Bulletin des Sciences Mathematiques最新文献

{"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}

{"title":"A new method based on the semi-tensor product of matrices for solving communicative quaternion matrix equation ∑i=1kAiXBi=C and its application","authors":"Mingcui Zhang,&nbsp;Ying Li,&nbsp;Jianhua Sun,&nbsp;Xueling Fan,&nbsp;Anli Wei","doi":"10.1016/j.bulsci.2025.103576","DOIUrl":"10.1016/j.bulsci.2025.103576","url":null,"abstract":"<div><div>This paper studies the least squares problem of the commutative quaternion matrix equation <span><span>(1.1)</span></span>, finds its minimal norm least squares (anti-)Hermitian solution. In the process of completing this work, we generalize the semi-tensor product of real matrices to the commutative quaternion matrices, then use it to extend the vector operators to the commutative quaternion matrix and propose the <em>L</em>-representation, which transforms the intricate commutative quaternion matrix equation into a solvable system of real linear equations, we also use <em>GH</em>-representation to reduce the complexity of the operation and greatly save the operation time. This can be illustrated by numerical examples in the paper. In addition, we take a special kind of commutative quaternion: reduced biquaternion as an example, and compare our method with another method in reference <span><span>[33]</span></span> to prove the effectiveness of our method. Finally, we apply the method used in this paper to symmetric color image restoration.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"199 ","pages":"Article 103576"},"PeriodicalIF":1.3,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143173502","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":"Characterizations of complex symmetric Toeplitz operators","authors":"Sudip Ranjan Bhuia,&nbsp;Deepak Pradhan,&nbsp;Jaydeb Sarkar","doi":"10.1016/j.bulsci.2025.103578","DOIUrl":"10.1016/j.bulsci.2025.103578","url":null,"abstract":"<div><div>We characterize Toeplitz operators that are complex symmetric. This follows as a by-product of characterizations of conjugations on Hilbert spaces. Notably, we prove that every conjugation admits a canonical factorization. As a consequence, we prove that a Toeplitz operator is complex symmetric if and only if the Toeplitz operator is <em>S</em>-Toeplitz for some unilateral shift <em>S</em> and the transpose of the Toeplitz operator matrix is equal to the matrix of the Toeplitz operator corresponding to the basis of the unilateral shift <em>S</em>. Also, we characterize complex symmetric Toeplitz operators on the Hardy space over the open unit polydisc. Our results are related to a question raised by K. Guo and S. Zhu <span><span>[9]</span></span>.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"199 ","pages":"Article 103578"},"PeriodicalIF":1.3,"publicationDate":"2025-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143173504","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}