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Discrete Mathematics and Applications最新文献

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Limit theorem for stationary distribution of a critical controlled branching process with immigration 有移民的临界受控分支过程静态分布的极限定理
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-10-01 DOI: 10.1515/dma-2023-0030
Vladimir I. Vinokurov
{"title":"Limit theorem for stationary distribution of a critical controlled branching process with immigration","authors":"Vladimir I. Vinokurov","doi":"10.1515/dma-2023-0030","DOIUrl":"https://doi.org/10.1515/dma-2023-0030","url":null,"abstract":"Abstract We consider the sequence {ξn,t}t≥1 of controlled critical branching processes with immigration, where n = 1, 2, … is an integer parameter limiting the population size. It is shown that for n → ∞ the stationary distributions of considered branching processes normalized by n $begin{array}{} sqrt{n} end{array} $ converge to the distribution of a random variable whose square has a gamma distribution.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"6 1","pages":"325 - 337"},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139328386","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
Limit theorem for a smoothed version of the spectral test for testing the equiprobability of a binary sequence 用于检验二进制序列等概率的平滑版频谱检验的极限定理
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-10-01 DOI: 10.1515/dma-2023-0029
M. P. Savelov
{"title":"Limit theorem for a smoothed version of the spectral test for testing the equiprobability of a binary sequence","authors":"M. P. Savelov","doi":"10.1515/dma-2023-0029","DOIUrl":"https://doi.org/10.1515/dma-2023-0029","url":null,"abstract":"Abstract We consider the problem of testing the hypothesis that the tested sequence is a sequence of independent random variables that take values 1 and –1 with equal probability. To solve this problem, the Discrete Fourier Transform (spectral) test of the NIST package uses the statistic TFourier, the exact limiting distribution of which is unknown. In this paper a new statistic is proposed and its limiting distribution is established. This new statistic is a slight modification of TFourier. A hypothesis about the limit distribution of TFourier is formulated, which is confirmed by numerical experiments presented by Pareschi F., Rovatti R. and Setti G.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"7 1","pages":"317 - 323"},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139330293","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
Classes of piecewise-quasiaffine transformations on the generalized 2-group of quaternions 广义四元组 2 上的片断-四元变换类
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-10-01 DOI: 10.1515/dma-2023-0028
B. Pogorelov, M. Pudovkina
{"title":"Classes of piecewise-quasiaffine transformations on the generalized 2-group of quaternions","authors":"B. Pogorelov, M. Pudovkina","doi":"10.1515/dma-2023-0028","DOIUrl":"https://doi.org/10.1515/dma-2023-0028","url":null,"abstract":"Abstract The class of nonabelian 2-groups H with cyclic subgroup of index 2 includes the dihedral group, the generalized quaternion group, the semidihedral group, and the modular maximal cyclic group, which have many various applications in discrete mathematics and cryptography. We introduce piecewise-quasiaffine transformations on a group H, and put forward criteria of their bijectivity. For the generalized group of quaternions of order 2m, we obtain a complete classification of orthomorphisms, complete transformations, and their left analogues in the class of piecewise-quasiaffine transformations under consideration. We also evaluate their cardinalities.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"5 1","pages":"299 - 316"},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139330860","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 polynomial-modular recursive sequences 关于多项式模块递归序列
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-10-01 DOI: 10.1515/dma-2023-0027
S. Marchenkov
{"title":"On polynomial-modular recursive sequences","authors":"S. Marchenkov","doi":"10.1515/dma-2023-0027","DOIUrl":"https://doi.org/10.1515/dma-2023-0027","url":null,"abstract":"Abstract We consider recursive sequences over the set of integers, where as rules of generation we take arbitrary superpositions of polynomial functions and the function |x|; such sequences are referred to as polynomial-modular recursive sequences. We show how evaluations on three-tape Minsky machines can be simulated via polynomial-modular recursive sequences. Based on this result, we formulate algorithmically unsolvable problems related to polynomial-modular recursive sequences. We also consider recursive sequences in which the rules of generation are functions formed by some superpositions of polynomial functions and the function [x]. $begin{array}{} displaystyle [sqrt{x}]. end{array}$ For the set of such recursive sequences, an algorithmically unsolvable problem is indicated.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"25 1","pages":"293 - 298"},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139328931","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 algebraicity of lattices of ω-fibred formations of finite groups 论有限群的ω纤维阵的网格代数性
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-10-01 DOI: 10.1515/dma-2023-0026
Serafim P. Maksakov, M. Sorokina
{"title":"On algebraicity of lattices of ω-fibred formations of finite groups","authors":"Serafim P. Maksakov, M. Sorokina","doi":"10.1515/dma-2023-0026","DOIUrl":"https://doi.org/10.1515/dma-2023-0026","url":null,"abstract":"Abstract For a nonempty set ω of primes, V. A. Vedernikov had constructed ω-fibred formations of groups via function methods. We study lattice properties of ω-fibred formations of finite groups with direction δ satisfying the condition δ0 ≤ δ. The lattice ωδFθ of all ω-fibred formations with direction δ and θ-valued ω-satellite is shown to be algebraic under the condition that the lattice of formations θ is algebraic. As a corollary, the lattices ωδF, ωδFτ, τωδF, ωδnF of ω-fibred formations of groups are shown to be algebraic.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"67 1","pages":"283 - 291"},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139330317","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 small distance-regular graphs with the intersection arrays {mn − 1, (m − 1)(n + 1), n − m + 1; 1, 1, (m − 1)(n + 1)} 在具有交集阵列 {mn - 1, (m - 1)(n + 1), n - m + 1; 1, 1, (m - 1)(n + 1)} 的小型距离不规则图上
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-10-01 DOI: 10.1515/dma-2023-0025
A. Makhnev, M. P. Golubyatnikov
{"title":"On small distance-regular graphs with the intersection arrays {mn − 1, (m − 1)(n + 1), n − m + 1; 1, 1, (m − 1)(n + 1)}","authors":"A. Makhnev, M. P. Golubyatnikov","doi":"10.1515/dma-2023-0025","DOIUrl":"https://doi.org/10.1515/dma-2023-0025","url":null,"abstract":"Abstract Let Γ be a diameter 3 distance-regular graph with a strongly regular graph Γ3, where Γ3 is the graph whose vertex set coincides with the vertex set of the graph Γ and two vertices are adjacent whenever they are at distance 3 in the graph Γ. Computing the parameters of Γ3 by the intersection array of the graph Γ is considered as the direct problem. Recovering the intersection array of the graph Γ by the parameters of Γ3 is referred to as the inverse problem. The inverse problem for Γ3 has been solved earlier by A. A. Makhnev and M. S. Nirova. In the case where Γ3 is a pseudo-geometric graph of a net, a series of admissible intersection arrays has been obtained: {c2(u2 − m2) + 2c2m − c2 − 1, c2(u2 − m2), (c2 − 1)(u2 − m2) + 2c2m − c2; 1, c2, u2 − m2} (A. A. Makhnev, Wenbin Guo, M. P. Golubyatnikov). The cases c2 = 1 and c2 = 2 have been examined by A. A. Makhnev, M. P. Golubyatnikov and A. A. Makhnev, M. S. Nirova, respectively. In this paper in the class of graphs with the intersection arrays {mn − 1, (m − 1)(n + 1)}, {n − m + 1}; 1, 1, (m − 1)(n + 1)} all admissible intersection arrays for {3 ≤ m ≤ 13} are found: {20,16,5; 1, 1,16}, {39,36,4; 1, 1,36}, {55,54,2; 1, 2,54}, {90,84,7; 1, 1,84}, {220,216,5; 1, 1,216}, {272,264,9; 1, 1,264} and {350,336,15; 1, 1,336}. It is demonstrated that graphs with the intersection arrays {20,16,5; 1, 1,16}, {39,36,4; 1, 1,36} and {90,84,7; 1, 1,84} do not exist.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"218 1","pages":"273 - 281"},"PeriodicalIF":0.5,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139331533","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
Nonlinearity of functions over finite fields 有限域上函数的非线性
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-08-01 DOI: 10.1515/dma-2023-0021
V. G. Ryabov
{"title":"Nonlinearity of functions over finite fields","authors":"V. G. Ryabov","doi":"10.1515/dma-2023-0021","DOIUrl":"https://doi.org/10.1515/dma-2023-0021","url":null,"abstract":"Abstract The nonlinearity and additive nonlinearity of a function are defined as the Hamming distances, respectively, to the set of all affine mappings and to the set of all mappings having nontrivial additive translators. On the basis of the revealed relation between the nonlinearities and the Fourier coefficients of the characters of a function, convenient formulas for nonlinearity evaluation for practically important classes of functions over an arbitrary finite field are found. In the case of a field of even characteristic, similar results were obtained for the additive nonlinearity in terms of the autocorrelation coefficients. The formulas obtained made it possible to present specific classes of functions with maximal possible and high nonlinearity and additive nonlinearity.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"33 1","pages":"231 - 246"},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48978494","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
Short complete diagnostic tests for circuits with two additional inputs in some basis 在某些基础上对具有两个附加输入的电路进行完整的短路诊断测试
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-08-01 DOI: 10.1515/dma-2023-0020
K. A. Popkov
{"title":"Short complete diagnostic tests for circuits with two additional inputs in some basis","authors":"K. A. Popkov","doi":"10.1515/dma-2023-0020","DOIUrl":"https://doi.org/10.1515/dma-2023-0020","url":null,"abstract":"Abstract We prove that any Boolean function in n variables can be modeled by a testable Boolean circuit with two additional inputs in the basis “conjunction, oblique conjunction, disjunction, negation” so that the circuit admits a complete diagnostic test of the length at most 2n + 3 with respect to stuck-at faults of the type 1 at gate outputs.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"33 1","pages":"219 - 230"},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41403232","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 properties of multiaffine predicates on a finite set 关于有限集上多仿射谓词的性质
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-08-01 DOI: 10.1515/dma-2023-0023
S. Selezneva
{"title":"On properties of multiaffine predicates on a finite set","authors":"S. Selezneva","doi":"10.1515/dma-2023-0023","DOIUrl":"https://doi.org/10.1515/dma-2023-0023","url":null,"abstract":"Abstract We consider predicates on a finite set that are invariant with respect to an affine operation fG, where G is some Abelian group. Such predicates are said to be multiaffine for the group G. Special attention is paid to predicates that are affine for a group Gq of addition modulo q=ps, where p is a prime number and s=1. We establish the predicate multiaffinity criterion for a group Gq. Then we introduce disjunctive normal forms (DNF) for predicates on a finite set and obtain properties of DNFs of predicates that are multiaffine for a group Gq. Finally we show how these properties can be used to design a polynomial algorithm that decides satisfiability of a system of predicates which are multiaffine for a group Gq, if predicates are specified by DNF.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"33 1","pages":"259 - 267"},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47853471","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 limit joint distributions of statistics of three tests of the NIST package NIST软件包三次测试统计的极限联合分布
IF 0.5
Discrete Mathematics and Applications Pub Date : 2023-08-01 DOI: 10.1515/dma-2023-0022
Maksim P. Savelov
{"title":"The limit joint distributions of statistics of three tests of the NIST package","authors":"Maksim P. Savelov","doi":"10.1515/dma-2023-0022","DOIUrl":"https://doi.org/10.1515/dma-2023-0022","url":null,"abstract":"Abstract For sequences of independent random variables having a Bernoulli distribution the joint distribution and the limit joint distribution of statistics of three tests of the NIST statistical package («Monobit Test», «Frequency Test within a Block», and «Cumulative Sums Test») are obtained. In the case when two blocks are used in «Frequency Test within a Block», pairwise covariance of these statistics is given.","PeriodicalId":11287,"journal":{"name":"Discrete Mathematics and Applications","volume":"33 1","pages":"247 - 257"},"PeriodicalIF":0.5,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43618843","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
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