained for n≥3. By using these results, a classification of Lagrangians into Poincaré–Cartan one-forms and Legendre transformations is obtained.
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  • 31
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3936-3958 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The quantum net model differs from other quantizations and discretizations of space-time in being founded upon quantum-logical principles. Fermions are envisaged as arising from defects in the net. Such defects are investigated and it is found that the attempt to vary them infinitesimally gives rise to a reticular version of the Dirac operator, which now has a simple interpretation in terms of quantum mechanical infinitesimal parallel transport. The analog of the usual massless Weyl equations are found to hold on the net, and algebraic solutions are deduced by exploiting its inherent logical structure. A correspondence principle then applies to show that these equations and their solutions correspond precisely to the ones expected in the continuum. (In the course of this, new basis-independent expressions for the complex Minkowski-space Dirac matrices are found.) Finally, an attempt is made to introduce gravity into the net, and the flat space Dirac Lagrangian is modified accordingly.
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  • 32
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4497-4504 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Exact analytic solutions are provided for a class of equations describing a composite scalar particle in constant electric and magnetic fields, and also in plane electromagnetic fields. The external fields are taken in both classical and quantum cases. A detailed physical analysis of the results is given.
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  • 33
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4534-4546 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is well known that quantum physics forbids the simultaneous measurement of two noncommuting projection operators. However, sometimes there exists a third projection (mirror projection) which may be measured together with the second one and whose outcomes are completely correlated, in the Einstein–Podolsky–Rosen sense, with the outcomes of the first projection. In this article the states for which such a mirror projection exists are characterized and a procedure for constructing the mirror is given. In particular, it is shown that for two noncommuting projections there are always states for which the mirror projection exists, but also states for which it does not exist.
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    Journal of Mathematical Physics 35 (1994), S. 4651-4660 
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    Notes: A Cauchy problem is formulated with data that describe the scattering of two vortices in a superconductor, and the following is proven: First, a unique global finite-energy solution exists. Second, the symmetry of the solution rules out all cases other than 0°, 90°, or 180° scattering. Third, a local analytic solution exists near the origin. The leading terms of this solution show that, of the three cases, 90° scattering is realized.
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    Journal of Mathematical Physics 35 (1994), S. 4739-4745 
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    Notes: A modified Korteweg–de Vries (mKdV)-type bilinear equation that has been shown to pass the three-soliton solution and the Painlevé tests [see, J. Math. Phys. 2094, 28 (1987); 2572, 31 (1990)] is considered herein. In this article, a Bäcklund transformation and a nonlinear superposition formula are proven rigorously. As an application of the obtained results, N-soliton solutions are obtained. Therefore, the integrability of this mKdV-type bilinear equation is confirmed.
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    Journal of Mathematical Physics 35 (1994), S. 4725-4738 
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    Notes: In this paper all the potential constraints (with or without first-order partial derivatives) of the KP system, from which the associated linear problem can be restricted into a (1+1)-dimensional Hamiltonian equation, are obtained by using the sufficient and necessary condition for a nonlinear equation to be a Hamiltonian system. Some well-known integrable systems, such as (1+1)-dimensional AKNS system, generalized NS system, and several new Hamiltonian equations, are deduced as particular examples.
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    Journal of Mathematical Physics 35 (1994), S. 4799-4808 
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    Notes: A more simple form than the one given by Vaklev [J. Math. Phys. 33, 4111 (1992)] for the soliton solutions related to the quadratic bundle [E. A. Kuznetzov and A. V. Mikhailov, Teor. Mat. Fiz. 30, 303 (1977); D. J. Kaup and A. C. Newell, J. Math. Phys. 19, 798 (1978); V. S. Gerdjikov, M. I. Ivanov, and P. P. Kulish, Teor. Mat. Fiz. 44, 342 (1980); V. S. Gerdjikov and M. I. Ivanov, Bulg. J. Phys. 10, 13 (1983); 10, 2, 129 (1983)] is obtained. The corresponding solutions for the gauge equivalent case are obtained as well. Among them one can find the N-soliton solutions for the derivative nonlinear Schrödinger equation, their gauge equivalents, etc. The method used in the article allows one to express some integrals by means of appropriate determinants and thus the result is obtained without integration.
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    Journal of Mathematical Physics 35 (1994), S. 4157-4177 
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    Notes: For an asymptotically flat initial-data set in general relativity, the total mass-momentum may be interpreted as a Hermitian quadratic form on the complex, two-dimensional vector space of "asymptotic spinors.'' A generalization to an arbitrary initial-data set is obtained. The mass-momentum is retained as a Hermitian quadratic form, but the space of "asymptotic spinors'' on which it is a function is modified. Indeed, the dimension of this space may range from zero to infinity, depending on the initial data. There is given a variety of examples and general properties of this generalized mass-momentum.
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    Journal of Mathematical Physics 35 (1994), S. 4217-4246 
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    Notes: The spectral function (also known as the Plancherel measure), which gives the spectral distribution of the eigenvalues of the Laplace–Beltrami operator, is calculated for a field of arbitrary integer spin (i.e., for a symmetric traceless and divergence-free tensor field) on the N-dimensional real hyperbolic space (HN). In odd dimensions the spectral function μ(λ) is analytic in the complex λ plane, while in even dimensions it is a meromorphic function with simple poles on the imaginary axis, as in the scalar case. For N even a simple relation between the residues of μ(λ) at these poles and the (discrete) degeneracies of the Laplacian on the N sphere (SN) is established. A similar relation between μ(λ) at discrete imaginary values of λ and the degeneracies on SN is found to hold for N odd. These relations are generalizations of known results for the scalar field. The zeta functions for fields of integer spin on HN are written down. Then a relation between the integer-spin zeta functions on HN and SN is obtained. Applications of the zeta functions presented here to quantum field theory of integer spin in anti-de Sitter space–time are pointed out.
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    Journal of Mathematical Physics 35 (1994), S. 4268-4276 
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    Notes: In this article the q-deformed gamma function and q-deformed beta function are discussed in detail. Three definitions for the q-gamma function are obtained and the q-deformed duplication and multiplication formulas are proven. The q-beta function is defined and its useful properties are derived.
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    Journal of Mathematical Physics 35 (1994), S. 4303-4333 
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    Notes: "Classical'' topological entropy is one of the main numerical invariants in topological dynamics on compact spaces. Here, the author's recent development of a noncommutative generalization of topological entropy, in the natural setting of general C*-algebras as the noncommutative counterpart of continuous function algebras on compact spaces, is presented in a slightly modified and improved form. This includes both a survey of earlier results with some important corrections, and also new general results in response to (and inspired by) a more recent counterproposal for a noncommutative topological entropy by Thomsen. Finally, some partially new examples for the calculation of the defined topological entropy are shown. The rather self-evident physical interpretation in the framework of (operator-algebraic) quantum statistical mechanics and of "chaotic'' quantum dynamical systems is briefly touched upon.
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    Journal of Mathematical Physics 35 (1994), S. 4383-4390 
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    Notes: For the fundamental boson realization of SU(N) in its principal SO(3) basis, the generators of SU(N) are SO(3) tensor operators constructed out of one single type of boson, namely a boson with SO(3) multiplet label (N−1)/2. Here, the adjoint boson realization of SU(N) is given: this time the SO(3) tensor operators are constructed by means of N−1 types of bosons [those with SO(3) labels 1,2,..., N−1]. The validity of this realization depends upon a new identity between 6j coefficients. From this realization, or equivalently from this new identity, one can deduce the existence of a family of structural zeros of 6j coefficients.
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    Journal of Mathematical Physics 35 (1994), S. 3817-3844 
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    Notes: This article presents a theory of scalar quantum fields based on nonstandard analysis. Free scalar momentum fields and free Klein–Gordon fields are treated first. It is shown that the nonrigorous formalism of the standard theory can be replaced by a mathematically rigorous nonstandard theory. The second quantized energy–momentum operators are derived and the free quantum fields are diagonalized. Interacting scalar fields are considered and a nonstandard scattering operator is derived. A nonstandard counterpart to Wick's theorem is developed and the φ4 interaction is briefly discussed.
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    Journal of Mathematical Physics 35 (1994), S. 3889-3915 
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    Notes: General adiabatic evolutions associated to Hamiltonians, which admit a holomorphic extension with respect to the time variable in a complex strip, and whose spectrum satisfies a gap condition are studied. An explicit rate of exponential decay is given, which is related to simple geometric quantities associated to the spectrum of the Hamiltonian, for the transition probability between the two parts of the spectrum when the evolution is taken from −∞ to +∞.
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    Journal of Mathematical Physics 35 (1994), S. 3959-3968 
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    Notes: The classical phase space structure of N SU(n+1) non-Abelian Chern-Simons (NACS) particles is investigated by first constructing the product space of associated SU(n+1) bundle with CPn as the fiber. The Poisson bracket is calculated using the symplectic structure on the associated bundle and it is found that the minimal substitution in the presence of external gauge fields is equivalent to the modification of symplectic structure by the addition of field strength two form. Then, a direct product of the associated bundle is taken by the space of all connections and a specific connection is chosen by the condition of vanishing momentum map corresponding to the gauge transformation, thus recovering the quantum mechanical model of NACS particles in Lee and Oh [Phys. Rev. Lett. 72, 1141 (1994)].
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    Journal of Mathematical Physics 35 (1994), S. 3998-4004 
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    Notes: A model is proposed for calculating the magnetic susceptibility of isotropic classical spin chains showing nearest neighbor correlated cationic distributions. It allows one to obtain a general closed-form expression: This expression formally looks like previous ones obtained in the case of random chains for which the neighboring cationic species are not correlated; but here the previous intervening scalar parameters are replaced by vectorial and matricial expressions.
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    Journal of Mathematical Physics 35 (1994), S. 4057-4066 
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    Notes: Recently a doubly periodic solution of the Kadomtsev–Petviashvili equation was deduced by summing over component solitons. The same solution was derived directly by the Hirota bilinear method. This alternate route enables one to obtain a new solution. Such a mechanism can also be applied to wavepacket dynamics, e.g., the Davey–Stewartson equation.
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    Journal of Mathematical Physics 35 (1994), S. 4178-4183 
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    Notes: The mass of gravitational sources differs by a factor of 2 when computed by the Komar superpotential and when computed in the gravitational weak field limit. The difference has been recognized for some time since both the linearized theory and the Einstein pseudotensor yield the same value, different by a factor of 2 from the Komar mass. The great advantage of the Komar superpotential over other methods is its tensorial formulation, however it fails to produce a Noether quantity. A different tensorial method is suggested that is free of the mass anomaly, namely, the zero and first Taub numbers [Phys. Rev. D 47, 474 (1993)] which are indeed Noether quantities. The zeroth Taub number is obtained from the Penrose–Goldberg superpotential [Phys. Rev. D 41, 410 (1990)].
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    Journal of Mathematical Physics 35 (1994), S. 4372-4382 
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    Notes: The power density estimation problem with a priori information about spectrum is considered. The problem is reduced to a power density estimation problem with spectral gaps. The solution of the problem is studied in the context of the trigonometric moment problem with gaps. The necessary and sufficient conditions are established for the existence of solution and all solutions are described in indeterminate cases. A new definition of the entropy functional is given. The effective algorithm to construct maximum entropy solution is proposed. A number of explicit illustrations are presented.
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    Journal of Mathematical Physics 35 (1994), S. 3253-3260 
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    Notes: A realization of the Heisenberg q-algebra whose generators are first-order difference operators on the full real line is discussed herein. The eigenfunctions of the corresponding q-oscillator Hamiltonian are given explicitly in terms of the q−1-Hermite polynomials. The nonuniqueness of the measure for these q-oscillator states is also studied.
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    Journal of Mathematical Physics 35 (1994), S. 3261-3272 
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    Notes: The osp(1,2) Gaudin algebra is defined and integrable models described by it are considered. The models include the osp(1,2) Gaudin magnet and the Dicke model related to it. Detailed discussion of the simplest cases of these models is presented. The effect of the presence of fermions on the separation of variables is indicated.
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    Journal of Mathematical Physics 35 (1994), S. 2978-2982 
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    Notes: In this article, a system of finite-dimensional involutive functions is presented and proven to be integrable in the Liouville sense. By using the nonlinearization method, the C. Neumann system associated with the modified Korteweg–de Vries (mKdV) hierarchy is obtained. Thus, the C. Neumann system is shown to be completely integrable via a gauge transformation between it and an integrable Hamiltonian system. Finally, the solution of a stationary mKdV equation and the involutive solutions of the mKdV hierarchy are secured. As two examples, the involutive solutions are given for the mKdV equation: vt+1/4vxxx−3/2v2vx=0 and the 5th mKdV equation vt−1/16vxxxxx+5/8v2vxxx +5/2vvxvxx +5/8v3x−3/40v4vx=0.
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    Journal of Mathematical Physics 35 (1994), S. 3025-3028 
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    Notes: An algebraically special solution of the Regge–Wheeler–Zerilli equation that has not been noticed is examined. This solution is proved to be related to Chandrasekhar's solution but has a simpler analytical expression.
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    Journal of Mathematical Physics 35 (1994), S. 3769-3769 
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    Journal of Mathematical Physics 35 (1994), S. 3043-3050 
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    Notes: The vacuum fluctuations for an impulsive spherical gravitational wave due to the snapping of a "rotating'' cosmic string are calculated herein. This is complementary to the previous calculation due to a snapping string, which had the null result. Although the mathematical expressions are different at the intermediate steps, the same null result is found.
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    Journal of Mathematical Physics 35 (1994), S. 3163-3177 
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    Notes: Vector coherent state theory is used to give an algorithm for constructing the so(5) irreps of type [N,0] and [N,N] in the physical so(3) basis. The construction is remarkably simple and permits the matrices of the so(5) operators, for irreps of low-dimension and/or small multiplicities, to be computed by hand. The construction is applied to the [2,0] and [2,2] irreps to illustrate the process.
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    Journal of Mathematical Physics 35 (1994), S. 3146-3162 
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    Notes: An analytical method to calculate invariants is developed, based on the theory of complete systems of simultaneous linear first order partial differential equations. The application of this algorithm to the general case, in which the invariants are not polynomials is included. For the case of Lie algebras with one invariant the procedure of finding the invariant can be computerized. As an example of this procedure, the algorithm is applied in the calculation of the invariants of the group SA(n,R). The explicit construction of its invariants for n=2, 3, 4 is given. A theorem determining the order of a polynomial invariant of a Lie group is proven allowing us to show that the invariant of SA(n,R) is a homogeneous polynomial of order 1/2n(n+1) in the generators. From this fact an immediate consequence is that the order in the generators of translations is n. The method is also applied in the calculation of invariants of the dimension six solvable Lie algebras, and dimension seven nilpotent.
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    Journal of Mathematical Physics 35 (1994), S. 2074-2082 
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    Notes: The structure of generalized supersymmetry with mutually commuting involutions for the meromorphic supersymmetric quantum mechanics on the compact Riemann surface is introduced. For this purpose a Riemann surface is considered as a self-conjugate complex manifold. On this basis the Witten index for the new involution is calculated.
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    Journal of Mathematical Physics 35 (1994), S. 2142-2156 
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    Notes: The connection between supersymmetric quantum mechanics and the Korteweg–de Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation of the conservation laws, and gives some insight into the Miura transformation that converts the KdV equation into the modified KdV equation. The construction of the τ function by means of supersymmetric quantum mechanics is discussed.
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    Journal of Mathematical Physics 35 (1994), S. 2210-2217 
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    Notes: A nonprincipal value prescription is used to define the spurious singularities of Yang–Mills theory in the temporal gauge. Typical one-loop dimensionally regularized temporal-gauge integrals in the prescription are explicitly calculated, and a regularization for the spurious gauge divergences is introduced. The divergent part of the one-loop self-energy is shown to be local and has the same form as that in the spatial axial gauge with the principal-value prescription. The renormalization of the theory is also briefly mentioned.
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    Journal of Mathematical Physics 35 (1994), S. 2233-2258 
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    Notes: In this paper, the classical two-fluid model for superconductors is used to determine the time-dependent partial differential equations (PDEs) which govern wave propagation in superconducting media. These equations are then solved exactly in both two and three dimensions using localized wave solutions rather than the traditional eigenfunction solutions. We have applied these localized wave solutions to the problem of a symmetric superconducting slab, neglecting the normally conducting current density, and found that the resultant focus wave mode magnetic field solution expels flux from the interior of the slab and can regain its initial amplitude as it travels along the surface of the slab. A comparison of the transverse part of the localized wave solution with the transverse part of the more usual plane wave solution shows remarkable agreement.
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    Journal of Mathematical Physics 35 (1994), S. 2309-2314 
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    Notes: The Dirac equation is rewritten in the framework of a Clifford algebra, revealing some new features, of which the most interesting is the U(1)×SU(2) symmetry of the corresponding Lagrangian.
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    Journal of Mathematical Physics 35 (1994), S. 2357-2370 
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    Notes: The field fluctuations are studied for the free and imperfect Bose gas. In the phase where there is condensation, these field fluctuations are abnormal, with critical exponents depending on the way the symmetry-breaking external field tends to zero in the thermodynamic limit. On the critical line there is also abnormal behavior, but the dependence on the way the field disappears, is slightly different. For densities below the critical density, the fluctuations are normal and independent of the way the external field goes to zero.
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    Journal of Mathematical Physics 35 (1994), S. 2390-2396 
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    Notes: Using the inverse strong symmetry of the Korteweg–de Vries (KdV) equation on the trivial symmetry and τ0 symmetry, one gets four new sets of symmetries of the KdV equation. These symmetries are expressed explicitly by the multi-integrations of the Jost function of the KdV equation and constitute an infinite dimensional Lie algebra together with two hierarchies of the known symmetries. Contrary to the general belief, the time-independent symmetry groups of the KdV and mKdV equations are non-Abelian and the infinite dimensional Lie algebras of the KdV and mKdV equations are nonisomorphic though two equations are related by the Miura transformation. Starting from these sets of symmetries, four hierarchies of the integrodifferential KdV equations, which can be solved by the Schrödinger inverse scattering transformation method, are obtained. Some of these hierarchies enjoy a common strong symmetry and/or same local conserved densities.
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    Journal of Mathematical Physics 35 (1994), S. 2397-2407 
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    Notes: From a bi-Hamiltonian viewpoint the equivalence of two supersymmetric Korteweg–deVries theories, introduced by Manin–Radul and Laberge–Mathieu, is discussed herein. It is shown that the transformation connecting the two theories (proposed recently in the literature) preserves the bi-Hamiltonian structures; moreover, another derivation of this transformation, stemming from bi-Hamiltonian reduction theory and strongly emphasizing the geometrical meaning of the above equivalence is presented.
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    Journal of Mathematical Physics 35 (1994), S. 2485-2489 
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    Notes: In this comment we obtain two types of solutions of the graded Yang–Baxter equation whose symmetry group is GLqs(1||1).
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    Journal of Mathematical Physics 35 (1994), S. 2505-2515 
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    Notes: The osp(1||2) algebra is first realized through one boson and two fermion pairs of creation annihilation operators and then both osp(1||2) and osp(3||2) are realized in terms of three boson and two fermion pairs. All these realizations are reducible, and the reduced states are labeled by the total occupation number.
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    Journal of Mathematical Physics 35 (1994), S. 2560-2569 
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    Notes: Algebras that represent a generalization of both quantum groups, quantum supergroups, and braided groups are defined. They are given by a pair of solutions of the Yang–Baxter equation that satisfy some additional conditions. Several examples are presented.
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    Journal of Mathematical Physics 35 (1994), S. 2617-2632 
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    Notes: An addition law is introduced for the usual quantum matrices A(R) by means of a coaddition Δ(underbar)t=t⊗1+1⊗t. It supplements the usual comultiplication Δt=t⊗t and together they obey a codistributivity condition. The coaddition does not form a usual Hopf algebra but a braided one. The same remarks apply for rectangular m×n quantum matrices. As an application, left-invariant vector fields are constructed on A(R) and other quantum spaces. They close in the form of a braided Lie algebra. As another application, the wave functions in the lattice approximation of Kac–Moody algebras and other lattice fields can be added and functionally differentiated.
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    Journal of Mathematical Physics 35 (1994), S. 3074-3088 
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    Notes: Representations of the n-braid group where generators are given by matrices whose elements belong to a noncommutative algebra are discussed. Representation of this algebra in a Hilbert space generalizes the Burau representation. Two algebras which are closely related and are physically indistinguishable provided that a particular eigenvalue is fine tuned are discussed. It is shown that the generalized oscillator system given by one of the algebras generates a hydrogenlike spectrum.
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    Journal of Mathematical Physics 35 (1994), S. 1513-1521 
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    Notes: The Wigner–Poisson (WP) system (or quantum Vlasov–Poisson system) is modified to include dissipative terms in the Hamiltonian. By utilizing the equivalence of the WP system to the Schrödinger–Poisson system, global existence and uniqueness are proved and regularity properties are deduced. The proof differs somewhat from that for the nondissipative case treated previously by Brezzi–Markowich and Illner et al.; in particular the Hille–Yosida Theorem is used since the linear evolution is not unitary, and a Liapunov function is introduced to replace the energy, which is not conserved.
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    Journal of Mathematical Physics 35 (1994), S. 1555-1572 
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    Notes: A quantum logic formulation of quantum measurements is introduced using Boolean powers of orthomodular σ-posets to the description of the coupled system. A comparison with the traditional Hilbert space approach to quantum measurements and a discussion of some important classes of measurements is given.
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    Journal of Mathematical Physics 35 (1994), S. 1634-1643 
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    Notes: Nonlinear wave equations describing forced vibrations of a string subject to random perturbations of intensity ε are studied herein. Two kinds of random perturbations are considered; one is Gaussian in the form of initial white noise and the other is a non-Gaussian random forcing which involves the formal derivative of a Brownian sheet. The solutions uε(t,x) of the complete forced equation are a stochastic process in space and time which has a unique stochastic equilibrium. The time variable t varies in a finite interval I:=[0, T], where T is a fixed positive time, and the space variable x varies in an interval J. Assuming that the initial conditions are of sufficient regularity, the fluctuations uε(t,x) from u0(t,x), the unperturbed solution, are analyzed as the intensity of perturbation ε↓0.
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    Journal of Mathematical Physics 35 (1994), S. 2423-2429 
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    Notes: Study of radial and circular geodesics including those of tachyons in two spherically symmetric vacuum five-dimensional space–time is done. One of them is of Schwarzschild type and the other the so-called soliton solution. We obtain results which are different from the usual analogous four-dimensional (4D) ones. It is found that all the circular geodesics irrespective of whether they are timelike, null, or spacelike will be stable in the region r(approximately-greater-than)6M. It has also been shown that in a homogeneous cosmological model where the isotropic 3 space expands but the extra space contracts with time, the existence of tachyon is possible. This is in contradiction to the analogous 4D result obtained previously.
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    Journal of Mathematical Physics 35 (1994), S. 2463-2484 
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    Notes: It is shown that Bäcklund transformations (BTs) and zero-curvature representations (ZCRs) of systems of partial differential equations (PDEs) are closely related. The connection is established by nonlinear representations of the symmetry group underlying the ZCR which induce gauge transformations relating different BTs. This connection is used to construct BTs from ZCRs (and vice versa). Furthermore a procedure is outlined which allows a systematic search for ZCRs of a given system of PDEs.
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    Journal of Mathematical Physics 35 (1994), S. 2516-2538 
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    Notes: Using the supersymplectic framework of Berezin, Kostant, and others, two types of supersymmetric extensions of the Schrödinger algebra (itself a conformal extension of the Galilei algebra) were constructed. An ‘I-type' extension exists in any space dimension, and for any pair of integers N+ and N−. It yields an N=N++N− superalgebra, which generalizes the N=1 supersymmetry Gauntlett et al. found for a free spin-1/2 particle, as well as the N=2 supersymmetry of the fermionic oscillator found by Beckers et al. In two space dimensions, new, ‘exotic' or ‘IJ-type' extensions arise for each pair of integers ν+ and ν−, yielding an N=2(ν++ν−) superalgebra of the type discovered recently by Leblanc et al. in nonrelativistic Chern–Simons theory. For the magnetic monopole the symmetry reduces to o(3)×osp(1/1), and for the magnetic vortex it reduces to o(2)×osp(1/2).
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    Journal of Mathematical Physics 35 (1994), S. 2583-2606 
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    Notes: In the present paper all typical finite-dimensional representations of the quantum Lie superalgebra Uq[gl(2/2)] are constructed at generic deformation parameter q. As in the nondeformed case, the finite-dimensional Uq[gl(2/2)]-module Wq obtained is irreducible and can be decomposed into finite-dimensional irreducible Uq[gl(2)⊕gl(2)]-submodules Vqk.
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    Journal of Mathematical Physics 35 (1994), S. 1463-1470 
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    Notes: The geometric phase has been defined as the holonomy of two bundles with different base spaces and different connections. In this article we establish the relation between the Berry–Simon and the Anandan–Aharonov definitions for a large class of cyclic Hamiltonians (with N-fold degeneracy) using the classifying theorem for principal fiber bundles.
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    Journal of Mathematical Physics 35 (1994), S. 1549-1554 
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    Notes: It is shown that the polynomials introduced recently by Aldaya, Bisquert, and Navarro-Salas [Phys. Lett. A 156, 381 (1991)] in connection with a relativistic generalization of the quantum harmonic oscillator can be expressed in terms of Gegenbauer polynomials. This fact is useful in the investigation of the properties of the corresponding wave function. Some examples are given, in particular, related to the asymptotic behavior and to the distribution of zeros of the polynomials for large quantum numbers.
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    Journal of Mathematical Physics 35 (1994), S. 1597-1621 
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    Notes: The eigenvalue problem for the radial Schrödinger equation with an "almost'' Coulomb potential is considered. This problem provides the simplest example of a system whose classical trajectories have singularities. Thus the standard semiclassical quantization procedure (in the sense of Einstein–Brillouin–Keller–Maslov) cannot be applied straightforwardly to this situation. The equation under consideration has two transition points on the half axis 0〈x〈∞: a regular singular point at the origin and a turning point for some x0(approximately-greater-than)0; these points coalesce at low energy levels. The well-known comparison equation method provides uniform asymptotics for equations of this kind, but has the following shortcomings: it does not appeal to the corresponding classical mechanical problem and the formulas for the eigenvalues and eigenfunctions contain phase integrals which are not analytic with respect to the parameter characterizing the closeness of the transition points. In the present article we derive new formulas for the eigenfunctions in the form of inverse Fourier transforms of rapidly oscillating exponentials multiplied by some powers of x, together with simple formulas for the eigenvalues. These formulas are directly connected with the classical trajectories and do not have the shortcomings of the comparison equation method, i.e., all the functions entering the asymptotic expansions are analytic in x and energy. As a by-product, an asymptotic expansion of integrals having two stationary phase points which coalesce for some value of the parameter and tend to infinity when the parameter tends to zero is obtained.
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    Journal of Mathematical Physics 35 (1994), S. 1668-1687 
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    Notes: Using the formulation in terms of principal fiber bundles, it is shown that the external symmetry implies the conservation of the energy-momentum tensor for a general gauge theory. When applying this theory to the case of Dirac fields, one is naturally forced to replace the dependence on the metric by the dependence on the underlying spin structure in the variational problems.
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    Journal of Mathematical Physics 35 (1994), S. 2570-2582 
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    Notes: A study of the superconformal covariantization of superdifferential operators defined on (1||1) superspace is presented. It is shown that a superdifferential operator with a particular type of constraint can be covariantized only when it is of odd order. In such a case, the action of superconformal transformation on the superdifferential operator is nothing but a Hamiltonian flow defined by the corresponding supersymmetric second Gelfand–Dickey bracket. The covariant form of a superdifferential operator of odd order is given.
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    Journal of Mathematical Physics 35 (1994), S. 2648-2656 
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    Notes: Inversion formulas are obtained for the restrictions of the Hartley and Hilbert transforms to R+. Regularity results are derived, and an illustrative example presented.
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    Journal of Mathematical Physics 35 (1994), S. 2633-2647 
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    Notes: The noncommutative geometry corresponding to arbitrary braidings is studied in a purely algebraical way. The new and original proposal of the geometry is given in terms of the theory of braided monoidal categories. The quantum oscillator is considered as an example of application of our geometry.
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    Journal of Mathematical Physics 35 (1994), S. 1445-1462 
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    Notes: Hamiltonians with strong Wigner–von Neumann potentials are known to possess bound states in the continuous spectrum. For smaller couplings these bound states become resonances, which appear as singularities of the m-function. These singularities are intimately connected with the decay of the corresponding subordinate eigenfunction. For Coulomb-type potentials with Schrödinger operators this has recently be shown by Atkinson, the author, and Hinton, Klaus and Shaw. Here these results are extended to a general class of Wigner–von Neumann potentials for Dirac and Schrödinger operators.
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    Journal of Mathematical Physics 35 (1994), S. 1487-1512 
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    Notes: A study is made of the real-energy limits of approximate solutions of the Chandler–Gibson equations, as well as the real-energy limits of the approximate equations themselves. It is proved that (1) the approximate time-independent transition operator Tπ(z) and an auxiliary operator Mπ(z), when restricted to finite energy intervals, are trace class operators and have limits in trace norm for almost all values of the real energy; (2) the basic dynamical equation that determines the operator Mπ(z), when restricted to the space of trace class operators, has a real-energy limit in trace norm for almost all values of the real energy; (3) the real-energy limit of Mπ(z) is a solution of the real-energy limit equation; (4) the diagonal (on-shell) elements of the kernels of the real-energy limit of Tπ(z) and of all solutions of the real-energy limit equation exactly equal the on-shell transition operator, implying that the real-energy limit equation uniquely determines the physical transition amplitude; and (5) a sequence of approximate on-shell transition operators converges strongly to the exact on-shell transition operator. These mathematically rigorous results are believed to be the most general of their type for nonrelativistic N-body quantum scattering theories.
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    Journal of Mathematical Physics 35 (1994), S. 1951-1975 
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    Notes: In his classic book on group representations and special functions Vilenkin studied the matrix elements of irreducible representations of the Euclidean and oscillator Lie algebras with respect to countable bases of eigenfunctions of the Cartan subalgebras, and he computed the summation identities for Bessel functions and Laguerre polynomials associated with the addition theorems for these matrix elements. He also studied matrix elements of the pseudo-Euclidean and pseudo-oscillator algebras with respect to the continuum bases of generalized eigenfunctions of the Cartan subalgebras of these Lie algebras and this resulted in realizations of the addition theorems for the matrix elements as integral transform identities for Bessel functions and for confluent hypergeometric functions. Here we work out q analogs of these results in which the usual exponential function mapping from the Lie algebra to the Lie group is replaced by the q-exponential mappings Eq and eq. This study of representations of the Euclidean quantum algebra and the q-oscillator algebra (not a quantum algebra) leads to summation, integral transform, and q-integral transform identities for q analogs of the Bessel and confluent hypergeometric functions, extending the results of Vilenkin for the q=1 case.
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    Journal of Mathematical Physics 35 (1994), S. 1998-2012 
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    Notes: The problem of the correspondence between symmetries and conservation laws for partial differential equations is considered. For Lagrangian systems the set of Noether (variational) symmetries can be shown to lead to the set of all local conservation laws. For partial differential equations without well-defined Lagrangian functions there is no universal correspondence between symmetries and conservation laws. In this article it is shown that for a large class of differential equations there is a natural way to associate conservation laws with symmetries. The class consists of many interesting equations, e.g., Korteweg–de Vries equation, Kadomtsev–Petviashvili equation, Boussinesq equation, nonlinear diffusion equation, Monge–Ampère equation, regularized long-wave equation, and Navier–Stokes equations. Characteristics of the corresponding conservation laws are calculated and examples are given. For Lagrangian systems the consistency of the approach with the standard Noether results is discussed.
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    Journal of Mathematical Physics 35 (1994), S. 1066-1094 
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    Notes: A rigorous derivation of the semiclassical Liouville equation for electrons which move in a crystal lattice (without the influence of an external field) is presented herein. The approach is based on carrying out the semiclassical limit in the band-structure Wigner equation. The semiclassical macroscopic densities are also obtained as limits of the corresponding quantum quantities.
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    Journal of Mathematical Physics 35 (1994), S. 1139-1170 
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    Notes: A formulation of the complete dynamics of electrons and nuclei is presented. The dynamical equations are derived using the time-dependent variational principle (TDVP). The approximate electronic state vectors are antisymmetrized geminal power (AGP) states parameterized as projected coherent states, while the nuclei are treated as classical point particles. This leads to a formulation of time-dependent AGP theory that generalizes time-dependent Hartree–Fock (TDHF) theory and explicitly includes the dynamics of the nuclei. The linear approximation to the evolution equations (the classical harmonic approximation) which corresponds to a generalized random phase approximation (RPA) based on an AGP electronic reference state and which explicitly includes the dynamics of the nuclei, is studied and presented in this paper. The equations are formulated in terms of the primitive nonorthogonal electronic atomic basis thus avoiding any transformation to orthonormal molecular orbitals during the evolution.
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    Journal of Mathematical Physics 35 (1994), S. 1202-1218 
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    Notes: Chaos in adiabatic Hamiltonian systems is a recent discovery and a pervasive phenomenon in physics. In this work, a geometric criterion is discussed based on the theory of action from classical mechanics to detect the existence of Smale horseshoe chaos in adiabatic systems. It is used to show that generic adiabatic planar Hamiltonian systems exhibit stochastic dynamics in large regions of phase space. To illustrate the method, results are obtained for three problems concerning relativistic particle dynamics, fluid mechanics, and passage through resonance, results which either could not be obtained with existing methods, or which were difficult and analytically impractical to obtain with them.
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    Journal of Mathematical Physics 35 (1994), S. 1302-1321 
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    Notes: The complete scheme of the application of one- and two-dimensional subspaces and the subgroups method to five-dimensional gravity with a G3 group of motion are presented here in space–time and in potential space formalisms. From this method one obtains the Kramer, Belinsky–Ruffini, Dobiasch–Maison, Clément, Gross–Perry–Sorkin solutions, etc., as special cases.
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    Journal of Mathematical Physics 35 (1994), S. 1348-1360 
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    Notes: The following inequality is established: ||Pn(cos cursive-theta)||〈 [(square root of)1+(π4/16)(n+1/2)4 sin4 cursive-theta]−1, 0〈cursive-theta〈π, n=1,2,..., where Pn(x) denotes the Legendre polynomial of degree n. The relation P2n(cos cursive-theta) + (4/π2)× Q2n(cos cursive-theta) 〈 [(square root of)1+(π4/16)(n+1/2)4 sin4 cursive-theta]−1, n=1,2,..., on [θn1,θn,n+1], is proven where Qn(x) denotes the Legendre function of second kind, cos θn1 the largest zero of Qn(x), and cos θn,n+1=−cos θn1. Similarly we obtain the inequalities ||J0(x)|| 〈 [(square root of)1+(π4/16)x4]−1, x≠0, and J20(x) + Y20(x)〈 [(square root of)1+(π4/16)x4]−1, x≥y1, where y1=0.893577... is the first positive zero of Y0(x), and J0(x), Y0(x) denote the Bessel functions of the first and second kind, respectively. The results of the present paper arise out of some problems of nuclear and particle physics.
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    Journal of Mathematical Physics 35 (1994), S. 1387-1398 
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    Notes: A new family of asymptotic solutions of the Helmholtz equation can be derived. It is shown that new solutions are regular at caustics and turning points and do not require any special functions.
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    Journal of Mathematical Physics 35 (1994), S. 2024-2035 
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    Notes: Operators of the form Tβf(x)=∑Jj=1 cursive-phij(βx)f(σj +ρjx) are considered herein where β is a real parameter; σj and ρj are real numbers, and {cursive-phij} are holomorphic functions which satisfy certain additional conditions. Transfer operators of this form appear in statistical physics: the leading eigenvalue may be interpreted as the free energy of a lattice of interacting particles, as a function of inverse temperature β. A method for obtaining Taylor series expansions in β of the leading and second leading eigenvalues, and the leading eigenfunction are given. The method may be extended to find series expansions for other eigenvalues and eigenfunctions. The radii of convergence of these series have not been found. These results generalize the author's findings in another article [J. Math. Phys. 32, 2718 (1991)].
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    Journal of Mathematical Physics 35 (1994), S. 1054-1065 
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    Notes: A description of the Fock space of a parabose oscillator of order p based on commutation relations bilinear in creation and annihilation operators rather than trilinear ones is developed. A new statement of the well-known Green's ansatz is introduced to help understand the significance of the bilinear commutation relations. It is also applied to show how all parabose oscillators of even order (respectively, odd order) can be obtained as irreducible constituents of the Fock space associated with a Green's ansatz of two (three) terms. Analogs of the form in which the parabose Green's ansatz is presented are provided for one parafermi oscillator and for systems of many parabose and parafermi oscillators of the same order. Methods used in the paper allow various new results for q-deformed parabose oscillators to be derived.
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    Journal of Mathematical Physics 35 (1994), S. 1185-1191 
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    Notes: The time independent Bateman model which describes the damped harmonic oscillator coupled to its dual is studied using the path integral approach. The related propagator is calculated by means of the matrix representation.
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    Journal of Mathematical Physics 35 (1994), S. 1219-1232 
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    Notes: A study of the existence of some integrable systems with nonlinear constants of motion is presented using the approach of the theory of generalized (dynamical or hidden) symmetries. Two Lagrangians are considered, both obtained by modifying the Toda Lagrangian. First a two-particle system is studied and then the results are generalized to a three-particle system. It is shown that in both cases the Lagrangians possess nonlinear constants of motion in involution and, thus, they are integrable.
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    Journal of Mathematical Physics 35 (1994), S. 646-655 
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    Notes: A finite subgroup of the conformal group SL(2,C) can be related to invariant polynomials on a hypersurface in C3. The latter then carries a simple singularity, which resolves by a finite iteration of basic cycles of deprojections. The homological intersection graph of these cycles is the Dynkin graph of an ADE Lie group, i.e., a Lie group from the cartan series A, D, or E. The deformation of the simple singularity corresponds to ADE symmetry breaking. A (3+1)-dimensional topological model of observation is constructed, transforming consistently under SL(2,C), as an evolving three-dimensional system of world tubes, which connect "possible points of observation.'' The existence of an initial singularity for the four-dimensional space–time is related to its global topological structure. Associating the geometry of ADE singularities to the vertex structure of the topological model puts forward the conjecture on a likewise relation of inner symmetries of elementary particles to local space–time structure.
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    Journal of Mathematical Physics 35 (1994), S. 6644-6657 
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    Notes: An exact asymptotically flat axisymmetric solution of the Einstein–Maxwell equations representing the exterior field of two arbitrary Kerr–Newman masses located on the symmetry axis is constructed in explicit form. In a particular case, when the solution describes two identical Kerr–Newman sources, simple analytical formulas are obtained which allow a straightforward analysis of the equilibrium of two charged rotating masses. Some arguments are given in favor of the possibility of the balance of stationary black holes due to their gravitational spin–spin interaction. © 1994 American Institute of Physics.
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