• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제24권3호
• /
• pp.321-330
• /
• 2020

Data classification and clustering is one of the most common applications of the machine learning. In this paper, we aim to provide the insight of the classification for Turing pattern image, which has high nonlinearity, with feature engineering using the machine learning without a multi-layered algorithm. For a given image data X whose fixel values are defined in [-1, 1], X - X³ and ∇X would be more meaningful feature than X to represent the interface and bulk region for a complex pattern image data. Therefore, we use X - X³ and ∇X in the neural network and clustering algorithm to classification. The results validate the feasibility of the proposed approach.

• Kyungpook Mathematical Journal
• /
• 제62권2호
• /
• pp.243-256
• /
• 2022

In 1914, Bohr proved that there is an r₀ ∈ (0, 1) such that if a power series ∑^∞_m=0 c_mz^m is convergent in the open unit disc and |∑^∞_m=0 c_mz^m| < 1 then, ∑^∞_m=0 |c_mz^m| < 1 for |z| < r₀. The largest value of such r₀ is called the Bohr radius. In this article, we find Bohr radius for some univalent harmonic mappings having different dilatations. We also compute the Bohr radius for functions that are convex in one direction.

• International Journal of Advanced Culture Technology
• /
• 제10권4호
• /
• pp.86-93
• /
• 2022

To combine the science and technology creativity necessary in the era of the 4th Industrial Revolution, it is necessary to cultivate talents who can discover new knowledge and create new values by combining various knowledge with self-directed mathematical competencies. This research attempted to lay the foundation for the curriculum for fostering future creative convergence talent by preparing, executing, and reflecting on the learning plan after learners themselves understand their level and status through self-directed learning. Firstly, We would like to present a teaching-learning plan based on the essential capabilities of the future society, where the development of a curriculum based on mathematics curriculum and intelligent informatization are accelerated. Secondly, an educational design model system diagram was presented to strengthen the self-directed learning ability of mathematics subjects in the electronic engineering curriculum. Consequently, through a survey, we would like to propose the establishment of an educational system necessary for the 4th industry by analyzing learning ability through self-directed learning teaching methods of subjects related to mathematics, probability, and statistics.

• Nonlinear Functional Analysis and Applications
• /
• 제27권3호
• /
• pp.533-551
• /
• 2022

In this paper, we introduce several types 𝛼-𝜓 interpolative proximal contractions and provide some sufficient conditions to prove the existence of best proximity points for these contractions in metric spaces. In the case of proximal contraction of the first kind, these metric spaces are not necessarily complete. Meanwhile, some new results can derive from our results. Finally, some examples are provided to show the validity of our results.

• Advances in nano research
• /
• 제15권1호
• /
• pp.15-23
• /
• 2023

Dynamics of protein filamentous has been an active area of research since the last few decades as the role of cytoskeletal components, microtubules, intermediate filaments and microfilaments is very important in cell functions. During cell functions, these components undergo the deformations like bending, buckling and vibrations. In the present paper, bending and buckling of microfilaments are studied by using Euler Bernoulli beam theory with nonlocal parametric effects in conjunction. The obtained results show that the nonlocal parametric effects are not ignorable and the applications of nonlocal parameters well agree with the experimental verifications.

• Kyungpook Mathematical Journal
• /
• 제64권1호
• /
• pp.57-68
• /
• 2024

Let V₃(z, f) and 𝜎⁽¹⁾₃(z, f) be the cubic polynomials representing, respectively, the 3rd de la Vallée Poussin mean and the 3rd Cesàro mean of order 1 of a power series f(z). If 𝒦 denotes the usual class of convex univalent functions in the open unit disk centered at the origin, we show that, in general, V₃(z, f) ⊀ 𝜎⁽¹⁾₃(z,f), for all f ∈ 𝒦. Making use of polylogarithms, we identify a transformation, Λ : 𝒦 → 𝒦, such that V₃(z, Λ(f)) ≺ 𝜎⁽¹⁾₃(z, Λ(f)) for all f ∈ 𝒦. Here '≺' stands for subordination between two analytic functions.

• 호남수학학술지
• /
• 제46권2호
• /
• pp.267-278
• /
• 2024

In this paper, we investigate the uniqueness of a meromorphic function f(z) and its difference polynomial of difference operator with two sharing values counting multiplicities. Our two results improve and generalize the recent results of Barki Mahesh, Dyavanal Renukadevi S and Bhoosnurmath Subhas S [4] and for the case q ≥ 2, this allows for a highly unique generalization. To further demonstrate the validity of our main result, we provide an example.

• Steel and Composite Structures
• /
• 제42권3호
• /
• pp.389-396
• /
• 2022

This investigation in fluid mechanics surrounds around the variety of flow problems for different fluids along the stretching cylinder. Numerical procedure is carried out for the obtained resultant equations by Keller-Box technique. Numerical study of laminar, steady, viscous and incompressible two dimensional boundary layer flow of effects of suction and blowing on boundary layer slip flow of Casson fluid along permeable exponentially stretching cylinder has been carried out in the present draft. physical parameters i.e., Nusselt number and skin friction coefficient, suction parameter and the local Reynold number are investigated on velocity profile and elaborated through proper graphs and table.

• 한국수학교육학회지시리즈D:수학교육연구
• /
• 제12권2호
• /
• pp.143-149
• /
• 2008

Before the 14th century, China had been thought as one of the countries with the most developed mathematics all along. But after the 16th century, Chinese mathematics increasingly walked up to the eclipse. The main reasons include the following points. First, the development of neoteric mathematics was closely associated with the social industrialization, but the lags in feudal China seriously blocked the development of the capitalistic seed, and China was still in the agricultural society then and couldn't step into the industrial society, which impeded the development of mathematics concerned with the industry and commerce. Second. the increasingly carrion feudalization was one of the essential reasons to block the development of Chinese neoteric mathematics. Finally, seeing about the developing logics of Chinese neoteric mathematics, we can find it was a scattered and experiential mathematical knowledge without strict and rational self-organizing structure system, which had the limitations existing in its interior mechanism.

• Advances in nano research
• /
• 제9권4호
• /
• pp.251-261
• /
• 2020

In this article, vibration attributes of single walled carbon nanotubes based on Galerkin's method have been investigated. The influence of power law index subjected to different end supports has been overtly examined. Application of the Hamilton's variational principal leads to the formation of partial differential equations. The effects of different physical and material parameters on the fundamental frequencies are investigated for armchair and zigzag carbon nanotubes with clamped-clamped, simply supported and clamped-free boundary conditions. By using volume fraction for power law index, the fundamental natural frequency spectra for two forms of Single-Walled Carbon Nanotubes (SWCNTs) are calculated. The influence of frequencies against length-to-diameter ratios with varying power law index are investigated in detail for these tubes. MATLAB software package has been utilized for extracting tube frequency spectra. The obtained results are confirmed by comparing with available literature.