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This chapter investigates the question which begings as follows. Suppose we have a geometrically irreducible middle extension sheaf G<\/italic> on \ud835\udd3e\u2098\/k<\/italic> which is pure of weight zero, such that the object N<\/italic> := G<\/italic>(1\/2)[1] \u025b Garith<\/sub> is \u201cdimension\u201d n<\/italic> and has G<\/italic>subscript geom,N<\/italic> = Garith,N<\/sub> = GL<\/italic>(n<\/italic>). Suppose in addition we are given s<\/italic> \u2264 2 distinct characters \u03c7\u200e\u1d62 of k<\/italic>\u02e3.<\/p>","DOI":"10.23943\/princeton\/9780691153308.003.0021","type":"book-chapter","created":{"date-parts":[[2017,11,21]],"date-time":"2017-11-21T12:38:12Z","timestamp":1511267892000},"source":"Crossref","is-referenced-by-count":5,"title":["GL(n) \u00d7 GL(n) \u00d7 \u2026 \u00d7 GL(n) Examples"],"prefix":"10.23943","author":[{"given":"Nicholas M.","family":"Katz","sequence":"first","affiliation":[]}],"member":"10341","published-online":{"date-parts":[[2017,10,19]]},"container-title":["Convolution and Equidistribution"],"original-title":["GL(n) \u00d7 GL(n) \u00d7 \u2026 \u00d7 GL(n) Examples"],"language":"en","deposited":{"date-parts":[[2022,7,28]],"date-time":"2022-07-28T14:08:19Z","timestamp":1659017299000},"score":18.173555,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/princeton-scholarship-online\/book\/21156\/chapter\/180785373"}},"issued":{"date-parts":[[2012,1,24]]},"ISBN":["9780691153308","9781400842704"],"references-count":0,"URL":"https:\/\/doi.org\/10.23943\/princeton\/9780691153308.003.0021","published":{"date-parts":[[2012,1,24]]}},{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T18:14:41Z","timestamp":1648836881756},"reference-count":0,"publisher":"Ovid Technologies (Wolters Kluwer Health)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Dimensions of Critical Care Nursing"],"published-print":{"date-parts":[[1986,11]]},"DOI":"10.1097\/00003465-198611000-00022","type":"journal-article","created":{"date-parts":[[2006,10,2]],"date-time":"2006-10-02T10:14:00Z","timestamp":1159784040000},"page":"377-378","source":"Crossref","is-referenced-by-count":0,"title":["Assessment of nutritional requirements of head-injured patients"],"prefix":"10.1097","volume":"5","author":[{"given":"Clifton","family":"GL","sequence":"first","affiliation":[]},{"given":"Robertson","family":"CS","sequence":"additional","affiliation":[]},{"given":"Choi","family":"SC","sequence":"additional","affiliation":[]}],"member":"276","container-title":["Dimensions of Critical Care Nursing"],"language":"en","link":[{"URL":"http:\/\/journals.lww.com\/00003465-198611000-00022","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,4,10]],"date-time":"2021-04-10T15:34:17Z","timestamp":1618068857000},"score":18.009666,"resource":{"primary":{"URL":"http:\/\/journals.lww.com\/00003465-198611000-00022"}},"subtitle":[""],"issued":{"date-parts":[[1986,11]]},"references-count":0,"journal-issue":{"issue":"6"},"URL":"https:\/\/doi.org\/10.1097\/00003465-198611000-00022","ISSN":["0730-4625"],"issn-type":[{"value":"0730-4625","type":"print"}],"published":{"date-parts":[[1986,11]]}},{"indexed":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T04:11:50Z","timestamp":1750911110394,"version":"3.41.0"},"reference-count":0,"publisher":"ASTM International100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959","isbn-type":[{"type":"print","value":"0803166583"},{"type":"print","value":"9780803166585"},{"type":"electronic","value":"9780803167292"}],"content-domain":{"domain":[],"crossmark-restriction":false},"published-print":{"date-parts":[[1972,1,1]]},"abstract":"The American Petroleum Institute has developed six lubricant Service Designations for Automotive Manual Transmissions and Axles. Each of these Designations states in qualitative terms the kind of service in which a gear lubricant is expected to perform satisfactorily. Both the type of gears and the operating conditions for the lubricant are included in each Service Designation. Supplementing of the qualitative API Designations with performance definitions is needed, particularly for Service Designations GL-4, GL-5, and GL-6. These performance definitions include a series of tests and associated minimum performance requirements. The tests and requirements for GL-4, GL-5, and GL-6 are presented in this publication. Appendix XIV presents the precision data related to these tests. Neither the lubricant classifications, nor the test techniques listed are ASTM Standards.<\/jats:p>","DOI":"10.1520\/stp45903s","type":"book-chapter","created":{"date-parts":[[2009,8,25]],"date-time":"2009-08-25T19:17:25Z","timestamp":1251227845000},"page":"1-11","source":"Crossref","is-referenced-by-count":0,"title":["Laboratory Performance Tests for Automotive Gear Lubricants intended for API GL-4, GL-5, and GL-6 Services"],"prefix":"10.1520","member":"381","container-title":["Laboratory Performance Tests for Automotive Gear Lubricants intended for API GL-4, GL-5, and GL-6 Services"],"language":"en","link":[{"URL":"https:\/\/dl.astm.org\/stps\/book\/chapter-pdf\/63187\/10_1520_stp45903s.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T23:08:39Z","timestamp":1750892919000},"score":17.005264,"resource":{"primary":{"URL":"https:\/\/dl.astm.org\/stps\/book\/910\/chapter\/136953\/Laboratory-Performance-Tests-for-Automotive-Gear"}},"issued":{"date-parts":[[1972,1,1]]},"ISBN":["0803166583","9780803166585","9780803167292"],"references-count":0,"URL":"https:\/\/doi.org\/10.1520\/stp45903s","published":{"date-parts":[[1972,1,1]]}},{"indexed":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T04:11:50Z","timestamp":1750911110765,"version":"3.41.0"},"reference-count":0,"publisher":"ASTM International100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959","isbn-type":[{"type":"print","value":"0803166583"},{"type":"print","value":"9780803166585"},{"type":"electronic","value":"9780803167292"}],"content-domain":{"domain":[],"crossmark-restriction":false},"published-print":{"date-parts":[[1972,1,1]]},"abstract":"Sufficient documentation is not available to provide absolute precision limits for these test procedures. However, sufficient data are available to provide the following general statements concerning the precision of these tests.<\/jats:p>","DOI":"10.1520\/stp45917s","type":"book-chapter","created":{"date-parts":[[2009,8,25]],"date-time":"2009-08-25T19:17:25Z","timestamp":1251227845000},"page":"69-71","source":"Crossref","is-referenced-by-count":1,"title":["Appendix XIV: Precision of Laboratory Tests for Automotive Gear Lubricants Intended for API GL-4, GL-5, and GL-6 Service"],"prefix":"10.1520","member":"381","container-title":["Laboratory Performance Tests for Automotive Gear Lubricants intended for API GL-4, GL-5, and GL-6 Services"],"language":"en","link":[{"URL":"https:\/\/dl.astm.org\/stps\/book\/chapter-pdf\/63216\/10_1520_stp45917s.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T23:08:42Z","timestamp":1750892922000},"score":16.63775,"resource":{"primary":{"URL":"https:\/\/dl.astm.org\/stps\/book\/910\/chapter\/137001\/Appendix-XIV-Precision-of-Laboratory-Tests-for"}},"issued":{"date-parts":[[1972,1,1]]},"ISBN":["0803166583","9780803166585","9780803167292"],"references-count":0,"URL":"https:\/\/doi.org\/10.1520\/stp45917s","published":{"date-parts":[[1972,1,1]]}},{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T02:51:28Z","timestamp":1771642288177,"version":"3.50.1"},"reference-count":0,"publisher":"American Physiological Society","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["American Journal of Physiology-Legacy Content"],"published-print":{"date-parts":[[1970,6,1]]},"DOI":"10.1152\/ajplegacy.1970.218.6.1718","type":"journal-article","created":{"date-parts":[[2017,12,22]],"date-time":"2017-12-22T20:50:39Z","timestamp":1513975839000},"page":"1718-1722","source":"Crossref","is-referenced-by-count":26,"title":["Dietary calcium and ultimobranchial body and parathyroid gland in the chicken"],"prefix":"10.1152","volume":"218","author":[{"given":"GL","family":"Mueller","sequence":"first","affiliation":[]},{"given":"CS","family":"Anast","sequence":"additional","affiliation":[]},{"given":"RP","family":"Breitenbach","sequence":"additional","affiliation":[]}],"member":"24","container-title":["American Journal of Physiology-Legacy Content"],"language":"en","link":[{"URL":"https:\/\/www.physiology.org\/doi\/pdf\/10.1152\/ajplegacy.1970.218.6.1718","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,8]],"date-time":"2019-09-08T19:06:31Z","timestamp":1567969591000},"score":16.581339,"resource":{"primary":{"URL":"https:\/\/www.physiology.org\/doi\/10.1152\/ajplegacy.1970.218.6.1718"}},"issued":{"date-parts":[[1970,6,1]]},"references-count":0,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1970,6,1]]}},"alternative-id":["10.1152\/ajplegacy.1970.218.6.1718"],"URL":"https:\/\/doi.org\/10.1152\/ajplegacy.1970.218.6.1718","ISSN":["0002-9513"],"issn-type":[{"value":"0002-9513","type":"print"}],"published":{"date-parts":[[1970,6,1]]}},{"indexed":{"date-parts":[[2023,11,1]],"date-time":"2023-11-01T11:47:35Z","timestamp":1698839255365},"reference-count":9,"publisher":"Elsevier BV","issue":"4","license":[{"start":{"date-parts":[[1977,4,1]],"date-time":"1977-04-01T00:00:00Z","timestamp":228700800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["The American Journal of Clinical Nutrition"],"published-print":{"date-parts":[[1977,4]]},"DOI":"10.1093\/ajcn\/30.4.579","type":"journal-article","created":{"date-parts":[[2018,1,17]],"date-time":"2018-01-17T09:44:42Z","timestamp":1516182282000},"page":"579-581","update-policy":"http:\/\/dx.doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":5,"title":["Failure of histidine supplementation to improve anemia in chronic dialysis patients"],"prefix":"10.1016","volume":"30","author":[{"given":"RD","family":"Reeves","sequence":"first","affiliation":[]},{"given":"GL","family":"Barbour","sequence":"additional","affiliation":[]},{"given":"CS","family":"Robertson","sequence":"additional","affiliation":[]},{"given":"CK","family":"Crumb","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1093\/ajcn\/30.4.579_bib1","doi-asserted-by":"crossref","first-page":"714","DOI":"10.1136\/bmj.4.5894.714","article-title":"Histidine for treatment of uraemicanaemia.","volume":"4","author":"GIORDANO","year":"1973","journal-title":"Brit. 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Published by Elsevier Inc. All rights reserved.","name":"copyright","label":"Copyright"}]},{"indexed":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T23:10:08Z","timestamp":1750893008625,"version":"3.41.0"},"reference-count":42,"publisher":"ASTM International100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959","isbn-type":[{"type":"print","value":"0803124740"},{"type":"print","value":"9780803124745"},{"type":"electronic","value":"9780803153707"}],"content-domain":{"domain":[],"crossmark-restriction":false},"published-print":{"date-parts":[[1997,1,1]]},"abstract":"An on-site biological assessment for soil toxicity was performed using a lumbricid earthworm, Eisenia foetida andrei(Bouche), at the Milltown Reservoir Superfund Site on the Clark Fork River near Missoula, MT. The assessment provided an opportunity to evaluate test containers and methodologies. Sixty-four field test stations, each consisting of three test containers of site soil, a control container of artificial soil, and a container to house soil moisture and temperature recording devices, were used. Laboratory tests were conducted on soil samples from selected field stations. The test containers were constructed from sections of polyvinyl chloride pipe and were found to be suitable in preventing escape of test organisms and damage by animals. The site soils had levels of arsenic, lead, cadmium, copper, and zinc higher than those in surrounding watersheds. Combined mortality for exposure to the site soil was similar in both the laboratory and field tests (1 to 3%). Combined sublethal responses to the site soil were also similar in both laboratory and field tests (3 to 4%). Artificial soil controls in both field and laboratory tests resulted in combined mortality rates of 1% or less. The methodologies employed proved successful in maintaining an adequate soil moisture level and allowed for measurement of soil temperature.<\/jats:p>","DOI":"10.1520\/stp12258s","type":"book-chapter","created":{"date-parts":[[2009,3,4]],"date-time":"2009-03-04T21:19:52Z","timestamp":1236201592000},"page":"490-517","source":"Crossref","is-referenced-by-count":0,"title":["A Field Screening Method Using Earthworms (Eisenia Foetida Andrei<\/i>) to Evaluate Contaminated Soils"],"prefix":"10.1520","author":[{"given":"DC","family":"Wilborn","sequence":"first","affiliation":[{"name":"Takena Ecological Services, Inc. 1 Biologist, biologist, microbiologist, chemist and ecotoxicologist , respectively, , 712 SW 3rd St., Corvallis, OR97333 ."}]},{"given":"MA","family":"Bollman","sequence":"additional","affiliation":[{"name":"Takena Ecological Services, Inc. 1 Biologist, biologist, microbiologist, chemist and ecotoxicologist , respectively, , 712 SW 3rd St., Corvallis, OR97333 ."}]},{"given":"CS","family":"Gillett","sequence":"additional","affiliation":[{"name":"Takena Ecological Services, Inc. 1 Biologist, biologist, microbiologist, chemist and ecotoxicologist , respectively, , 712 SW 3rd St., Corvallis, OR97333 ."}]},{"given":"SL","family":"Ott","sequence":"additional","affiliation":[{"name":"Takena Ecological Services, Inc. 1 Biologist, biologist, microbiologist, chemist and ecotoxicologist , respectively, , 712 SW 3rd St., Corvallis, OR97333 ."}]},{"given":"GL","family":"Linder","sequence":"additional","affiliation":[{"name":"Takena Ecological Services, Inc. 1 Biologist, biologist, microbiologist, chemist and ecotoxicologist , respectively, , 712 SW 3rd St., Corvallis, OR97333 ."}]}],"member":"381","reference":[{"key":"2025062516114649100_p490_c1","unstructured":"ASTM, 1995, \u201cStandard Guide For Conducting a Laboratory Soil Toxicity Test With Lumbricid Earthworm Eisenia Foetida,\u201d American Society for Testing and Materials, ASTM Standard No. E 1676-95, Philadelphia, PA."},{"article-title":"Earthworm Toxicological Tests, Hazard Assessment and Biomonitoring: A Methodological Approach","year":"1988","author":"Bouche","key":"2025062516114649100_p490_c2"},{"key":"2025062516114649100_p490_c3","article-title":"The Nature and Properties of Soils","author":"Buckman","year":"1969","edition":"7th Ed."},{"key":"2025062516114649100_p490_c4","doi-asserted-by":"crossref","unstructured":"Callahan, C. 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To simplify design and aerodynamic analysis process, a method of obtaining 3D aerodynamic characteristics from 2D airfoil with spoiler simulation is developed. 3D CFD simulations is used as a validation and to develop correcting factors. 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