{"title":"Multiplicative structures on the minimal resolution of determinantal rings","authors":"Ruud Pellikaan","doi":"10.1016/1385-7258(89)90010-3","DOIUrl":"https://doi.org/10.1016/1385-7258(89)90010-3","url":null,"abstract":"<div><p>It is shown that the minimal resolution of a determinantal ring has the structure of an associative differential graded algebra.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 4","pages":"Pages 471-478"},"PeriodicalIF":0.0,"publicationDate":"1989-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/1385-7258(89)90010-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"137201486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Compact-like operators between non-archimedean normed spaces","authors":"N. de Grande-de Kimpe , J. Martinez-Maurica","doi":"10.1016/1385-7258(89)90005-X","DOIUrl":"10.1016/1385-7258(89)90005-X","url":null,"abstract":"<div><p>The Fredholm theory for compact operators on a non-archimedean Banach space <em>E</em>, as recently developed by W. Schikhof, does not work if the hypothesis of the completeness of E is dropped. This observation led the authors to introduce two new ideals of operators between non-archimedean normed spaces which, in the case of Banach spaces coincide with the ideal of the compact operators. They also investigate in various ways the possible equality of the three operator ideals.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"92 4","pages":"Pages 421-433"},"PeriodicalIF":0.0,"publicationDate":"1989-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/1385-7258(89)90005-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"111136948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A characterization of harmonic functions","authors":"Josip Globevnik , Walter Rudin","doi":"10.1016/S1385-7258(88)80020-9","DOIUrl":"https://doi.org/10.1016/S1385-7258(88)80020-9","url":null,"abstract":"<div><p>Gauss' mean value characterization of harmonic functions involves circles (or spheres) centered at every point of the domain of the function. The present paper gives a criterion of this type which involves only one point of the domain; to make up for this, circles or spheres are replaced by a larger family of convex curves or surfaces which surround this point.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 4","pages":"Pages 419-426"},"PeriodicalIF":0.0,"publicationDate":"1988-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80020-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72227966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Vector measures on orthocomplemented lattices","authors":"P. Kruszyński","doi":"10.1016/S1385-7258(88)80021-0","DOIUrl":"https://doi.org/10.1016/S1385-7258(88)80021-0","url":null,"abstract":"<div><p>A relatively orthocomplemented lattice <em>L</em> is a lattice in which every interval is an orthocomplemented sublattice. An orthogonally scattered measure ξ on <em>L</em> is a Hilbert space valued abstract measure over <em>L</em> such that ξ(<em>e</em>) ⊥ ξ(<em>f</em>) whenever <em>e</em> ⊥ <em>f</em>in <em>L</em>. The properties of so generalized c.a.o.s. measures are studied, the representation theorem has been proved: every <em>H</em>-valued c.a.o.s. measure ξ on <em>L</em> is of the form <em>ξ(e) = Φ(e)x</em>, where <em>x ε H</em>, and Φ is a lattice orthohomomorphism from <em>L</em> into Proj (<em>H</em>). The results generalize those in [21]. Their suitability for many applications has been demonstrated, including duality theory for some inductive-projective limits of Hilbert spaces and quantum probability.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 4","pages":"Pages 427-442"},"PeriodicalIF":0.0,"publicationDate":"1988-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80021-0","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72243389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Stanley decomposition of the harmonic oscillator","authors":"L.J. Billera , R. Cushman , J.A. Sanders","doi":"10.1016/S1385-7258(88)80017-9","DOIUrl":"https://doi.org/10.1016/S1385-7258(88)80017-9","url":null,"abstract":"<div><p>This paper gives a new decomposition for the ring of polynomial functions on the variety of (<em>n</em> + 1) × (<em>n</em> + 1) complex matrices of rank less than or equal to one. This involves decomposing the monoid <span><span><span><math><mrow><msub><mo>M</mo><mi>n</mi></msub><mo>=</mo><mo>{</mo><mo>(</mo><mi>j</mi><mo>,</mo><mi>k</mi><mo>)</mo><mo>∈</mo><msup><mi>ℕ</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>×</mo><msup><mi>ℕ</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mrow><mo>|</mo><mrow><mo>|</mo><mi>j</mi><mo>|</mo><mo>=</mo><mo>|</mo><mi>k</mi><mo>|</mo></mrow></mrow><mo>}</mo></mrow></math></span></span></span> into a finite disjoint union of translates of ℕ cones based on certain 2<em>n</em> simplices in ℝ<sup>2n+2</sup>. As a consequence we have a method for writing the normal form of a perturbed <em>n</em>+1 dimensional harmonic oscillator in a unique way.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 4","pages":"Pages 375-393"},"PeriodicalIF":0.0,"publicationDate":"1988-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80017-9","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72243387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Ungleichungen für geometrische und arithmetische Mittelwerte","authors":"Horst Alzer","doi":"10.1016/S1385-7258(88)80016-7","DOIUrl":"https://doi.org/10.1016/S1385-7258(88)80016-7","url":null,"abstract":"<div><p>Wir bezeichnen mit <em>G<sub>n</sub></em> und <em>A<sub>n</sub></em> (bzw. <em>G′<sub>n</sub></em> und <em>A′<sub>n</sub></em>) das ungewichtete geometrische und arithmetische Mittel der Zahlen <em>χ<sub>1</sub>,,χ<sub>n</sub></em> (bzw. <em>1−χ<sub>1</sub>,,1−χ<sub>n</sub>), χ<sub>i</sub>ε[0,1/2], i=1,...,n</em>. Das Ziel dieser Note ist es, die beiden Differenzen <span><span><span><math><mrow><msub><mi>A</mi><mi>n</mi></msub><mo>/</mo><msubsup><mi>A</mi><mi>n</mi><mo>'</mo></msubsup><mo>−</mo><msub><mi>G</mi><mi>n</mi></msub><mo>/</mo><msubsup><mi>G</mi><mi>n</mi><mo>'</mo></msubsup><mtext></mtext><mi>u</mi><mi>n</mi><mi>d</mi><mtext></mtext><mo>(</mo><msub><mi>A</mi><mi>n</mi></msub><mo>−</mo><msubsup><mi>A</mi><mi>n</mi><mo>'</mo></msubsup><mo>)</mo><mo>−</mo><mo>(</mo><msub><mi>G</mi><mi>n</mi></msub><mo>−</mo><msubsup><mi>G</mi><mi>n</mi><mo>'</mo></msubsup><mo>)</mo></mrow></math></span></span></span> bestmöglich nach oben und nach unten abzuschätzen. Wir werden die Gültigkeit der Ungleichungen <span><span><span><math><mrow><mo>(</mo><mo>*</mo><mo>)</mo><mo>0</mo><mo>≤</mo><msub><mi>A</mi><mi>n</mi></msub><mo>/</mo><msubsup><mi>A</mi><mi>n</mi><mo>'</mo></msubsup><mo>−</mo><msub><mi>G</mi><mi>n</mi></msub><mo>/</mo><msubsup><mi>G</mi><mi>n</mi><mo>'</mo></msubsup><mo>≤</mo><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo><mo>/</mo><mo>(</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span></span></span> und <span><span><span><math><mrow><mn>0</mn><mo>≤</mo><mo>(</mo><msub><mi>A</mi><mi>n</mi></msub><mo>−</mo><msubsup><mi>A</mi><mi>n</mi><mo>'</mo></msubsup><mo>)</mo><mo>−</mo><mo>(</mo><msub><mi>G</mi><mi>n</mi></msub><mo>−</mo><msubsup><mi>G</mi><mi>n</mi><mo>'</mo></msubsup><mo>)</mo><mo>≤</mo><msup><mn>2</mn><mrow><mo>(</mo><mi>1</mi><mo>−</mo><mi>n</mi><mo>)</mo><mo>/</mo><mi>n</mi></mrow></msup><mo>−</mo><mn>1</mn><mo>/</mo><mi>n</mi></mrow></math></span></span></span> für alle <em>χ<sub>i</sub>ε[0,1/2], i=1,...,n</em>, nachweisen und zeigen, daß sich die angegebenen Schranken nicht verschärfen lassen. Bei der linken Seite von (*) handelt es sich um die bekannte Ungleichung von Ky Fan.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 4","pages":"Pages 365-374"},"PeriodicalIF":0.0,"publicationDate":"1988-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80016-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72243386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On the problem of rationality for some cubic complexes","authors":"A. Alzati , M. Bertolini","doi":"10.1016/S1385-7258(88)80015-5","DOIUrl":"https://doi.org/10.1016/S1385-7258(88)80015-5","url":null,"abstract":"<div><p>Let <em>V</em> be the complete intersection of smooth, generic quadric and cubic hypersurfaces in ℙ<sup>5</sup>(ℂ). <em>V</em> is a non rational Fano threefold. It is interesting to study the rationality of <em>V</em> when it contains <em>n</em> planes. This problem has been solved when the planes meet two by two in one point only. We consider and solve all remaining cases.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 4","pages":"Pages 349-364"},"PeriodicalIF":0.0,"publicationDate":"1988-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80015-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72205761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fast and rigorous factorization under the generalized Riemann hypothesis","authors":"A.K. Lenstra","doi":"10.1016/S1385-7258(88)80022-2","DOIUrl":"https://doi.org/10.1016/S1385-7258(88)80022-2","url":null,"abstract":"<div><p>We present an algorithm that finds a non-trivial factor of an odd composite integer <em>n</em> with probability <em>⩾1/2 - o(1)</em> in expected time bounded by <span><math><mrow><msup><mi>e</mi><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>o</mi><mo>(</mo><mn>1</mn><mo>)</mo><mo>)</mo><msqrt><mrow><mi>log</mi><mo></mo><mi>n</mi><mi>log</mi><mo></mo><mi>log</mi><mo></mo><mi>n</mi></mrow></msqrt></mrow></msup></mrow></math></span>. This result can be <em>rigorously</em> proved under the sole assumption of the generalized Riemann hypothesis. The time bound matches the <em>heuristic</em> time bounds for the continued fraction algorithm, the quadratic sieve algorithm, the Schnorr-Lenstra class group algorithm, and the worst case of the elliptic curve method. The algorithm is based on Seysen's factoring algorithm [14], and the elliptic curve smoothness test from [12].</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 4","pages":"Pages 443-454"},"PeriodicalIF":0.0,"publicationDate":"1988-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80022-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72243388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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