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A Note on 3-Distance Coloring of Planar Graphs 平面图的三维着色说明
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-03-19 DOI: 10.1007/s41980-023-00848-7
Morteza Hasanvand, Kenta Ozeki
{"title":"A Note on 3-Distance Coloring of Planar Graphs","authors":"Morteza Hasanvand, Kenta Ozeki","doi":"10.1007/s41980-023-00848-7","DOIUrl":"https://doi.org/10.1007/s41980-023-00848-7","url":null,"abstract":"<p>Thomassen (J. Combin. Theory Ser B 128:192–218, 2018) showed that every subcubic planar graph has 2-distance chromatic number at most 7, which was originally conjectured by Wegner (graphs with given diameter and a coloring problem, University of Dortmund, preprint, 1977). In this note, we consider 3-distance colorings of this family of graphs, and prove that every subcubic planar graph has 3-distance chromatic number at most 17, and we conjecture that this number can be reduced to 12. In addition, we show that every planar graph with maximum degree at most <span>(Delta )</span> has 3-distance chromatic number at most <span>((6+o(1))Delta )</span>.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140169431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Cesàro $$mathfrak {q}$$ -Difference Sequence Spaces and Spectrum of Weighted $$mathfrak {q}$$ -Difference Operator Cesàro $$mathfrak {q}$ -差分序列空间和加权 $$mathfrak {q}$ -差分算子的频谱
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-03-15 DOI: 10.1007/s41980-024-00862-3
Taja Yaying, Bipan Hazarika, Pinakadhar Baliarsingh, Mohammad Mursaleen
{"title":"Cesàro $$mathfrak {q}$$ -Difference Sequence Spaces and Spectrum of Weighted $$mathfrak {q}$$ -Difference Operator","authors":"Taja Yaying, Bipan Hazarika, Pinakadhar Baliarsingh, Mohammad Mursaleen","doi":"10.1007/s41980-024-00862-3","DOIUrl":"https://doi.org/10.1007/s41980-024-00862-3","url":null,"abstract":"<p>In this research paper, we undertake an investigation into Cesàro <span>(mathfrak {q})</span>-difference sequence spaces <span>(mathfrak {X}(mathfrak {C}_1^{delta ;mathfrak {q}}))</span>, where <span>(mathfrak {X} in {ell _{infty },c,c_0}.)</span> These spaces are generated using the matrix <span>(mathfrak {C}_1^{delta ,mathfrak {q}})</span>, which is a product of the Cesàro matrix <span>(mathfrak {C}_1)</span> of the first-order and the second-order <span>(mathfrak {q})</span>-difference operator <span>(nabla ^2_mathfrak {q})</span> defined by </p><span>$$begin{aligned} (nabla ^2_mathfrak {q} mathfrak {f})_k=mathfrak {f}_k-(1+mathfrak {q})mathfrak {f}_{k-1}+mathfrak {q}mathfrak {f}_{k-2},~(kin mathbb {N}_0), end{aligned}$$</span><p>where <span>(mathfrak {q}in (0,1))</span> and <span>(mathfrak {f}_k=0)</span> for <span>(k&lt;0.)</span> Our endeavor includes the establishment of significant inclusion relationships, the determination of bases for these spaces, the investigation of their <span>(alpha )</span>-, <span>(beta )</span>-, and <span>(gamma )</span>-duals, and the formulation of characterization results pertaining to matrix classes <span>((mathfrak {X},mathfrak {Y}))</span>, with <span>(mathfrak {X})</span> chosen from the set <span>({ell _{infty }(mathfrak {C}_1^{delta ;mathfrak {q}}), c(mathfrak {C_1^{delta ;mathfrak {q}}}), c_0(mathfrak {C}_1^{delta ;mathfrak {q}})})</span> and <span>(mathfrak {Y})</span> chosen from the set <span>({ell _{infty },c,c_0,ell _{1}}.)</span> The final section of our study is dedicated to the meticulous spectral analysis of the weighted <span>(mathfrak {q})</span>-difference operator <span>(nabla ^{2;mathfrak {z}}_{mathfrak {q}})</span> over the space <span>(c_0)</span> of null sequences.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140149518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global and Local Solutions of Stochastic Nonlinear Schrödinger System With Quadratic Interaction 具有二次交互作用的随机非线性薛定谔系统的全局和局部解决方案
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-03-15 DOI: 10.1007/s41980-024-00863-2
Masaru Hamano, Shunya Hashimoto, Shuji Machihara
{"title":"Global and Local Solutions of Stochastic Nonlinear Schrödinger System With Quadratic Interaction","authors":"Masaru Hamano, Shunya Hashimoto, Shuji Machihara","doi":"10.1007/s41980-024-00863-2","DOIUrl":"https://doi.org/10.1007/s41980-024-00863-2","url":null,"abstract":"<p>Global and local existence results for the solutions of systems of stochastic Schrödinger equations with multiplicative noise and quadratic nonlinear terms are discussed in this paper. The same system in the deterministic treatment was studied in [23] where the mass and energy are conserved. In our stochastic situation, those are not conserved.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140149274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Adjustment to the Fowler Equation 调整福勒方程
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-03-15 DOI: 10.1007/s41980-024-00864-1
Borys Álvarez-Samaniego, Wilson P. Álvarez-Samaniego, Kevin Lloacana-Unda
{"title":"Adjustment to the Fowler Equation","authors":"Borys Álvarez-Samaniego, Wilson P. Álvarez-Samaniego, Kevin Lloacana-Unda","doi":"10.1007/s41980-024-00864-1","DOIUrl":"https://doi.org/10.1007/s41980-024-00864-1","url":null,"abstract":"<p>Following closely the analysis performed by Andrew C. Fowler to derive the first canonical equation for nonlinear dune dynamics, but considering some appropriate changes of variables, suitable scalings, and by neglecting higher-order terms, we obtain an adaptation of the aforementioned equation, which contains an additional term, to describe dune morphodynamics.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140149345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Strongly Nonnil-Coherent Rings and Strongly Nonnil-Noetherian Rings 论强无相干环和强无非ether环
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-03-10 DOI: 10.1007/s41980-023-00856-7
Khaled Alhazmy, Fuad Ali Ahmed Almahdi, Younes El Haddaoui, Najib Mahdou
{"title":"On Strongly Nonnil-Coherent Rings and Strongly Nonnil-Noetherian Rings","authors":"Khaled Alhazmy, Fuad Ali Ahmed Almahdi, Younes El Haddaoui, Najib Mahdou","doi":"10.1007/s41980-023-00856-7","DOIUrl":"https://doi.org/10.1007/s41980-023-00856-7","url":null,"abstract":"<p>The first part of this paper introduces and studies the class of strongly nonnil-coherent rings, a subclass of the already defined and studied class of nonnil-coherent rings. Contrary to the classical result that every Noetherian ring is coherent, a nonnil-Noetherian ring need not be nonnil-coherent. To remedy this, the second part introduces and studies the class of strongly nonnil-Noetherian rings, a subclass of the class of nonnil-Noetherian rings. Some examples are also given to illustrate the results.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140098341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Long-Time Existence of the Finslerian Ricci Flow 芬斯勒利玛窦流的长期存在
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-03-04 DOI: 10.1007/s41980-023-00857-6
{"title":"The Long-Time Existence of the Finslerian Ricci Flow","authors":"","doi":"10.1007/s41980-023-00857-6","DOIUrl":"https://doi.org/10.1007/s41980-023-00857-6","url":null,"abstract":"<h3>Abstract</h3> <p>In this study, we demonstrate that any solution to the Finslerian Ricci flow encountering a singularity on a compact manifold is invariably associated with an unbounded <em>hh</em>-curvature tensor. Furthermore, we establish the extended temporal viability of the Finslerian Ricci flow under the constraint of bounded curvature. To achieve this, we derive the evolution equation for the <em>hh</em>-curvature tensor and establish precise estimates for the covariant derivatives of the Cartan curvature tensor.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The S-Relative Pólya Groups and S-Ostrowski Quotients of Number Fields 数域的 S 相对波利亚群和 S-Ostrowski 之商
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-03-02 DOI: 10.1007/s41980-023-00858-5
Ehsan Shahoseini, Abbas Maarefparvar
{"title":"The S-Relative Pólya Groups and S-Ostrowski Quotients of Number Fields","authors":"Ehsan Shahoseini, Abbas Maarefparvar","doi":"10.1007/s41980-023-00858-5","DOIUrl":"https://doi.org/10.1007/s41980-023-00858-5","url":null,"abstract":"<p>Let <i>K</i>/<i>F</i> be a finite extension of number fields and <i>S</i> be a finite set of primes of <i>F</i>, including all the Archimedean ones. In this paper, using some results of González-Avilés (J Reine Angew Math 613:75–97, 2007), we generalize the notions of the relative Pólya group <span>({{,textrm{Po},}}(K/F))</span> (Chabert in J Number Theory 203:360–375, 2019; Maarefparvar and Rajaei in J Number Theory 207:367-384, 2020) and the Ostrowski quotient <span>({{,textrm{Ost},}}(K/F))</span> (Shahoseini et al. in Pac J Math 321(2):415–429, 2022) to their <i>S</i>-versions. Using this approach, we obtain generalizations of some well-known results on the <i>S</i>-capitulation map, including an <i>S</i>-version of Hilbert’s Theorem 94.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140025756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Remark on a Result of Huber and Kahn 关于胡贝尔和卡恩一个结果的评论
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-02-29 DOI: 10.1007/s41980-024-00861-4
Somayeh Habibi, Farhad Rahmati
{"title":"A Remark on a Result of Huber and Kahn","authors":"Somayeh Habibi, Farhad Rahmati","doi":"10.1007/s41980-024-00861-4","DOIUrl":"https://doi.org/10.1007/s41980-024-00861-4","url":null,"abstract":"<p>A. Huber and B. Kahn construct a relative slice filtration on the motive <i>M</i>(<i>X</i>) associated to a principal <i>T</i>-bundle <span>(Xrightarrow Y)</span> for a smooth scheme <i>Y</i>. As a consequence of their result, one can observe that the mixed Tateness of the motive <i>M</i>(<i>Y</i>) implies that the motive <i>M</i>(<i>X</i>) is mixed Tate. In this note we prove the inverse implication for a principal <i>G</i>-bundle, for a split reductive group <i>G</i>.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140003152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Holomorphic Statistical Structures of Constant Holomorphic Sectional Curvature on Complex Space Forms 复杂空间形式上恒定全态截面曲率的全态统计结构
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-02-27 DOI: 10.1007/s41980-023-00855-8
Mingming Yan, Xinlei Wu, Liang Zhang
{"title":"The Holomorphic Statistical Structures of Constant Holomorphic Sectional Curvature on Complex Space Forms","authors":"Mingming Yan, Xinlei Wu, Liang Zhang","doi":"10.1007/s41980-023-00855-8","DOIUrl":"https://doi.org/10.1007/s41980-023-00855-8","url":null,"abstract":"<p>In this paper, we prove the non-existence of non-trivial statistical structures of constant holomorphic sectional curvature based on complex space forms with dimension greater than 2. For 2-dimensional complex space forms we show an example to illustrate there do exist non-trivial statistical structures of constant holomorphic sectional curvature, and we also obtain a rigidity theorem in this case. Finally, in contrast to complex space forms, we construct some new examples of non-trivial statistical structures of constant sectional curvature based on real space forms.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139978503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Dunkl–Williams Constant Related to Birkhoff Orthogonality in Banach Spaces 与巴拿赫空间中的伯克霍夫正交性有关的邓克尔-威廉斯常数
IF 0.7 4区 数学
Bulletin of The Iranian Mathematical Society Pub Date : 2024-02-26 DOI: 10.1007/s41980-023-00853-w
Yuankang Fu, Huayou Xie, Yongjin Li
{"title":"The Dunkl–Williams Constant Related to Birkhoff Orthogonality in Banach Spaces","authors":"Yuankang Fu, Huayou Xie, Yongjin Li","doi":"10.1007/s41980-023-00853-w","DOIUrl":"https://doi.org/10.1007/s41980-023-00853-w","url":null,"abstract":"<p>In this paper, we shall consider a new constant <span>(DW_B(X))</span> which is the Dunkl–Williams constant related to Birkhoff orthogonality, and a constant <span>(DW^p_B(X))</span> that is a generalization of <span>(DW_B(X))</span>. Interestingly, the upper bounds of <span>(DW_B(X))</span> and the Dunkl–Williams constant are different. The connections between these two constants and other well-known constants are exhibited. Some characterizations of Hilbert space and uniformly non-square Banach space in terms of these two constants are established. Furthermore, we also give a characterization of the Radon plane with an affine regular hexagonal unit sphere and calculate the value of <span>(DW^p_B(l_infty -l_1))</span>.</p>","PeriodicalId":9395,"journal":{"name":"Bulletin of The Iranian Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139978839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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