Bulletin des Sciences Mathematiques最新文献

{"title":"Direct sums and abstract Kadets–Klee properties","authors":"Tomasz Kiwerski,&nbsp;Paweł Kolwicz","doi":"10.1016/j.bulsci.2025.103587","DOIUrl":"10.1016/j.bulsci.2025.103587","url":null,"abstract":"<div><div>Let <span><math><mi>X</mi><mo>=</mo><msub><mrow><mo>{</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>}</mo></mrow><mrow><mi>γ</mi><mo>∈</mo><mi>Γ</mi></mrow></msub></math></span> be a family of Banach spaces and let <span><math><mi>E</mi></math></span> be a Banach sequence space defined on Γ. The main aim of this work is to investigate the abstract Kadets–Klee properties, that is, the Kadets–Klee type properties in which the weak convergence of sequences is replaced by the convergence with respect to some linear Hausdorff topology, for the direct sum construction <span><math><msub><mrow><mo>(</mo><msub><mrow><mo>⨁</mo></mrow><mrow><mi>γ</mi><mo>∈</mo><mi>Γ</mi></mrow></msub><msub><mrow><mi>X</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>)</mo></mrow><mrow><mi>E</mi></mrow></msub></math></span>. As we will show, and this seems to be quite atypical behavior when compared to some other geometric properties, to lift the Kadets–Klee properties from the components to whole direct sum it is not enough to assume that all involved spaces have the appropriate Kadets–Klee property. Actually, to complete the picture one must add a dichotomy in the form of the Schur type properties for <span><math><msub><mrow><mi>X</mi></mrow><mrow><mi>γ</mi></mrow></msub></math></span>'s supplemented by the variant of strict monotonicity for <span><math><mi>E</mi></math></span>. Back down to earth, this general machinery naturally provides a blue print for other topologies like, for example, the weak topology or the topology of local convergence in measure, that are perhaps more commonly associated with this type of considerations. Furthermore, by limiting ourselves to direct sums in which the family <span><math><mi>X</mi></math></span> is constant, that is, <span><math><msub><mrow><mi>X</mi></mrow><mrow><mi>γ</mi></mrow></msub><mo>=</mo><mi>X</mi></math></span> for all <span><math><mi>γ</mi><mo>∈</mo><mi>Γ</mi></math></span> and some Banach space <em>X</em>, we return to the well-explored ground of Köthe–Bochner sequence spaces <span><math><mi>E</mi><mo>(</mo><mi>X</mi><mo>)</mo></math></span>. Doing all this, we will reproduce, but sometimes also improve, essentially all existing results about the classical Kadets–Klee properties in Köthe–Bochner sequence spaces.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"200 ","pages":"Article 103587"},"PeriodicalIF":1.3,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adams-type inequalities with logarithmic weights in fractional dimensions and the existence of extremals","authors":"Rou Jiang ,&nbsp;Wenyan Xu ,&nbsp;Caifeng Zhang ,&nbsp;Maochun Zhu","doi":"10.1016/j.bulsci.2025.103586","DOIUrl":"10.1016/j.bulsci.2025.103586","url":null,"abstract":"<div><div>In this paper, we proved a sharp Adams-type inequality with logarithmic weights <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo><mo>=</mo><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>r</mi></mrow></mfrac><mo>)</mo></mrow><mrow><mi>β</mi><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span> or <span><math><msub><mrow><mi>ω</mi></mrow><mrow><mi>β</mi></mrow></msub><mo>(</mo><mi>r</mi><mo>)</mo><mo>=</mo><msup><mrow><mo>(</mo><mi>log</mi><mo>⁡</mo><mfrac><mrow><mi>e</mi></mrow><mrow><mi>r</mi></mrow></mfrac><mo>)</mo></mrow><mrow><mi>β</mi><mo>(</mo><mi>p</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow></msup></math></span>, <span><math><mi>β</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> in the fractional dimensions. Furthermore, we show the existence of extremals for this kind of inequalities.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"200 ","pages":"Article 103586"},"PeriodicalIF":1.3,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143509434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exact bounds to the Toeplitz determinants of certain order, Zalcman conjecture and Krushkals inequalities for the functions associated with the lemniscate of Bernoulli","authors":"Winne Bareh ,&nbsp;D. Vamshee Krishna ,&nbsp;Biswajit Rath","doi":"10.1016/j.bulsci.2025.103585","DOIUrl":"10.1016/j.bulsci.2025.103585","url":null,"abstract":"<div><div>The main object of this article is to investigate sharp bounds of the Toeplitz determinants of certain order, Zalcman conjecture and Krushkals inequalities for normalized analytic functions in the open unit disk <span><math><mi>D</mi></math></span>, associated with the familiar subfamily of starlike functions associated with the right half of lemniscate of Bernoulli. The practical tools applied in the derivation of our main results are the coefficient inequalities of the Carathéodory class <span><math><mi>P</mi></math></span>.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"199 ","pages":"Article 103585"},"PeriodicalIF":1.3,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143438013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Diagonal property and weak point property of higher rank divisors and certain Hilbert schemes","authors":"Arijit Mukherjee,&nbsp;D.S. Nagaraj","doi":"10.1016/j.bulsci.2024.103541","DOIUrl":"10.1016/j.bulsci.2024.103541","url":null,"abstract":"<div><div>In this paper, we introduce the notion of the diagonal property and the weak point property for an ind-variety. We prove that the ind-varieties of higher rank divisors of integral slopes on a smooth projective curve have the weak point property. Moreover, we show that the ind-variety of <span><math><mo>(</mo><mn>1</mn><mo>,</mo><mi>n</mi><mo>)</mo></math></span>-divisors has the diagonal property and is a locally complete linear ind-variety and calculate its Picard group. Furthermore, we obtain that the Hilbert schemes of a curve associated to the good partitions of a constant polynomial satisfy the diagonal property. In the process of obtaining this, we provide the exact number of such Hilbert schemes up to isomorphism by proving that the multi symmetric products associated to two distinct partitions of a positive integer <em>n</em> are not isomorphic.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"198 ","pages":"Article 103541"},"PeriodicalIF":1.3,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143103542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global well-posedness of a class of weakly hyperbolic Cauchy problems with variable multiplicities on Rd","authors":"Sandro Coriasco ,&nbsp;Giovanni Girardi ,&nbsp;N. Uday Kiran","doi":"10.1016/j.bulsci.2025.103584","DOIUrl":"10.1016/j.bulsci.2025.103584","url":null,"abstract":"<div><div>We study a class of weakly hyperbolic Cauchy problems on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, involving linear operators with characteristics of variable multiplicities, whose coefficients are unbounded in the space variable. The behavior in the time variable is governed by a suitable “shape function”. We develop a parameter-dependent symbolic calculus, corresponding to an appropriate subdivision of the phase space. By means of such calculus, a parametrix can be constructed, in terms of (generalized) Fourier integral operators naturally associated with the employed symbol class. Further, employing the parametrix, we prove <span><math><mi>S</mi><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>)</mo></math></span>-well-posedness and give results about the global regularity of the solution, within a scale of weighted Sobolev space, encoding both smoothness and decay at infinity of temperate distributions. In particular, loss of decay appears, together with the well-known phenomenon of loss of smoothness.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"199 ","pages":"Article 103584"},"PeriodicalIF":1.3,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143394499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Length distortion of curves under meromorphic univalent mappings","authors":"Bappaditya Bhowmik ,&nbsp;Deblina Maity","doi":"10.1016/j.bulsci.2025.103583","DOIUrl":"10.1016/j.bulsci.2025.103583","url":null,"abstract":"<div><div>Let <em>f</em> be a conformal (analytic and univalent) map defined on the open unit disk <span><math><mi>D</mi></math></span> of the complex plane <span><math><mi>C</mi></math></span> that is continuous on the semi-circle <span><math><mo>∂</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>=</mo><mo>{</mo><mi>z</mi><mo>∈</mo><mi>C</mi><mo>:</mo><mo>|</mo><mi>z</mi><mo>|</mo><mo>=</mo><mn>1</mn><mo>,</mo><mrow><mi>Im</mi></mrow><mspace></mspace><mi>z</mi><mo>&gt;</mo><mn>0</mn><mo>}</mo></math></span>. The existence of a uniform upper bound for the ratio of the length of the image of the horizontal diameter <span><math><mo>(</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span> to the length of the image of <span><math><mo>∂</mo><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span> under <em>f</em> was proved by Gehring and Hayman. In this article, at first, we generalize this result by introducing a simple pole for <em>f</em> in <span><math><mi>D</mi></math></span> and considering the ratio of the length of the image of the vertical diameter <span><math><mi>I</mi><mo>=</mo><mo>{</mo><mi>z</mi><mo>:</mo><mrow><mi>Re</mi></mrow><mspace></mspace><mi>z</mi><mo>=</mo><mn>0</mn><mo>;</mo><mspace></mspace><mo>|</mo><mrow><mi>Im</mi></mrow><mspace></mspace><mi>z</mi><mo>|</mo><mo>&lt;</mo><mn>1</mn><mo>}</mo></math></span> to the length of the image of the semi-circle <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>=</mo><mo>{</mo><mi>z</mi><mo>:</mo><mo>|</mo><mi>z</mi><mo>|</mo><mo>=</mo><mn>1</mn><mo>;</mo><mspace></mspace><mrow><mi>Re</mi></mrow><mspace></mspace><mi>z</mi><mo>&lt;</mo><mn>0</mn><mo>}</mo></math></span> under such <em>f</em>. Finally, we further generalize this result by replacing the vertical diameter <em>I</em> with a hyperbolic geodesic symmetric with respect to the real line, and by replacing <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> with the corresponding arc of the unit circle passing through the point −1.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"199 ","pages":"Article 103583"},"PeriodicalIF":1.3,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143174298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Disproving a weaker form of Hooley's conjecture","authors":"Mounir Hayani","doi":"10.1016/j.bulsci.2025.103582","DOIUrl":"10.1016/j.bulsci.2025.103582","url":null,"abstract":"<div><div>Hooley conjectured that <span><math><mi>G</mi><mo>(</mo><mi>x</mi><mo>;</mo><mi>q</mi><mo>)</mo><mo>≪</mo><mi>x</mi><mi>log</mi><mo>⁡</mo><mi>q</mi></math></span>, as soon as <span><math><mi>q</mi><mo>→</mo><mo>+</mo><mo>∞</mo></math></span>, where <span><math><mi>G</mi><mo>(</mo><mi>x</mi><mo>;</mo><mi>q</mi><mo>)</mo></math></span> represents the variance of primes <span><math><mi>p</mi><mo>≤</mo><mi>x</mi></math></span> in arithmetic progressions modulo <em>q</em>, weighted by <span><math><mi>log</mi><mo>⁡</mo><mi>p</mi></math></span>. In this paper, we study <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>η</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>;</mo><mi>q</mi><mo>)</mo></math></span>, a function similar to <span><math><mi>G</mi><mo>(</mo><mi>x</mi><mo>;</mo><mi>q</mi><mo>)</mo></math></span>, but including the weighting factor <span><math><mi>η</mi><mrow><mo>(</mo><mfrac><mrow><mi>p</mi></mrow><mrow><mi>x</mi></mrow></mfrac><mo>)</mo></mrow></math></span>, which has a dampening effect on the values of <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>η</mi></mrow></msub></math></span>. Our study is motivated by the disproof of Hooley's conjecture by Fiorilli and Martin in the range <span><math><mi>q</mi><mo>≍</mo><mi>log</mi><mo>⁡</mo><mi>log</mi><mo>⁡</mo><mi>x</mi></math></span>. Even though this weighting factor dampens the values, we still prove that an estimation of the form <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>η</mi></mrow></msub><mo>(</mo><mi>x</mi><mo>;</mo><mi>q</mi><mo>)</mo><mo>≪</mo><mi>x</mi><mi>log</mi><mo>⁡</mo><mi>q</mi></math></span> is false in the same range.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"199 ","pages":"Article 103582"},"PeriodicalIF":1.3,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143174299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Maps of the plane with a finite number of fixed points","authors":"Rafael Ortega ,&nbsp;Xingchen Yu","doi":"10.1016/j.bulsci.2025.103581","DOIUrl":"10.1016/j.bulsci.2025.103581","url":null,"abstract":"<div><div>In this paper, we find two families of planar maps with a finite number of fixed points. Further we apply our results to study the number of periodic solutions of some forced second order differential equations. In this way we obtain a refinement of a result due to Nakajima and Seifert. In their paper these authors assumed that the periodic system was dissipative and defined in the whole plane. Now we can deal with non-dissipative equations defined on proper subsets of the plane and such that some solutions of the initial value problem blow up in finite time.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"199 ","pages":"Article 103581"},"PeriodicalIF":1.3,"publicationDate":"2025-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143174297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Topologically torsion elements of the circle group for arithmetic-type sequences","authors":"Pratulananda Das ,&nbsp;Ayan Ghosh ,&nbsp;Tamim Aziz","doi":"10.1016/j.bulsci.2025.103580","DOIUrl":"10.1016/j.bulsci.2025.103580","url":null,"abstract":"<div><div>A subgroup <em>H</em> of the circle group <span><math><mi>T</mi></math></span> is called characterized by a sequence of integers <span><math><mo>(</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span> if <span><math><mi>H</mi><mo>=</mo><mo>{</mo><mi>x</mi><mo>∈</mo><mi>T</mi><mo>:</mo><munder><mi>lim</mi><mrow><mi>n</mi><mo>→</mo><mo>∞</mo></mrow></munder><mo>⁡</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>n</mi></mrow></msub><mi>x</mi><mo>=</mo><mn>0</mn><mo>}</mo></math></span>, denoted by <span><math><msub><mrow><mi>t</mi></mrow><mrow><mo>(</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow></msub><mo>(</mo><mi>T</mi><mo>)</mo></math></span> whereas the elements of <span><math><msub><mrow><mi>t</mi></mrow><mrow><mo>(</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow></msub><mo>(</mo><mi>T</mi><mo>)</mo></math></span> are called topologically torsion elements (corresponding to the sequence <span><math><mo>(</mo><msub><mrow><mi>u</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span>). In this article, we primarily consider a class of sequences which can be extracted from a given arithmetic sequence (we call these extracted sequences “arithmetic-type” sequences) and investigate the corresponding characterized subgroups thoroughly. The primary result of this article is the characterization of topologically torsion elements corresponding to an “arithmetic-type” sequence and thus generalizing the main result of Dikranjan and Impieri (2014) <span><span>[11, Theorem 2.3]</span></span> where the characterization of topologically torsion elements for a given arithmetic sequence was established. It is important to note that in the literature there has not been any characterization result for non-arithmetic sequences. This consequently helps us to understand certain cardinality aspects of the characterized subgroups characterized by arithmetic-type sequences all of which happen to be contained in the characterized subgroup characterized by the generating arithmetic sequence. Eventually we are able to establish an interesting fact that given an arithmetic sequence <span><math><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></math></span>, it is always possible to construct a tower of such subgroups of height <span><math><mi>c</mi></math></span> each characterized by an arithmetic-type sequence whose union is still properly contained in <span><math><msub><mrow><mi>t</mi></mrow><mrow><mo>(</mo><msub><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>)</mo></mrow></msub><mo>(</mo><mi>T</mi><mo>)</mo></math></span>.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"199 ","pages":"Article 103580"},"PeriodicalIF":1.3,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143174300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Smooth invariant manifolds and foliations for the differential equations with piecewise constant argument","authors":"Weijie Lu ,&nbsp;Donal O'Regan ,&nbsp;Yonghui Xia","doi":"10.1016/j.bulsci.2025.103579","DOIUrl":"10.1016/j.bulsci.2025.103579","url":null,"abstract":"<div><div>In this work, we establish the theory of smooth invariant manifolds and smooth invariant foliations for the differential equations with piecewise constant argument of a generalized type (DEPCAGs). Suppose that the linear DEPCAGs admits a <em>α</em>-exponential dichotomy, we obtain the existence of Lipschitz stable (unstable) invariant manifolds and Lipschitz stable (unstable) invariant foliations, which are based on the Lyapunov-Perron integrals with piecewise constant argument and other non-trivial techniques (such as, dichotomy inequalities with piecewise constant argument). Furthermore, we formulate and prove the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-smoothness of these manifolds and foliations for DEPCAGs by means of the fiber contraction theorem.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"199 ","pages":"Article 103579"},"PeriodicalIF":1.3,"publicationDate":"2025-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143173505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}