Research in the Mathematical Sciences最新文献_第2页

Duality for Poincaré series of surfaces and delta invariant of curves 曲面的波恩卡列数列和曲线的德尔塔不变量的对偶性

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-06-26 DOI: 10.1007/s40687-024-00457-8

José Ignacio Cogolludo-Agustín, Tamás László, Jorge Martín-Morales, András Némethi

引用次数: 0

Homotopy prefactorization algebras 同调预因子代数

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-06-24 DOI: 10.1007/s40687-024-00456-9

Najib Idrissi, Eugene Rabinovich

引用次数: 0

Geometry of the parabolic subset of generically immersed 3-manifolds in $$mathbb {R}^4$$ $$mathbb{R}^4$$中泛浸3-manifolds的抛物线子集几何学

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-05-18 DOI: 10.1007/s40687-024-00450-1

A. C. Nabarro, M. C. Romero Fuster, M. C. Zanardo

引用次数: 0

Quantum q-series and mock theta functions 量子 Q 序列和模拟 Theta 函数

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-05-11 DOI: 10.1007/s40687-024-00447-w

Amanda Folsom, David Metacarpa

{"title":"Quantum q-series and mock theta functions","authors":"Amanda Folsom, David Metacarpa","doi":"10.1007/s40687-024-00447-w","DOIUrl":"https://doi.org/10.1007/s40687-024-00447-w","url":null,"abstract":"Our results investigate mock theta functions and quantum modular forms via quantum q-series identities. After Lovejoy, quantum q-series identities are such that they do not hold as an equality between power series inside the unit disc in the classical sense, but do hold at dense sets of roots of unity on the boundary. We establish several general (multivariable) quantum q-series identities and apply them to various settings involving (universal) mock theta functions. As a consequence, we surprisingly show that limiting, finite, universal mock theta functions at roots of unity for which their infinite counterparts do not converge are quantum modular. Moreover, we show that these finite limiting universal mock theta functions play key roles in (generalized) Ramanujan radial limits. A further corollary of our work reveals that the finite Kontsevich–Zagier series is a kind of “universal quantum mock theta function,” in that it may be used to evaluate odd-order Ramanujan mock theta functions at roots of unity. (We also offer a similar result for even-order mock theta functions.) Finally, to complement the notion of a quantum q-series identity and the results of this paper, we also define what we call an “antiquantum q-series identity’ and offer motivating general results with applications to third-order mock theta functions.","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"18 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140941901","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}

引用次数: 0

Some remarks about $$ rho $$ -regularity for real analytic maps 关于实解析映射的 $$ rho $$ 规则性的几点评论

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-05-05 DOI: 10.1007/s40687-024-00453-y

Maico Ribeiro, Ivan Santamaria, Thiago da Silva

引用次数: 0

Matroid products in tropical geometry 热带几何中的 Matroid 乘积

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-05-02 DOI: 10.1007/s40687-024-00452-z

Nicholas Anderson

引用次数: 0

Higher derivatives of functions with given critical points and values 给定临界点和临界值的函数高导数

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-05-02 DOI: 10.1007/s40687-024-00448-9

G. Goldman, Y. Yomdin

{"title":"Higher derivatives of functions with given critical points and values","authors":"G. Goldman, Y. Yomdin","doi":"10.1007/s40687-024-00448-9","DOIUrl":"https://doi.org/10.1007/s40687-024-00448-9","url":null,"abstract":"Let (f: B^n rightarrow {{mathbb {R}}}) be a (d+1) times continuously differentiable function on the unit ball (B^n), with (mathrm{max,}_{zin B^n} Vert f(z) Vert =1). A well-known fact is that if f vanishes on a set (Zsubset B^n) with a non-empty interior, then for each (k=1,ldots ,d+1) the norm of the k-th derivative (||f^{(k)}||) is at least (M=M(n,k)>0). A natural question to ask is “what happens for other sets Z?”. This question was partially answered in Goldman and Yomdin (Lower bounds for high derivatives of smooth functions with given zeros. arXiv:2402.01388), Yomdin (Anal Math Phys 11:89, 2021), Yomdin (J Singul 25:443–455, 2022) and Yomdin (Higher derivatives of functions vanishing on a given set. arXiv:2108.02459v1). In the present paper, we ask a similar (and closely related) question: what happens with the high-order derivatives of f, if its gradient vanishes on a given set (Sigma )? And what conclusions for the high-order derivatives of f can be obtained from the analysis of the metric geometry of the “critical values set” (f(Sigma ))? In the present paper, we provide some initial answers to these questions.","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"27 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140937301","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}

引用次数: 0

Closed orientable surfaces and fold Gauss maps 封闭可定向曲面和折叠高斯图

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-04-26 DOI: 10.1007/s40687-024-00451-0

C. Mendes de Jesus, Pantaleón D. Romero, E. Sanabria-Codesal

引用次数: 0

Saddle point braids of braided fibrations and pseudo-fibrations 辫状纤维和伪纤维的鞍点辫状结构

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-04-17 DOI: 10.1007/s40687-024-00446-x

Benjamin Bode, Mikami Hirasawa

{"title":"Saddle point braids of braided fibrations and pseudo-fibrations","authors":"Benjamin Bode, Mikami Hirasawa","doi":"10.1007/s40687-024-00446-x","DOIUrl":"https://doi.org/10.1007/s40687-024-00446-x","url":null,"abstract":"Let (g_t) be a loop in the space of monic complex polynomials in one variable of fixed degree n. If the roots of (g_t) are distinct for all t, they form a braid (B_1) on n strands. Likewise, if the critical points of (g_t) are distinct for all t, they form a braid (B_2) on (n-1) strands. In this paper we study the relationship between (B_1) and (B_2). Composing the polynomials (g_t) with the argument map defines a pseudo-fibration map on the complement of the closure of (B_1) in ({mathbb {C}}times S^1), whose critical points lie on (B_2). We prove that for (B_1) a T-homogeneous braid and (B_2) the trivial braid this map can be taken to be a fibration map. In the case of homogeneous braids we present a visualization of this fact. Our work implies that for every pair of links (L_1) and (L_2) there is a mixed polynomial (f:{mathbb {C}}^2rightarrow {mathbb {C}}) in complex variables u, v and the complex conjugate (overline{v}) such that both f and the derivative (f_u) have a weakly isolated singularity at the origin with (L_1) as the link of the singularity of f and (L_2) as a sublink of the link of the singularity of (f_u).","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"9 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140610487","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}

引用次数: 0

The crossing numbers of amphicheiral knots 双螺旋结的交叉数

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-04-17 DOI: 10.1007/s40687-024-00440-3

A. Stoimenow

引用次数: 0