Sharp local LpL^p estimates for the Hermite eigenfunctions

We investigate the concentration of eigenfunctions for the Hermite operator $H=-\Delta+|x|^2$ in $\mathbb{R}^n$ by establishing local $L^p$ bounds over the compact sets with arbitrary dilations and translations. These new results extend the local estimates by Thangavelu and improve those derived from Koch-Tataru, and explain the special phenomenon that the global $L^p$ bounds decrease in $p$ when $2\le p\le \frac{2n+6}{n+1}$. The key $L^2$-estimates show that the local probabilities decrease away from the boundary $\{|x|=\lambda\}$, and then they satisfy Bohr's correspondence principle in any dimension. The proof uses the Hermite spectral projection operator represented by Mehler's formula for the Hermite-Schr\"odinger propagator $e^{-it H}$, and the strategy developed by Thangavelu and Jeong-Lee-Ryu. We also exploit an explicit version of the stationary phase lemma and H\"ormander's $L^2$ oscillatory integral theorem. Using Koch-Tataru's strategy, we construct appropriate examples to illustrate the possible concentrations and show the optimality of our local estimates.Comment: 35 pages, 6 figure

Multiple scattering effects on heavy meson production in p+A collisions at backward rapidity

We study the incoherent multiple scattering effects on heavy meson production in the backward rapidity region of p+A collisions within the generalized high-twist factorization formalism. We calculate explicitly the double scattering contributions to the heavy meson differential cross sections by taking into account both initial-state and final-state interactions, and find that these corrections are positive. We further evaluate the nuclear modification factor for muons that come form the semi-leptonic decays of heavy flavor mesons. Phenomenological applications in d+Au collisions at a center-of-mass energy $\sqrt{s}=200$ GeV at RHIC and in p+Pb collisions at $\sqrt{s}=5.02$ TeV at the LHC are presented. We find that incoherent multiple scattering can describe rather well the observed nuclear enhancement in the intermediate $p_T$ region for such reactions.Comment: 10 pages, 6 figures, published version in PL

Resilient neural network training for accelerators with computing errors

—With the advancements of neural networks, customized accelerators are increasingly adopted in massive AI applications. To gain higher energy efficiency or performance, many hardware design optimizations such as near-threshold logic or overclocking can be utilized. In these cases, computing errors may happen and the computing errors are difficult to be captured by conventional training on general purposed processors (GPPs). Applying the offline trained neural network models to the accelerators with errors directly may lead to considerable prediction accuracy loss. To address this problem, we explore the resilience of neural network models and relax the accelerator design constraints to enable aggressive design options. First of all, we propose to train the neural network models using the accelerators’ forward computing results such that the models can learn both the data and the computing errors. In addition, we observe that some of the neural network layers are more sensitive to the computing errors. With this observation, we schedule the most sensitive layer to the attached GPP to reduce the negative influence of the computing errors. According to the experiments, the neural network models obtained from the proposed training outperform the original models significantly when the CNN accelerators are affected by computing errors

Overgroups of the elementary unitary group in linear group over commutative rings

AbstractFor a commutative ring with identity, we give a complete description of all overgroups of the elementary unitary group EU2nR (n⩾5) in linear group GL2nR

Controllable Andreev retroreflection and specular Andreev reflection in a four-terminal graphene-superconductor hybrid system

We report the investigation of electron transport through a four-terminal graphene-superconductor hybrid system. Due to the quantum interference of the reflected holes from two graphene-superconductor interfaces with phase difference $\theta$, it is found that the specular Andreev reflection vanishes at $\theta=0$ while the Andreev retroreflection disappears at $\theta=\pi$. This means that the retroreflection and specular reflection can be easily controlled and separated in this device. In addition, due to the diffraction effect in the narrow graphene nanoribbon, the reflected hole can exit from both graphene terminals. As the width of nanoribbon increases, the diffraction effect gradually disappears and the reflected hole eventually exits from a particular graphene terminal depending on the type of Andreev reflection.Comment: 4 pages, 5 figure

Three-dimensional numerical study of flow characteristic and membrane fouling evolution in an enzymatic membrane reactor

In order to enhance the understanding of membrane fouling mechanism, the hydrodynamics of granular flow in a stirred enzymatic membrane reactor was numerically investigated in the present study. A three-dimensional Euler-Euler model, coupled with k-e mixture turbulence model and drag function for interphase momentum exchange, was applied to simulate the two-phase (fluid-solid) turbulent flow. Numerical simulations of single- or two-phase turbulent flow under various stirring speed were implemented. The numerical results coincide very well with some published experimental data. Results for the distributions of velocity, shear stress and turbulent kinetic energy were provided. Our results show that the increase of stirring speed could not only enlarge the circulation loops in the reactor, but it can also increase the shear stress on the membrane surface and accelerate the mixing process of granular materials. The time evolution of volumetric function of granular materials on the membrane surface has qualitatively explained the evolution of membrane fouling.Comment: 10 panges, 8 figure

Manipulation of pH Shift to Enhance the Growth and Antibiotic Activity of Xenorhabdus nematophila

To evaluate the effects of pH control strategy on cell growth and the production of antibiotic (cyclo(2-Me-BABA-Gly)) by Xenorhabdus nematophila and enhance the antibiotic activity. The effects of uncontrolled- (different initial pH) and controlled-pH (different constant pH and pH-shift) operations on cell growth and antibiotic activity of X. nematophila YL00I were examined. Experiments showed that the optimal initial pH for cell growth and antibiotic production of X. nematophila YL001 occurred at 7.0. Under different constant pH, a pH level of 7.5 was found to be optimal for biomass and antibiotic activity at 23.71 g/L and 100.0 U/mL, respectively. Based on the kinetic information relating to the different constant pH effects on the fermentation of X. nematophila YL001, a two-stage pH control strategy in which pH 6.5 was maintained for the first 24 h, and then switched to 7.5 after 24 h, was established to improve biomass production and antibiotic activity. By applying this pH-shift strategy, the maximal antibiotic activity and productivity were significantly improved and reaching 185.0 U/mL and 4.41 U/mL/h, respectively, compared to values obtained from constant pH operation (100.0 U/mL and 1.39 U/mL/h)