首页 > 最新文献

Random Operators and Stochastic Equations最新文献

英文 中文
The main probability G-density of the theory of non-Hermitian random matrices, VICTORIA transform, RESPECT and REFORM methods 非埃尔米特随机矩阵理论的主概率G密度、VICTORIA变换、RESPECT和REFORM方法
IF 0.4 Q4 Mathematics Pub Date : 2022-03-01 DOI: 10.1515/rose-2022-2071
V. Girko
Abstract The main probability G-density of the global law for random matrices whose entries are independent is founded.
摘要建立了条目独立的随机矩阵全局律的主概率G密度。
{"title":"The main probability G-density of the theory of non-Hermitian random matrices, VICTORIA transform, RESPECT and REFORM methods","authors":"V. Girko","doi":"10.1515/rose-2022-2071","DOIUrl":"https://doi.org/10.1515/rose-2022-2071","url":null,"abstract":"Abstract The main probability G-density of the global law for random matrices whose entries are independent is founded.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45045429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
The G-pencil law under G-Lindeberg condition. The canonical equation K_98 and G-logarithmic law G-Lindeberg条件下的G-铅笔定律。正则方程K_98与G-对数律
IF 0.4 Q4 Mathematics Pub Date : 2022-03-01 DOI: 10.1515/rose-2022-2072
V. Girko, B. Shevchuk, L. Shevchuk
Abstract The examples of the pencil law for two random matrices whose pairs of entries are independent are considered.
摘要考虑了两个元素对独立的随机矩阵的铅笔律的例子。
{"title":"The G-pencil law under G-Lindeberg condition. The canonical equation K_98 and G-logarithmic law","authors":"V. Girko, B. Shevchuk, L. Shevchuk","doi":"10.1515/rose-2022-2072","DOIUrl":"https://doi.org/10.1515/rose-2022-2072","url":null,"abstract":"Abstract The examples of the pencil law for two random matrices whose pairs of entries are independent are considered.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42275278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solving equations with semimartingale noise 求解带有半鞅噪声的方程
IF 0.4 Q4 Mathematics Pub Date : 2022-01-23 DOI: 10.1515/rose-2021-2070
Jonathan Gutierrez-Pavón, Carlos G. Pacheco
Abstract In this work we focus on a method for solving equations with a coefficient formally given in terms of the derivative of a continuous semimartingale. This generalizes the case of coefficients being the white noise. The idea for solving the equation is to find explicitly the inverse of the ill-posed differential operator, which boils down to finding the associated Green kernel. To find the kernel we give explicitly two homogeneous solutions in terms of the so-called Dolean–Dade exponential. The general idea to define rigorously differential operators lies on dealing with them through bilinear forms. We give several examples with explicit calculations.
摘要在这项工作中,我们重点讨论了一种用连续半鞅的导数形式给出系数的方程组的求解方法。这推广了系数是白噪声的情况。求解方程的想法是明确地找到不适定微分算子的逆,这归结为找到相关的格林核。为了找到核,我们根据所谓的Dolean–Dade指数明确给出了两个齐次解。定义严格微分算子的一般思想在于通过双线性形式处理它们。我们给出了几个带有显式计算的例子。
{"title":"Solving equations with semimartingale noise","authors":"Jonathan Gutierrez-Pavón, Carlos G. Pacheco","doi":"10.1515/rose-2021-2070","DOIUrl":"https://doi.org/10.1515/rose-2021-2070","url":null,"abstract":"Abstract In this work we focus on a method for solving equations with a coefficient formally given in terms of the derivative of a continuous semimartingale. This generalizes the case of coefficients being the white noise. The idea for solving the equation is to find explicitly the inverse of the ill-posed differential operator, which boils down to finding the associated Green kernel. To find the kernel we give explicitly two homogeneous solutions in terms of the so-called Dolean–Dade exponential. The general idea to define rigorously differential operators lies on dealing with them through bilinear forms. We give several examples with explicit calculations.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48218477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Multivalued and random version of Perov fixed point theorem in generalized gauge spaces 广义规范空间中Perov不动点定理的多值和随机版本
IF 0.4 Q4 Mathematics Pub Date : 2022-01-06 DOI: 10.1515/rose-2021-2068
A. Laadjel, J. Nieto, A. Ouahab, R. Rodríguez-López
Abstract In this paper, we present some random fixed point theorems in complete gauge spaces. We establish then a multivalued version of a Perov–Gheorghiu’s fixed point theorem in generalized gauge spaces. Finally, some examples are given to illustrate the results.
摘要本文给出了完备规范空间中的一些随机不动点定理。然后,我们在广义规范空间中建立了Perov–Gheorghiu不动点定理的多值版本。最后,通过实例说明了结果。
{"title":"Multivalued and random version of Perov fixed point theorem in generalized gauge spaces","authors":"A. Laadjel, J. Nieto, A. Ouahab, R. Rodríguez-López","doi":"10.1515/rose-2021-2068","DOIUrl":"https://doi.org/10.1515/rose-2021-2068","url":null,"abstract":"Abstract In this paper, we present some random fixed point theorems in complete gauge spaces. We establish then a multivalued version of a Perov–Gheorghiu’s fixed point theorem in generalized gauge spaces. Finally, some examples are given to illustrate the results.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44703902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Deplay BSDEs driven by fractional Brownian motion 分数布朗运动驱动的Deplay BSDE
IF 0.4 Q4 Mathematics Pub Date : 2022-01-06 DOI: 10.1515/rose-2021-2069
Sadibou Aidara, Ibrahima Sané
Abstract This paper deals with a class of deplay backward stochastic differential equations driven by fractional Brownian motion (with Hurst parameter H greater than 1 2 {frac{1}{2}} ). In this type of equation, a generator at time t can depend not only on the present but also the past solutions. We essentially establish existence and uniqueness of a solution in the case of Lipschitz coefficients and non-Lipschitz coefficients. The stochastic integral used throughout this paper is the divergence-type integral.
摘要研究一类分数阶布朗运动驱动的后向随机微分方程(赫斯特参数H大于1 2 {frac{1}{2}})。在这种类型的方程中,时刻t的生成器不仅依赖于现在的解,也依赖于过去的解。我们从本质上建立了在Lipschitz系数和非Lipschitz系数情况下解的存在唯一性。本文所使用的随机积分是散度型积分。
{"title":"Deplay BSDEs driven by fractional Brownian motion","authors":"Sadibou Aidara, Ibrahima Sané","doi":"10.1515/rose-2021-2069","DOIUrl":"https://doi.org/10.1515/rose-2021-2069","url":null,"abstract":"Abstract This paper deals with a class of deplay backward stochastic differential equations driven by fractional Brownian motion (with Hurst parameter H greater than 1 2 {frac{1}{2}} ). In this type of equation, a generator at time t can depend not only on the present but also the past solutions. We essentially establish existence and uniqueness of a solution in the case of Lipschitz coefficients and non-Lipschitz coefficients. The stochastic integral used throughout this paper is the divergence-type integral.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2022-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43966204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
L 1 and L ∞ stability of transition densities of perturbed diffusions 扰动扩散跃迁密度的L1和L∞稳定性
IF 0.4 Q4 Mathematics Pub Date : 2021-11-20 DOI: 10.1515/rose-2021-2067
I. Bitter, V. Konakov
Abstract In this paper, we derive a stability result for L 1 {L_{1}} and L ∞ {L_{infty}} perturbations of diffusions under weak regularity conditions on the coefficients. In particular, the drift terms we consider can be unbounded with at most linear growth, and the estimates reflect the transport of the initial condition by the unbounded drift through the corresponding flow. Our approach is based on the study of the distance in L 1 {L_{1}} - L 1 {L_{1}} metric between the transition densities of a given diffusion and the perturbed one using the McKean–Singer parametrix expansion. In the second part, we generalize the well-known result on the stability of diffusions with bounded coefficients to the case of at most linearly growing drift.
摘要本文给出了扩散的L1{L_{1}}和L∞{L_{{infty}扰动在弱正则性条件下的稳定性结果。特别是,我们考虑的漂移项最多可以是线性增长的无界漂移项,并且估计反映了无界漂移通过相应流对初始条件的传输。我们的方法是基于使用McKean–Singer参数展开来研究给定扩散的跃迁密度和扰动扩散的跃迁浓度之间在L1{L_{1}}-L1{L_{1}}度量中的距离。在第二部分中,我们将关于有界系数扩散稳定性的众所周知的结果推广到漂移至多线性增长的情况。
{"title":"L 1 and L ∞ stability of transition densities of perturbed diffusions","authors":"I. Bitter, V. Konakov","doi":"10.1515/rose-2021-2067","DOIUrl":"https://doi.org/10.1515/rose-2021-2067","url":null,"abstract":"Abstract In this paper, we derive a stability result for L 1 {L_{1}} and L ∞ {L_{infty}} perturbations of diffusions under weak regularity conditions on the coefficients. In particular, the drift terms we consider can be unbounded with at most linear growth, and the estimates reflect the transport of the initial condition by the unbounded drift through the corresponding flow. Our approach is based on the study of the distance in L 1 {L_{1}} - L 1 {L_{1}} metric between the transition densities of a given diffusion and the perturbed one using the McKean–Singer parametrix expansion. In the second part, we generalize the well-known result on the stability of diffusions with bounded coefficients to the case of at most linearly growing drift.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44174105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Coupled fractional differential systems with random effects in Banach spaces Banach空间中具有随机效应的耦合分数阶微分系统
IF 0.4 Q4 Mathematics Pub Date : 2021-10-27 DOI: 10.1515/rose-2021-2064
O. Zentar, M. Ziane, S. Khelifa
Abstract The purpose of this work is to investigate the existence of solutions for a system of random differential equations involving the Riemann–Liouville fractional derivative. The existence result is established by means of a random abstract formulation to Sadovskii’s fixed point theorem principle [A. Baliki, J. J. Nieto, A. Ouahab and M. L. Sinacer, Random semilinear system of differential equations with impulses, Fixed Point Theory Appl. 2017 2017, Paper No. 27] combined with a technique based on vector-valued metrics and convergent to zero matrices. An example is also provided to illustrate our result.
摘要本文的目的是研究一类含有Riemann-Liouville分数阶导数的随机微分方程组解的存在性。通过对Sadovskii不动点定理原理的一个随机抽象表述,建立了存在性结果。Baliki, J. J. Nieto, a . Ouahab和M. L. Sinacer,随机半线性脉冲微分方程系统,不动点理论应用,2017,No. 27]。最后给出了一个例子来说明我们的结果。
{"title":"Coupled fractional differential systems with random effects in Banach spaces","authors":"O. Zentar, M. Ziane, S. Khelifa","doi":"10.1515/rose-2021-2064","DOIUrl":"https://doi.org/10.1515/rose-2021-2064","url":null,"abstract":"Abstract The purpose of this work is to investigate the existence of solutions for a system of random differential equations involving the Riemann–Liouville fractional derivative. The existence result is established by means of a random abstract formulation to Sadovskii’s fixed point theorem principle [A. Baliki, J. J. Nieto, A. Ouahab and M. L. Sinacer, Random semilinear system of differential equations with impulses, Fixed Point Theory Appl. 2017 2017, Paper No. 27] combined with a technique based on vector-valued metrics and convergent to zero matrices. An example is also provided to illustrate our result.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41356211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Small double limit with reflecting Wentzel boundary condition 具有反映Wentzel边界条件的小双极限
IF 0.4 Q4 Mathematics Pub Date : 2021-10-21 DOI: 10.1515/rose-2021-2066
Ibrahima Sané, A. Diédhiou
Abstract We provide a large deviation principle on the stochastic differential equations with reflecting Wentzel boundary condition if δ ε {frac{delta}{varepsilon}} tends to 0 when the two parameters δ (homogenization parameter) and ε (the large deviations parameter) tend to zero. Here, we suppose that the homogenization parameter converges sufficiently quickly more than the large deviations parameter. Furthermore, we will make explicit the associated rate function.
摘要给出了反映Wentzel边界条件的随机微分方程在均匀化参数δ和大偏差参数ε趋于零时δ ε {frac{delta}{varepsilon}}趋于0的大偏差原理。这里,我们假设均匀化参数比大偏差参数收敛得足够快。此外,我们将明确相关的速率函数。
{"title":"Small double limit with reflecting Wentzel boundary condition","authors":"Ibrahima Sané, A. Diédhiou","doi":"10.1515/rose-2021-2066","DOIUrl":"https://doi.org/10.1515/rose-2021-2066","url":null,"abstract":"Abstract We provide a large deviation principle on the stochastic differential equations with reflecting Wentzel boundary condition if δ ε {frac{delta}{varepsilon}} tends to 0 when the two parameters δ (homogenization parameter) and ε (the large deviations parameter) tend to zero. Here, we suppose that the homogenization parameter converges sufficiently quickly more than the large deviations parameter. Furthermore, we will make explicit the associated rate function.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48675819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Maximum likelihood estimation for sub-fractional Vasicek model 亚分数阶Vasicek模型的最大似然估计
IF 0.4 Q4 Mathematics Pub Date : 2021-10-10 DOI: 10.1515/rose-2021-2065
B. Prakasa Rao
Abstract We investigate the asymptotic properties of maximum likelihood estimators of the drift parameters for the fractional Vasicek model driven by a sub-fractional Brownian motion.
研究了由次分数阶布朗运动驱动的分数阶Vasicek模型漂移参数的极大似然估计的渐近性质。
{"title":"Maximum likelihood estimation for sub-fractional Vasicek model","authors":"B. Prakasa Rao","doi":"10.1515/rose-2021-2065","DOIUrl":"https://doi.org/10.1515/rose-2021-2065","url":null,"abstract":"Abstract We investigate the asymptotic properties of maximum likelihood estimators of the drift parameters for the fractional Vasicek model driven by a sub-fractional Brownian motion.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47762263","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Controllability of impulsive neutral stochastic integro-differential systems driven by a Rosenblatt process with unbounded delay 具有无界时滞的Rosenblatt过程驱动的脉冲中立型随机积分微分系统的可控性
IF 0.4 Q4 Mathematics Pub Date : 2021-09-25 DOI: 10.1515/rose-2021-2063
Youssef Benkabdi, E. Lakhel
Abstract In this paper, the controllability of a class of impulsive neutral stochastic integro-differential systems with infinite delay driven by Rosenblatt process in a separable Hilbert space is studied. The controllability result is obtained by using stochastic analysis and a fixed-point strategy. A practical example is provided to illustrate the viability of the abstract result of this work.
摘要本文研究了一类由Rosenblatt过程驱动的具有无限时滞的脉冲中立型随机积分微分系统在可分离Hilbert空间中的可控性。利用随机分析和定点策略得到了可控性结果。通过一个实例说明了这项工作抽象结果的可行性。
{"title":"Controllability of impulsive neutral stochastic integro-differential systems driven by a Rosenblatt process with unbounded delay","authors":"Youssef Benkabdi, E. Lakhel","doi":"10.1515/rose-2021-2063","DOIUrl":"https://doi.org/10.1515/rose-2021-2063","url":null,"abstract":"Abstract In this paper, the controllability of a class of impulsive neutral stochastic integro-differential systems with infinite delay driven by Rosenblatt process in a separable Hilbert space is studied. The controllability result is obtained by using stochastic analysis and a fixed-point strategy. A practical example is provided to illustrate the viability of the abstract result of this work.","PeriodicalId":43421,"journal":{"name":"Random Operators and Stochastic Equations","volume":null,"pages":null},"PeriodicalIF":0.4,"publicationDate":"2021-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45449721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
期刊
Random Operators and Stochastic Equations
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