Transactions of the American Mathematical Society最新文献_第8页

3-2-1 foliations for Reeb flows on the tight 3-sphere 紧密三球面上里布流的 3-2-1 叶形

IF 1.3 2区数学

Transactions of the American Mathematical Society Pub Date : 2024-01-17 DOI: 10.1090/tran/9119

Carolina de Oliveira

引用次数: 0

The ratios conjecture for real Dirichlet characters and multiple Dirichlet series 实狄利克特字符和多重狄利克特数列的比率猜想

IF 1.3 2区数学

Transactions of the American Mathematical Society Pub Date : 2024-01-03 DOI: 10.1090/tran/9113

Martin Čech

{"title":"The ratios conjecture for real Dirichlet characters and multiple Dirichlet series","authors":"Martin Čech","doi":"10.1090/tran/9113","DOIUrl":"https://doi.org/10.1090/tran/9113","url":null,"abstract":"Conrey, Farmer and Zirnbauer introduced a recipe to find asymptotic formulas for the sum of ratios of products of shifted L-functions. These ratios conjectures are very powerful and can be used to determine many statistics of L-functions, including moments or statistics about the distribution of zeros. We consider the family of real Dirichlet characters, and use multiple Dirichlet series to prove the ratios conjectures with one shift in the numerator and denominator in some range of the shifts. This range can be improved by extending the family to include non-primitive characters. All of the results are conditional under the Generalized Riemann hypothesis. This extended range is good enough to enable us to compute an asymptotic formula for the sum of shifted logarithmic derivatives near the critical line. As an application, we compute the one-level density for test functions whose Fourier transform is supported in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis negative 2 comma 2 right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo>(</mml:mo> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">left (-2,2right )</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, including lower-order terms.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"24 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934796","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}

引用次数: 0

BPS invariants of symplectic log Calabi-Yau fourfolds 对称对数 Calabi-Yau 四围的 BPS 不变量

IF 1.3 2区数学

Transactions of the American Mathematical Society Pub Date : 2024-01-03 DOI: 10.1090/tran/9114

Mohammad Farajzadeh-Tehrani

引用次数: 0

On the constant of Lipschitz approximability 关于 Lipschitz 近似性常数

IF 1.3 2区数学

Transactions of the American Mathematical Society Pub Date : 2024-01-03 DOI: 10.1090/tran/9110

Rubén Medina

{"title":"On the constant of Lipschitz approximability","authors":"Rubén Medina","doi":"10.1090/tran/9110","DOIUrl":"https://doi.org/10.1090/tran/9110","url":null,"abstract":"In this note we find <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"lamda greater-than 1\"> <mml:semantics> <mml:mrow> <mml:mi>λ</mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">lambda >1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and give an explicit construction of a separable Banach space <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> such that there is no <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"lamda\"> <mml:semantics> <mml:mi>λ</mml:mi> <mml:annotation encoding=\"application/x-tex\">lambda</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Lipschitz retraction from <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> onto any compact convex subset of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula> whose closed linear span is <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. This is closely related to a well-known open problem raised by Godefroy and Ozawa in 2014 and represents the first known example of a Banach space with such a property.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"26 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934867","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}

引用次数: 0

Higher rank (𝑞,𝑡)-Catalan polynomials, affine Springer fibers, and a finite rational shuffle theorem 高阶(△,𝑡)-卡塔兰多项式、仿射 Springer 纤维和有限有理洗牌定理

IF 1.3 2区数学

Transactions of the American Mathematical Society Pub Date : 2024-01-03 DOI: 10.1090/tran/9115

Nicolle González, José Simental, Monica Vazirani

{"title":"Higher rank (𝑞,𝑡)-Catalan polynomials, affine Springer fibers, and a finite rational shuffle theorem","authors":"Nicolle González, José Simental, Monica Vazirani","doi":"10.1090/tran/9115","DOIUrl":"https://doi.org/10.1090/tran/9115","url":null,"abstract":"We introduce the higher rank <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis q comma t right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>q</mml:mi> <mml:mo>,</mml:mo> <mml:mi>t</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">(q,t)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Catalan polynomials and prove they equal truncations of the Hikita polynomial to a finite number of variables. Using affine compositions and a certain standardization map, we define a <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"monospace d monospace i monospace n monospace v\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"monospace\">d</mml:mi> <mml:mi mathvariant=\"monospace\">i</mml:mi> <mml:mi mathvariant=\"monospace\">n</mml:mi> <mml:mi mathvariant=\"monospace\">v</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathtt {dinv}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> statistic on rank <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> semistandard <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis m comma n right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>m</mml:mi> <mml:mo>,</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">(m,n)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-parking functions and prove <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"monospace c monospace o monospace d monospace i monospace n monospace v\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"monospace\">c</mml:mi> <mml:mi mathvariant=\"monospace\">o</mml:mi> <mml:mi mathvariant=\"monospace\">d</mml:mi> <mml:mi mathvariant=\"monospace\">i</mml:mi> <mml:mi mathvariant=\"monospace\">n</mml:mi> <mml:mi mathvariant=\"monospace\">v</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathtt {codinv}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> counts the dimension of an affine space in an affine paving of a parabolic affine Springer fiber. Combining these results, we give a finite analogue of the Rational Shuffle Theorem in the context of double affine Hecke algebras. Lastly, we also give a Bizley-type formula for the higher rank Catalan numbers in the non-coprime case.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"7 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141060602","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}

引用次数: 0

Weierstrass bridges 魏尔斯特拉斯桥梁

IF 1.3 2区数学

Transactions of the American Mathematical Society Pub Date : 2024-01-03 DOI: 10.1090/tran/9116

Alexander Schied, Zhenyuan Zhang

{"title":"Weierstrass bridges","authors":"Alexander Schied, Zhenyuan Zhang","doi":"10.1090/tran/9116","DOIUrl":"https://doi.org/10.1090/tran/9116","url":null,"abstract":"We introduce a new class of stochastic processes called fractional Wiener–Weierstraß bridges. They arise by applying the convolution from the construction of the classical, fractal Weierstraß functions to an underlying fractional Brownian bridge. By analyzing the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"p\"> <mml:semantics> <mml:mi>p</mml:mi> <mml:annotation encoding=\"application/x-tex\">p</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-th variation of the fractional Wiener–Weierstraß bridge along the sequence of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"b\"> <mml:semantics> <mml:mi>b</mml:mi> <mml:annotation encoding=\"application/x-tex\">b</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-adic partitions, we identify two regimes in which the processes exhibit distinct sample path properties. We also analyze the critical case between those two regimes for Wiener–Weierstraß bridges that are based on a standard Brownian bridge. We furthermore prove that fractional Wiener–Weierstraß bridges are never semimartingales, and we show that their covariance functions are typically fractal functions. Some of our results are extended to Weierstraß bridges based on bridges derived from a general continuous Gaussian martingale.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"207 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140935215","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}

引用次数: 0

Effects of NGF and Photobiomodulation Therapy on Crush Nerve Injury and Fracture Healing: A Stereological and Histopathological Study in an Animal Model. 神经生长因子和光生物调节治疗对挤压神经损伤和骨折愈合的影响:动物模型的体视学和组织病理学研究。

IF 1.2 2区数学

Transactions of the American Mathematical Society Pub Date : 2023-12-01 Epub Date: 2022-11-15 DOI: 10.1177/19433875221138175

Esengül Şen, Nilüfer Özkan, Mehmet Emin Önger, Süleyman Kaplan

{"title":"Effects of NGF and Photobiomodulation Therapy on Crush Nerve Injury and Fracture Healing: A Stereological and Histopathological Study in an Animal Model.","authors":"Esengül Şen, Nilüfer Özkan, Mehmet Emin Önger, Süleyman Kaplan","doi":"10.1177/19433875221138175","DOIUrl":"10.1177/19433875221138175","url":null,"abstract":"Study design: A stereological and histopathological study in an animal model.Objective: This study explores the effects of the nerve growth factor and photobiomodulation therapy on the damaged nerve tissue and fracture healing.Methods: A total of 24 rabbits were divided into 4 groups: control group (n = 5), nerve growth factor (NGF) group (n = 7), photobiomodulation (PBMT) group (n = 6), and nerve growth factor and photobiomodulation therapy (NGF+PBMT) group (n = 6). The vertical fracture was performed between the mental foramen and the first premolar, and the mental nerve was crushed for 30 seconds with a standard serrated clamp with a force of approximately 50 N in all groups. The control group received an isotonic solution (.02 mL, .09% NaCl) to the operation site locally. The NGF group received 1 μg human NGF-β/.9% .2 mL NaCl solution for 7 days locally. The PBMT group received PBMT treatment (GaAlAs laser, 810 nm, .3 W, 18 J/cm2) every 48 hours for 14 sessions following the surgery. The NGF+PBMT group received both NGF and PBMT treatment as described above. After 28 days, the bone tissues and mental nerves from all groups were harvested and histologically and stereologically analyzed.Results: According to the stereological results, the volume of the new vessel and the volume of the new bone were significantly higher in the PBMT group than in other groups (P < .001). According to the histopathological examinations, higher myelinated axons were observed in experimental groups than in the control group.Conclusions: As a result, PBMT has beneficial effects on bone regeneration. Based on the light microscopic evaluation, more regenerated axon populations were observed in the NGF group than in the PBMT and PBMT + NGF groups in terms of myelinated axon content.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":"184 1","pages":"281-291"},"PeriodicalIF":1.2,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10693267/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82690653","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}

引用次数: 0

On the rôle of singular functions in extending the probabilistic symbol to its most general class 论奇异函数的rôle将概率符号扩展到它的最一般类

2区数学

Transactions of the American Mathematical Society Pub Date : 2023-11-09 DOI: 10.1090/tran/9064

Sebastian Rickelhoff, Alexander Schnurr

{"title":"On the rôle of singular functions in extending the probabilistic symbol to its most general class","authors":"Sebastian Rickelhoff, Alexander Schnurr","doi":"10.1090/tran/9064","DOIUrl":"https://doi.org/10.1090/tran/9064","url":null,"abstract":"The probabilistic symbol is the right-hand side derivative of the characteristic functions corresponding to the one-dimensional marginals of a stochastic process. This object, as long as the derivative exists, provides crucial information concerning the stochastic process. For a Lévy process, one obtains the characteristic exponent while the symbol of a (rich) Feller process coincides with the classical symbol which is well known from the theory of pseudodifferential operators. Leaving these classes behind, the most general class of processes for which the symbol still exists are Lévy-type processes. It has been an open question, whether further generalizations are possible within the framework of Markov processes. We answer this question in the present article: within the class of Hunt semimartingales, Lévy-type processes are exactly those for which the probabilistic symbol exists. Leaving Hunt behind, one can construct processes admitting a symbol. However, we show, that the applicability of the symbol might be lost for these processes. Surprisingly, in our proofs the upper and lower Dini derivatives corresponding to certain singular functions play an important rôle.","PeriodicalId":23209,"journal":{"name":"Transactions of the American Mathematical Society","volume":" 92","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135191250","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}

引用次数: 0

A solution operator for the overline{∂} equation in Sobolev spaces of negative index 负指标Sobolev空间中overline{∂}方程的解算子

2区数学

Transactions of the American Mathematical Society Pub Date : 2023-11-09 DOI: 10.1090/tran/9066

Ziming Shi, Liding Yao

引用次数: 0

Moduli spaces of Lie algebras and foliations 李代数与叶形的模空间

2区数学

Transactions of the American Mathematical Society Pub Date : 2023-11-09 DOI: 10.1090/tran/9072

Sebastián Velazquez

引用次数: 0