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CATEGORIFYING RATIONALIZATION
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- CLARK BARWICK, SAUL GLASMAN, MARC HOYOIS, DENIS NARDIN, JAY SHAH
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- Journal:
- Forum of Mathematics, Sigma / Volume 7 / 2019
- Published online by Cambridge University Press:
- 09 January 2020, e42
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- Article
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We construct, for any set of primes $S$, a triangulated category (in fact a stable $\infty$-category) whose Grothendieck group is $S^{-1}\mathbf{Z}$. More generally, for any exact $\infty$-category $E$, we construct an exact $\infty$-category $S^{-1}E$ of equivariant sheaves on the Cantor space with respect to an action of a dense subgroup of the circle. We show that this $\infty$-category is precisely the result of categorifying division by the primes in $S$. In particular, $K_{n}(S^{-1}E)\cong S^{-1}K_{n}(E)$.
Crop Rotation, Cover Crop, and Weed Management Effects on Weed Seedbanks and Yields in Snap Bean, Sweet Corn, and Cabbage
- Daniel C. Brainard, Robin R. Bellinder, Russell R. Hahn, Denis A. Shah
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- Journal:
- Weed Science / Volume 56 / Issue 3 / June 2008
- Published online by Cambridge University Press:
- 20 January 2017, pp. 434-441
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Three major hypotheses were examined in this study: (1) the density of summer annual weeds is reduced in crop rotation systems that include winter wheat compared to those with strictly summer annual crops, (2) the integration of a red clover in cropping systems reduces weed seedbank densities, and (3) changes in weed seedbanks due to crop rotation system have greater impact on future crops that are managed with cultivation alone, compared to those managed with herbicides. To test these hypotheses, five 3-yr rotation sequences were examined in central New York state: continuous field corn (FC); field corn with red clover (FC + CL); field corn–oats–wheat (FC/O/W); sweet corn–peas–wheat (SC/P/W), and SC/P/W with red clover (SC/P/W + CL). In the fourth year, sweet corn, snap beans, and cabbage were planted in subplots with three levels of weed management as sub-subplots: cultivation alone, reduced-rate herbicides (1/2×), and full-rate herbicides (1×). The trial was carried out in two separate cycles, from 1997 to 2000 (cycle 1) and from 1998 to 2001 (cycle 2). Crop rotations with strictly summer annual crops (FC) did not result in consistently higher weed seedbank densities of summer annual weeds compared to rotations involving winter wheat (FC/O/W; SC/P/W; SC/P/W + CL). Integration of red clover in continuous field corn resulted in higher weed seedbanks (cycle 1) or emergence (cycle 2) of several summer annual weeds compared to field corn alone. In contrast, integration of red clover in the SC/P/W rotation led to a 96% reduction in seedbank density of winter annuals in cycle 1, although this effect was not detected in cycle 2. Observed changes in weed seedbank density and emergence due to crop rotation resulted in increased weed biomass in the final year in only one case (sweet corn, cycle 2), and did not result in detectable differences in crop yields. In contrast, final year weed management had a strong effect on weed biomass and yield; cultivation alone resulted in yield losses for sweet corn (32 to 34%) and cabbage (0 to 7%), but not snap beans compared to either 1/2× or 1× herbicides.
Effect of weed growth stage and adjuvant on the efficacy of fomesafen and bentazon
- Robin R. Bellinder, Marija Arsenovic, Denis A. Shah, Bradley J. Rauch
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- Journal:
- Weed Science / Volume 51 / Issue 6 / December 2003
- Published online by Cambridge University Press:
- 20 January 2017, pp. 1016-1021
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The efficacies of bentazon and fomesafen in controlling annual weeds in dry and edible pod beans in New York State were investigated in greenhouse and field experiments. Dose responses to bentazon and fomesafen were studied for four weed species (ragweed, velvetleaf, eastern black nightshade, and hairy nightshade) under greenhouse conditions. Herbicides were applied at cotyledon to two-, two- to four-, and four- to six–true leaf stages, both with and without a crop oil concentrate (bentazon) or a nonionic surfactant (fomesafen). Field studies were conducted for 2 yr for all weed species except eastern black nightshade, for which no adequate field populations were found. Field studies confirmed greenhouse results, indicating that weed control could be improved by the use of an adjuvant, but there were exceptions. In general, adjuvant usage improved the efficacy of fomesafen more than it did with bentazon. The minimum rates of herbicide required for effective and consistent control was dependent on the particular combination of weed species, herbicide and its rate of application, growth stage at which the application was made, and adjuvant usage.
Contributors
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- By Lenard A. Adler, Pinky Agarwal, Rehan Ahmed, Jagga Rao Alluri, Fawaz Al-Mufti, Samuel Alperin, Michael Amoashiy, Michael Andary, David J. Anschel, Padmaja Aradhya, Vandana Aspen, Esther Baldinger, Jee Bang, George D. Baquis, John J. Barry, Jason J. S. Barton, Julius Bazan, Amanda R. Bedford, Marlene Behrmann, Lourdes Bello-Espinosa, Ajay Berdia, Alan R. Berger, Mark Beyer, Don C. Bienfang, Kevin M. Biglan, Thomas M. Boes, Paul W. Brazis, Jonathan L. Brisman, Jeffrey A. Brown, Scott E. Brown, Ryan R. Byrne, Rina Caprarella, Casey A. Chamberlain, Wan-Tsu W. Chang, Grace M. Charles, Jasvinder Chawla, David Clark, Todd J. Cohen, Joe Colombo, Howard Crystal, Vladimir Dadashev, Sarita B. Dave, Jean Robert Desrouleaux, Richard L. Doty, Robert Duarte, Jeffrey S. Durmer, Christyn M. Edmundson, Eric R. Eggenberger, Steven Ender, Noam Epstein, Alberto J. Espay, Alan B. Ettinger, Niloofar (Nelly) Faghani, Amtul Farheen, Edward Firouztale, Rod Foroozan, Anne L. Foundas, David Elliot Friedman, Deborah I. Friedman, Steven J. Frucht, Oded Gerber, Tal Gilboa, Martin Gizzi, Teneille G. Gofton, Louis J. Goodrich, Malcolm H. Gottesman, Varda Gross-Tsur, Deepak Grover, David A. Gudis, John J. Halperin, Maxim D. Hammer, Andrew R. Harrison, L. Anne Hayman, Galen V. Henderson, Steven Herskovitz, Caitlin Hoffman, Laryssa A. Huryn, Andres M. Kanner, Gary P. Kaplan, Bashar Katirji, Kenneth R. Kaufman, Annie Killoran, Nina Kirz, Gad E. Klein, Danielle G. Koby, Christopher P. Kogut, W. Curt LaFrance, Patrick J.M. Lavin, Susan W. Law, James L. Levenson, Richard B. Lipton, Glenn Lopate, Daniel J. Luciano, Reema Maindiratta, Robert M. Mallery, Georgios Manousakis, Alan Mazurek, Luis J. Mejico, Dragana Micic, Ali Mokhtarzadeh, Walter J. Molofsky, Heather E. Moss, Mark L. Moster, Manpreet Multani, Siddhartha Nadkarni, George C. Newman, Rolla Nuoman, Paul A. Nyquist, Gaia Donata Oggioni, Odi Oguh, Denis Ostrovskiy, Kristina Y. Pao, Juwen Park, Anastas F. Pass, Victoria S. Pelak, Jeffrey Peterson, John Pile-Spellman, Misha L. Pless, Gregory M. Pontone, Aparna M. Prabhu, Michael T. Pulley, Philip Ragone, Prajwal Rajappa, Venkat Ramani, Sindhu Ramchandren, Ritesh A. Ramdhani, Ramses Ribot, Heidi D. Riney, Diana Rojas-Soto, Michael Ronthal, Daniel M. Rosenbaum, David B. Rosenfield, Durga Roy, Michael J. Ruckenstein, Max C. Rudansky, Eva Sahay, Friedhelm Sandbrink, Jade S. Schiffman, Angela Scicutella, Maroun T. Semaan, Robert C. Sergott, Aashit K. Shah, David M. Shaw, Amit M. Shelat, Claire A. Sheldon, Anant M. Shenoy, Yelizaveta Sher, Jessica A. Shields, Tanya Simuni, Rajpaul Singh, Eric E. Smouha, David Solomon, Mehri Songhorian, Steven A. Sparr, Egilius L. H. Spierings, Eve G. Spratt, Beth Stein, S.H. Subramony, Rosa Ana Tang, Cara Tannenbaum, Hakan Tekeli, Amanda J. Thompson, Michael J. Thorpy, Matthew J. Thurtell, Pedro J. Torrico, Ira M. Turner, Scott Uretsky, Ruth H. Walker, Deborah M. Weisbrot, Michael A. Williams, Jacques Winter, Randall J. Wright, Jay Elliot Yasen, Shicong Ye, G. Bryan Young, Huiying Yu, Ryan J. Zehnder
- Edited by Alan B. Ettinger, Albert Einstein College of Medicine, New York, Deborah M. Weisbrot, State University of New York, Stony Brook
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- Book:
- Neurologic Differential Diagnosis
- Published online:
- 05 June 2014
- Print publication:
- 17 April 2014, pp xi-xx
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