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A Top-Down Approach to Algebraic Renormalization in Regularity Structures Based on Multi-indices 基于多指数的正则结构中代数重正化的自顶向下方法
IF 2.6 1区 数学
Archive for Rational Mechanics and Analysis Pub Date : 2024-11-10 DOI: 10.1007/s00205-024-02041-4
Yvain Bruned, Pablo Linares
{"title":"A Top-Down Approach to Algebraic Renormalization in Regularity Structures Based on Multi-indices","authors":"Yvain Bruned,&nbsp;Pablo Linares","doi":"10.1007/s00205-024-02041-4","DOIUrl":"10.1007/s00205-024-02041-4","url":null,"abstract":"<div><p>We provide an algebraic framework to describe renormalization in regularity structures based on multi-indices for a large class of semi-linear stochastic PDEs. This framework is “top-down”, in the sense that we postulate the form of the counterterm and use the renormalized equation to build a canonical smooth model for it. The core of the construction is a generalization of the Hopf algebra of derivations in Linares et al. (Commun Am Math Soc 3:1–64, 2023, https://doi.org/10.1090/cams/16), which is extended beyond the structure group to describe the model equation via an exponential map; this allow us to implement a renormalization procedure which resembles the preparation map approach in our context.</p></div>","PeriodicalId":55484,"journal":{"name":"Archive for Rational Mechanics and Analysis","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142598940","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Further investigation on differential properties of the generalized Ness–Helleseth function 广义奈斯-赫勒塞斯函数微分性质的进一步研究
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2024-11-10 DOI: 10.1007/s10623-024-01525-4
Yongbo Xia, Chunlei Li, Furong Bao, Shaoping Chen, Tor Helleseth
{"title":"Further investigation on differential properties of the generalized Ness–Helleseth function","authors":"Yongbo Xia, Chunlei Li, Furong Bao, Shaoping Chen, Tor Helleseth","doi":"10.1007/s10623-024-01525-4","DOIUrl":"https://doi.org/10.1007/s10623-024-01525-4","url":null,"abstract":"<p>Let <i>n</i> be an odd positive integer, <i>p</i> be an odd prime with <span>(pequiv 3pmod 4)</span>, <span>(d_{1} = {{p^{n}-1}over {2}} -1 )</span> and <span>(d_{2} =p^{n}-2)</span>. The function defined by <span>(f_u(x)=ux^{d_{1}}+x^{d_{2}})</span> is called the generalized Ness–Helleseth function over <span>(mathbb {F}_{p^n})</span>, where <span>(uin mathbb {F}_{p^n})</span>. It was initially studied by Ness and Helleseth in the ternary case. In this paper, for <span>(p^n equiv 3 pmod 4)</span> and <span>(p^n ge 7)</span>, we provide the necessary and sufficient condition for <span>(f_u(x))</span> to be an APN function. In addition, for each <i>u</i> satisfying <span>(chi (u+1) = chi (u-1))</span>, the differential spectrum of <span>(f_u(x))</span> is investigated, and it is expressed in terms of some quadratic character sums of cubic polynomials, where <span>(chi (cdot ))</span> denotes the quadratic character of <span>({mathbb {F}}_{p^n})</span>.\u0000</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142597482","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
Pullback Measure Attractors for Non-autonomous Fractional Stochastic Reaction-Diffusion Equations on Unbounded Domains 无界域上非自治分式随机反应-扩散方程的回拉测度吸引子
IF 1.6 2区 数学
Applied Mathematics and Optimization Pub Date : 2024-11-10 DOI: 10.1007/s00245-024-10196-5
Shaoyue Mi, Ran Li, Dingshi Li
{"title":"Pullback Measure Attractors for Non-autonomous Fractional Stochastic Reaction-Diffusion Equations on Unbounded Domains","authors":"Shaoyue Mi,&nbsp;Ran Li,&nbsp;Dingshi Li","doi":"10.1007/s00245-024-10196-5","DOIUrl":"10.1007/s00245-024-10196-5","url":null,"abstract":"<div><p>This paper is concerned with the pullback measure attractors of the non-autonomous fractional reaction-diffusion equations defined on <span>(mathbb {R}^{n})</span>. We first prove the existence and uniqueness of pullback measure attractors for such equations. Then we establish the upper semi-continuity of these attractors as the noise intensity <span>(varepsilon )</span> tends to zero. Specifically, we apply the uniform estimates on the tails of solutions to prove the asymptotic compactness of a family of probability distributions of solutions to overcome the non-compactness of usual Sobolev embeddings on unbounded domains.</p></div>","PeriodicalId":55566,"journal":{"name":"Applied Mathematics and Optimization","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142598978","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
Issue Information ‐ TOC 发行信息 - TOC
IF 3 1区 数学
Communications on Pure and Applied Mathematics Pub Date : 2024-11-09 DOI: 10.1002/cpa.22208
{"title":"Issue Information ‐ TOC","authors":"","doi":"10.1002/cpa.22208","DOIUrl":"https://doi.org/10.1002/cpa.22208","url":null,"abstract":"","PeriodicalId":10601,"journal":{"name":"Communications on Pure and Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":3.0,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142598162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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
Improved key recovery attacks on reduced-round Salsa20 改进对减圆 Salsa20 的密钥恢复攻击
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2024-11-09 DOI: 10.1007/s10623-024-01522-7
Sabyasachi Dey, Gregor Leander, Nitin Kumar Sharma
{"title":"Improved key recovery attacks on reduced-round Salsa20","authors":"Sabyasachi Dey, Gregor Leander, Nitin Kumar Sharma","doi":"10.1007/s10623-024-01522-7","DOIUrl":"https://doi.org/10.1007/s10623-024-01522-7","url":null,"abstract":"<p>In this paper, we present an improved attack on the stream cipher Salsa20. Our improvements are based on two technical contributions. First, we make use of a distribution of a linear combination of several random variables that are derived from different differentials and explain how to exploit this in order to improve the attack complexity. Secondly, we study and exploit how to choose the actual value for so-called probabilistic neutral bits optimally. Because of the limited influence of these key bits on the computation, in the usual attack approach, these are fixed to a constant value, often zero for simplicity. As we will show, despite the fact that their influence is limited, the constant can be chosen in significantly better ways, and intriguingly, zero is the worst choice. Using this, we propose the first-ever attack on 7.5-round of the 128-bit key version of Salsa20. Also, we provide improvements in the attack against the 8-round of the 256-bit key version of Salsa20 and the 7-round of the 128-bit key version of Salsa20.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142597483","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
Parallel construction for constant dimension codes from mixed dimension construction 从混合维度结构并行构建恒定维度代码
IF 1.6 2区 数学
Designs, Codes and Cryptography Pub Date : 2024-11-09 DOI: 10.1007/s10623-024-01518-3
Xianmang He, Zusheng Zhang, Si Tian, Jingli Wang, Yindong Chen
{"title":"Parallel construction for constant dimension codes from mixed dimension construction","authors":"Xianmang He, Zusheng Zhang, Si Tian, Jingli Wang, Yindong Chen","doi":"10.1007/s10623-024-01518-3","DOIUrl":"https://doi.org/10.1007/s10623-024-01518-3","url":null,"abstract":"<p>The community has been pursuing improvements in the cardinalities for constant dimensional codes (CDC for short) for the past decade. Lao et al. (IEEE Trans Inf Theory 69(7):4333–4344, 2023) has shown that mixed dimension subspace codes can be used to construct large constant dimension subspace codes. The exploration of the CDCs’ construction is transformed into finding mixed dimension/distance subspace codes with large dimension distributions. In this paper, we apply the parallel construction to this mixed dimension construction, which allows us to contribute approximately more than 80 new constant dimension codes.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142598203","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
On entire solutions of certain partial differential equations 论某些偏微分方程的全解
IF 1.4 3区 数学
Analysis and Mathematical Physics Pub Date : 2024-11-09 DOI: 10.1007/s13324-024-00988-x
Feng Lü, Wenqi Bi
{"title":"On entire solutions of certain partial differential equations","authors":"Feng Lü,&nbsp;Wenqi Bi","doi":"10.1007/s13324-024-00988-x","DOIUrl":"10.1007/s13324-024-00988-x","url":null,"abstract":"<div><p>We firstly describe entire solutions of variation of the well-known PDE of tubular surfaces. In addition, we consider entire solutions of certain partial differential equations, which are related with the Picard’s little theorem. Moreover, we obtain a Tumura-Clunie type theorem in <span>({mathbb {C}}^{m})</span>, which is an improvement of a result given by Hu-Yang (Bull Aust Math Soc 90: 444-456, 2014).</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2024-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142598863","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
Network transformation-based analysis of biochemical systems. 基于网络转换的生化系统分析。
IF 2.2 4区 数学
Journal of Mathematical Biology Pub Date : 2024-11-08 DOI: 10.1007/s00285-024-02152-2
Dylan Antonio Talabis, Eduardo Mendoza
{"title":"Network transformation-based analysis of biochemical systems.","authors":"Dylan Antonio Talabis, Eduardo Mendoza","doi":"10.1007/s00285-024-02152-2","DOIUrl":"https://doi.org/10.1007/s00285-024-02152-2","url":null,"abstract":"<p><p>A dynamical system obtains a wide variety of kinetic realizations, which is advantageous for the analysis of biochemical systems. A reaction network, derived from a dynamical system, may or may not possess some properties needed for a thorough analysis. We improve and extend the work of Johnston and Hong et al. on network translations to network transformations, where the network is modified while preserving the dynamical system. These transformations can shrink, extend, or retain the stoichiometric subspace. Here, we show that a positive dependent network can be translated to a weakly reversible network. Using the kinetic realizations of (1) calcium signaling in the olfactory system and (2) metabolic insulin signaling, we demonstrate the benefits of transformed systems with positive deficiency for analyzing biochemical systems. Furthermore, we present an algorithm for a network transformation of a weakly reversible non-complex factorizable kinetic (NFK) system to a weakly reversible complex factorizable kinetic (CFK) system, thereby enhancing the Subspace Coincidence Theorem for NFK systems of Nazareno et al. Finally, using the transformed kinetic realization of monolignol biosynthesis in Populus xylem, we study the structural and kinetic properties of transformed systems, including the invariance of concordance and variation of injectivity and mono-/multi-stationarity under network transformation.</p>","PeriodicalId":50148,"journal":{"name":"Journal of Mathematical Biology","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142606880","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
Any Two-Coloring of the Plane Contains Monochromatic 3-Term Arithmetic Progressions 平面的任意双色包含单色三项算术级数
IF 1.1 2区 数学
Combinatorica Pub Date : 2024-11-07 DOI: 10.1007/s00493-024-00122-2
Gabriel Currier, Kenneth Moore, Chi Hoi Yip
{"title":"Any Two-Coloring of the Plane Contains Monochromatic 3-Term Arithmetic Progressions","authors":"Gabriel Currier, Kenneth Moore, Chi Hoi Yip","doi":"10.1007/s00493-024-00122-2","DOIUrl":"https://doi.org/10.1007/s00493-024-00122-2","url":null,"abstract":"<p>A conjecture of Erdős, Graham, Montgomery, Rothschild, Spencer, and Straus states that, with the exception of equilateral triangles, any two-coloring of the plane will have a monochromatic congruent copy of every three-point configuration. This conjecture is known only for special classes of configurations. In this manuscript, we confirm one of the most natural open cases; that is, every two-coloring of the plane admits a monochromatic congruent copy of any 3-term arithmetic progression.</p>","PeriodicalId":50666,"journal":{"name":"Combinatorica","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142594653","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
Sandpiles and Dunes: Mathematical Models for Granular Matter 沙堆和沙丘：颗粒物质的数学模型
IF 10.2 1区 数学
SIAM Review Pub Date : 2024-11-07 DOI: 10.1137/23m1583673
Piermarco Cannarsa, Stefano Finzi Vita
{"title":"Sandpiles and Dunes: Mathematical Models for Granular Matter","authors":"Piermarco Cannarsa, Stefano Finzi Vita","doi":"10.1137/23m1583673","DOIUrl":"https://doi.org/10.1137/23m1583673","url":null,"abstract":"SIAM Review, Volume 66, Issue 4, Page 751-777, November 2024. <br/> Granular materials are everywhere, in the environment but also in our pantry. Their properties are different from those of any solid material, due to the possibility of sudden phenomena such as avalanches or landslides. Here we present a brief survey on their characteristics and on what can be found (from the past thirty years) in the recent mathematics literature in order to reproduce their behavior. We discuss, in particular, differential models proposed for the growth of a sandpile on a table and, when wind comes into play, for the formation and dynamics of sand dunes. This field of research is still of great interest since there is no consolidated general model for the dynamics of granular matter, but rather only standalone models adapted to specific situations.","PeriodicalId":49525,"journal":{"name":"SIAM Review","volume":null,"pages":null},"PeriodicalIF":10.2,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142594678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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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