Elliptic systems with measurable coefficients of the type of Lam\'e system in three dimensions

We study the $3 \times 3$ elliptic systems $\nabla \times (a(x) \nabla\times u)-\nabla (b(x) \nabla \cdot u)=f$, where the coefficients $a(x)$ and $b(x)$ are positive scalar functions that are measurable and bounded away from zero and infinity. We prove that weak solutions of the above system are H\"older continuous under some minimal conditions on the inhomogeneous term $f$. We also present some applications and discuss several related topics including estimates of the Green's functions and the heat kernels of the above systems.Comment: Proof of Theorem 3.1 is correcte

3D Reconstruction & Assessment Framework based on affordable 2D Lidar

Lidar is extensively used in the industry and mass-market. Due to its measurement accuracy and insensitivity to illumination compared to cameras, It is applied onto a broad range of applications, like geodetic engineering, self driving cars or virtual reality. But the 3D Lidar with multi-beam is very expensive, and the massive measurements data can not be fully leveraged on some constrained platforms. The purpose of this paper is to explore the possibility of using cheap 2D Lidar off-the-shelf, to preform complex 3D Reconstruction, moreover, the generated 3D map quality is evaluated by our proposed metrics at the end. The 3D map is constructed in two ways, one way in which the scan is performed at known positions with an external rotary axis at another plane. The other way, in which the 2D Lidar for mapping and another 2D Lidar for localization are placed on a trolley, the trolley is pushed on the ground arbitrarily. The generated maps by different approaches are converted to octomaps uniformly before the evaluation. The similarity and difference between two maps will be evaluated by the proposed metrics thoroughly. The whole mapping system is composed of several modular components. A 3D bracket was made for assembling of the Lidar with a long range, the driver and the motor together. A cover platform made for the IMU and 2D Lidar with a shorter range but high accuracy. The software is stacked up in different ROS packages.Comment: 7 pages, 9 Postscript figures. Accepted by 2018 IEEE International Conference on Advanced Intelligent Mechatronic

Design of generalized fractional order gradient descent method

This paper focuses on the convergence problem of the emerging fractional order gradient descent method, and proposes three solutions to overcome the problem. In fact, the general fractional gradient method cannot converge to the real extreme point of the target function, which critically hampers the application of this method. Because of the long memory characteristics of fractional derivative, fixed memory principle is a prior choice. Apart from the truncation of memory length, two new methods are developed to reach the convergence. The one is the truncation of the infinite series, and the other is the modification of the constant fractional order. Finally, six illustrative examples are performed to illustrate the effectiveness and practicability of proposed methods.Comment: 8 pages, 16 figure

Quantum memory and non-demolition measurement of single phonon state with nitrogen-vacancy centers ensemble

In diamond, the mechanical vibration induced strain can lead to interaction between the mechanical mode and the nitrogen-vecancy (NV) centers. In this work, we propose to utilize the strain induced coupling for the quantum non-demolition (QND) single phonon measurement and memory in diamond. The single phonon in a diamond mechanical resonator can be perfectly absorbed and emitted by the NV centers ensemble (NVE) with adiabatically tuning the microwave driving. An optical laser drives the NVE to the excited states, which have much larger coupling strength to the mechanical mode. By adiabatically eliminating the excited states under large detuning limit, the effective coupling between the mechanical mode and the NVE can be used for QND measurement of the single phonon state. Under realistic experimental conditions, we numerically simulate the scheme. It is found that the fidelity of the absorbing and emitting process can reach a much high value. The overlap between the input and the output phonon shapes can reach $98.57\%$.Comment: 7 pages, 3 figure

Extracting Product Features from Online Consumer Reviews

Along with the exponential growth of user-generated content online comes the need of making sense of such content. Online consumer review is one type of user-generated content that has been more important. Thus, there is a demand for uncovering hidden patterns, unknown relationships and other useful information. The focal problem of this research is product feature extraction. Few existing studies has looked into detailed categorization of review features and explored how to adjust extraction methods by taking account of the characteristics of different categories of features. This paper begins with the introduction of a new scheme of feature classification and then introduces new extraction methods for each type of features separately. These methods were design to not only recognize new features but also filter irrelevant features. The experimental results show that our proposed methods outperform the state-of-the-art techniques

Molecular Dynamics Simulation of Strong Shock Waves Propagating in Dense Deuterium With the Effect of Excited Electrons

We present a molecular dynamics simulation of shock waves propagating in dense deuterium with the electron force field method [J. T. Su and W. A. Goddard, Phys. Rev. Lett. 99, 185003 (2007)], which explicitly takes the excitation of electrons into consideration. Non-equilibrium features associated with the excitation of electrons are systematically investigated. We show that chemical bonds in D$_2$ molecules lead to a more complicated shock wave structure near the shock front, compared with the results of classical molecular dynamics simulation. Charge separation can bring about accumulation of net charges on the large scale, instead of the formation of a localized dipole layer, which might cause extra energy for the shock wave to propagate. In addition, the simulations also display that molecular dissociation at the shock front is the major factor corresponding to the "bump" structure in the principal Hugoniot. These results could help to build a more realistic picture of shock wave propagation in fuel materials commonly used in the inertial confinement fusion

Moisture-triggered physically transient electronics

Physically transient electronics, a form of electronics that can physically disappear in a controllable manner, is very promising for emerging applications. Most of the transient processes reported so far only occur in aqueous solutions or biofluids, offering limited control over the triggering and degradation processes. We report novel moisture-triggered physically transient electronics, which exempt the needs of resorption solutions and can completely disappear within well-controlled time frames. The triggered transient process starts with the hydrolysis of the polyanhydride substrate in the presence of trace amounts of moisture in the air, a process that can generate products of corrosive organic acids to digest various inorganic electronic materials and components. Polyanhydride is the only example of polymer that undergoes surface erosion, a distinct feature that enables stable operation of the functional devices over a predefined time frame. Clear advantages of this novel triggered transience mode include that the lifetime of the devices can be precisely controlled by varying the moisture levels and changing the composition of the polymer substrate. The transience time scale can be tuned from days to weeks. Various transient devices, ranging from passive electronics (such as antenna, resistor, and capacitor) to active electronics ( such as transistor, diodes, optoelectronics, and memories), and an integrated system as a platform demonstration have been developed to illustrate the concept and verify the feasibility of this design strategy