Current Issue : October-December Volume : 2023 Issue Number : 4 Articles : 5 Articles
Vague graphs (VGs), which are a family of fuzzy graphs (FGs), are a well-organized and useful tool for capturing and resolving a range of real-world scenarios involving ambiguous data. In graph theory, a dominating set (DS) for a graph G∗ = ðX, EÞ is a subset S of the vertices X such that every vertex not in S is adjacent to at least one member of S. The concept of DS in FGs has received the attention of many researchers due to its many applications in various fields such as computer science and electronic networks. In this paper, we introduce the notion of ððϵ1, ϵ2Þ, 2Þ-Regular vague dominating set and provide some examples to explain various concepts introduced. Also, some results were discussed. Additionally, the ððϵ1, ϵ2Þ, 2Þ-Regular strong (weak) and independent strong (weak) domination sets for vague domination set (VDS) were presented with some theorems to support the context....
In article, I present a study on upper and lower statistical convergence, and upper and lower strong fractional weighted mean convergence by moduli for triple sequences. One of the generalizations of the discrete operator Cesàro, was weighted mean operators, which are linear operators, too. Given a modulus function f , I established that a triple sequence that is f -upper or lower strong fractional weighted mean convergent, in some supplementary conditions, is also f -lower or upper statistically convergent. The results of this paper adapt the results obtained in [1] and [2] to upper and lower strong fractional weighted mean convergence and to triple sequence concept. Furthermore, new concepts can be applied to the approximation theory, topology, Fourier analysis, analysis interdisciplinary with applications electrical engineering, robotics and other domains....
It is commonly accepted that, on social networks, the opinion of the agents with a higher connectivity, i.e. , a larger number of followers, results in more convincing than that of the agents with a lower number of followers. By kinetic modeling approach, a kinetic model of opinion formation on social networks is derived, in which the distribution function depends on both the opinion and the connectivity of the agents. The opinion exchange process is governed by a Sznajd type model with three opinions, ±1, 0, and the social network is represented statistically with connectivity denoting the number of contacts of a given individual. The asymptotic mean opinion of a social network is determined in terms of the initial opinion and the connectivity of the agents....
Based on the standard definition of the product (concatenation), the natural non-negative degree of the language is introduced. Root extraction is the reverse operation to it, and it can be defined in several different ways. Despite the simplicity of the formulation of the problem of extracting the root, the authors could not find any description of it in the literature (as well as on the Internet), including even its formulation. Most of the material in this article is devoted to the simplest version of the formulation: the root of the 2nd degree for the 1-letter alphabet, but many of the provisions of the article are generalized to more complex cases. Apparently, for a possible future description of a polynomial algorithm for solving at least one of the described statements of root extraction problems, it is first necessary to really analyze in detail such a special case, that is: either describe the necessary polynomial algorithm, or, conversely, show that the problem belongs to the class of NP-complete problems. Thus, in this article, we do not propose a polynomial algorithm for the problems under consideration; however, the models described here should help in constructing appropriate heuristic algorithms for their solution. A detailed description of the possible further application of such heuristic algorithms is beyond the scope of this article....
It is not generally known that the inequality that Bell derived using three random variables must be identically satisfied by any three corresponding data sets of ±1’s that are writable on paper. This surprising fact is not immediately obvious from Bell’s inequality derivation based on causal random variables, but follows immediately if the same mathematical operations are applied to finite data sets. For laboratory data, the inequality is identically satisfied as a fact of pure algebra, and its satisfaction is independent of whether the processes generating the data are local, non-local, deterministic, random, or nonsensical. It follows that if predicted correlations violate the inequality, they represent no three cross-correlated data sets that can exist, or can be generated from valid probability models. Reported data that violate the inequality consist of probabilistically independent data-pairs and are thus inconsistent with inequality derivation. In the case of random variables as Bell assumed, the correlations in the inequality may be expressed in terms of the probabilities that give rise to them. A new inequality is then produced: The Wigner inequality, that must be satisfied by quantum mechanical probabilities in the case of Bell experiments. If that were not the case, predicted quantum probabilities and correlations would be inconsistent with basic algebra....
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