Regularity Criteria for Navier-Stokes Equations with Slip Boundary Conditions on Non-flat Boundaries via Two Velocity Components

H.-O. Bae and H.J. Choe, in a 1997 paper, established a regularity criteria for the incompressible Navier-Stokes equations in the whole space $\R^3$ based on two velocity components. Recently, one of the present authors extended this result to the half-space case $\R^3_+\,.$ Further, this author in collaboration with J. Bemelmans and J. Brand extended the result to cylindrical domains under physical slip boundary conditions. In this note we obtain a similar result in the case of smooth arbitrary boundaries, but under a distinct, apparently very similar, slip boundary condition. They coincide just on flat portions of the boundary. Otherwise, a reciprocal reduction between the two results looks not obvious, as shown in the last section below.Comment: 15 page

Exploring Dynamic Development of Listening Comprehension Difficulties: A Longitudinal Case Study of EFL Learners

 This study employed Dynamic Systems Theory to investigate the Listening Comprehension Difficulties (LCD) trajectories of two EFL learners. Through a longitudinal case study spanning a semester, LCD in five listening tasks was assessed using four indicators: vocabulary difficulties, familiar word difficulties, weak form difficulties, and chunk difficulties. Key findings included: 1) distinct nonlinear and intricate trajectories were observed for both learners, diverging from group averages; 2) semi-structured interview showed that individual pathways were influenced by interwoven factors including environmental variables (language policy, linguistic milieu, learning environment, etc.), linguistic factors (task complexity, language apprehension, native language transfer, etc.), and individual differences (e.g., self-regulation strategies, language anxiety, etc.)

Analyzing perceived value among immigrants to develop a marketing approach

Over the past decade, the world has witnessed a huge growth rate on immigrants. As immigrants holding with divergent backgrounds, leading to disparate identities and self-value, a luxury firm need to consider cultural diversity not only at the cross-country level, but also at the single-country level. Based on previous studies, a new model was created to probe into luxury value perception for immigrants from three facets. This thesis empirically analyzed immigrants by a survey, mainly determining perceived value

Food Watch: Helping People to Live a Healthy Life

Food is one of the great pleasures of life. However, due to cultural backgrounds and physical conditions, the same food is not suitable for all consumers. Peanuts, dairy products, and wheat can be deadly for people with food allergies. These consumers must carefully check the ingredients of all of their food. This article outlines a system that combines product labeling and mobile technology to help those with food allergies and food intolerances easily manage their diet and protect their health. With this new system, a user with dietary restrictions only needs to scan a label barcode with a mobile phone app to quickly assess a food product’s appropriateness for their needs. This system not only provides users with a functional, time-saving solution, it will also provide peace of mind to improve their quality of life

LRF-Net: Learning Local Reference Frames for 3D Local Shape Description and Matching

The local reference frame (LRF) acts as a critical role in 3D local shape description and matching. However, most of existing LRFs are hand-crafted and suffer from limited repeatability and robustness. This paper presents the first attempt to learn an LRF via a Siamese network that needs weak supervision only. In particular, we argue that each neighboring point in the local surface gives a unique contribution to LRF construction and measure such contributions via learned weights. Extensive analysis and comparative experiments on three public datasets addressing different application scenarios have demonstrated that LRF-Net is more repeatable and robust than several state-of-the-art LRF methods (LRF-Net is only trained on one dataset). In addition, LRF-Net can significantly boost the local shape description and 6-DoF pose estimation performance when matching 3D point clouds.Comment: 28 pages, 14 figure

Energy-efficient Amortized Inference with Cascaded Deep Classifiers

Deep neural networks have been remarkable successful in various AI tasks but often cast high computation and energy cost for energy-constrained applications such as mobile sensing. We address this problem by proposing a novel framework that optimizes the prediction accuracy and energy cost simultaneously, thus enabling effective cost-accuracy trade-off at test time. In our framework, each data instance is pushed into a cascade of deep neural networks with increasing sizes, and a selection module is used to sequentially determine when a sufficiently accurate classifier can be used for this data instance. The cascade of neural networks and the selection module are jointly trained in an end-to-end fashion by the REINFORCE algorithm to optimize a trade-off between the computational cost and the predictive accuracy. Our method is able to simultaneously improve the accuracy and efficiency by learning to assign easy instances to fast yet sufficiently accurate classifiers to save computation and energy cost, while assigning harder instances to deeper and more powerful classifiers to ensure satisfiable accuracy. With extensive experiments on several image classification datasets using cascaded ResNet classifiers, we demonstrate that our method outperforms the standard well-trained ResNets in accuracy but only requires less than 20% and 50% FLOPs cost on the CIFAR-10/100 datasets and 66% on the ImageNet dataset, respectively