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Symmetry, Volume 13, Issue 12

December 2021 - 221 articles

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Cover Story: Laws of large numbers (LLNs) are theorems of great importance for probability and chance theory. Within chance theory the notion of an uncertain random variable was defined to model phenomena where both uncertainty and randomness are present. This work considers uncertain random variables as functions of random variables and uncertain variables, introduced within uncertainty theory. Sequences of uncertain random variables are defined for a fixed continuous function, strictly monotone with respect to its second argument, as are sequences of pairwise independent or independent, identically distributed random variables and regular, independent, and identically distributed uncertain variables. Some LLNs for such defined sequences of uncertain random variables are formulated and proven. Two of their counterparts for uncertain variables are also discussed. View this paper

Articles (221)

  • Article
  • Open Access
2,449 Views
19 Pages

20 December 2021

In this paper, a new subspace gradient method is proposed in which the search direction is determined by solving an approximate quadratic model in which a simple symmetric matrix is used to estimate the Hessian matrix in a three-dimensional subspace....

  • Article
  • Open Access
5 Citations
3,885 Views
14 Pages

20 December 2021

The U-shaped metal bellows expansion joint compensates for the pipeline displacement by its own deformation. The compensation performance of the metal bellows in the initial stage of tension and compression deformation is unstable. In this paper, the...

  • Article
  • Open Access
12 Citations
3,106 Views
13 Pages

Modelling Artificial Immunization Processes to Counter Cyberthreats

  • Dmitry Zegzhda,
  • Evgeny Pavlenko and
  • Elena Aleksandrova

20 December 2021

This paper looks at the problem of cybersecurity in modern cyber-physical and information systems and proposes an immune-like approach to the information security of modern complex systems. This approach is based on the mathematical modeling in infor...

  • Article
  • Open Access
2,573 Views
17 Pages

20 December 2021

This article presents the methodology and tools to evaluate the reliability of quantitative sociological research data. The problem of filtering unreliable data is usually solved by statistical methods. This article proposes an improved method for fi...

  • Article
  • Open Access
2 Citations
2,325 Views
12 Pages

Stabilization of Periodical Discrete Feedback Control for Markov Jumping Stochastic Systems

  • Zhiyou Liu,
  • Lichao Feng,
  • Xinbin Li,
  • Zhigang Lu and
  • Xianhui Meng

19 December 2021

Motivated by the two strategies of intermittent control and discrete feedback control, this paper aims to introduce a periodically intermittent discrete feedback control in the drift part to stabilize an unstable Markov jumping stochastic differentia...

  • Article
  • Open Access
2 Citations
3,333 Views
16 Pages

Radius of Star-Likeness for Certain Subclasses of Analytic Functions

  • Caihuan Zhang,
  • Mirajul Haq,
  • Nazar Khan,
  • Muhammad Arif,
  • Khurshid Ahmad and
  • Bilal Khan

19 December 2021

In this paper, we investigate a normalized analytic (symmetric under rotation) function, f, in an open unit disk that satisfies the condition ℜfzgz>0, for some analytic function, g, with ℜz+1−2nzgz>0,∀n∈N. We calcula...

  • Article
  • Open Access
7 Citations
5,709 Views
12 Pages

18 December 2021

A multi-purpose image-based QR code is designed in this paper. There are four purposes for the generated image-based QR code. In the first purpose, the basic image-based QR code with the look of a host image is with an ingenious layout to be identifi...

  • Article
  • Open Access
7 Citations
2,830 Views
25 Pages

17 December 2021

In order to guide the optimization design of the nozzle of the aircraft-fixed gas fire extinguishing system, we studied the influence of nozzle geometric parameters including outlet–inlet area ratio, length–diameter aspect ratio, and wall...

  • Article
  • Open Access
11 Citations
3,073 Views
17 Pages

17 December 2021

The crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main purpose of this paper is to determine the crossing numbers of the join products of six symmetric graphs on six vertices with paths...

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