29,751 research outputs found
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 and with .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
and the generalized hyperbolic sine function
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 usersβ 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
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