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On scatter properties of modular addition operation over imprimitivity systems of the translation group of the binary vector space 二元向量空间平移群非基系统上模加法运算的散射性质
IF 0.5 Q4 Mathematics Pub Date : 2023-06-01 DOI: 10.1515/dma-2023-0013
D. A. Burov
Abstract We study scatter properties of the modular addition operation for imprimitivity systems of the translation group of the binary vector space Vn = {0, 1}n. We describe all the subspaces of the space Vn that induce imprimitivity systems with worst possible scatter by the modular addition operation.
摘要我们研究了二元向量空间Vn={0,1}n平移群的有迹系统的模加法运算的散射性质。我们描述了空间Vn的所有子空间,这些子空间通过模加法运算引入了具有最差可能散射的无微性系统。
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引用次数: 0
On the equality problem of finitely generated classes of exponentially-polynomial functions 有限生成类指数多项式函数的等式问题
IF 0.5 Q4 Mathematics Pub Date : 2023-06-01 DOI: 10.1515/dma-2023-0015
S. Marchenkov
Abstract We consider the class EPℕ of exponentially-polynomial functions which can be obtained by arbitrary superpositions of the constants 0, 1 and arithmetic operations of addition, multiplication, and powering. For this class, we solve the algorithmic equality problem of two functions that assume a finite number of values. Next, this class is restricted to the class PEPℕ, in which the function xy is replaced by a sequence of functions { pix $begin{array}{} displaystyle p_i^x end{array}$}, where p0, p1, … are all prime numbers. For the class PEPℕ, the problem of membership of a function to a finitely generated class is effectively reduced to the equality problem of two functions. In turn, the last problem is effectively solved for the set of all one-place PEPℕ-functions.
摘要考虑一类指数多项式函数ep_1,该类函数可由常数0、1的任意叠加和加法、乘法、乘幂等算术运算得到。对于这门课,我们解决了两个假设有限个数的函数的算法等式问题。接下来,该类被限制为类PEP∈,其中函数xy被函数序列{pix$begin{array}{} displaystyle p_i^x end{array}$}取代,其中p0, p1,…都是素数。对于PEP类,将函数与有限生成类的隶属关系问题有效地简化为两个函数的相等问题。反过来,最后一个问题有效地解决了所有单位PEP -函数的集合。
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引用次数: 0
Fault-tolerant resolvability of some graphs of convex polytopes 一些凸多面体图的容错可分解性
IF 0.5 Q4 Mathematics Pub Date : 2023-06-01 DOI: 10.1515/dma-2023-0016
S. Sharma, H. Raza, V. K. Bhat
Abstract The fault-tolerant resolvability is an extension of metric resolvability in graphs with several intelligent systems applications, for example, network optimization, robot navigation, and sensor networking. The graphs of convex polytopes, which are rotationally symmetric, are essential in intelligent networks due to the uniform rate of data transformation to all nodes. A resolving set is an ordered set 𝕎 of vertices of a connected graph G in which the vector of distances to the vertices in 𝕎 uniquely determines all the vertices of the graph G. The minimum cardinality of a resolving set of G is known as the metric dimension of G. If 𝕎 ∖ ρ is also a resolving set for each ρ in 𝕎. In that case, 𝕎 is said to be a fault-tolerant resolving set. The fault-tolerant metric dimension of G is the minimum cardinality of such a set 𝕎. The metric dimension and the fault-tolerant metric dimension for three families of convex polytope graphs are studied. Our main results affirm that three families, as mentioned above, have constant fault-tolerant resolvability structures.
容错可解析性是度量可解析性在图中的扩展,在网络优化、机器人导航和传感器网络等智能系统中有广泛的应用。由于数据到所有节点的转换速率一致,凸多面体图是旋转对称的,在智能网络中是必不可少的。解析集是连通图G的顶点的有序集,其中到顶点的距离向量唯一地决定了图G的所有顶点。G的解析集的最小基数被称为G的度量维数。如果∈ρ也是中每个ρ的解析集。在这种情况下,说它是一个容错解析集。G的容错度量维数是这样一个集合的最小基数。研究了三种凸多面体图族的度量维数和容错度量维数。我们的主要结果证实,如上所述,三个家庭具有恒定的容错可解性结构。
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引用次数: 1
Mutually Orthogonal Latin Squares as Group Transversals 作为群截线的相互正交的拉丁正方形
IF 0.5 Q4 Mathematics Pub Date : 2023-03-01 DOI: 10.1515/dma-2023-0010
R. Pradhan, V. K. Jain
Abstract In this paper, we give a method to determine a complete set of mutually orthogonal Latin squares of order m, where m is an odd prime or power of a prime, as a group transversal of a Frobenius group.
摘要在本文中,我们给出了一种确定m阶相互正交的完备拉丁平方集的方法,其中m是奇素数或素数的幂,是Frobenius群的横切群。
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引用次数: 0
Criteria for maximal nonlinearity of a function over a finite field 有限域上函数最大非线性的判据
IF 0.5 Q4 Mathematics Pub Date : 2023-03-01 DOI: 10.1515/dma-2023-0012
V. G. Ryabov
Abstract An n-place function over a field with q elements is called maximally nonlinear if it has the greatest nonlinearity among all such functions. Criteria and necessary conditions for maximal nonlinearity are obtained, which imply that, for even n, the maximally nonlinear functions are bent functions, but, for q > 2, the known families of bent functions are not maximally nonlinear. For an arbitrary finite field, a relationship between the Hamming distances from a function to all affine mappings and the Fourier spectra of the nontrivial characters of the function are found.
具有q个元素的域上的n位函数如果在所有这些函数中具有最大的非线性,则称为最大非线性。得到了最大非线性的判据和必要条件,这意味着,对于偶数n,最大非线性函数是bent函数,而对于q > 2,已知的bent函数族不是最大非线性的。对于任意有限域,得到了函数到所有仿射映射的Hamming距离与函数非平凡特征的傅立叶谱之间的关系。
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引用次数: 1
Decomposition of polynomials using the shift-composition operation 多项式的移位合成分解
IF 0.5 Q4 Mathematics Pub Date : 2023-03-01 DOI: 10.1515/dma-2023-0009
V. Nozdrunov
Abstract V. I. Solodovnikov had employed the shift-composition operation to investigate homomorphisms of shift registers into linear automata; in his papers, conditions for the absence of nontrivial inner homomorphisms of shift registers were derived. An essential role was played by the condition of linearity of the left component of the shift-composition operation in the corresponding polynomial decomposition. In this paper we consider the case where the left component is a function belonging to a wider class, which includes the class of linear functions.
摘要V.I.Solodovnikov利用移位合成运算将移位寄存器的同态研究成线性自动机;在他的论文中,导出了移位寄存器不存在非平凡内同态的条件。移位合成运算的左分量的线性条件在相应的多项式分解中发挥了重要作用。在本文中,我们考虑左分量是属于更广泛类的函数的情况,该类包括线性函数类。
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引用次数: 0
Explicit basis for admissible rules in K-saturated tabular logics K饱和表逻辑中可容许规则的显式基
IF 0.5 Q4 Mathematics Pub Date : 2023-03-01 DOI: 10.1515/dma-2023-0011
V. V. Rimatskiĭ
Abstract We construct an explicit finite basis for admissible rules in K-saturated tabular logics that extend the logic Grz.
本文构造了k饱和表逻辑中可容许规则的显式有限基,扩展了逻辑Grz。
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引用次数: 0
On the existence of special nonlinear invariants for round functions of XSL-ciphers XSL密码的圆函数的特殊非线性不变量的存在性
IF 0.5 Q4 Mathematics Pub Date : 2023-03-01 DOI: 10.1515/dma-2023-0007
D. Burov
Abstract Nonlinear invariants of round transformations in XSL-schemes are studied. The emphasis is on invariants which may be found by means of the approach suggested at the conference ASIACRYPT 2016. Some known results on the inertia groups of decomposable functions are used to describe conditions on S-boxes and matrices of XSL-schemes which are necessary for the existence of such invariants. It is shown that for a number of schemes these conditions are not satisfied.
摘要研究了xsl格式中圆变换的非线性不变量。重点是可以通过2016年ASIACRYPT会议上建议的方法找到的不变量。利用可分解函数惯性群的一些已知结果,描述了s -box和xsl - schema矩阵上存在这种不变量所必需的条件。结果表明,对于许多方案,这些条件是不满足的。
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引用次数: 1
Frontmatter 头版头条
Q4 Mathematics Pub Date : 2023-03-01 DOI: 10.1515/dma-2023-frontmatter2
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引用次数: 0
Asymptotic local probabilities of large deviations for branching process in random environment with geometric distribution of descendants 子体几何分布随机环境中分支过程大偏差的渐近局部概率
IF 0.5 Q4 Mathematics Pub Date : 2023-03-01 DOI: 10.1515/dma-2023-0008
Konstantin Yu. Denisov
Abstract We consider the branching process Zn=Xn,1+⋯+XnZn−1 $ Z_{n} =X_{n, 1} + dotsb +X_{nZ_{n-1}} $, in random environmentsη, where η is a sequence of independent identically distributedvariables, for fixed η the random variables Xi, j areindependent, have the geometric distribution. We suppose that the associated random walk Sn=ξ1+⋯+ξn $ S_n = xi_1 + dotsb + xi_n $ has positive meanμ,0 < h (μ;μ+) and someμ+.
摘要我们考虑了在随机环境η中的分支过程Zn=Xn,1+…+XnZn−1$Z_{n}=X_{n,1}+dotsb+X_{nZ_{n-1}}$,其中η是独立的同分布变量序列,对于固定的η,随机变量Xi,j是独立的,具有几何分布。我们假设相关的随机行走Sn=ξ1+ξ+ξn$S_n=xi_1+dotsb+xi_n$具有正平均μ  μ+)和一些μ+。
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引用次数: 0
期刊
Discrete Mathematics and Applications
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