Local linear convergence analysis of Primal–Dual splitting methods

In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these methods. More precisely, in our framework, we first show that (i) the sequences generated by Primal–Dual splitting methods identify a pair of primal and dual smooth manifolds in a finite number of iterations, and then (ii) enter a local linear convergence regime, which is characterized based on the structure of the underlying active smooth manifolds. We also show how our results for Primal–Dual splitting can be specialized to cover existing ones on Forward–Backward splitting and Douglas–Rachford splitting/ADMM (alternating direction methods of multipliers). Moreover, based on these obtained local convergence analysis result, several practical acceleration techniques are discussed. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from fields including signal/image processing, inverse problems and machine learning. The demonstration not only verifies the local linear convergence behaviour of Primal–Dual splitting methods, but also the insights on how to accelerate them in practice.     

一种新型彩色三维光学成像系统

提出一种新型三维彩色光学数字成像系统。此系统利用投影结构光对现实世界中的物体进行数字化，同时得到对应的彩色纹理。详细介绍了系统的硬件设计和软件体系结构设计，得到物体彩色纹理的两种不同方法；直接获取和从编码条纹中提取，给出了用该系统得到的实验结果并简单评价了系统的性能。此系统在反求工程、影视制作、三维游戏制作、医学应用等方面有远大的应用前景。     

Effects of diamines and their fluorinated groups on the color lightness and preparation of organosoluble aromatic polyimides from 2,2‐bis[4‐(4‐amino‐2‐trifluoromethylphenoxy)phenyl]‐hexafluoropropane

To investigate the position and amount of the CF₃ group affecting the coloration of polyimides (PIs), we prepared 2,2‐bis[4‐(4‐amino‐2‐trifluoromethylphenoxy)phenyl]hexafluoropropane ( 2 ) with four CF₃ groups with 2‐chloro‐5‐nitrobenzotrifluoride and 2,2‐bis(4‐hydroxyphenol)hexafluoropropane. A series of soluble and light‐colored fluorinated PIs ( 5 ) were synthesized from 2 and various aromatic dianhydrides ( 3a – 3f ). 5a – 5f had inherent viscosities ranging from 0.80 to 1.19 dL/g and were soluble in amide polar solvents and even in less polar solvents. The glass‐transition temperatures of 5 were 221–265 °C, and the 10% weight‐loss temperatures were above 493 °C. Their films had cutoff wavelengths between 343 and 390 nm, b* values (a yellowness index) ranging from 5 to 41, dielectric constants of 2.68–3.01 (1 MHz), and moisture absorptions of 0.03–0.29 wt %. In a comparison of the PI series 6 – 8 based on 2,2‐bis[4‐(4‐aminophenoxy)phenyl]hexafluoropropane, 2,2‐bis[4‐(4‐amino‐2‐trifluoromethylphenoxy)phenyl]propane, and 2,2‐bis[4‐(4‐aminophenoxy)phenyl]propane, we found that the CF₃ group close to the imide group was more effective in lowering the color; this means that CF₃ of 5 , 7 , and 8f was more effective than that of 6c . The color intensity of the four PI series was lowered in the following order: 5 > 7 > 6 > 8 . The PI 5f , synthesized from diamine 2 and 4,4′‐hexafluoroisopropylidenediphthalic anhydride, had six CF₃ groups in a repeated segment, so it exhibited the lightest color among the four series. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 922–938, 2003     

γ-辐照对纯Y_2SiO_5和Eu~(3+)∶Y_2SiO_5晶体光谱性能的影响

研究了γ-辐照前后纯Y2SiO5和Eu3+掺杂的Y2SiO5晶体吸收光谱的变化,辐照后,未退火和氢气退火的纯Y2SiO5晶体在260~270 nm和320 nm波段产生了附加吸收峰,分别是由F心和O-心的吸收引起的;经过空气退火的纯YSO晶体中,由于消除了氧空位,因此辐照后没有出现色心吸收峰。在Eu3+∶Y2SiO5晶体中,不但有相同的F心和O-心吸收峰,而且还有Eu2+离子在300 nm和390 nm的吸收峰。随着辐照剂量的增加,色心附加吸收峰增强。空气退火能减少Eu3+∶Y2SiO5晶体中的色心,而氢气退火能增加色心。     

Color Zone Map in Peripheral Vision at Various Illuminance Levels

We measured the entire region of mesopic and photopic vision to determine the color zone covering the visual field with unique red, yellow, green, and blue hue components. Eight kinds of test stimuli in the natural color system (NCS) color notation system were used. These stimuli were presented at horizontal and vertical meridians, and at meridians inclined at 45° angles. The illuminance level was set at six levels: 0.01 lx-1000 lx. The evaluation method measured chromatic, white, and black components as well as the hue component of the stimuli. Results show that the color zone of the retina extended further into the periphery with increasing illuminance; the response of opponent colors y-b was shown to be greater than that of the opponent colors r-g.     

Changes in the near-edge X-ray absorption fine structure spectra of long-chain diacetylene derivatives through photopolymerization in Langmuir–Blodgett films

Photopolymerization of cadmium 10,12-pentacosadiynoate (CdDA) in Langmuir–Blodgett (LB) films, with the molecular packing well arranged by moderate preannealing, was investigated with near-edge X-ray absorption fine structure (NEXAFS) spectroscopy. Greenish films of polydiacetylene with an absorption wavelength of 705 nm were obtained through the photopolymerization of preannealed monomer LB films, and this resulted in an extended π-conjugate system based on the well-ordered monomer in a two-dimensional arrangement. The electronic structures of the polydiacetylenes were found to be correlated to the variation of the molecular arrangements in the films from the changes in the NEXAFS spectra through photopolymerization in the LB films. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2329–2336, 2004     

Robust linear optimization under general norms

We explicitly characterize the robust counterpart of a linear programming problem with uncertainty set described by an arbitrary norm. Our approach encompasses several approaches from the literature and provides guarantees for constraint violation under probabilistic models that allow arbitrary dependencies in the distribution of the uncertain coefficients.     

Investigation and optimization of the covering power and coloristic properties of paint coatings of complex composition

A method for finding the optimum sizes of pigment particles, their volume concentration, and the paint coating thickness that provide the covering power and the required coloristic characteristics of reflected light for the minimum flow rate of pigments is based on using a four-flow approximation of the solution to the equation of radiation transfer in dispersion media and is extended to coatings of complex composition. The capabilities of the method are demonstrated by examples of coatings of mixtures of hematite and rutile particles in a binder with n=1.5 for variations of the modal size and the half-width of the size distribution of the pigment particles. B. I. Stepanov Institute of Physics, Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 1, pp. 90–96, January–February, 1997.     

Modules over Operator Algebras and Its Module Maps

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F／Cl比与Eu~（2＋）：BaFCl中F色心的浓度和光激励截面的关系

研究了Ｅｕ（２＋）：ＢａＦｘＣｌ２在紫外线辐照下的光激励发光。通过改变激励方式及激励光的扫描方向，给出了Ｅｕ（２＋）：ＢａＦｘＣｌ２－ｘ光激励发光过程中，两种Ｆ色心的浓度比值与光激励截面比值的测定方法。利用这种测定方法，进一步研究了两种Ｆ色心的浓度比值和光激励截面比值与Ｆ／ＣＩ比值的关系。