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B 457 (1995) 175\u2013201]","name":"articletitle","label":"Article Title"},{"value":"Nuclear Physics B","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/0550-3213(96)00258-1","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"https:\/\/doi.org\/10.1016\/0550-3213(95)00518-8","name":"associatedlink","label":"CrossRef DOI link to the associated document"},{"value":"converted-article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 1996 Published by Elsevier B.V.","name":"copyright","label":"Copyright"}]},{"indexed":{"date-parts":[[2025,9,10]],"date-time":"2025-09-10T21:44:53Z","timestamp":1757540693290},"reference-count":17,"publisher":"AIP Publishing","issue":"8","content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"published-print":{"date-parts":[[1973,8,1]]},"abstract":"<jats:p>We investigate necessary and sufficient conditions under which the difference of the resolvents Rz \u2212 R0z of two self-adjoint operators of the form H01 \u2261 F(P) and H \u2261 F(P) + V(Q) is nuclear. Here F(P) denotes a positive and continuous function of the usual momentum observables P and V(Q) a function of the conjugate coordinate observables. Roughly speaking, we prove that Rz \u2212 R0z is nuclear if and only if F(P) increases faster than |P|3\/2 at large |P| and V(Q) falls off to zero faster than 1\/|Q|3 at large |Q|. (For a precise statement of this result Sec. 3.) In particular, it is noticed that if H0 = (|P|2 + m2)1\/2 the relativistic free Hamiltonian, then Rz \u2212 R0z is not nuclear for any of the (suitably regular) potential V(QN.W.) where QN.W. denotes the usual Newton-Wigner position operator of the relativistic particle. We also investigate in Sec. 3 the necessary and sufficient conditions for Rz\u03b2 V Rz0\u03b2(\u03b2&amp;gt;0;\u03b2\u22601) to be nuclear. The implications of these results for the asymptotic behavior of the total scattering cross sections at high energy is discussed in Sec. 4.<\/jats:p>","DOI":"10.1063\/1.1666455","type":"journal-article","created":{"date-parts":[[2004,2,10]],"date-time":"2004-02-10T17:31:28Z","timestamp":1076434288000},"page":"997-1005","update-policy":"http:\/\/dx.doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":12,"title":["On trace-class operators of scattering theory and the asymptotic behavior of scattering cross section at high energy"],"prefix":"10.1063","volume":"14","author":[{"given":"Ph.","family":"Martin","sequence":"first","affiliation":[{"name":"Department of Mathematics, Denver University, Denver, Colorado"}]},{"given":"B.","family":"Misra","sequence":"additional","affiliation":[{"name":"Department of Physics and Astrophysics, University of Colorado, Boulder, Colorado 80302"}]}],"member":"317","reference":[{"key":"2024021015433442900_r1"},{"key":"2024021015433442900_r2","first-page":"475","volume":"144","year":"1962","journal-title":"Dokl. 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See also Supplementary file 1-Table S2 for the particle numbers."],"issued":{"date-parts":[[null]]},"references-count":0,"URL":"https:\/\/doi.org\/10.7554\/elife.35419.010"},{"institution":[{"name":"bioRxiv"}],"indexed":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T23:46:52Z","timestamp":1768520812751,"version":"3.49.0"},"posted":{"date-parts":[[2025,3,12]]},"group-title":"Microbiology","reference-count":39,"publisher":"openRxiv","license":[{"start":{"date-parts":[[2025,3,12]],"date-time":"2025-03-12T00:00:00Z","timestamp":1741737600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.biorxiv.org\/about\/FAQ#license"}],"funder":[{"award":["R35-GM127331"],"award-info":[{"award-number":["R35-GM127331"]}],"id":[{"id":"https:\/\/ror.org\/01cwqze88","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"accepted":{"date-parts":[[2025,3,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                <jats:p>\n                  <jats:italic>Klebsiella pneumoniae<\/jats:italic>\n                  is a leading cause of global deaths due to antibiotic resistance. Of particular concern, is the rapid expansion of resistance to beta-lactam antibiotics within\n                  <jats:italic>K. pneumoniae<\/jats:italic>\n                  lineages. The environmental factors that influence pathogen physiology and, subsequently, antibiotic resistance remain poorly understood. Here we demonstrate that physiologically-relevant reductions in pH increased antibiotic resistance as much as 64-fold, with the most dramatic increases observed for beta-lactams that inhibit cell division. We identified two genes that contribute to acid-dependent beta-lactam resistance, the class A PBP, PBP1b, and the paralogous class B PBP, PBP3\n                  <jats:sub>PARA<\/jats:sub>\n                  . Loss of either gene increases\n                  <jats:italic>K. pneumoniae<\/jats:italic>\n                  susceptibility to beta-lactams at low pH. Our data supports previous work from our group and others indicating that functional redundancy among cell wall synthesis enzymes allows for specialization and ensures robust cell wall synthesis across a range of environmental conditions.\n                <\/jats:p>","DOI":"10.1101\/2025.03.12.642896","type":"posted-content","created":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T12:54:49Z","timestamp":1741870489000},"source":"Crossref","is-referenced-by-count":0,"title":["pH-dependent beta-lactam resistance in\n                  <i>Klebsiella pneumoniae<\/i>\n                  is mediated by paralogous class B PBPs and the class A PBP, PBP1b"],"prefix":"10.64898","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6193-6721","authenticated-orcid":false,"given":"Sarah","family":"Beagle","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2071-0547","authenticated-orcid":false,"given":"Petra Anne","family":"Levin","sequence":"additional","affiliation":[]}],"member":"54368","reference":[{"key":"2025031911593680000_2025.03.12.642896v1.1","doi-asserted-by":"publisher","DOI":"10.1038\/s41579-020-0366-3"},{"key":"2025031911593680000_2025.03.12.642896v1.2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mib.2017.01.006"},{"key":"2025031911593680000_2025.03.12.642896v1.3","doi-asserted-by":"publisher","DOI":"10.1007\/BF00425435"},{"key":"2025031911593680000_2025.03.12.642896v1.4","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.75.2.664"},{"key":"2025031911593680000_2025.03.12.642896v1.5","doi-asserted-by":"publisher","DOI":"10.1099\/00221287-131-10-2839"},{"key":"2025031911593680000_2025.03.12.642896v1.6","doi-asserted-by":"publisher","DOI":"10.1074\/jbc.274.45.32031"},{"key":"2025031911593680000_2025.03.12.642896v1.7","doi-asserted-by":"publisher","DOI":"10.1101\/cshperspect.a025247"},{"key":"2025031911593680000_2025.03.12.642896v1.8","doi-asserted-by":"crossref","unstructured":"Mueller, E. 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