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

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

Information Potential Fields Navigation in Wireless Ad-Hoc Sensor Networks

As wireless sensor networks (WSNs) are increasingly being deployed in some important applications, it becomes imperative that we consider application requirements in in-network processes. We intend to use a WSN to aid information querying and navigation within a dynamic and real-time environment. We propose a novel method that relies on the heat diffusion equation to finish the navigation process conveniently and easily. From the perspective of theoretical analysis, our proposed work holds the lower constraint condition. We use multiple scales to reach the goal of accurate navigation. We present a multi-scale gradient descent method to satisfy users’ requirements in WSNs. Formula derivations and simulations show that the method is accurately and efficiently able to solve typical sensor network configuration information navigation problems. Simultaneously, the structure of heat diffusion equation allows more flexibility and adaptability in searching algorithm designs