{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:15:24Z","timestamp":1753884924645,"version":"3.41.2"},"reference-count":27,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Open Syst. Inf. Dyn."],"published-print":{"date-parts":[[2025,3]]},"abstract":"<jats:p> A one-parameter family of hermiticity-preserving superoperators is a time-dependent family [Formula: see text] of hermiticity-preserving superoperators determined, in a certain sense, by real and complex polynomial functions in the variable [Formula: see text]. The paper studies sufficient computable criteria for nonpositivity of superoperators in one-parameter families. More precisely, we give sufficient conditions for the following assertions to hold: [Formula: see text] every [Formula: see text] is not positive, [Formula: see text] [Formula: see text] is not positive for [Formula: see text] in some [Formula: see text] and [Formula: see text] there is some [Formula: see text] which is not positive. We show that [Formula: see text] implies [Formula: see text]. Our approach to the problem is based on the Descartes rule of signs and the Sturm-Tarski theorem. In order to apply these facts, we introduce the sign variation formulas. These formulas are first order logical formulas in one variable [Formula: see text], generalising sign sequences of polynomials used in Descartes rule of signs. <\/jats:p>","DOI":"10.1142\/s1230161225500040","type":"journal-article","created":{"date-parts":[[2025,5,16]],"date-time":"2025-05-16T06:27:59Z","timestamp":1747376879000},"source":"Crossref","is-referenced-by-count":0,"title":["On One-Parameter Families of Hermiticity-Preserving Superoperators which Are Not Positive"],"prefix":"10.1142","volume":"32","author":[{"given":"Grzegorz","family":"Pastuszak","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toru\u0144, Poland"}]},{"given":"Alicja","family":"Jaworska-Pastuszak","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toru\u0144, Poland"}]},{"given":"Takeo","family":"Kamizawa","sequence":"additional","affiliation":[{"name":"Department of Informatics and Data Science, Sanyo-Onoda City University, Sanyo-Onoda, Japan"}]}],"member":"219","published-online":{"date-parts":[[2025,5,15]]},"reference":[{"key":"S1230161225500040BIB001","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.75.3020"},{"key":"S1230161225500040BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/0004-3702(88)90049-5"},{"key":"S1230161225500040BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(86)90029-2"},{"volume-title":"Algorithms in Real Algebraic Geometry","year":"2016","author":"Basu S.","key":"S1230161225500040BIB004"},{"key":"S1230161225500040BIB005","doi-asserted-by":"crossref","unstructured":"L. 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