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We prove a new characterization of weakly regular ternary bent functions via partial difference sets. Partial difference sets are combinatorial objects corresponding to strongly regular graphs. Using known families of bent functions, we obtain in this way new families of strongly regular graphs, some of which were previously unknown. One of the families includes an example in [N. Hamada, T. Helleseth, A characterization of some {3v 2 + v 3 , 3v 1 + v 2 , 3, 3}-minihypers and some [15, 4, 9; 3]-codes with B 2 = 0, J. Statist.Plann. Inference 56 (1996) 129-146], which was considered to be sporadic; using our results, this strongly regular graph is now a member of an infinite family. Moreover, this paper contains a new proof that the Coulter-Matthews and ternary quadratic bent functions are weakly regular.

The present study demonstrated that perceived urban built environment attributes significantly correlate with leisure-time physical activity in Hangzhou, China.

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In this paper, we generalize the construction of strongly regular graphs in Tan et al. (J. Comb. Theory, Ser. A 117:668-682, 2010) from ternary bent functions to p-ary bent functions, where p is an odd prime. We obtain strongly regular graphs with three types of parameters. Using certain non-quadratic p-ary bent functions, our constructions can give rise to new strongly regular graphs for small parameters.

We present a carbon-nanotube-deposited long period fiber grating for refractive index sensing applications in liquid. Carbon nanotubes are deposited around the surface of a long period fiber grating to form the refractive index sensing element. The sensing mechanism relies mainly on the high refractive index properties of the carbon nanotube thin film, which enhances the cladding mode of the long period fiber grating in order to have a significant interaction between the propagating light and the target medium. A sensitivity of 31 dB/ RIU and 47 dB/ RIU are obtained for the refractive index ranges of 1.33 to 1.38 and 1.38 to 1.42, respectively, which have not been demonstrated with normal long period fiber gratings as the sensing element. As the sensing mechanism is based on the change of the transmitted optical power, our proposed scheme can intrinsically solve the limitations of the free spectral range commonly seen in other reported schemes, and continuous and repeatable measurements can be obtained while only acquiring errors mainly from the power fluctuations from the light source. The fiber grating also does not require any further mechanical modification like etching or tapering, which allows the sensing *Manuscript Click here to view linked References Y. C. Tan et. al., "Carbon-Nanotube-Deposited Long Period Fiber Grating ……" p. 2 element to have the advantage of mechanical strength for practical applications. The experimental results are consistent with the modeling of the sensing mechanism.

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