首页 > 最新文献

Journal of Complexity最新文献

英文 中文
Computing approximate roots of monotone functions
IF 1.8 2区 数学 Q1 MATHEMATICS
Journal of Complexity
Pub Date : 2025-01-28 DOI: 10.1016/j.jco.2025.101930
Alexandros Hollender , Chester Lawrence, Erel Segal-Halevi
We are given a value-oracle for a d-dimensional function f that satisfies the conditions of Miranda's theorem, and therefore has a root. Our goal is to compute an approximate root using a number of evaluations that is polynomial in the number of accuracy digits. For d=1 this is always possible using the bisection method, but for d≥2 this is impossible in general.
We show that, if d=2 and f satisfies a single monotonicity condition, then the number of required evaluations is polynomial in the accuracy. The same holds if d≥3 and f satisfies some particular d2−d monotonicity conditions. We show that, if d=2 and f satisfies a single monotonicity condition, then the number of required evaluations is polynomial in the accuracy. The same holds if d≥3 and f satisfies some particular d2−d monotonicity conditions. In contrast, if even two of these monotonicity conditions are missing, then the required number of evaluations might be exponential.
As an example application, we show that approximate roots of monotone functions can be used for approximate envy-free cake-cutting.
{"title":"Computing approximate roots of monotone functions","authors":"Alexandros Hollender ,&nbsp;Chester Lawrence,&nbsp;Erel Segal-Halevi","doi":"10.1016/j.jco.2025.101930","DOIUrl":"10.1016/j.jco.2025.101930","url":null,"abstract":"<div><div>We are given a value-oracle for a <em>d</em>-dimensional function <em>f</em> that satisfies the conditions of Miranda's theorem, and therefore has a root. Our goal is to compute an approximate root using a number of evaluations that is polynomial in the number of accuracy digits. For <span><math><mi>d</mi><mo>=</mo><mn>1</mn></math></span> this is always possible using the bisection method, but for <span><math><mi>d</mi><mo>≥</mo><mn>2</mn></math></span> this is impossible in general.</div><div>We show that, if <span><math><mi>d</mi><mo>=</mo><mn>2</mn></math></span> and <em>f</em> satisfies a single monotonicity condition, then the number of required evaluations is polynomial in the accuracy. The same holds if <span><math><mi>d</mi><mo>≥</mo><mn>3</mn></math></span> and <em>f</em> satisfies some particular <span><math><msup><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>d</mi></math></span> monotonicity conditions. We show that, if <span><math><mi>d</mi><mo>=</mo><mn>2</mn></math></span> and <em>f</em> satisfies a single monotonicity condition, then the number of required evaluations is polynomial in the accuracy. The same holds if <span><math><mi>d</mi><mo>≥</mo><mn>3</mn></math></span> and <em>f</em> satisfies some particular <span><math><msup><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>−</mo><mi>d</mi></math></span> monotonicity conditions. In contrast, if even two of these monotonicity conditions are missing, then the required number of evaluations might be exponential.</div><div>As an example application, we show that approximate roots of monotone functions can be used for approximate envy-free cake-cutting.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"88 ","pages":"Article 101930"},"PeriodicalIF":1.8,"publicationDate":"2025-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143157479","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 complexity of orbit word problems
IF 1.8 2区 数学 Q1 MATHEMATICS
Journal of Complexity
Pub Date : 2025-01-16 DOI: 10.1016/j.jco.2025.101929
Michael Maller
In previous work we defined a computational saddle transition problem which arises in the dynamics of diffeomorphisms of the 2−dimensional torus, and proved this problem is in Oracle NP, working in a model of computation appropriate for Turing machine computations on problems defined over the real numbers. In this note we report further work on these problems, studying orbit descriptions represented as finite words in periodic points. We show these Orbit Word Problems are again in Oracle NP, in our model. Our methods also reveal structures in the set of realized orbit words, suggesting further applications in complexity.
{"title":"On the complexity of orbit word problems","authors":"Michael Maller","doi":"10.1016/j.jco.2025.101929","DOIUrl":"10.1016/j.jco.2025.101929","url":null,"abstract":"<div><div>In previous work we defined a computational saddle transition problem which arises in the dynamics of diffeomorphisms of the 2−dimensional torus, and proved this problem is in Oracle <strong>NP</strong>, working in a model of computation appropriate for Turing machine computations on problems defined over the real numbers. In this note we report further work on these problems, studying orbit descriptions represented as finite words in periodic points. We show these Orbit Word Problems are again in Oracle <strong>NP</strong>, in our model. Our methods also reveal structures in the set of realized orbit words, suggesting further applications in complexity.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"88 ","pages":"Article 101929"},"PeriodicalIF":1.8,"publicationDate":"2025-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143157480","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
Fast interpolation of multivariate polynomials with sparse exponents
IF 1.8 2区 数学 Q1 MATHEMATICS
Journal of Complexity
Pub Date : 2024-12-16 DOI: 10.1016/j.jco.2024.101922
Joris van der Hoeven, Grégoire Lecerf
Consider a sparse multivariate polynomial f with integer coefficients. Assume that f is represented as a “modular black box polynomial”, e.g. via an algorithm to evaluate f at arbitrary integer points, modulo arbitrary positive integers. The problem of sparse interpolation is to recover f in its usual sparse representation, as a sum of coefficients times monomials. For the first time we present a quasi-optimal algorithm for this task in term of the product of the number of terms of f by the maximum of the bit-size of the terms of f.
{"title":"Fast interpolation of multivariate polynomials with sparse exponents","authors":"Joris van der Hoeven,&nbsp;Grégoire Lecerf","doi":"10.1016/j.jco.2024.101922","DOIUrl":"10.1016/j.jco.2024.101922","url":null,"abstract":"<div><div>Consider a sparse multivariate polynomial <em>f</em> with integer coefficients. Assume that <em>f</em> is represented as a “modular black box polynomial”, e.g. via an algorithm to evaluate <em>f</em> at arbitrary integer points, modulo arbitrary positive integers. The problem of sparse interpolation is to recover <em>f</em> in its usual sparse representation, as a sum of coefficients times monomials. For the first time we present a quasi-optimal algorithm for this task in term of the product of the number of terms of <em>f</em> by the maximum of the bit-size of the terms of <em>f</em>.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"87 ","pages":"Article 101922"},"PeriodicalIF":1.8,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180614","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 procedure for increasing the convergence order of iterative methods from p to 5p for solving nonlinear system
IF 1.8 2区 数学 Q1 MATHEMATICS
Journal of Complexity
Pub Date : 2024-12-06 DOI: 10.1016/j.jco.2024.101921
Santhosh George , Muniyasamy M , Manjusree Gopal , Chandhini G , Ioannis K. Argyros
In this paper, we propose a procedure to obtain an iterative method that increases its convergence order from p to 5p for solving nonlinear systems. Our analysis is given in more general Banach space settings and uses assumptions on the derivative of the involved operator only up to order max⁡{k,2}. Here, k is the order of the highest derivative used in the convergence analysis of the iterative method with convergence order p. A particular case of our analysis includes an existing fifth-order method and improves its applicability to more problems than the problems covered by the method's analysis in earlier study.
{"title":"A procedure for increasing the convergence order of iterative methods from p to 5p for solving nonlinear system","authors":"Santhosh George ,&nbsp;Muniyasamy M ,&nbsp;Manjusree Gopal ,&nbsp;Chandhini G ,&nbsp;Ioannis K. Argyros","doi":"10.1016/j.jco.2024.101921","DOIUrl":"10.1016/j.jco.2024.101921","url":null,"abstract":"<div><div>In this paper, we propose a procedure to obtain an iterative method that increases its convergence order from <em>p</em> to 5<em>p</em> for solving nonlinear systems. Our analysis is given in more general Banach space settings and uses assumptions on the derivative of the involved operator only up to order <span><math><mi>max</mi><mo>⁡</mo><mo>{</mo><mi>k</mi><mo>,</mo><mn>2</mn><mo>}</mo></math></span>. Here, <em>k</em> is the order of the highest derivative used in the convergence analysis of the iterative method with convergence order <em>p</em>. A particular case of our analysis includes an existing fifth-order method and improves its applicability to more problems than the problems covered by the method's analysis in earlier study.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"87 ","pages":"Article 101921"},"PeriodicalIF":1.8,"publicationDate":"2024-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180612","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 revisit on Nesterov acceleration for linear ill-posed problems
IF 1.8 2区 数学 Q1 MATHEMATICS
Journal of Complexity
Pub Date : 2024-12-04 DOI: 10.1016/j.jco.2024.101920
Duo Liu , Qin Huang , Qinian Jin
In recent years, Nesterov acceleration has been introduced to enhance the efficiency of Landweber iteration for solving ill-posed problems. For linear ill-posed problems in Hilbert spaces, Nesterov acceleration has been analyzed with a discrepancy principle proposed to terminate the iterations. However, the existing approach requires computing residuals along two distinct iterative sequences, resulting in increased computational costs. In this paper, we propose an alternative discrepancy principle for Nesterov acceleration that eliminates the need to compute the residuals for one of the iterative sequences, thereby reducing computational time by approximately one-third per iteration. We provide a convergence analysis of the proposed method, establishing both its convergence and convergence rates. The effectiveness of our approach is demonstrated through numerical simulations.
{"title":"A revisit on Nesterov acceleration for linear ill-posed problems","authors":"Duo Liu ,&nbsp;Qin Huang ,&nbsp;Qinian Jin","doi":"10.1016/j.jco.2024.101920","DOIUrl":"10.1016/j.jco.2024.101920","url":null,"abstract":"<div><div>In recent years, Nesterov acceleration has been introduced to enhance the efficiency of Landweber iteration for solving ill-posed problems. For linear ill-posed problems in Hilbert spaces, Nesterov acceleration has been analyzed with a discrepancy principle proposed to terminate the iterations. However, the existing approach requires computing residuals along two distinct iterative sequences, resulting in increased computational costs. In this paper, we propose an alternative discrepancy principle for Nesterov acceleration that eliminates the need to compute the residuals for one of the iterative sequences, thereby reducing computational time by approximately one-third per iteration. We provide a convergence analysis of the proposed method, establishing both its convergence and convergence rates. The effectiveness of our approach is demonstrated through numerical simulations.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"87 ","pages":"Article 101920"},"PeriodicalIF":1.8,"publicationDate":"2024-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180615","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
Changes of the Editorial Board 编辑委员会的变动
IF 1.8 2区 数学 Q1 MATHEMATICS
Journal of Complexity
Pub Date : 2024-11-29 DOI: 10.1016/j.jco.2024.101908
Erich Novak
{"title":"Changes of the Editorial Board","authors":"Erich Novak","doi":"10.1016/j.jco.2024.101908","DOIUrl":"10.1016/j.jco.2024.101908","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"87 ","pages":"Article 101908"},"PeriodicalIF":1.8,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142745321","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
Succinct obituary in memoriam of Joos Heintz 简练的讣告，纪念乔·海因茨
IF 1.8 2区 数学 Q1 MATHEMATICS
Journal of Complexity
Pub Date : 2024-11-29 DOI: 10.1016/j.jco.2024.101919
Luis M. Pardo
{"title":"Succinct obituary in memoriam of Joos Heintz","authors":"Luis M. Pardo","doi":"10.1016/j.jco.2024.101919","DOIUrl":"10.1016/j.jco.2024.101919","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"87 ","pages":"Article 101919"},"PeriodicalIF":1.8,"publicationDate":"2024-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142742866","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
Direct estimates for adaptive time-stepping finite element methods
IF 1.8 2区 数学 Q1 MATHEMATICS
Journal of Complexity
Pub Date : 2024-11-28 DOI: 10.1016/j.jco.2024.101918
Marcelo Actis , Fernando Gaspoz , Pedro Morin , Cornelia Schneider , Nick Schneider
We study direct estimates for adaptive time-stepping finite element methods for time-dependent partial differential equations. Our results generalize previous findings from “On approximation classes for adaptive time-stepping finite element methods” by Actis et al. (2023), where the approximation error was only measured in L2([0,T],L2(Ω)). In particular, we now also cover the error norms L∞([0,T],L2(Ω)) and L2([0,T],H1(Ω)) which are more natural in this context.
{"title":"Direct estimates for adaptive time-stepping finite element methods","authors":"Marcelo Actis ,&nbsp;Fernando Gaspoz ,&nbsp;Pedro Morin ,&nbsp;Cornelia Schneider ,&nbsp;Nick Schneider","doi":"10.1016/j.jco.2024.101918","DOIUrl":"10.1016/j.jco.2024.101918","url":null,"abstract":"<div><div>We study direct estimates for adaptive time-stepping finite element methods for time-dependent partial differential equations. Our results generalize previous findings from “On approximation classes for adaptive time-stepping finite element methods” by Actis et al. (2023), where the approximation error was only measured in <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>Ω</mi><mo>)</mo><mo>)</mo></math></span>. In particular, we now also cover the error norms <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>Ω</mi><mo>)</mo><mo>)</mo></math></span> and <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo><mo>,</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo><mo>)</mo></math></span> which are more natural in this context.</div></div>","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"87 ","pages":"Article 101918"},"PeriodicalIF":1.8,"publicationDate":"2024-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143180611","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
Stefan Heinrich is the Winner of the 2024 Best Paper Award of the Journal of Complexity 斯特凡-海因里希荣获《复杂性期刊》2024 年度最佳论文奖
IF 1.8 2区 数学 Q1 MATHEMATICS
Journal of Complexity
Pub Date : 2024-11-05 DOI: 10.1016/j.jco.2024.101905
Erich Novak, Mario Ullrich, Jan Vybíral
{"title":"Stefan Heinrich is the Winner of the 2024 Best Paper Award of the Journal of Complexity","authors":"Erich Novak,&nbsp;Mario Ullrich,&nbsp;Jan Vybíral","doi":"10.1016/j.jco.2024.101905","DOIUrl":"10.1016/j.jco.2024.101905","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"86 ","pages":"Article 101905"},"PeriodicalIF":1.8,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586490","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
Best Paper Award of the Journal of Complexity 复杂性期刊》最佳论文奖
IF 1.8 2区 数学 Q1 MATHEMATICS
Journal of Complexity
Pub Date : 2024-11-05 DOI: 10.1016/j.jco.2024.101904
{"title":"Best Paper Award of the Journal of Complexity","authors":"","doi":"10.1016/j.jco.2024.101904","DOIUrl":"10.1016/j.jco.2024.101904","url":null,"abstract":"","PeriodicalId":50227,"journal":{"name":"Journal of Complexity","volume":"86 ","pages":"Article 101904"},"PeriodicalIF":1.8,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586491","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
下一页 尾页
类型
全部 化学•材料 生命科学 医学 物理 工程技术 环境•农林 材料科学 地球科学 法学 管理学 化学 环境科学与生态学 计算机科学 教育学 经济学 农林科学 人文科学 生物学 数学 物理与天体物理 心理学 综合性期刊 其他 工业工程 理学 历史学 农学 文学 信息工程
数据库
全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley
期刊
Journal of Complexity
全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.
﹀
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们：info@booksci.cn
Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1