Temperature dependent friction and wear of magnetron sputtered coating TiAlN/VN

In this paper, a magnetron sputtered nano-structured multilayer coating TiAlN/VN, grown on hardened tool steel substrate, has been investigated in un-lubricated ball-on-disk sliding tests against an alumina counterface, to study the friction and wear behaviours at a broad range of testing temperatures from 25 to 700 ◦C, followed by comprehensive analysis of the worn samples using FEG-SEM, cross-sectional TEM, EDX, as well as micro/nano indentations. The experiment results indicated significant temperature dependent friction and wear properties of the coating investigated. Below 100 ◦C, the coating showed low friction coefficient at �≤0.6 and low wear rate in the scale of 10−17m3 N−1m−1 dominated by mild oxidation wear. From 100 to 200 ◦C, a progressive transition to higher friction coefficient occurred. After that, the coating exhibited high friction of �= 0.9 at temperatures between 200 and 400 ◦C, and simultaneously higher wear rates of (10−16 to 10−15) m3 N−1m−1. The associated wear mechanism changed to severe wear dominated by cracking and spalling. From 500 ◦C and so on, accelerated oxidation of the TiAlN/VN became the controlling process. This led first to the massive generation of oxide debris and maximum friction of �= 1.1 at 500 ◦C, and then to fast deterioration of the coating despite the lowest friction coefficient of �< 0.3 at 700 ◦C

On the Hecke Eigenvalues of Maass Forms

Let $\phi$ denote a primitive Hecke-Maass cusp form for $\Gamma_o(N)$ with the Laplacian eigenvalue $\lambda_\phi=1/4+t_{\phi}^2$. In this work we show that there exists a prime $p$ such that $p\nmid N$, $|\alpha_{p}|=|\beta_{p}| = 1$, and $p\ll(N(1+|t_{\phi}|))^c$, where $\alpha _{p},\;\beta _{p}$ are the Satake parameters of $\phi$ at $p$, and $c$ is an absolute constant with $0<c<1$. In fact, $c$ can be taken as $0.27332$. In addition, we prove that the natural density of such primes $p$ ($p\nmid N$ and $|\alpha_{p}|=|\beta_{p}| = 1$) is at least $34/35$.Comment: Version 2: typos corrected and a new section on natural density adde

Multi-consensus Decentralized Accelerated Gradient Descent

This paper considers the decentralized optimization problem, which has applications in large scale machine learning, sensor networks, and control theory. We propose a novel algorithm that can achieve near optimal communication complexity, matching the known lower bound up to a logarithmic factor of the condition number of the problem. Our theoretical results give affirmative answers to the open problem on whether there exists an algorithm that can achieve a communication complexity (nearly) matching the lower bound depending on the global condition number instead of the local one. Moreover, the proposed algorithm achieves the optimal computation complexity matching the lower bound up to universal constants. Furthermore, to achieve a linear convergence rate, our algorithm \emph{doesn't} require the individual functions to be (strongly) convex. Our method relies on a novel combination of known techniques including Nesterov's accelerated gradient descent, multi-consensus and gradient-tracking. The analysis is new, and may be applied to other related problems. Empirical studies demonstrate the effectiveness of our method for machine learning applications

Estimate for the 0++0^{++} glueball mass in QCD

We obtain accurate result for the lightest glueball mass of QCD in 3 dimensions from lattice Hamiltonian field theory. Using the dimensional reduction argument, a good approximation for confining theories, we suggest that the $0^{++}$ glueball mass in 3+1 dimensional QCD be about $1.71$ GeV.Comment: 10 Latex page