Indagationes Mathematicae (Proceedings)最新文献

{"title":"Discrete measures for spherical designs, eutactic stars and lattices","authors":"A. Neumaier , J.J. Seidel","doi":"10.1016/S1385-7258(88)80011-8","DOIUrl":"10.1016/S1385-7258(88)80011-8","url":null,"abstract":"","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 3","pages":"Pages 321-334"},"PeriodicalIF":0.0,"publicationDate":"1988-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80011-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"103801025","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":"Remarks on the equation 1k + 2k + + (x − 1)k= xk","authors":"Jerzy Urbanowicz","doi":"10.1016/S1385-7258(88)80014-3","DOIUrl":"10.1016/S1385-7258(88)80014-3","url":null,"abstract":"<div><p>For every <em>t</em> there is an explicitly given number <em>k</em>₀ such that the equation 1^<em>k</em> + 2^<em>k</em> + + (x − 1)^<em>k</em>= x^<em>k</em> has no integer solutions <em>x</em>≥2 for all <em>k</em>₀ for which the denominator of the <em>k</em>th Bernoulli number <em>B</em>_khas at most <em>t</em> distinct prime factors.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 3","pages":"Pages 343-348"},"PeriodicalIF":0.0,"publicationDate":"1988-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80014-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"93387736","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 space of all regular operators from C(K) into C(K)","authors":"A. Andreu,&nbsp;J.M. Mazón,&nbsp;S. Segura de Léon","doi":"10.1016/S1385-7258(88)80001-5","DOIUrl":"https://doi.org/10.1016/S1385-7258(88)80001-5","url":null,"abstract":"<div><p>It is known that <em>L^r(E, C(K))</em>, the space of all regular operators from <em>E</em> into <em>C(K)</em>, is a Riesz space for all Riesz spaces <em>E</em> if and only if <em>K</em> is Stonian. We prove that this statement holds if <em>E</em> is replaced by <em>C(K)</em>, where <em>K</em> is a compact space, the cardinal number of which satisfies a certain condition.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 3","pages":"Pages 225-230"},"PeriodicalIF":0.0,"publicationDate":"1988-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80001-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90124928","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":"F-algebras in which order ideals are ring ideals","authors":"M. Basly,&nbsp;A. Triki","doi":"10.1016/S1385-7258(88)80002-7","DOIUrl":"10.1016/S1385-7258(88)80002-7","url":null,"abstract":"","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 3","pages":"Pages 231-234"},"PeriodicalIF":0.0,"publicationDate":"1988-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80002-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"99119905","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":"Field invariants under totally positive quadratic extensions","authors":"E.A.M. Hornix","doi":"10.1016/S1385-7258(88)80008-8","DOIUrl":"https://doi.org/10.1016/S1385-7258(88)80008-8","url":null,"abstract":"<div><p><em>K</em> = F(√d) is a formally real field and a totally positive quadratic extension of <em>F</em>. A decomposition theorem for quadratic forms in Fed (<em>K</em>) is given. The invariants <em>r(q)</em> and <em>ud(KF)</em> are defined and relations between the invariants <em>β_F(i)</em>, <em>β_K(i)</em>, <em>ud(F), ud(K), l(F), l(K)</em> are studied, using the theory of quadratic forms.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 3","pages":"Pages 277-291"},"PeriodicalIF":0.0,"publicationDate":"1988-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80008-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91756098","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 remark on spaces of bounded continuous functions","authors":"Jan Pelant","doi":"10.1016/S1385-7258(88)80012-X","DOIUrl":"10.1016/S1385-7258(88)80012-X","url":null,"abstract":"<div><p>We show that <em>C_p^*</em>(ℚ) and <em>C_p^*(T)</em> are not linearly homeomorphic, thus answering a question of van Mill.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 3","pages":"Pages 335-338"},"PeriodicalIF":0.0,"publicationDate":"1988-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80012-X","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92956378","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":"New extension of the Banach contraction principle to locally convex spaces and applications","authors":"Kazimierz Włlodarczyk","doi":"10.1016/S1385-7258(88)80029-5","DOIUrl":"https://doi.org/10.1016/S1385-7258(88)80029-5","url":null,"abstract":"<div><p>In the paper, an important tool from fixed point theory, the Banach contraction principle, is extended to the more general setting where the spaces are Hausdorff locally convex and sequentially complete with calibrations Γ and the maps are not necessarily Γ-continuous. Applications are given for Γ-strictly pseudo-contractive maps.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 2","pages":"Pages 211-221"},"PeriodicalIF":0.0,"publicationDate":"1988-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80029-5","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92087760","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":"Simultaneous weighted sums of elements of finitely generated multiplicative groups","authors":"R. Tijdeman ,&nbsp;Lianxiang Wang","doi":"10.1016/S1385-7258(88)80028-3","DOIUrl":"10.1016/S1385-7258(88)80028-3","url":null,"abstract":"<div><p>Let <em>{G_j}_jεJ</em> be a finite set of finitely generated subgroups of the multiplicative group of complex numbers <em>C</em>^x. Write <em>H=∩ _jεJ G_j</em>. Let <em>n</em> be a positive integer and <em>a_ij</em> a complex number for <em>i</em> = 1, ..., <em>n</em> and <em>j ε J</em>. Then there exists a set <em>W</em> with the following properties. The cardinality of <em>W</em> depends only on <em>{G_j}_jεJ</em> and <em>n</em>. If, for each <em>jεJ, α</em> has a representation <em>α = Σ _iⁿ = ₁a _ijg_ij</em> in elements <em>g_ij</em> of <em>G_j</em>, then α has a representation <em>a= Σ_k=1ⁿ w_kh_k</em> with <em>w_kεW, h_k εH</em> for <em>k = 1,..., n</em>. The theorem in this note gives information on such representations.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 2","pages":"Pages 205-209"},"PeriodicalIF":0.0,"publicationDate":"1988-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80028-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"112640462","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 classical orthogonal Laurent polynomials","authors":"E. Hendriksen","doi":"10.1016/S1385-7258(88)80025-8","DOIUrl":"10.1016/S1385-7258(88)80025-8","url":null,"abstract":"<div><p>In [3] certain Laurent polynomials of <em>₂F₁</em> genus were called “Jacobi Laurent polynomials”. These Laurent polynomials belong to systems which are orthogonal with respect to a moment sequence <em>((a)_n/(c)_n)_nεℤ</em> where <em>a, c</em> are certain real numbers. Together with their confluent forms, belonging to systems which are orthogonal with respect to <em>1/(c)_n)_nεℤ</em> respectively <em>((a)_n)_nεℤ</em>, these Laurent polynomials will be called “classical”. The main purpose of this paper is to determine all the simple (see section 1) orthogonal systems of Laurent polynomials of which the members satisfy certain second order differential equations with polynomial coefficients, analogously to the well known characterization of S. Bochner [1] for ordinary polynomials.</p></div>","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 2","pages":"Pages 165-180"},"PeriodicalIF":0.0,"publicationDate":"1988-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80025-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"100006126","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":"Stable n-pointed trees of projective lines","authors":"L. Gerritzen ,&nbsp;F. Herrlich,&nbsp;M. van der Put","doi":"10.1016/S1385-7258(88)80024-6","DOIUrl":"10.1016/S1385-7258(88)80024-6","url":null,"abstract":"<div><p>Stable <em>n</em>-pointed trees arise in a natural way if one tries to find moduli for totally degenerate curves: Let <em>C</em> be a totally degenerate stable curve of genus <em>g ≥ 2</em> over a field k. This means that <em>C</em> is a connected projective curve of arithmetic genus <em>g</em> satisfying<span>o<ol><li><span><p>(a) every irreducible component of <em>C</em> is a rational curve over κ.</p></span></li><li><span><p>(b) every singular point of <em>C</em> is a κ-rational ordinary double point.</p></span></li><li><span><p>(c) every nonsingular component <em>L</em> of <em>C</em> meets <em>C−L</em> in at least three points. It is always possible to find g singular points <em>P₁,..., P_g</em> on <em>C</em> such that the blow up <em>C</em> of <em>C</em> at <em>P₁,..., P_g</em> is a connected projective curve with the following properties:<span>o<ol><li><span><p>(i) every irreducible component of <em>C</em> is isomorphic to P_k¹</p></span></li><li><span><p>(ii) the components of <em>C</em> intersect in ordinary κ-rational double points</p></span></li><li><span><p>(iii) the intersection graph of <em>C</em> is a tree.</p></span></li></ol></span></p></span></li></ol></span></p><p>The morphism φ : C → C is an isomorphism outside 2<em>g</em> regular points <em>Q₁, Q₁′, Q_g, Q_g′</em> and identifies <em>Q_i</em> with <em>Q_j′</em>. is uniquely determined by the g pairs of regular κ-rational points (<em>Q_i, Q_i′</em>). A curve <em>C</em> satisfying (i)-(iii) together with <em>n</em> κ-rational regular points on it is called a <em>n</em>-pointed tree of projective lines. <em>C</em> is stable if on every component there are at least three points which are either singular or marked. The object of this paper is the classification of stable <em>n</em>-pointed trees. We prove in particular the existence of a fine moduli space <em>B_n</em> of stable <em>n</em>-pointed trees. The discussion above shows that there is a surjective map <em>πB_2g → D_g</em> of <em>B_2g</em> onto the closed subscheme <em>D_g</em> of the coarse moduli scheme <em>M_g</em> of stable curves of genus <em>g</em> corresponding to the totally degenerate curves. By the universal property of <em>M_g</em>, π is a (finite) morphism. π factors through <em>B_2g = B_2g</em> mod the action of the group of pair preserving permutations of 2<em>g</em> elements (a group of order 2<em>^gg</em>, isomorphic to a wreath product of <em>S_g</em> and ℤ/2ℤ</p><p>The induced morphism <em>π: B_2g → D_g</em> is an isomorphism on the open subscheme of irreducible curves in <em>D_g</em>, but in general there may be nonequivalent choices of <em>g</em> singular points on a totally degenerated curve for the above constructio","PeriodicalId":100664,"journal":{"name":"Indagationes Mathematicae (Proceedings)","volume":"91 2","pages":"Pages 131-163"},"PeriodicalIF":0.0,"publicationDate":"1988-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/S1385-7258(88)80024-6","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134566863","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}