A characterization of two weight norm inequality for Littlewood-Paley gλ∗g_{\lambda}^{*}-function

Let $n\ge 2$ and $g_{\lambda}^{*}$ be the well-known high dimensional Littlewood-Paley function which was defined and studied by E. M. Stein, \begin{align*} g_{\lambda}^{*}(f)(x) =\bigg(\iint_{\mathbb R^{n+1}_{+}} \Big(\frac{t}{t+|x-y|}\Big)^{n\lambda} |\nabla P_tf(y,t)|^2 \frac{dy dt}{t^{n-1}}\bigg)^{1/2}, \ \quad \lambda > 1, \end{align*} where $P_tf(y,t)=p_t*f(y)$, $p_t(y)=t^{-n}p(y/t)$ and $p(x) = (1+|x|^2)^{-(n+1)/2}$, $\nabla =(\frac{\partial}{\partial y_1},\ldots,\frac{\partial}{\partial y_n},\frac{\partial}{\partial t})$. In this paper, we give a characterization of two-weight norm inequality for $g_{\lambda}^{*}$-function. We show that, $\big\| g_{\lambda}^{*}(f \sigma) \big\|_{L^2(w)} \lesssim \big\| f \big\|_{L^2(\sigma)}$ if and only if the two-weight Muchenhoupt $A_2$ condition holds, and a testing condition holds : \begin{align*} \sup_{Q : cubes \ in \mathbb R^n} \frac{1}{\sigma(Q)} \int_{\mathbb R^n} \iint_{\widehat{Q}} \Big(\frac{t}{t+|x-y|}\Big)^{n\lambda}|\nabla P_t(\mathbf{1}_Q \sigma)(y,t)|^2 \frac{w dx dt}{t^{n-1}} dy < \infty, \end{align*} where $\widehat{Q}$ is the Carleson box over $Q$ and $(w, \sigma)$ is a pair of weights. We actually prove this characterization for $g_{\lambda}^{*}$-function associated with more general fractional Poisson kernel $p^\alpha(x) = (1+|x|^2)^{-{(n+\alpha)}/{2}}$. Moreover, the corresponding results for intrinsic $g_{\lambda}^*$-function are also presented.Comment: 21 pages, to appear in Journal of Geometric Analysi

Development of Drilling Control Technology to Reduce Drilling Noise during Roof Bolting Operations

Noise induced hearing loss is a serious health issue among coal mine workers. The roof bolting operation is one of the noisiest underground mining operations. It is second among all equipment in underground coal mines whose operators exceed 100% noise dosage according to MSHA data. In roof bolting, the noise generated in the roof drilling normally contributes a major proportion to the noise exposure to this particular group of miners. This study is to develop a drilling control technology to reduce noise generated during roof bolting drilling.;Previous research shows that the specific energy consumed in drilling bolt holes is inversely proportional to the bite depth (i.e., penetration per drill revolution). Less specific energy at a reasonably high bite depth means less energy is wasted in the drilling process for producing heat, bit wear, and noise. Properly controlled drilling will not only maintain good drilling productivity, but also significantly reduce the sound power level, noise dosage, and the required drilling energy. Rational drilling control is implemented through properly chosen penetration and rotational rates according to the specific rock strength, drill bit, and steel.;Several efforts are investigated in this research. The first one is to explore the feasibility of the drilling control technology for reducing drilling noise. Drilling experiments have been conducted in the laboratory. Different drilling parameters (penetration rate and rotational rate) and different drill bits and steels were utilized through drilling medium hard rock. The results show that significant reduction in noise dose can be achieved at a reasonably high bite depth when drilling medium hard rock. This research indicates that through proper control of the drilling parameters with regarded to rock type, the noise exposure to the roof bolter operators can be significantly reduced. At the same time, drilling productivity is not affected or even improved. Then an algorithm has been developed for finding the rational drilling control parameters that can minimize the noise dose of the bolter operators in roof bolting drilling. Also, a mathematical model for simulating roof bolt drilling has been improved to include the noise generation. This model can be used to estimate the rock strength as well as required drilling thrust and torque, specific energy, energy efficiency, and noise dose for a given rock strength. The safety check of drilling operation is also included in this model. As an additional effect of this drill control technology, the dust size distributions of drilling at different parameters were analyzed. This noise control algorithm can be incorporated into the existing drill control unit for potential drilling automation

Role Playing Learning for Socially Concomitant Mobile Robot Navigation

In this paper, we present the Role Playing Learning (RPL) scheme for a mobile robot to navigate socially with its human companion in populated environments. Neural networks (NN) are constructed to parameterize a stochastic policy that directly maps sensory data collected by the robot to its velocity outputs, while respecting a set of social norms. An efficient simulative learning environment is built with maps and pedestrians trajectories collected from a number of real-world crowd data sets. In each learning iteration, a robot equipped with the NN policy is created virtually in the learning environment to play itself as a companied pedestrian and navigate towards a goal in a socially concomitant manner. Thus, we call this process Role Playing Learning, which is formulated under a reinforcement learning (RL) framework. The NN policy is optimized end-to-end using Trust Region Policy Optimization (TRPO), with consideration of the imperfectness of robot's sensor measurements. Simulative and experimental results are provided to demonstrate the efficacy and superiority of our method

Response of Coastal Upwelling East of Hainan Island in the South China Sea to Sudden Impact and Long-Term Variability of Atmospheric Forcing

The wind-driven coastal upwelling east of Hainan Island (UEH) in the northwestern South China Sea (SCS) is sensitive to the multi-scale variability of atmospheric forcing. This chapter focuses on two ends of time scales of atmospheric forcing: very short-time or sudden impact, i.e., typhoon passages; and long-term variability associated with El Niño events. The response of the sea surface temperature (SST) associated with the UEH to typhoon passages was investigated based on concurrent satellite SST and wind products. The long-term variability and response of the UEH to super El Niño events were analyzed based on recent 30 years of satellite data. The results show that the UEH has significant responses to atmospheric forcing. Meanwhile, the ocean circulation also plays an important role in modulation of the coastal upwelling

From Material Collection to Ideological Presentation: A Paradigm Shift in Museum Practice

Under the impetus of the New Museum Movement, the definition of museum has been updated. Museums are no longer merely places of “collection, storage and exhibition”, but also have functions of “research, education and pleasure”. Although “comprehensive and scarce” collection is important, it is no longer the only standard for museum exhibition. At the same time, new ideas have emerged that emphasize “human” subjectivity, multiple expressions, and situational narratives. As a result, the paradigm shift from material collection to ideological presentation has become a specific direction for museum practice in China today

Multiple Scale Impacts of Nomad Settlement on Social-Ecological Systems

There are complex interactions and feedback mechanisms between human and natural systems within the coupled social-ecological systems (SESs) (Liu et al. 2007, Li and Li 2012). Human society is the major driving force that changes ecosystem dynamics from local environments to the biosphere (Liu et al. 2007, Kirch 2005). Grasslands, especially the vulnerable arid and semi-arid grassland ecosystems upon which pastoralists live and graze livestock, can be considered as SESs; pastoral activities influence the biophysical environment and set up interactions between the components of these systems (Robinson 2009). In recent years, the ecosystem services provided by grasslands and the problem of poverty in grassland communities have attracted increasing attention from governments and society in China. One response has been the Nomad Settlement Projects (NSPs), implemented as a development strategy in pastoral areas to find solutions to the prevailing ecological and social problems. Nomadic people were provided with houses and farmland in some place, and encouraged to settle down and modernize the “backward” pastoralism. In this paper, we explored the impacts of China’s Nomad Sedentarization Project (NSP) for pastoral areas on coupled social and ecological systems by evaluating the consequences of these projects at different scales (village scale, county scale and catchment scale) undertaken in grassland SESs, including the ecological and social consequences. China\u27s government is now promoting the NSP in large areas of grassland as a solution for ecological restoration and poverty alleviation. To determine the effects of this policy, we conducted in-depth interviews at two of the project\u27s sites and examined the social and ecological systems at village, county, and catchment scales