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    Jones polynomial for graphs of twist knots
    (PRAIRIE VIEW A & M UNIV, DEPT MATHEMATICS, 2019) Şahin, Abdulgani.; Şahin, Bünyamin.
    We frequently encounter knots in the flow of our daily life. Either we knot a tie or we tie a knot on our shoes. We can even see a fisherman knotting the rope of his boat. Of course, the knot as a mathematical model is not that simple. These are the reflections of knots embedded in three-dimensional space in our daily lives. In fact, the studies on knots are meant to create a complete classification of them. This has been achieved for a large number of knots today. But we cannot say that it has been terminated yet. There are various effective instruments while carrying out all these studies. One of these effective tools is graphs. Graphs are have made a great contribution to the development of algebraic topology. Along with this support, knot theory has taken an important place in low dimensional manifold topology. In 1984, Jones introduced a new polynomial for knots. The discovery of that polynomial opened a new era in knot theory. In a short time, this polynomial was defined by algebraic arguments and its combinatorial definition was made. The Jones polynomials of knot graphs and their applications were introduced by Murasugi. T. Ugur and A. Kopuzlu found an algorithm for the Jones polynomials of torus knots K(2, q) in 2006. In this paper, first of all, it has been obtained signed graphs of the twist knots which are a special family of knots. We subsequently compute the Jones polynomials for graphs of twist knots. We will consider signed graphs associated with each twist knot diagrams.
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    Variation of the key morphological, structural, optical and electrical properties of SILAR CdO with alkaline earth Ca2+ ions doping
    (ELSEVIER SCI LTD, 2019) Şahin, Bünyamin.; Aydın, Raşit.; Çetin, Hidayet.
    Pristine and alkaline earth Ca2+ ions doped (CaxCd1-xO (0 <= x <= 0.025)) CdO films were fabricated by SILAR technique on the soda lime glass substrates. The influence of increasing Ca content on the morphological, structural, optical and electrical properties of deposited films was analyzed. Metallurgical Microscope (MM), Scanning Electron Microscope (SEM) and Atomic Force Microscopy (AFM) images of the samples exhibited that the morphology was dramatically changed with the addition of Ca to the synthesis solution when compared to the pristine CdO film. Energy Dispersive Spectrometry (EDS) analyses confirmed the presence of Ca in the doped films. X-ray diffraction (XRD) analysis of the pristine and Ca-doped CdO films exhibited cubic crystalline structure with preferred orientation of (111) and (200) direction. The existence of chemical bonding was confirmed by Fourier Transform Infrared Spectroscopy (FTIR) study. Optical studies revealed that the energy band gap were dependent on Ca-doping content in accordance with both Vegard's relation and Tauc's law calculations. The impedance analysis and four-point probe measurement results of CdO thin films were studied. Sheet resistances of the thin films were increased by Ca doping up to doping level of 1.5%. Further doping level causes degradation in sheet resistance.