Using COMSOL Multiphysics To Simulate Radiation from Dipole Antenna and First Iteration Cantor Set Shape Antenna

The method of electromotive force (emf) for calculation of antenna impedance is applicable to a very limited number of antenna configurations such as monopole and dipole antenna. In more general antenna structures, especially when complicated geometry such as fractals is involved numerical techniques are essential. There are Electromagnetic (EM) simulation softwares such as G-NEC, XFDTD for the modelling studies in which is essential an understanding of the fundamental theory behind these numerical techniques in creating the antenna models. In this paper, we compare the radiation from dipole antenna and the antenna with shape of the first iteration of Cantor set. The simulation of this problem has been done by COMSOL Multi-physics software

The impact of words in mathematics education – Case of ‎symbols

The development of standardized forms of symbolic notation is a long and complicated process and the selection of symbolic notation is frequently based on factors other than merit. As multiple representations are common in math education, we examined a different representation of the symbol in mathematics education. In a teaching experiment, we investigated whether participants benefit from words instead of standard symbols and whether the different representation affects performance. For the teaching experiment, students were divided into two groups: the "word" group, and the "sign" group. We utilized words instead of the formal symbol in the "word" group and examined student's understanding and mathematics reasoning. Results indicate that the multiple symbolic representations (word instead of sign) are helpful. The study also indicates that some math symbols may mislead students. According to sociocultural perspectives and linguistic approaches, our study illustrates that using words instead of formal symbols improves student's understanding and reasoning and indicates that the use of words can block common errors made by students. This research emphasizes the importance of various forms of multiple representations in mathematics learning

F(ψ,φ) F(ψ,φ)F(\psi,\varphi)-Contractions for α-admissible mappings on M-metric spaces

Abstract In this paper, we introduce certain α-admissible mappings which are F(ψ,φ) $F(\psi,\varphi)$-contractions on M-metric spaces, and we establish some fixed point results. Our results generalize and extend some well-known results on this topic in the literature

The impact of words in mathematics education – Case of ‎symbols

The development of standardized forms of symbolic notation is a long and complicated process and the selection of symbolic notation is frequently based on factors other than merit. As multiple representations are common in math education, we examined a different representation of the symbol in mathematics education. In a teaching experiment, we investigated whether participants benefit from words instead of standard symbols and whether the different representation affects performance. For the teaching experiment, students were divided into two groups: the "word" group, and the "sign" group. We utilized words instead of the formal symbol in the "word" group and examined student's understanding and mathematics reasoning. Results indicate that the multiple symbolic representations (word instead of sign) are helpful. The study also indicates that some math symbols may mislead students. According to sociocultural perspectives and linguistic approaches, our study illustrates that using words instead of formal symbols improves student's understanding and reasoning and indicates that the use of words can block common errors made by students. This research emphasizes the importance of various forms of multiple representations in mathematics learning