Construction of Multivariate Tight Framelet Packets Associated with Dilation Matrix

In this paper, we present a method for constructing multivariate tight framelet packets associated with an arbitrary dilation matrix using unitary extension principles.We also prove how to construct various tight frames for L2(Rd) by replac-ing some mother framelets.     

Optical asymmetric watermarking using modified wavelet fusion and diffractive imaging

In most of the existing image encryption algorithms the generated keys are in the form of a noise like distribution with a uniform distributed histogram. However, the noise like distribution is an apparent sign indicating the presence of the keys. If the keys are to be transferred through some communication channels, then this may lead to a security problem. This is because; the noise like features may easily catch people׳s attention and bring more attacks. To address this problem it is required to transfer the keys to some other meaningful images to disguise the attackers. The watermarking schemes are complementary to image encryption schemes. In most of the iterative encryption schemes, support constraints play an important role of the keys in order to decrypt the meaningful data. In this article, we have transferred the support constraints which are generated by axial translation of CCD camera using amplitude-, and phase- truncation approach, into different meaningful images. This has been done by developing modified fusion technique in wavelet transform domain. The second issue is, in case, the meaningful images are caught by the attacker then how to solve the copyright protection. To resolve this issue, watermark detection plays a crucial role. For this purpose, it is necessary to recover the original image using the retrieved watermarks/support constraints. To address this issue, four asymmetric keys have been generated corresponding to each watermarked image to retrieve the watermarks. For decryption, an iterative phase retrieval algorithm is applied to extract the plain-texts from corresponding retrieved watermarks.     

Signal enhancement of a novel multi-address coding lidar backscatters based on a combined technique of demodulation and wavelet de-noising

Multi-address coding (MAC) lidar is a novel lidar system recently developed by our laboratory. By applying a new combined technique of multi-address encoding, multiplexing and decoding, range resolution is effectively improved. In data processing, a signal enhancement method involving laser signal demodulation and wavelet de-noising in the downlink is proposed to improve the signal to noise ratio (SNR) of raw signal and the capability of remote application. In this paper, the working mechanism of MAC lidar is introduced and the implementation of encoding and decoding is also illustrated. We focus on the signal enhancement method and provide the mathematical model and analysis of an algorithm on the basis of the combined method of demodulation and wavelet de-noising. The experimental results and analysis demonstrate that the signal enhancement approach improves the SNR of raw data. Overall, compared with conventional lidar system, MAC lidar achieves a higher resolution and better de-noising performance in long-range detection.     

Multiphase Thermohaline Convection in the Earth’s Crust: I. A New Finite Element – Finite Volume Solution Technique Combined With a New Equation of State for NaCl–H2O

We present a new finite element – finite volume (FEFV) method combined with a realistic equation of state for NaCl–H₂O to model fluid convection driven by temperature and salinity gradients. This method can deal with the nonlinear variations in fluid properties, separation of a saline fluid into a high-density, high-salinity brine phase and low-density, low-salinity vapor phase well above the critical point of pure H₂O, and geometrically complex geological structures. Similar to the well-known implicit pressure explicit saturation formulation, this approach decouples the governing equations. We formulate a fluid pressure equation that is solved using an implicit finite element method. We derive the fluid velocities from the updated pressure field and employ them in a higher-order, mass conserving finite volume formulation to solve hyperbolic parts of the conservation laws. The parabolic parts are solved by finite element methods. This FEFV method provides for geometric flexibility and numerical efficiency. The equation of state for NaCl–H₂O is valid from 0 to 750°C, 0 to 4000 bar, and 0–100 wt.% NaCl. This allows the simulation of thermohaline convection in high-temperature and high-pressure environments, such as continental or oceanic hydrothermal systems where phase separation is common.     

广义双剪应力准则角隅模型

本文将广义双剪应力准则变换为π平面和静水应力轴的柱坐标方程,然后将其角隅光滑化,得到了新的光滑、外凸的广义双剪应力准则角隅模型,研究结果表明,近年来作为光滑化Mohr-Coulomb理论提出的各种角隅模型,实际上并不是光滑化的Mohr-Coulomb理论,而是光滑化的广义双剪应力理论。     

Intertwining wavelets or multiresolution analysis on graphs through random forests

We propose a new method for performing multiscale analysis of functions defined on the vertices of a finite connected weighted graph. Our approach relies on a random spanning forest to downsample the set of vertices, and on approximate solutions of Markov intertwining relation to provide a subgraph structure and a filter bank leading to a wavelet basis of the set of functions. Our construction involves two parameters q and $q^{\prime }$. The first one controls the mean number of kept vertices in the downsampling, while the second one is a tuning parameter between space localization and frequency localization. We provide an explicit reconstruction formula, bounds on the reconstruction operator norm and on the error in the intertwining relation, and a Jackson-like inequality. These bounds lead to recommend a way to choose the parameters q and $q^{\prime }$. We illustrate the method by numerical experiments.     

Review of wavelet methods for the solution of reaction–diffusion problems in science and engineering

Wavelet method is a recently developed tool in applied mathematics. Investigation of various wavelet methods, for its capability of analyzing various dynamic phenomena through waves gained more and more attention in engineering research. Starting from ‘offering good solution to differential equations’ to capturing the nonlinearity in the data distribution, wavelets are used as appropriate tools at various places to provide good mathematical model for scientific phenomena, which are usually modeled through linear or nonlinear differential equations. Review shows that the wavelet method is efficient and powerful in solving wide class of linear and nonlinear reaction–diffusion equations. This review intends to provide the great utility of wavelets to science and engineering problems which owes its origin to 1919. Also, future scope and directions involved in developing wavelet algorithm for solving reaction–diffusion equations are addressed.     

Direct observations of the leaching of a simulated nuclear waste glass in a radiation environment

The durability of the media proposed for the containment of commercial nuclear waste will be affected not only by the differences in groundwater composition that they might encounter but also by the changes that their own irradiation fields will make to these solutions. Experimental results that question the ability of current leaching experiments to predict the stability of nuclear waste composites are presented.     

超宽带聚合物调制器的优化设计

设计了一种以聚合物作为材料的低损耗、宽带宽的Mach—Zehnder光波导调制器。分析了调制器的脊波导的模式特性,设计了脊波导的结构,并使用BPM软件模拟了脊形波导的光场分布;通过对光场分布的分析,优化了脊形波导的宽度Wg,脊高6,芯层高度H。同时对聚合物调制器的电极进行了优化,包括电极宽度W和电极间距D,使得调制器有较小的导体损耗以及较好的阻抗匹配。并结合了脊波导的结构参数和电极的优化参数,给出了优化结果,它能够使微波的有效折射率与光波的有效折射率达到匹配,从而使带宽达到177GHz,导体损耗为0．2569dB／cm·GHz1／2。