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A Survey in Mathematics for Industry: Two-timing and matched asymptotic expansions for singular perturbation problems
- R. E. O'MALLEY, Jr., E. KIRKINIS
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- Journal:
- European Journal of Applied Mathematics / Volume 22 / Issue 6 / December 2011
- Published online by Cambridge University Press:
- 12 August 2011, pp. 613-629
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Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems. Stud. Appl. Math. 124, 383–410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations.
Contributors
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- By Rose Teteki Abbey, K. C. Abraham, David Tuesday Adamo, LeRoy H. Aden, Efrain Agosto, Victor Aguilan, Gillian T. W. Ahlgren, Charanjit Kaur AjitSingh, Dorothy B E A Akoto, Giuseppe Alberigo, Daniel E. Albrecht, Ruth Albrecht, Daniel O. Aleshire, Urs Altermatt, Anand Amaladass, Michael Amaladoss, James N. Amanze, Lesley G. Anderson, Thomas C. Anderson, Victor Anderson, Hope S. Antone, María Pilar Aquino, Paula Arai, Victorio Araya Guillén, S. Wesley Ariarajah, Ellen T. Armour, Brett Gregory Armstrong, Atsuhiro Asano, Naim Stifan Ateek, Mahmoud Ayoub, John Alembillah Azumah, Mercedes L. García Bachmann, Irena Backus, J. Wayne Baker, Mieke Bal, Lewis V. Baldwin, William Barbieri, António Barbosa da Silva, David Basinger, Bolaji Olukemi Bateye, Oswald Bayer, Daniel H. Bays, Rosalie Beck, Nancy Elizabeth Bedford, Guy-Thomas Bedouelle, Chorbishop Seely Beggiani, Wolfgang Behringer, Christopher M. Bellitto, Byard Bennett, Harold V. Bennett, Teresa Berger, Miguel A. Bernad, Henley Bernard, Alan E. Bernstein, Jon L. Berquist, Johannes Beutler, Ana María Bidegain, Matthew P. Binkewicz, Jennifer Bird, Joseph Blenkinsopp, Dmytro Bondarenko, Paulo Bonfatti, Riet en Pim Bons-Storm, Jessica A. Boon, Marcus J. Borg, Mark Bosco, Peter C. Bouteneff, François Bovon, William D. Bowman, Paul S. Boyer, David Brakke, Richard E. Brantley, Marcus Braybrooke, Ian Breward, Ênio José da Costa Brito, Jewel Spears Brooker, Johannes Brosseder, Nicholas Canfield Read Brown, Robert F. Brown, Pamela K. Brubaker, Walter Brueggemann, Bishop Colin O. Buchanan, Stanley M. Burgess, Amy Nelson Burnett, J. Patout Burns, David B. Burrell, David Buttrick, James P. Byrd, Lavinia Byrne, Gerado Caetano, Marcos Caldas, Alkiviadis Calivas, William J. Callahan, Salvatore Calomino, Euan K. Cameron, William S. Campbell, Marcelo Ayres Camurça, Daniel F. Caner, Paul E. Capetz, Carlos F. Cardoza-Orlandi, Patrick W. Carey, Barbara Carvill, Hal Cauthron, Subhadra Mitra Channa, Mark D. 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- The Cambridge Dictionary of Christianity
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- 05 August 2012
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- 20 September 2010, pp xi-xliv
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Perturbation Methods. By A. H. NAYFEH. Wiley, 1973. 425 pp. £9 (hardback) or £3.75 (paperback).
- R. E. O'malley
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- Journal of Fluid Mechanics / Volume 63 / Issue 3 / 29 April 1974
- Published online by Cambridge University Press:
- 29 March 2006, p. 623
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Co-morbidity and familial aggregation of alcoholism and anxiety disorders
- K. R. MERIKANGAS, D. E. STEVENS, B. FENTON, M. STOLAR, S. O'MALLEY, S. W. WOODS, N. RISCH
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- Psychological Medicine / Volume 28 / Issue 4 / July 1998
- Published online by Cambridge University Press:
- 01 July 1998, pp. 773-788
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Background. This study examined the patterns of familial aggregation and co-morbidity of alcoholism and anxiety disorders in the relatives of 165 probands selected for alcoholism and/or anxiety disorders compared to those of 61 unaffected controls.
Methods. Probands were either selected from treatment settings or at random from the community. DSM-III-R diagnoses were obtained for all probands and their 1053 first-degree relatives, based on direct interview or family history information.
Results. The findings indicate that: (1) alcoholism was associated with anxiety disorders in the relatives, particularly among females; (2) both alcoholism and anxiety disorders were highly familial; (3) the familial aggregation of alcoholism was attributable to alcohol dependence rather than to alcohol abuse, particularly among male relatives; and (4) the pattern of co-aggregation of alcohol dependence and anxiety disorders in families differed according to the subtype of anxiety disorder; there was evidence of a partly shared diathesis underlying panic and alcoholism, whereas social phobia and alcoholism tended to aggregate independently.
Conclusions. The finding that the onset of social phobia tended to precede that of alcoholism, when taken together with the independence of familial aggregation of social phobia and alcoholism support a self-medication hypothesis as the explanation for the co-occurrence of social phobia and alcoholism. In contrast, the lack of a systematic pattern in the order of onset of panic and alcoholism among subjects with both disorders as well as evidence for shared underlying familial risk factors suggests that co-morbidity between panic disorder and alcoholism is not a consequence of self-medication of panic symptoms. The results of this study emphasize the importance of examining co-morbid disorders and subtypes thereof in identifying sources of heterogeneity in the pathogenesis of alcoholism.
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