Transactions of the American Mathematical Society最新文献

{"title":"Semi-integral Brauer–Manin obstruction and quadric orbifold pairs","authors":"Vladimir Mitankin, Masahiro Nakahara, Sam Streeter","doi":"10.1090/tran/9170","DOIUrl":"https://doi.org/10.1090/tran/9170","url":null,"abstract":"<p>We study local-global principles for two notions of semi-integral points, termed Campana points and Darmon points. In particular, we develop a semi-integral version of the Brauer–Manin obstruction interpolating between Manin’s classical version for rational points and the integral version developed by Colliot-Thélène and Xu. We determine the status of local-global principles, and obstructions to them, in two families of orbifolds naturally associated to quadric hypersurfaces. Further, we establish a quantitative result measuring the failure of the semi-integral Brauer–Manin obstruction to account for its integral counterpart for affine quadrics.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"36 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140931971","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cuntz algebra automorphisms: Graphs and stability of permutations","authors":"Francesco Brenti, Roberto Conti, Gleb Nenashev","doi":"10.1090/tran/9159","DOIUrl":"https://doi.org/10.1090/tran/9159","url":null,"abstract":"<p>We characterize the permutative automorphisms of the Cuntz algebra <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper O Subscript n\"> <mml:semantics> <mml:msub> <mml:mrow> <mml:mi mathvariant=\"script\">O</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msub> <mml:annotation encoding=\"application/x-tex\">mathcal {O}_n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> (namely, stable permutations) in terms of two sequences of graphs that we associate to any permutation of a discrete hypercube <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-bracket n right-bracket Superscript t\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">[</mml:mo> <mml:mi>n</mml:mi> <mml:msup> <mml:mo stretchy=\"false\">]</mml:mo> <mml:mi>t</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">[n]^t</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. As applications we show that in the limit of large <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"t\"> <mml:semantics> <mml:mi>t</mml:mi> <mml:annotation encoding=\"application/x-tex\">t</mml:annotation> </mml:semantics> </mml:math> </inline-formula> (resp. <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"n\"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding=\"application/x-tex\">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>) almost all permutations are not stable, thus proving Conj. 12.5 of Brenti and Conti [Adv. Math. 381 (2021), p. 60], characterize (and enumerate) stable quadratic <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"4\"> <mml:semantics> <mml:mn>4</mml:mn> <mml:annotation encoding=\"application/x-tex\">4</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"5\"> <mml:semantics> <mml:mn>5</mml:mn> <mml:annotation encoding=\"application/x-tex\">5</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-cycles, as well as a notable class of stable quadratic <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"r\"> <mml:semantics> <mml:mi>r</mml:mi> <mml:annotation encoding=\"application/x-tex\">r</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-cycles, i.e. those admitting a compatible cyclic factorization by stable transpositions. Some of our results use new combinatorial concepts that may be of independent interest.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"215 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effective approximation to complex algebraic numbers by algebraic numbers of bounded degree","authors":"Prajeet Bajpai, Yann Bugeaud","doi":"10.1090/tran/9190","DOIUrl":"https://doi.org/10.1090/tran/9190","url":null,"abstract":"<p>We establish the first effective improvements on the Liouville inequality for approximation to complex non-real algebraic numbers by complex algebraic numbers of degree at most <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"4\"> <mml:semantics> <mml:mn>4</mml:mn> <mml:annotation encoding=\"application/x-tex\">4</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"2015 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Surface counterexamples to the Eisenbud-Goto conjecture","authors":"Jong In Han, Sijong Kwak","doi":"10.1090/tran/9192","DOIUrl":"https://doi.org/10.1090/tran/9192","url":null,"abstract":"<p>It is well known that the Eisenbud-Goto regularity conjecture is true for arithmetically Cohen-Macaulay varieties, projective curves, smooth surfaces, smooth threefolds in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper P Superscript 5\"> <mml:semantics> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">P</mml:mi> </mml:mrow> <mml:mn>5</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">mathbb {P}^5</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and toric varieties of codimension two. After J. McCullough and I. Peeva constructed counterexamples in 2018, it has been an interesting question to find the categories such that the Eisenbud-Goto conjecture holds. So far, surface counterexamples have not been found while counterexamples of any dimension greater or equal to 3 are known.</p> <p>In this paper, we construct counterexamples to the Eisenbud-Goto conjecture for projective surfaces in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper P Superscript 4\"> <mml:semantics> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">P</mml:mi> </mml:mrow> <mml:mn>4</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">mathbb {P}^4</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and investigate projective invariants, cohomological properties, and geometric properties. The counterexamples are constructed via binomial rational maps between projective spaces.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"21 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Witt rings of many flag varieties are exterior algebras","authors":"Tobias Hemmert, Marcus Zibrowius","doi":"10.1090/tran/9188","DOIUrl":"https://doi.org/10.1090/tran/9188","url":null,"abstract":"<p>The Witt ring of a complex flag variety describes the interesting – i.e. torsion – part of its topological KO-theory. We show that for a large class of flag varieties, these Witt rings are exterior algebras, and that the degrees of the generators can be determined by Dynkin diagram combinatorics. Besides a few well-studied examples such as full flag varieties and projective spaces, this class includes many flag varieties whose Witt rings were previously unknown, including many flag varieties of exceptional types. In particular, it includes all flag varieties of types <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G 2\"> <mml:semantics> <mml:msub> <mml:mi>G</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:annotation encoding=\"application/x-tex\">G_2</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper F 4\"> <mml:semantics> <mml:msub> <mml:mi>F</mml:mi> <mml:mn>4</mml:mn> </mml:msub> <mml:annotation encoding=\"application/x-tex\">F_4</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. The results also extend to flag varieties over other algebraically closed fields.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"61 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141519506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Locally trivial monodromy of moduli spaces of sheaves on K3 surfaces","authors":"Claudio Onorati, Arvid Perego, Antonio Rapagnetta","doi":"10.1090/tran/9185","DOIUrl":"https://doi.org/10.1090/tran/9185","url":null,"abstract":"&lt;p&gt;In this paper we study monodromy operators on moduli spaces &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M Subscript v Baseline left-parenthesis upper S comma upper H right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;M&lt;/mml:mi&gt; &lt;mml:mi&gt;v&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;S&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mi&gt;H&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;M_v(S,H)&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; of sheaves on K3 surfaces with non-primitive Mukai vectors &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"v\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;v&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;v&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;. If we write &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"v equals m w\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;v&lt;/mml:mi&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:mi&gt;m&lt;/mml:mi&gt; &lt;mml:mi&gt;w&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;v=mw&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;, with &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"m greater-than 1\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;m&lt;/mml:mi&gt; &lt;mml:mo&gt;&gt;&lt;/mml:mo&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;m&gt;1&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; and &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"w\"&gt; &lt;mml:semantics&gt; &lt;mml:mi&gt;w&lt;/mml:mi&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;w&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; primitive, then our main result is that the inclusion &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M Subscript w Baseline left-parenthesis upper S comma upper H right-parenthesis right-arrow upper M Subscript v Baseline left-parenthesis upper S comma upper H right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;M&lt;/mml:mi&gt; &lt;mml:mi&gt;w&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;S&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mi&gt;H&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;mml:mo stretchy=\"false\"&gt;→&lt;/mml:mo&gt; &lt;mml:msub&gt; &lt;mml:mi&gt;M&lt;/mml:mi&gt; &lt;mml:mi&gt;v&lt;/mml:mi&gt; &lt;/mml:msub&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;S&lt;/mml:mi&gt; &lt;mml:mo&gt;,&lt;/mml:mo&gt; &lt;mml:mi&gt;H&lt;/mml:mi&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;M_w(S,H)to M_v(S,H)&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; as the most singular locus induces an isomorphism between the monodromy groups of these symplectic varieties, allowing us to extend to the non-primitive case ","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"65 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141746168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the failure of Ornstein theory in the finitary category","authors":"Uri Gabor","doi":"10.1090/tran/8776","DOIUrl":"https://doi.org/10.1090/tran/8776","url":null,"abstract":"<p>We show the invalidity of finitary counterparts for three classification theorems: The preservation of being a Bernoulli shift through factors, Sinai’s factor theorem, and the weak Pinsker property. We construct a finitary factor of an i.i.d. process which is not finitarily isomorphic to an i.i.d. process, showing that being finitarily Bernoulli is not preserved through finitary factors. This refutes a conjecture of M. Smorodinsky [<italic>Finitary isomorphism of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"m\"> <mml:semantics> <mml:mi>m</mml:mi> <mml:annotation encoding=\"application/x-tex\">m</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-dependent processes</italic>, Amer. Math. Soc., Birkhauser, Providence, RI, 1992, pp. 373–376], which was first suggested by D. Rudolph [<italic>A characterization of those processes finitarily isomorphic to a Bernoulli shift</italic>, Birkhäuser, Boston, Mass., 1981, pp. 1–64]. We further show that any ergodic system is isomorphic to a process none of whose finitary factors are i.i.d. processes, and in particular, there is no general finitary Sinai’s factor theorem for ergodic processes. Another consequence of this result is the invalidity of a finitary weak Pinsker property, answering a question of G. Pete and T. Austin [Math. Inst. Hautes Études Sci. 128 (2018), 1–119].</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"131 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140932111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Equivariant 3-manifolds with positive scalar curvature","authors":"Tsz-Kiu Aaron Chow, Yangyang Li","doi":"10.1090/tran/9181","DOIUrl":"https://doi.org/10.1090/tran/9181","url":null,"abstract":"<p>In this paper, for any compact Lie group <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we show that the space of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-equivariant Riemannian metrics with positive scalar curvature (PSC) on any closed three-manifold is either empty or contractible. In particular, we prove the generalized Smale conjecture for spherical three-orbifolds. Moreover, for connected <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we make a classification of all PSC <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-equivariant three-manifolds.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"20 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141532723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Identification of Genetic Variants in Exon 4 of TP53 in Lung Carcinoma and in Silico Prediction of Their Significance.","authors":"Rajendra Prasad, Kirti Sharma, Karanpreet Bhutani, Suvarna Prasad, Sunita Manhas, Jai Kishan","doi":"10.1007/s12291-022-01099-9","DOIUrl":"10.1007/s12291-022-01099-9","url":null,"abstract":"<p><p>Lung cancer is a severe and the leading cause of cancer related deaths in men and women all over the world. Tumor suppressor protein (TP53) encoded by the TP53 gene which plays a pivotal role in various cellular tumor suppression processes viz cell cycle arrest and apoptosis. Henceforth, the present study was aimed to TP53 exon4 variants from lung carcinoma. Histopathologic and clinically proven 20 patients of lung cancer were enrolled in this study the average age of patients was 45 ± 8 years which categorized as early onset of lung cancer. Genomic DNA was isolated from the blood specimen of patients. Extracted DNA was subjected to PCR amplification for exon 4 of TP53 using appropriate primers and subsequently amplified products were applied to nucleotide alterations via using the DNA sanger sequencing. The genetic analysis documented five variants in exon4 of TP53 which include viz. 4 substitutions [c.215 > C at codon 72, C. 358-359AA > GG at codon 120] were highly prevalent, occurring in 63% and 25% frequency in patients. Other two variants viz. C. 358 A > C at codon 120, C. 365T > G at codon 122 were present at frequency of 15% whilst one deletion variant [152 del C] was found with 5% frequency. Furthermore, alterations on codon 72, 120,122 and 51 were characterized as possibly damaging by Poly Phen-2 and decreased stability using stability bioinformatic tool. Taken together all these findings infer that TP53 gene involved in modulation and susceptibility to lung cancer.</p>","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"91 1","pages":"276-282"},"PeriodicalIF":1.2,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10987423/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82685530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sharp weighted log-Sobolev inequalities: Characterization of equality cases and applications","authors":"Zoltán Balogh, Sebastiano Don, Alexandru Kristály","doi":"10.1090/tran/9163","DOIUrl":"https://doi.org/10.1090/tran/9163","url":null,"abstract":"&lt;p&gt;By using optimal mass transport theory, we provide a direct proof to the sharp &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript p\"&gt; &lt;mml:semantics&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;L&lt;/mml:mi&gt; &lt;mml:mi&gt;p&lt;/mml:mi&gt; &lt;/mml:msup&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;L^p&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-log-Sobolev inequality &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis p greater-than-or-equal-to 1 right-parenthesis\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mo stretchy=\"false\"&gt;(&lt;/mml:mo&gt; &lt;mml:mi&gt;p&lt;/mml:mi&gt; &lt;mml:mo&gt;≥&lt;/mml:mo&gt; &lt;mml:mn&gt;1&lt;/mml:mn&gt; &lt;mml:mo stretchy=\"false\"&gt;)&lt;/mml:mo&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;(pgeq 1)&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; involving a log-concave homogeneous weight on an open convex cone &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E subset-of-or-equal-to double-struck upper R Superscript n\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;E&lt;/mml:mi&gt; &lt;mml:mo&gt;⊆&lt;/mml:mo&gt; &lt;mml:msup&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;R&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:msup&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;Esubseteq mathbb R^n&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;. The perk of this proof is that it allows to characterize the extremal functions realizing the equality cases in the &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript p\"&gt; &lt;mml:semantics&gt; &lt;mml:msup&gt; &lt;mml:mi&gt;L&lt;/mml:mi&gt; &lt;mml:mi&gt;p&lt;/mml:mi&gt; &lt;/mml:msup&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;L^p&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;-log-Sobolev inequality. The characterization of the equality cases is new for &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p greater-than-or-equal-to n\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;p&lt;/mml:mi&gt; &lt;mml:mo&gt;≥&lt;/mml:mo&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;pgeq n&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt; even in the unweighted setting and &lt;inline-formula content-type=\"math/mathml\"&gt; &lt;mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper E equals double-struck upper R Superscript n\"&gt; &lt;mml:semantics&gt; &lt;mml:mrow&gt; &lt;mml:mi&gt;E&lt;/mml:mi&gt; &lt;mml:mo&gt;=&lt;/mml:mo&gt; &lt;mml:msup&gt; &lt;mml:mrow&gt; &lt;mml:mi mathvariant=\"double-struck\"&gt;R&lt;/mml:mi&gt; &lt;/mml:mrow&gt; &lt;mml:mi&gt;n&lt;/mml:mi&gt; &lt;/mml:msup&gt; &lt;/mml:mrow&gt; &lt;mml:annotation encoding=\"application/x-tex\"&gt;E=mathbb R^n&lt;/mml:annotation&gt; &lt;/mml:semantics&gt; &lt;/mml:math&gt; &lt;/inline-formula&gt;. As an application, we provide a sharp weighted hypercontractivity estimate for the Hopf-Lax semigroup related to the Hamilton-Jacobi equation, characterizing also t","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"19 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141152915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}