A Novel Gesture-based CAPTCHA Design for Smart Devices

CAPTCHAs have been widely used in Web applications to prevent service abuse. With the evolution of computing environment from desktop computing to ubiquitous computing, more and more users are accessing Web applications on smart devices where touch based interactions are dominant. However, the majority of CAPTCHAs are designed for use on computers and laptops which do not reflect the shift of interaction style very well. In this paper, we propose a novel CAPTCHA design to utilise the convenience of touch interface while retaining the needed security. This is achieved through using a hybrid challenge to take advantages of human’s cognitive abilities. A prototype is also developed and found to be more user friendly than conventional CAPTCHAs in the preliminary user acceptance test

Geometric convexity of the generalized sine and the generalized hyperbolic sine

In the paper, the authors prove that the generalized sine function $\sin_{p,q}(x)$ and the generalized hyperbolic sine function $\sinh_{p,q}(x)$ are geometrically concave and geometrically convex, respectively. Consequently, the authors verify a conjecture posed in the paper "B. A. Bhayo and M. Vuorinen, On generalized trigonometric functions with two parameters, J. Approx. Theory 164 (2012), no.~10, 1415\nobreakdash--1426; Available online at \url{http://dx.doi.org/10.1016/j.jat.2012.06.003}".Comment: 5 page

Some sharp inequalities involving Seiffert and other means and their concise proofs

In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide concise proofs of some known inequalities and find some new sharp inequalities involving the Seiffert, contra-harmonic, centroidal, arithmetic, geometric, harmonic, and root-square means of two positive real numbers $a$ and $b$ with $a\ne b$.Comment: 10 page