13 results
Cultural contributions to adults' self-rated mental health problems and strengths: 7 culture clusters, 28 societies, 16 906 adults
- William E. Copeland, Masha Y. Ivanova, Thomas M. Achenbach, Lori V. Turner, Guangyu Tong, Adelina Ahmeti-Pronaj, Alma Au, Monica Bellina, J. Carlos Caldas, Yi-Chuen Chen, Ladislav Csemy, Marina M. da Rocha, Anca Dobrean, Lourdes Ezpeleta, Yasuko Funabiki, Valerie S. Harder, Felipe Lecannelier, Marie Leiner de la Cabada, Patrick Leung, Jianghong Liu, Safia Mahr, Sergey Malykh, Jasminka Markovic, David M. Ndetei, Kyung Ja Oh, Jean-Michel Petot, Geylan Riad, Direnc Sakarya, Virginia C. Samaniego, Sandra Sebre, Mimoza Shahini, Edwiges Silvares, Roma Simulioniene, Elvisa Sokoli, Joel B. Talcott, Natalia Vazquez, Tomasz Wolanczyk, Ewa Zasepa
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- Journal:
- Psychological Medicine / Volume 53 / Issue 16 / December 2023
- Published online by Cambridge University Press:
- 19 May 2023, pp. 7581-7590
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Background
It is unknown how much variation in adult mental health problems is associated with differences between societal/cultural groups, over and above differences between individuals.
MethodsTo test these relative contributions, a consortium of indigenous researchers collected Adult Self-Report (ASR) ratings from 16 906 18- to 59-year-olds in 28 societies that represented seven culture clusters identified in the Global Leadership and Organizational Behavioral Effectiveness study (e.g. Confucian, Anglo). The ASR is scored on 17 problem scales, plus a personal strengths scale. Hierarchical linear modeling estimated variance accounted for by individual differences (including measurement error), society, and culture cluster. Multi-level analyses of covariance tested age and gender effects.
ResultsAcross the 17 problem scales, the variance accounted for by individual differences ranged from 80.3% for DSM-oriented anxiety problems to 95.2% for DSM-oriented avoidant personality (mean = 90.7%); by society: 3.2% for DSM-oriented somatic problems to 8.0% for DSM-oriented anxiety problems (mean = 6.3%); and by culture cluster: 0.0% for DSM-oriented avoidant personality to 11.6% for DSM-oriented anxiety problems (mean = 3.0%). For strengths, individual differences accounted for 80.8% of variance, societal differences 10.5%, and cultural differences 8.7%. Age and gender had very small effects.
ConclusionsOverall, adults' self-ratings of mental health problems and strengths were associated much more with individual differences than societal/cultural differences, although this varied across scales. These findings support cross-cultural use of standardized measures to assess mental health problems, but urge caution in assessment of personal strengths.
3 - The spt-function of Andrews
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- By William Y. C. Chen, Tianjin University
- Edited by Anders Claesson, University of Iceland, Reykjavik, Mark Dukes, University College Dublin, Sergey Kitaev, University of Strathclyde, David Manlove, University of Glasgow, Kitty Meeks, University of Glasgow
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- Surveys in Combinatorics 2017
- Published online:
- 21 July 2017
- Print publication:
- 30 June 2017, pp 141-203
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Zeta Functions and the Log Behaviour of Combinatorial Sequences
- William Y. C. Chen, Jeremy J. F. Guo, Larry X. W. Wang
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 58 / Issue 3 / October 2015
- Published online by Cambridge University Press:
- 21 July 2015, pp. 637-651
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In this paper, we use the Riemann zeta function ζ(x) and the Bessel zeta function ζμ(x) to study the log behaviour of combinatorial sequences. We prove that ζ(x) is log-convex for x > 1. As a consequence, we deduce that the sequence {|B2n|/(2n)!}n ≥ 1 is log-convex, where Bn is the nth Bernoulli number. We introduce the function θ(x) = (2ζ(x)Γ(x + 1)) 1/x, where Γ(x) is the gamma function, and we show that logθ(x) is strictly increasing for x ≥ 6. This confirms a conjecture of Sun stating that the sequence is strictly increasing. Amdeberhan et al. defined the numbers an(μ) = 2 2n+1 (n + 1)!(μ+ 1)nζμ(2n) and conjectured that the sequence {an(μ)}n≥1 is log-convex for μ = 0 and μ = 1. By proving that ζμ(x) is log-convex for x > 1 and μ > -1, we show that the sequence {an(≥)}n>1 is log-convex for any μ > - 1. We introduce another function θμ,(x) involving ζμ(x) and the gamma function Γ(x) and we show that logθμ(x) is strictly increasing for x > 8e(μ + 2)2. This implies that
Based on Dobinski’s formula, we prove that
where Bn is the nth Bell number. This confirms another conjecture of Sun. We also establish a connection between the increasing property of and Holder’s inequality in probability theory.
Contributors
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- By Hamid M. Abdolmaleky, Cory Adamson, Paola Allavena, Dimitrios Anastasiou, Johanna Apfel, Surinder K. Batra, Mark E. Burkard, Amancio Carnero, Michael J. Clemens, Jeanette Gowen Cook, Isabel Dominguez, Jeremy S. Edwards, Wafik S. El-Deiry, Androulla Elia, Mohammad R. Eskandari, Aurora Esquela-Kerscher, Manel Esteller, Rob M. Ewing, Douglas V. Faller, Kristopher Frese, Xijin Ge, Giovanni Germano, Daniel A. Haber, William C. Hahn, Antoine Ho, Christine Iacobuzio-Donahue, Sergii Ivakhno, Prasad V. Jallepalli, Rosanne Jones, Sharyn Katz, Arnaud Krebs, Karl Krueger, Arthur W. Lambert, Adam Lerner, Holly Lewis, Jason W. Locasale, Giselle Y. López, Shyamala Maheswaran, Alberto Mantovani, José Ignacio Martín-Subero, Simon J. Morley, Oliver Müller, Kathleen R. Nevis, Sait Ozturk, Panagiotis Papageorgis, Jignesh R. Parikh, Steven M. Powell, Kimberly L. Raiford, Andrew M. Rankin, Patricia Reischmann, Simon Rosenfeld, Marc Samsky, Anthony Scott, Shantibhusan Senapati, Yashaswi Shrestha, Anurag Singh, Rakesh K. Singh, Gromoslaw A. Smolen, Sudhir Srivastava, Simon Tavaré, Sam Thiagalingam, László Tora, David Tuveson, Asad Umar, Matthew G. Vander Heiden, Cyrus Vaziri, Zhenghe John Wang, Kevin Webster, Chen Khuan Wong, Yu Xia, Hai Yan, Jian Yu, Lihua Yu, Min Yu, Lin Zhang, Jin-Rong Zhou
- Edited by Sam Thiagalingam
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- Book:
- Systems Biology of Cancer
- Published online:
- 05 April 2015
- Print publication:
- 09 April 2015, pp ix-xiv
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2-Log-Concavity of the Boros–Moll Polynomials
- William Y. C. Chen, Ernest X. W. Xia
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- Proceedings of the Edinburgh Mathematical Society / Volume 56 / Issue 3 / October 2013
- Published online by Cambridge University Press:
- 21 August 2013, pp. 701-722
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The Boros–Moll polynomials Pm (a) arise in the evaluation of a quartic integral. It has been conjectured by Boros and Moll that these polynomials are infinitely log-concave. In this paper, we show that Pm (a) is 2-log-concave for any m ≥ 2. Let di (m) be the coefficient of ai in Pm (a). We also show that the sequence is log-concave.
Real-Time Classification of Transient Events in Synoptic Sky Surveys
- Ashish A. Mahabal, C. Donalek, S. G. Djorgovski, A. J. Drake, M. J. Graham, R. Williams, Y. Chen, B. Moghaddam, M. Turmon
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- Journal:
- Proceedings of the International Astronomical Union / Volume 7 / Issue S285 / September 2011
- Published online by Cambridge University Press:
- 20 April 2012, pp. 355-357
- Print publication:
- September 2011
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An automated rapid classification of the transient events detected in modern synoptic sky surveys is essential for their scientific utility and effective follow-up when resources are scarce. This problem will grow by orders of magnitude with the next generation of surveys. We are exploring a variety of novel automated classification techniques, mostly Bayesian, to respond to those challenges, using the ongoing CRTS sky survey as a testbed. We describe briefly some of the methods used.
Recurrence Relations for Strongly q-Log-Convex Polynomials
- William Y. C. Chen, Larry X. W. Wang, Arthur L. B. Yang
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- Journal:
- Canadian Mathematical Bulletin / Volume 54 / Issue 2 / 01 June 2011
- Published online by Cambridge University Press:
- 20 November 2018, pp. 217-229
- Print publication:
- 01 June 2011
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We consider a class of strongly $q$-log-convex polynomials based on a triangular recurrence relation with linear coefficients, and we show that the Bell polynomials, the Bessel polynomials, the Ramanujan polynomials and the Dowling polynomials are strongly $q$-log-convex. We also prove that the Bessel transformation preserves log-convexity.
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. Chapman, James H. Charlesworth, Kenneth R. Chase, Chen Zemin, Luciano Chianeque, Philip Chia Phin Yin, Francisca H. Chimhanda, Daniel Chiquete, John T. Chirban, Soobin Choi, Robert Choquette, Mita Choudhury, Gerald Christianson, John Chryssavgis, Sejong Chun, Esther Chung-Kim, Charles M. A. Clark, Elizabeth A. Clark, Sathianathan Clarke, Fred Cloud, John B. Cobb, W. Owen Cole, John A Coleman, John J. Collins, Sylvia Collins-Mayo, Paul K. Conkin, Beth A. Conklin, Sean Connolly, Demetrios J. Constantelos, Michael A. Conway, Paula M. Cooey, Austin Cooper, Michael L. Cooper-White, Pamela Cooper-White, L. William Countryman, Sérgio Coutinho, Pamela Couture, Shannon Craigo-Snell, James L. Crenshaw, David Crowner, Humberto Horacio Cucchetti, Lawrence S. Cunningham, Elizabeth Mason Currier, Emmanuel Cutrone, Mary L. Daniel, David D. Daniels, Robert Darden, Rolf Darge, Isaiah Dau, Jeffry C. Davis, Jane Dawson, Valentin Dedji, John W. de Gruchy, Paul DeHart, Wendy J. Deichmann Edwards, Miguel A. De La Torre, George E. Demacopoulos, Thomas de Mayo, Leah DeVun, Beatriz de Vasconcellos Dias, Dennis C. Dickerson, John M. Dillon, Luis Miguel Donatello, Igor Dorfmann-Lazarev, Susanna Drake, Jonathan A. Draper, N. Dreher Martin, Otto Dreydoppel, Angelyn Dries, A. J. Droge, Francis X. D'Sa, Marilyn Dunn, Nicole Wilkinson Duran, Rifaat Ebied, Mark J. Edwards, William H. Edwards, Leonard H. Ehrlich, Nancy L. Eiesland, Martin Elbel, J. Harold Ellens, Stephen Ellingson, Marvin M. Ellison, Robert Ellsberg, Jean Bethke Elshtain, Eldon Jay Epp, Peter C. Erb, Tassilo Erhardt, Maria Erling, Noel Leo Erskine, Gillian R. Evans, Virginia Fabella, Michael A. Fahey, Edward Farley, Margaret A. Farley, Wendy Farley, Robert Fastiggi, Seena Fazel, Duncan S. Ferguson, Helwar Figueroa, Paul Corby Finney, Kyriaki Karidoyanes FitzGerald, Thomas E. FitzGerald, John R. Fitzmier, Marie Therese Flanagan, Sabina Flanagan, Claude Flipo, Ronald B. Flowers, Carole Fontaine, David Ford, Mary Ford, Stephanie A. Ford, Jim Forest, William Franke, Robert M. Franklin, Ruth Franzén, Edward H. Friedman, Samuel Frouisou, Lorelei F. Fuchs, Jojo M. Fung, Inger Furseth, Richard R. Gaillardetz, Brandon Gallaher, China Galland, Mark Galli, Ismael García, Tharscisse Gatwa, Jean-Marie Gaudeul, Luis María Gavilanes del Castillo, Pavel L. Gavrilyuk, Volney P. Gay, Metropolitan Athanasios Geevargis, Kondothra M. George, Mary Gerhart, Simon Gikandi, Maurice Gilbert, Michael J. Gillgannon, Verónica Giménez Beliveau, Terryl Givens, Beth Glazier-McDonald, Philip Gleason, Menghun Goh, Brian Golding, Bishop Hilario M. Gomez, Michelle A. Gonzalez, Donald K. Gorrell, Roy Gottfried, Tamara Grdzelidze, Joel B. Green, Niels Henrik Gregersen, Cristina Grenholm, Herbert Griffiths, Eric W. Gritsch, Erich S. Gruen, Christoffer H. Grundmann, Paul H. Gundani, Jon P. Gunnemann, Petre Guran, Vidar L. Haanes, Jeremiah M. Hackett, Getatchew Haile, Douglas John Hall, Nicholas Hammond, Daphne Hampson, Jehu J. Hanciles, Barry Hankins, Jennifer Haraguchi, Stanley S. Harakas, Anthony John Harding, Conrad L. Harkins, J. William Harmless, Marjory Harper, Amir Harrak, Joel F. Harrington, Mark W. Harris, Susan Ashbrook Harvey, Van A. Harvey, R. Chris Hassel, Jione Havea, Daniel Hawk, Diana L. Hayes, Leslie Hayes, Priscilla Hayner, S. Mark Heim, Simo Heininen, Richard P. Heitzenrater, Eila Helander, David Hempton, Scott H. Hendrix, Jan-Olav Henriksen, Gina Hens-Piazza, Carter Heyward, Nicholas J. Higham, David Hilliard, Norman A. Hjelm, Peter C. Hodgson, Arthur Holder, M. Jan Holton, Dwight N. Hopkins, Ronnie Po-chia Hsia, Po-Ho Huang, James Hudnut-Beumler, Jennifer S. Hughes, Leonard M. Hummel, Mary E. Hunt, Laennec Hurbon, Mark Hutchinson, Susan E. Hylen, Mary Beth Ingham, H. Larry Ingle, Dale T. Irvin, Jon Isaak, Paul John Isaak, Ada María Isasi-Díaz, Hans Raun Iversen, Margaret C. Jacob, Arthur James, Maria Jansdotter-Samuelsson, David Jasper, Werner G. Jeanrond, Renée Jeffery, David Lyle Jeffrey, Theodore W. Jennings, David H. Jensen, Robin Margaret Jensen, David Jobling, Dale A. Johnson, Elizabeth A. Johnson, Maxwell E. Johnson, Sarah Johnson, Mark D. Johnston, F. Stanley Jones, James William Jones, John R. Jones, Alissa Jones Nelson, Inge Jonsson, Jan Joosten, Elizabeth Judd, Mulambya Peggy Kabonde, Robert Kaggwa, Sylvester Kahakwa, Isaac Kalimi, Ogbu U. Kalu, Eunice Kamaara, Wayne C. Kannaday, Musimbi Kanyoro, Veli-Matti Kärkkäinen, Frank Kaufmann, Léon Nguapitshi Kayongo, Richard Kearney, Alice A. Keefe, Ralph Keen, Catherine Keller, Anthony J. Kelly, Karen Kennelly, Kathi Lynn Kern, Fergus Kerr, Edward Kessler, George Kilcourse, Heup Young Kim, Kim Sung-Hae, Kim Yong-Bock, Kim Yung Suk, Richard King, Thomas M. King, Robert M. Kingdon, Ross Kinsler, Hans G. Kippenberg, Cheryl A. Kirk-Duggan, Clifton Kirkpatrick, Leonid Kishkovsky, Nadieszda Kizenko, Jeffrey Klaiber, Hans-Josef Klauck, Sidney Knight, Samuel Kobia, Robert Kolb, Karla Ann Koll, Heikki Kotila, Donald Kraybill, Philip D. W. Krey, Yves Krumenacker, Jeffrey Kah-Jin Kuan, Simanga R. Kumalo, Peter Kuzmic, Simon Shui-Man Kwan, Kwok Pui-lan, André LaCocque, Stephen E. Lahey, John Tsz Pang Lai, Emiel Lamberts, Armando Lampe, Craig Lampe, Beverly J. Lanzetta, Eve LaPlante, Lizette Larson-Miller, Ariel Bybee Laughton, Leonard Lawlor, Bentley Layton, Robin A. Leaver, Karen Lebacqz, Archie Chi Chung Lee, Marilyn J. Legge, Hervé LeGrand, D. L. LeMahieu, Raymond Lemieux, Bill J. Leonard, Ellen M. Leonard, Outi Leppä, Jean Lesaulnier, Nantawan Boonprasat Lewis, Henrietta Leyser, Alexei Lidov, Bernard Lightman, Paul Chang-Ha Lim, Carter Lindberg, Mark R. Lindsay, James R. Linville, James C. Livingston, Ann Loades, David Loades, Jean-Claude Loba-Mkole, Lo Lung Kwong, Wati Longchar, Eleazar López, David W. Lotz, Andrew Louth, Robin W. Lovin, William Luis, Frank D. Macchia, Diarmaid N. J. MacCulloch, Kirk R. MacGregor, Marjory A. MacLean, Donald MacLeod, Tomas S. Maddela, Inge Mager, Laurenti Magesa, David G. Maillu, Fortunato Mallimaci, Philip Mamalakis, Kä Mana, Ukachukwu Chris Manus, Herbert Robinson Marbury, Reuel Norman Marigza, Jacqueline Mariña, Antti Marjanen, Luiz C. L. Marques, Madipoane Masenya (ngwan'a Mphahlele), Caleb J. D. Maskell, Steve Mason, Thomas Massaro, Fernando Matamoros Ponce, András Máté-Tóth, Odair Pedroso Mateus, Dinis Matsolo, Fumitaka Matsuoka, John D'Arcy May, Yelena Mazour-Matusevich, Theodore Mbazumutima, John S. McClure, Christian McConnell, Lee Martin McDonald, Gary B. McGee, Thomas McGowan, Alister E. McGrath, Richard J. McGregor, John A. McGuckin, Maud Burnett McInerney, Elsie Anne McKee, Mary B. McKinley, James F. McMillan, Ernan McMullin, Kathleen E. McVey, M. Douglas Meeks, Monica Jyotsna Melanchthon, Ilie Melniciuc-Puica, Everett Mendoza, Raymond A. Mentzer, William W. Menzies, Ina Merdjanova, Franziska Metzger, Constant J. Mews, Marvin Meyer, Carol Meyers, Vasile Mihoc, Gunner Bjerg Mikkelsen, Maria Inêz de Castro Millen, Clyde Lee Miller, Bonnie J. Miller-McLemore, Alexander Mirkovic, Paul Misner, Nozomu Miyahira, R. W. L. Moberly, Gerald Moede, Aloo Osotsi Mojola, Sunanda Mongia, Rebeca Montemayor, James Moore, Roger E. Moore, Craig E. Morrison O.Carm, Jeffry H. Morrison, Keith Morrison, Wilson J. Moses, Tefetso Henry Mothibe, Mokgethi Motlhabi, Fulata Moyo, Henry Mugabe, Jesse Ndwiga Kanyua Mugambi, Peggy Mulambya-Kabonde, Robert Bruce Mullin, Pamela Mullins Reaves, Saskia Murk Jansen, Heleen L. Murre-Van den Berg, Augustine Musopole, Isaac M. T. Mwase, Philomena Mwaura, Cecilia Nahnfeldt, Anne Nasimiyu Wasike, Carmiña Navia Velasco, Thulani Ndlazi, Alexander Negrov, James B. Nelson, David G. Newcombe, Carol Newsom, Helen J. Nicholson, George W. E. Nickelsburg, Tatyana Nikolskaya, Damayanthi M. A. Niles, Bertil Nilsson, Nyambura Njoroge, Fidelis Nkomazana, Mary Beth Norton, Christian Nottmeier, Sonene Nyawo, Anthère Nzabatsinda, Edward T. Oakes, Gerald O'Collins, Daniel O'Connell, David W. Odell-Scott, Mercy Amba Oduyoye, Kathleen O'Grady, Oyeronke Olajubu, Thomas O'Loughlin, Dennis T. Olson, J. Steven O'Malley, Cephas N. Omenyo, Muriel Orevillo-Montenegro, César Augusto Ornellas Ramos, Agbonkhianmeghe E. Orobator, Kenan B. Osborne, Carolyn Osiek, Javier Otaola Montagne, Douglas F. Ottati, Anna May Say Pa, Irina Paert, Jerry G. Pankhurst, Aristotle Papanikolaou, Samuele F. Pardini, Stefano Parenti, Peter Paris, Sung Bae Park, Cristián G. Parker, Raquel Pastor, Joseph Pathrapankal, Daniel Patte, W. Brown Patterson, Clive Pearson, Keith F. Pecklers, Nancy Cardoso Pereira, David Horace Perkins, Pheme Perkins, Edward N. Peters, Rebecca Todd Peters, Bishop Yeznik Petrossian, Raymond Pfister, Peter C. Phan, Isabel Apawo Phiri, William S. F. Pickering, Derrick G. Pitard, William Elvis Plata, Zlatko Plese, John Plummer, James Newton Poling, Ronald Popivchak, Andrew Porter, Ute Possekel, James M. Powell, Enos Das Pradhan, Devadasan Premnath, Jaime Adrían Prieto Valladares, Anne Primavesi, Randall Prior, María Alicia Puente Lutteroth, Eduardo Guzmão Quadros, Albert Rabil, Laurent William Ramambason, Apolonio M. Ranche, Vololona Randriamanantena Andriamitandrina, Lawrence R. Rast, Paul L. Redditt, Adele Reinhartz, Rolf Rendtorff, Pål Repstad, James N. Rhodes, John K. Riches, Joerg Rieger, Sharon H. Ringe, Sandra Rios, Tyler Roberts, David M. Robinson, James M. Robinson, Joanne Maguire Robinson, Richard A. H. Robinson, Roy R. Robson, Jack B. Rogers, Maria Roginska, Sidney Rooy, Rev. Garnett Roper, Maria José Fontelas Rosado-Nunes, Andrew C. Ross, Stefan Rossbach, François Rossier, John D. Roth, John K. Roth, Phillip Rothwell, Richard E. Rubenstein, Rosemary Radford Ruether, Markku Ruotsila, John E. Rybolt, Risto Saarinen, John Saillant, Juan Sanchez, Wagner Lopes Sanchez, Hugo N. Santos, Gerhard Sauter, Gloria L. Schaab, Sandra M. Schneiders, Quentin J. Schultze, Fernando F. Segovia, Turid Karlsen Seim, Carsten Selch Jensen, Alan P. F. Sell, Frank C. Senn, Kent Davis Sensenig, Damían Setton, Bal Krishna Sharma, Carolyn J. Sharp, Thomas Sheehan, N. Gerald Shenk, Christian Sheppard, Charles Sherlock, Tabona Shoko, Walter B. Shurden, Marguerite Shuster, B. Mark Sietsema, Batara Sihombing, Neil Silberman, Clodomiro Siller, Samuel Silva-Gotay, Heikki Silvet, John K. Simmons, Hagith Sivan, James C. Skedros, Abraham Smith, Ashley A. Smith, Ted A. Smith, Daud Soesilo, Pia Søltoft, Choan-Seng (C. S.) Song, Kathryn Spink, Bryan Spinks, Eric O. Springsted, Nicolas Standaert, Brian Stanley, Glen H. Stassen, Karel Steenbrink, Stephen J. Stein, Andrea Sterk, Gregory E. Sterling, Columba Stewart, Jacques Stewart, Robert B. Stewart, Cynthia Stokes Brown, Ken Stone, Anne Stott, Elizabeth Stuart, Monya Stubbs, Marjorie Hewitt Suchocki, David Kwang-sun Suh, Scott W. Sunquist, Keith Suter, Douglas Sweeney, Charles H. Talbert, Shawqi N. Talia, Elsa Tamez, Joseph B. Tamney, Jonathan Y. Tan, Yak-Hwee Tan, Kathryn Tanner, Feiya Tao, Elizabeth S. Tapia, Aquiline Tarimo, Claire Taylor, Mark Lewis Taylor, Bishop Abba Samuel Wolde Tekestebirhan, Eugene TeSelle, M. Thomas Thangaraj, David R. Thomas, Andrew Thornley, Scott Thumma, Marcelo Timotheo da Costa, George E. “Tink” Tinker, Ola Tjørhom, Karen Jo Torjesen, Iain R. Torrance, Fernando Torres-Londoño, Archbishop Demetrios [Trakatellis], Marit Trelstad, Christine Trevett, Phyllis Trible, Johannes Tromp, Paul Turner, Robert G. Tuttle, Archbishop Desmond Tutu, Peter Tyler, Anders Tyrberg, Justin Ukpong, Javier Ulloa, Camillus Umoh, Kristi Upson-Saia, Martina Urban, Monica Uribe, Elochukwu Eugene Uzukwu, Richard Vaggione, Gabriel Vahanian, Paul Valliere, T. J. Van Bavel, Steven Vanderputten, Peter Van der Veer, Huub Van de Sandt, Louis Van Tongeren, Luke A. Veronis, Noel Villalba, Ramón Vinke, Tim Vivian, David Voas, Elena Volkova, Katharina von Kellenbach, Elina Vuola, Timothy Wadkins, Elaine M. Wainwright, Randi Jones Walker, Dewey D. Wallace, Jerry Walls, Michael J. Walsh, Philip Walters, Janet Walton, Jonathan L. Walton, Wang Xiaochao, Patricia A. Ward, David Harrington Watt, Herold D. Weiss, Laurence L. Welborn, Sharon D. Welch, Timothy Wengert, Traci C. West, Merold Westphal, David Wetherell, Barbara Wheeler, Carolinne White, Jean-Paul Wiest, Frans Wijsen, Terry L. Wilder, Felix Wilfred, Rebecca Wilkin, Daniel H. Williams, D. Newell Williams, Michael A. Williams, Vincent L. Wimbush, Gabriele Winkler, Anders Winroth, Lauri Emílio Wirth, James A. Wiseman, Ebba Witt-Brattström, Teofil Wojciechowski, John Wolffe, Kenman L. Wong, Wong Wai Ching, Linda Woodhead, Wendy M. Wright, Rose Wu, Keith E. Yandell, Gale A. Yee, Viktor Yelensky, Yeo Khiok-Khng, Gustav K. K. Yeung, Angela Yiu, Amos Yong, Yong Ting Jin, You Bin, Youhanna Nessim Youssef, Eliana Yunes, Robert Michael Zaller, Valarie H. Ziegler, Barbara Brown Zikmund, Joyce Ann Zimmerman, Aurora Zlotnik, Zhuo Xinping
- Edited by Daniel Patte, Vanderbilt University, Tennessee
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- Book:
- The Cambridge Dictionary of Christianity
- Published online:
- 05 August 2012
- Print publication:
- 20 September 2010, pp xi-xliv
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Non-Terminating Basic Hypergeometric Series and the q-Zeilberger Algorithm
- William Y. C. Chen, Qing-Hu Hou, Yan-Ping Mu
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 51 / Issue 3 / October 2008
- Published online by Cambridge University Press:
- 12 December 2008, pp. 609-633
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We present a systematic method for proving non-terminating basic hypergeometric identities. Assume that k is the summation index. By setting a parameter x to xqn, we may find a recurrence relation of the summation by using the q-Zeilberger algorithm. This method applies to almost all non-terminating basic hypergeometric summation formulae in the work of Gasper and Rahman. Furthermore, by comparing the recursions and the limit values, we may verify many classical transformation formulae, including the Sears–Carlitz transformation, transformations of the very well-poised 8φ7 series, the Rogers–Fine identity and the limiting case of Watson's formula that implies the Rogers–Ramanujan identities.
Contributors
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- By Graham Allan, Donna M. Allen, Irwin Altman, Arthur Aron, Donald H. Baucom, Steven R. H. Beach, Ellen Berscheid, Rosemary Blieszner, Jeffrey Boase, Tyfany M. J. Boettcher, Barbara B. Brown, Abraham P. Buunk, Lorne Campbell, Daniel J. Canary, Rodney Cate, John P. Caughlin, Mahnaz Charania, Jennie Y. Chen, F. Scott Christopher, Jennifer A. Clarke, Marilyn Coleman, W. Andrew Collins, Michael K. Coolsen, Nathan R. Cottle, Carolyn E. Cutrona, Marianne Dainton, Valerian J. Derlega, Lisa M. Diamond, Pieternel Dijkstra, Steve Duck, Pearl A. Dykstra, Norman B. Epstein, Beverley Fehr, Frank D. Fincham, Helen E. Fisher, Julie Fitness, Garth J. O. Fletcher, Myron D. Friesen, Lawrence Ganong, Kelli A. Gardner, Jenny de Jong Gierveld, Robin Goodwin, Christine R. Gray, Kathryn Greene, David W. Harris, Willard W. Hartup, John H. Harvey, Kathi L. Heffner, Ted L. Huston, William J. Ickes, Emily A. Impett, Michael P. Johnson, Deborah J. Jones, Deborah A. Kashy, Janice K. Kiecolt‐Glaser, Jeffrey L. Kirchner, Brighid M. Kleinman, Galena H. Kline, Mark L. Knapp, Ascan Koerner, Jean‐Philippe Laurenceau, Kim Leon, Timothy J. Loving, Stephanie D. Madsen, Howard J. Markman, Alicia Mathews, Mario Mikulincer, Patricia Noller, Nickola C. Overall, Letitia Anne Peplau, Daniel Perlman, Sally Planalp, Urmila Pillay, Nicole D. Pleasant, Caryl E. Rusbult, Barbara R. Sarason, Irwin G. Sarason, Phillip R. Shaver, Alan L. Sillars, Jeffry A. Simpson, Susan Sprecher, Susan Stanton, Greg Strong, Catherine A. Surra, Anita L. Vangelisti, C. Arthur VanLear, Theo van Tilburg, Barry Wellman, Amy Wenzel, Carol M. Werner, Adam R. West, Sarah W. Whitton, Heike A. Winterheld
- Edited by Anita L. Vangelisti, University of Texas, Austin, Daniel Perlman, University of British Columbia, Vancouver
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- Book:
- The Cambridge Handbook of Personal Relationships
- Published online:
- 05 June 2012
- Print publication:
- 05 June 2006, pp xvii-xxii
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DNA Damage and Repair in Human Spinal Cord Ischemia-Reperfusion Injury
- G Roseborough, D Gao, R Lin, L Chen, Y Park, E Chu, G M Williams, C Wei
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- Journal:
- Microscopy and Microanalysis / Volume 11 / Issue S02 / August 2005
- Published online by Cambridge University Press:
- 01 August 2005, pp. 1006-1007
- Print publication:
- August 2005
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Extended abstract of a paper presented at Microscopy and Microanalysis 2005 in Honolulu, Hawaii, USA, July 31--August 4, 2005
CAUCHY AUGMENTATION FOR BASIC HYPERGEOMETRIC SERIES
- WILLIAM Y. C. CHEN, AMY M. FU
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- Journal:
- Bulletin of the London Mathematical Society / Volume 36 / Issue 2 / March 2004
- Published online by Cambridge University Press:
- 02 February 2004, pp. 169-175
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- March 2004
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The authors present a technique of deriving basic hypergeometric identities from specializations using fewer parameters, by using the classical Cauchy identity on the expansion of the power of $x$ in terms of the $q$-binomial coefficients. This method is referred to as ‘Cauchy augmentation’. Despite its simple appearance, the Cauchy identity plays a key role in parameter augmentation. For example, one can reach the $q$-Gauss summation formula from the Euler identity by using the Cauchy augmentation twice. This idea also applies to Jackson's $_2\phi_1$ to $_3\phi_1$ transformation formula. Moreover, a transformation formula analogous to Jackson's formula is obtained.
Transport and Microstructure of Microcrystalline Silicon Alloys
- G. Lucovsky, C. Wang, M. J. Williams, Y. L. Chen, D. M. Mauer
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- Journal:
- MRS Online Proceedings Library Archive / Volume 283 / 1992
- Published online by Cambridge University Press:
- 28 February 2011, 443
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- 1992
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The microstructure and electrical properties of μc-Si and μc-Si,C prepared by remote plasma-enhanced chemical-vapor deposition, PECVD, are reviewed. The microstructure has been characterized by transmission electron microscopy, TEM, infrared, IR, absorption and Raman scattering. The electrical properties were characterized by temperature-dependent dark-conductivity measurements. These studies have explained significant quantitative differences between the carrier transport properties of μc-Si and μc-Si,C alloys in terms of a band offset model for the interfacial potential steps between the amorphous and crystalline constituents of these material systems.