Abstract: In this paper a mathematical proof of the new Binary-to-RNS Non-Coprime moduli set in RNS [1] of the form { 2n - 2, 2n, 2n + 2 } is presented. The modulies 2n - 2, 2n + 2 are known to be called conjugates of each other and has been discussed in previous literature [1 - 4]. Co-prime moduli sets are known to offer these benefits: 1) Large dynamic ranges. II) Fast RNS arithmetic. III) Simple and efficient RNS processing hardware. IV) Efficient weighted-to-RNS and RNS-to-Weighted converters. When comparing the Non-Coprime ones to them the DR (Dynamic Range) is the dominant. The dynamic range achieved by the set above is defined by the least common multiple ( LCM ) of the moduli and the non-coprime set was carefully chosen to do the mathematical calculations upon. This new non-coprime moduli set is unique and the only one of its shape.

• Publication Date: 10-Dec-2017
• DOI: 10.15224/978-1-63248-138-2-05
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Abstract: In this paper, structural and optical properties of undoped and sliver doped titanium dioxide film have been studied. By using Sol-gel method undoped and sliver doped titanium dioxide (TiO2) thin film synthesis on FTO glass substrate. Sliver has been doped 3%,7%, concentration in titanium dioxide (TiO2) .Different properties such as, crystal structure, phase identification, thickness, band gap, transmission and absorption spectrum have been studied using X-ray diffraction (XRD), Raman spectroscopy, UV/Vis spectrophotometry. The results showed that undoped and Ag doped TiO2 thin film annealed at 450oc had anatase phases and there is no Ag peaks in X-ray diffraction.

• Publication Date: 10-Dec-2017
• DOI: 10.15224/978-1-63248-138-2-06
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