首页 > 最新文献

Discrete Mathematics and Applications最新文献

英文 中文
On the complexity of monotone circuits for threshold symmetric Boolean functions 关于阈值对称布尔函数单调电路的复杂性
IF 0.5 Q4 MATHEMATICS, APPLIED Pub Date : 2021-10-01 DOI: 10.1515/dma-2021-0031
I. Sergeev
Abstract The complexity of implementation of a threshold symmetric n-place Boolean function with threshold k = O(1) via circuits over the basis {∨, ∧} is shown not to exceed 2 log2 k ⋅ n + o(n). Moreover, the complexity of a threshold-2 function is proved to be 2n + Θ( n $begin{array}{} sqrt n end{array} $), and the complexity of a threshold-3 function is shown to be 3n + O(log n), the corresponding lower bounds are put forward.
摘要通过基{∧,∧}上的电路实现阈值k=O(1)的阈值对称n位布尔函数的复杂性不超过2 log2k·n+O(n)。此外,还证明了阈值-2函数的复杂度为2n+θ(n$begin{array}{}sqrt nend{array}$),并证明了阈值-3函数的复杂性为3n+O(logn),给出了相应的下界。
{"title":"On the complexity of monotone circuits for threshold symmetric Boolean functions","authors":"I. Sergeev","doi":"10.1515/dma-2021-0031","DOIUrl":"https://doi.org/10.1515/dma-2021-0031","url":null,"abstract":"Abstract The complexity of implementation of a threshold symmetric n-place Boolean function with threshold k = O(1) via circuits over the basis {∨, ∧} is shown not to exceed 2 log2 k ⋅ n + o(n). Moreover, the complexity of a threshold-2 function is proved to be 2n + Θ( n $begin{array}{} sqrt n end{array} $), and the complexity of a threshold-3 function is shown to be 3n + O(log n), the corresponding lower bounds are put forward.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"31 1","pages":"345 - 366"},"PeriodicalIF":0.5,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43093321","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
Boolean analogues of the Pascal triangle with maximal possible number of ones 具有最大可能数目的帕斯卡三角形的布尔类比
IF 0.5 Q4 MATHEMATICS, APPLIED Pub Date : 2021-10-01 DOI: 10.1515/dma-2021-0029
F. M. Malyshev
Abstract The aim of the paper is to find the maximal possible number ξ of units in Boolean triangular array Ts formed by s(s+1)2 $begin{array}{} displaystyle frac{s(s+1)}{2} end{array}$ elements of the field GF(2) defined by the top row of s elements. Each element of each row except the top one is the sum (as in the Pascal’s triangle) of two elements of the above row. It is proved that ξ ⩽ ⌈ s(s+1)3 $begin{array}{} displaystyle frac{s(s+1)}{3} end{array}$⌉ and this value is attained only on triangles having the upper row as the Fibonacci series mod 2.
摘要本文的目的是在由s元素的顶行定义的域GF(2)的s(s+1)2$begin{array}{}displaystylefrac{s(s+1)}{2}end{array}$元素形成的布尔三角数组Ts中找到单元的最大可能数ξ。除了最上面的一行之外,每行的每个元素都是上面一行的两个元素的和(如Pascal三角形)。证明了ξ⩽s(s+1)3$begin{array}{}displaystylefrac{s(s+1)}{3}end{array}$,并且该值仅在具有作为斐波那契级数mod 2的上排的三角形上获得。
{"title":"Boolean analogues of the Pascal triangle with maximal possible number of ones","authors":"F. M. Malyshev","doi":"10.1515/dma-2021-0029","DOIUrl":"https://doi.org/10.1515/dma-2021-0029","url":null,"abstract":"Abstract The aim of the paper is to find the maximal possible number ξ of units in Boolean triangular array Ts formed by s(s+1)2 $begin{array}{} displaystyle frac{s(s+1)}{2} end{array}$ elements of the field GF(2) defined by the top row of s elements. Each element of each row except the top one is the sum (as in the Pascal’s triangle) of two elements of the above row. It is proved that ξ ⩽ ⌈ s(s+1)3 $begin{array}{} displaystyle frac{s(s+1)}{3} end{array}$⌉ and this value is attained only on triangles having the upper row as the Fibonacci series mod 2.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"31 1","pages":"319 - 325"},"PeriodicalIF":0.5,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47623873","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
The limited deficit method and the problem of constructing orthomorphisms and almost orthomorphisms of Abelian groups 有限亏缺法与构造阿贝尔群的正态和几乎正态问题
IF 0.5 Q4 MATHEMATICS, APPLIED Pub Date : 2021-10-01 DOI: 10.1515/dma-2021-0030
A. V. Menyachikhin
Abstract The limited deficit method is described, which allows constructing new orthomorphisms (almost orthomorphisms) of groups with the use of those already known. A class of transformations is described under which the set of all orthomorphisms (almost orthomorphisms) remains invariant. It is conjectured that the set of all orthomorphisms (almost orthomorphisms) is generated by transformations implemented by the limited deficit method. This conjecture is verified for all Abelian groups of order at most 12. The spectral-linear method and the spectral-differential method of design of permutations over the additive group of the field 𝔽2m (m = 4, …, 8) are used to construct orthomorphisms with sufficiently high values of the most important cryptographic parameters.
摘要描述了利用已知群的正态构造群的新正态(几乎正态)的有限亏缺方法。描述了一类变换,在该类变换下,所有正态(几乎正态)的集合保持不变。我们推测所有正态(几乎正态)集合是由有限亏缺法实现的变换生成的。这个猜想在所有不超过12阶的阿贝尔群上都得到了验证。利用谱-线性法和谱-微分法设计域𝔽2m (m = 4,…,8)加性群上的置换,构造了具有足够高值的最重要密码参数的正态。
{"title":"The limited deficit method and the problem of constructing orthomorphisms and almost orthomorphisms of Abelian groups","authors":"A. V. Menyachikhin","doi":"10.1515/dma-2021-0030","DOIUrl":"https://doi.org/10.1515/dma-2021-0030","url":null,"abstract":"Abstract The limited deficit method is described, which allows constructing new orthomorphisms (almost orthomorphisms) of groups with the use of those already known. A class of transformations is described under which the set of all orthomorphisms (almost orthomorphisms) remains invariant. It is conjectured that the set of all orthomorphisms (almost orthomorphisms) is generated by transformations implemented by the limited deficit method. This conjecture is verified for all Abelian groups of order at most 12. The spectral-linear method and the spectral-differential method of design of permutations over the additive group of the field 𝔽2m (m = 4, …, 8) are used to construct orthomorphisms with sufficiently high values of the most important cryptographic parameters.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"31 1","pages":"327 - 343"},"PeriodicalIF":0.5,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46061616","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
On the average-case complexity of Boolean functions under binomial distribution on their domains 二项分布布尔函数在其定义域上的平均情况复杂度
IF 0.5 Q4 MATHEMATICS, APPLIED Pub Date : 2021-10-01 DOI: 10.1515/dma-2021-0028
A. V. Chashkin
Abstract Given a binomial probability distribution on the n-dimensional Boolean cube, the complexity of implementation of Boolean functions by straight line programs with conditional stop is considered. The order, as n → ∞, of the average-case complexity of almost all n-place Boolean functions is established.
摘要给定n维布尔立方体上的二项式概率分布,考虑了带条件停止的直线程序实现布尔函数的复杂性。顺序,如n→ ∞, 建立了几乎所有n位布尔函数的平均情况复杂度。
{"title":"On the average-case complexity of Boolean functions under binomial distribution on their domains","authors":"A. V. Chashkin","doi":"10.1515/dma-2021-0028","DOIUrl":"https://doi.org/10.1515/dma-2021-0028","url":null,"abstract":"Abstract Given a binomial probability distribution on the n-dimensional Boolean cube, the complexity of implementation of Boolean functions by straight line programs with conditional stop is considered. The order, as n → ∞, of the average-case complexity of almost all n-place Boolean functions is established.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"31 1","pages":"315 - 318"},"PeriodicalIF":0.5,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42189872","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
Large deviations of branching process in a random environment 随机环境中分支过程的大偏差
IF 0.5 Q4 MATHEMATICS, APPLIED Pub Date : 2021-08-01 DOI: 10.1515/dma-2021-0025
A. V. Shklyaev
Abstract In this first part of the paper we find the asymptotic formulas for the probabilities of large deviations of the sequence defined by the random difference equation Yn+1=AnYn + Bn, where A1, A2, … are independent identically distributed random variables and Bn may depend on {(Ak,Bk),0⩽k
摘要本文第一部分给出了由随机差分方程Yn+1=AnYn + Bn定义的序列的大偏差概率的渐近公式,其中A1, A2,…是独立的同分布随机变量,对于任意n≥1,Bn可能依赖于{(Ak,Bk),0≤k
{"title":"Large deviations of branching process in a random environment","authors":"A. V. Shklyaev","doi":"10.1515/dma-2021-0025","DOIUrl":"https://doi.org/10.1515/dma-2021-0025","url":null,"abstract":"Abstract In this first part of the paper we find the asymptotic formulas for the probabilities of large deviations of the sequence defined by the random difference equation Yn+1=AnYn + Bn, where A1, A2, … are independent identically distributed random variables and Bn may depend on {(Ak,Bk),0⩽k<n} $ {(A_k,B_k),0leqslant k lt n} $ for any n≥1. In the second part of the paper this results are applied to the large deviations of branching processes in a random environment.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"31 1","pages":"281 - 291"},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44535506","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: 4
On closed classes in partial k-valued logic that contain all polynomials 关于包含所有多项式的部分k值逻辑中的闭类
IF 0.5 Q4 MATHEMATICS, APPLIED Pub Date : 2021-08-01 DOI: 10.1515/dma-2021-0020
V. Alekseev
Abstract Let Polk be the set of all functions of k-valued logic representable by a polynomial modulo k, and let Int (Polk) be the family of all closed classes (with respect to superposition) in the partial k-valued logic containing Polk and consisting only of functions extendable to some function from Polk. Previously the author showed that if k is the product of two different primes, then the family Int (Polk) consists of 7 closed classes. In this paper, it is proved that if k has at least 3 different prime divisors, then the family Int (Polk) contains an infinitely decreasing (with respect to inclusion) chain of different closed classes.
摘要设Polk是可由多项式模k表示的k值逻辑的所有函数的集合,并且设Int(Polk)是包含Polk并且仅由可从Polk扩展到某个函数的函数组成的部分k值逻辑中的所有闭类(关于叠加)的族。先前作者证明,如果k是两个不同素数的乘积,那么Int(Polk)族由7个闭类组成。本文证明了如果k至少有3个不同的素数,则族Int(Polk)包含一个不同闭类的无限递减(关于包含)链。
{"title":"On closed classes in partial k-valued logic that contain all polynomials","authors":"V. Alekseev","doi":"10.1515/dma-2021-0020","DOIUrl":"https://doi.org/10.1515/dma-2021-0020","url":null,"abstract":"Abstract Let Polk be the set of all functions of k-valued logic representable by a polynomial modulo k, and let Int (Polk) be the family of all closed classes (with respect to superposition) in the partial k-valued logic containing Polk and consisting only of functions extendable to some function from Polk. Previously the author showed that if k is the product of two different primes, then the family Int (Polk) consists of 7 closed classes. In this paper, it is proved that if k has at least 3 different prime divisors, then the family Int (Polk) contains an infinitely decreasing (with respect to inclusion) chain of different closed classes.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"31 1","pages":"231 - 240"},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42312171","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
Collisions and incidence of vertices and components in the graph of k-fold iteration of the uniform random mapping 图中k次迭代的一致随机映射的顶点和分量的碰撞和关联
IF 0.5 Q4 MATHEMATICS, APPLIED Pub Date : 2021-08-01 DOI: 10.1515/dma-2021-0023
V. O. Mironkin
Abstract The probabilistic characteristics of the graph of k-fold iteration of uniform random mapping are studied. Formulas for the distribution of the length of the aperiodicity segment of an arbitrary vertex with some restrictions are calculated. We obtain exact expressions for the probabilities that two arbitrary vertices belong to the same connected component, that an arbitrary vertex belongs to the preimage set of another vertex and that there exists a collision in the considered graph.
摘要研究了均匀随机映射的k次迭代图的概率特征。在一定的限制条件下,计算了任意顶点的非周期段长度的分布公式。我们得到了两个任意顶点属于同一连通分量的概率、任意顶点属于另一个顶点的原像集的概率以及图中存在碰撞的概率的精确表达式。
{"title":"Collisions and incidence of vertices and components in the graph of k-fold iteration of the uniform random mapping","authors":"V. O. Mironkin","doi":"10.1515/dma-2021-0023","DOIUrl":"https://doi.org/10.1515/dma-2021-0023","url":null,"abstract":"Abstract The probabilistic characteristics of the graph of k-fold iteration of uniform random mapping are studied. Formulas for the distribution of the length of the aperiodicity segment of an arbitrary vertex with some restrictions are calculated. We obtain exact expressions for the probabilities that two arbitrary vertices belong to the same connected component, that an arbitrary vertex belongs to the preimage set of another vertex and that there exists a collision in the considered graph.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"31 1","pages":"259 - 269"},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48654805","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
Alphabetic points in compositions and words 作文和单词中的字母点
IF 0.5 Q4 MATHEMATICS, APPLIED Pub Date : 2021-08-01 DOI: 10.1515/dma-2021-0021
M. Archibald, A. Blecher, A. Knopfmacher
Abstract We use generating functions to account for alphabetic points (or the lack thereof) in compositions and words. An alphabetic point is a value j such that all the values to its left are not larger than j and all the values to its right are not smaller than j. We also provide the asymptotics for compositions and words which have no alphabetic points, as the size tends to infinity. This is achieved by the construction of upper and lower bounds which converge to each other, and in the latter case by probabilistic arguments.
我们使用生成函数来解释作文和单词中的字母点(或缺少字母点)。字母点是一个值j,使得它左边的所有值都不大于j,它右边的所有值都不小于j。我们还提供了没有字母点的组合和单词的渐近性,因为大小趋于无穷大。这是通过构造彼此收敛的上界和下界来实现的,在后一种情况下通过概率论证来实现。
{"title":"Alphabetic points in compositions and words","authors":"M. Archibald, A. Blecher, A. Knopfmacher","doi":"10.1515/dma-2021-0021","DOIUrl":"https://doi.org/10.1515/dma-2021-0021","url":null,"abstract":"Abstract We use generating functions to account for alphabetic points (or the lack thereof) in compositions and words. An alphabetic point is a value j such that all the values to its left are not larger than j and all the values to its right are not smaller than j. We also provide the asymptotics for compositions and words which have no alphabetic points, as the size tends to infinity. This is achieved by the construction of upper and lower bounds which converge to each other, and in the latter case by probabilistic arguments.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"31 1","pages":"241 - 250"},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45452622","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: 3
Frontmatter Frontmatter
IF 0.5 Q4 MATHEMATICS, APPLIED Pub Date : 2021-08-01 DOI: 10.1515/dma-2021-frontmatter4
{"title":"Frontmatter","authors":"","doi":"10.1515/dma-2021-frontmatter4","DOIUrl":"https://doi.org/10.1515/dma-2021-frontmatter4","url":null,"abstract":"","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":" ","pages":""},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47119490","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
Local limit theorems for generalized scheme of allocation of particles into ordered cells 广义粒子有序单元分配方案的局部极限定理
IF 0.5 Q4 MATHEMATICS, APPLIED Pub Date : 2021-08-01 DOI: 10.1515/dma-2021-0026
A. N. Timashev
Abstract A generalized scheme of allocation of n particles into ordered cells (components). Some statements containing sufficient conditions for the weak convergence of the number of components with given cardinality and of the total number of components to the negative binomial distribution as n → ∞ are presented as hypotheses. Examples supporting the validity of these statements in particular cases are considered. For some examples we prove local limit theorems for the total number of components which partially generalize known results on the convergence of this distribution to the normal law.
摘要一种将n个粒子分配到有序单元(组件)中的广义方案。一些含有给定基数的分量数和分量总数弱收敛于负二项分布的充分条件的语句为n→ ∞ 作为假设提出。考虑了在特定情况下支持这些陈述有效性的例子。对于一些例子,我们证明了分量总数的局部极限定理,这些定理部分地推广了关于该分布收敛到正态律的已知结果。
{"title":"Local limit theorems for generalized scheme of allocation of particles into ordered cells","authors":"A. N. Timashev","doi":"10.1515/dma-2021-0026","DOIUrl":"https://doi.org/10.1515/dma-2021-0026","url":null,"abstract":"Abstract A generalized scheme of allocation of n particles into ordered cells (components). Some statements containing sufficient conditions for the weak convergence of the number of components with given cardinality and of the total number of components to the negative binomial distribution as n → ∞ are presented as hypotheses. Examples supporting the validity of these statements in particular cases are considered. For some examples we prove local limit theorems for the total number of components which partially generalize known results on the convergence of this distribution to the normal law.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"31 1","pages":"293 - 307"},"PeriodicalIF":0.5,"publicationDate":"2021-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46045268","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
期刊
Discrete Mathematics and Applications
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
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