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

Performance Evaluation and Modeling of HPC I/O on Non-Volatile Memory

HPC applications pose high demands on I/O performance and storage capability. The emerging non-volatile memory (NVM) techniques offer low-latency, high bandwidth, and persistence for HPC applications. However, the existing I/O stack are designed and optimized based on an assumption of disk-based storage. To effectively use NVM, we must re-examine the existing high performance computing (HPC) I/O sub-system to properly integrate NVM into it. Using NVM as a fast storage, the previous assumption on the inferior performance of storage (e.g., hard drive) is not valid any more. The performance problem caused by slow storage may be mitigated; the existing mechanisms to narrow the performance gap between storage and CPU may be unnecessary and result in large overhead. Thus fully understanding the impact of introducing NVM into the HPC software stack demands a thorough performance study. In this paper, we analyze and model the performance of I/O intensive HPC applications with NVM as a block device. We study the performance from three perspectives: (1) the impact of NVM on the performance of traditional page cache; (2) a performance comparison between MPI individual I/O and POSIX I/O; and (3) the impact of NVM on the performance of collective I/O. We reveal the diminishing effects of page cache, minor performance difference between MPI individual I/O and POSIX I/O, and performance disadvantage of collective I/O on NVM due to unnecessary data shuffling. We also model the performance of MPI collective I/O and study the complex interaction between data shuffling, storage performance, and I/O access patterns.Comment: 10 page