Augmented Lagrangian Methods for $p$-Harmonic Flows with the Generalized Penalization Terms and Application to Image Processing

In this paper, we propose a generalized penalization technique and a convex constraint minimization approach for the $p$-harmonic flow problem following the ideas in [Kang & March, IEEE T. Image Process., 16 (2007), 2251-2261]. We use fast algorithms to solve the subproblems, such as the dual projection methods, primal-dual methods and augmented Lagrangian methods. With a special penalization term, some special algorithms are presented. Numerical experiments are given to demonstrate the performance of the proposed methods. We successfully show that our algorithms are effective and efficient due to two reasons: the solver for subproblem is fast in essence and there is no need to solve the subproblem accurately (even 2 inner iterations of the subproblem are enough). It is also observed that better PSNR values are produced using the new algorithms.     

岩体卸荷渗流特性的试验

岩体破坏可能是由于各类岩体工程的开挖引起的,同时影响其失稳破坏的主要外界因素就是地下水及其在岩体中的渗流.为了分析岩石卸荷量与渗透系数的关系,提出了岩石卸荷试验的方法和步骤.通过试验得到了不同阶段卸荷量与渗透系数之间的关系曲线.根据试验结果,建立了卸荷应力-渗透系数关系方程,探讨了岩石渗透系数与卸荷量之间的变化规律:在卸荷过程中的弹性阶段,其渗透系数基本无变化;当进入卸荷的塑性阶段,其渗透系数发生较大变化,尤其当卸荷量达到极限卸荷量的80%以上.渗透系数增长较快.     

Keggin type heteropolyacids-catalyzed synthesis of quinoxaline derivatives in water

Keggin type heteropolyacids was found to be an efficient and reusable catalyst for the synthesis of biologically active quinoxaline derivatives from the condensation of 1,2-diamine with 1,2-dicarbonyl compounds in excellent yields in water.This method provides a new and efficient protocol in terms of small quantity of catalyst,a wide scope of substrates,and simple work-up procedure.     

Sample introduction in gas chromatography using a coiled wire filament

A simple device for field sampling and concentration of analytes for subsequent introduction into an injection port for gas chromatographic (GC) analysis has been developed. It consists of a tiny, coiled platinum wire filament (CWF) that is attached to a retractable plunger wire, which fits inside a syringe needle housing. Sampling is accomplished by dipping the end of the CWF in a liquid sample, which is drawn into the wire coil by capillary action, and introducing it into the injection port either before or after allowing the solvent to evaporate. The CWF can be used with or without a nonvolatile chemical coating. A major advantage of this sampling device is that nonvolatile sample matrix components remain on the wire coil, reducing the required injection port and liner cleaning frequency and contamination of the head of the chromatographic column. The coil itself can be easily cleaned between analyses by rinsing and/or burning off residual material in a small flame. The sampling coil facilitates specifically designed chemical reactions in the injection port, such as thermochemolysis and methylation. Applications demonstrated in this work include: (1) direct introduction of samples with little or no pre-treatment, (2) simultaneous thermochemolysis and methylation of lipid-containing samples such as bacteria and bacterial endospores for analysis of biomarkers, and (3) solid phase micro-extraction (SPME) using temporary wire coatings. The CWF allowed for significant reduction in sample preparation time, in most cases to less than a few minutes. The peak shapes examined for polycyclic aromatic hydrocarbon analytes (PAHs) were significantly better (asymmetry factors <1.3) when using the CWF sampling technique compared to splitless and on-column injection techniques (asymmetry factors >1.3). Extraction efficiencies for SPME (especially for high boiling point components such as PAHs) improved by an average of 2.5 times when using the CWF compared to the performance of commercially available SPME fibers. Coiled wire filaments and GC injection port liners were used for more than 100 Bacillus endospore thermochemolysis methylation analyses without the need for cleaning or replacement.     

Synthesis,structural characterization and antitumor activity of a Ca(II) coordination polymer based on 4-formyl-1,3-benzenedisulfonate-2-furoic acid hydrazide ligands

A new Ca(II) coordination polymer, {[CaL(H₂O)₄] · (H₂O)₄} _n (L = 4-formyl-1,3-benzenedisulfonate-2-furoic acid hydrazide) has been prepared by one-pot synthesis method. And it was characterized by elemental analysis, IR and thermal analysis. The result of X-ray single-crystal diffraction analysis shows that the Ca(II) complex molecules form one-dimensional chain structure by the bridging oxygen atoms. The anti-tumor activity of L ligand and the Ca(II) coordination polymer has also been studied.     

Effects of temperature,mechanical motion and source positional jitter on the resolving power of beamline 02B at the SSRF

A detailed analysis of the effects of temperature excursions, instrumental mechanical motion and source position jitter on the energy‐resolving power of beamline 02B at the Shanghai Synchrotron Radiation Facility (SSRF) is presented in this study. This beamline uses a bending‐magnet‐based source and includes a variable‐line‐spacing grating monochromator with additional optics. Expressions are derived for the monochromator output photon energy shifts for each of the performance challenges considered. The calculated results indicate that measured temperature excursions of ±1 K produce an energy shift of less than 11% of the system's energy resolution. Mechanical displacements and vibrations measured at amplitudes of less than 0.5 µm produce changes of less than 5%, while measured source location jitter results in a change of less than 10%. Spectroscopic test experiments at 250 and 400 eV provide energy resolutions of over 10⁴. This analysis, combined with the measured results, confirms the operational stability of the beamline, indicating that it meets the performance requirements for experimental use.     

Li2CO3对0.7CaTiO3-0.3SmAlO3陶瓷性能的影响

采用固相反应法,以0.7CaTiO3-0.3SmAlO3 (CSTA)为基础配方,研究了Li2CO3对CSTA微波介质陶瓷性能的影响.结果表明:添加适量的Li2CO3可有效的降低CSTA的烧结温度,由1500℃降低到1380℃.XRD分析表明:Li2CO3的引入未改变陶瓷的的晶相组成.SEM分析表明,添加Li2CO3会抑制晶粒长大,当添加0.lwt;时,晶粒尺寸小,分布均匀;随着添加量的增加,玻璃相增加,部分晶粒长大,分布不均匀,从而降低品质因数.添加0.lwt;的Li2CO3的CSTA陶瓷在1380 ℃烧结时获得最佳介电性能:εr=45.09,Q·f=61600 GHz (f=6.417 GHz),тf=+7.54×10-6/℃.     

Efficient Convex Optimization Approaches to Variational Image Fusion

Image fusion is an imaging technique to visualize information from multiple imaging sources in one single image, which is widely used in remote sensing, medical imaging etc. In this work, we study two variational approaches to image fusion which are closely related to the standard TV-$L_2$ and TV-$L_1$ image approximation methods. We investigate their convex optimization formulations, under the perspective of primal and dual, and propose their associated new image decomposition models. In addition, we consider the TV-$L_1$ based image fusion approach and study the specified problem of fusing two discrete-constrained images $f_1(x) ∈\mathcal{L}_1$ and $f_2(x) ∈\mathcal{L}_2$, where$\mathcal{L}_1$ and$\mathcal{L}_2$ are the sets of linearly-ordered discrete values. We prove that the TV-$L_1$ based image fusion actually gives rise to the exact convex relaxation to the corresponding nonconvex image fusion constrained by the discrete-valued set $u(x) ∈\mathcal{L}_1 ∪\mathcal{L}_2$. This extends the results for the global optimization of the discrete-constrained TV-$L_1$ image approximation [8, 36] to the case of image fusion. As a big numerical advantage of the two proposed dual models, we show both of them directly lead to new fast and reliable algorithms, based on modern convex optimization techniques. Experiments with medical images, remote sensing images and multi-focus images visibly show the qualitative differences between the two studied variational models of image fusion. We also apply the new variational approaches to fusing 3D medical images.     

On the asymptotic behavior of radial entire solutions for the equation (−Δ)3u = up in Rn

Our main task in this note is to prove the existence and to classify the exact growth at infinity of radial positive $C^6$-solutions of ${(?\mathrm{\Delta })}^{3}u=u^p$ in ${\mathbf{R}}^n$, where $n?15$ and p is bounded from below by the sixth-order Joseph–Lundgren exponent. Following the main work of Winkler, we introduce the sub- and super-solution method and comparison principle to conclude the asymptotic behavior of solutions.     

多复变数一类α次星形映射齐次展开式各项的精细估计

本文首先给出复Banach空间单位球上一类α次星形映射齐次展开式各项的精细估计,特别当这些映射又是k折对称映射时,估计还是精确的.其次建立C~n中单位多圆柱上上述推广映射齐次展开式各项的精细估计,同样当这些映射又是k折对称映射时,估计仍是精确的.由此证明了多复变数中关于α次星形映射的弱Bieberbach猜想,且所得到的估计都能回到单复变数的情形.