A unified approach to error bounds for structured convex optimization problems

Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for solving optimization problems. In this paper, we present a new framework for establishing error bounds for a class of structured convex optimization problems, in which the objective function is the sum of a smooth convex function and a general closed proper convex function. Such a class encapsulates not only fairly general constrained minimization problems but also various regularized loss minimization formulations in machine learning, signal processing, and statistics. Using our framework, we show that a number of existing error bound results can be recovered in a unified and transparent manner. To further demonstrate the power of our framework, we apply it to a class of nuclear-norm regularized loss minimization problems and establish a new error bound for this class under a strict complementarity-type regularity condition. We then complement this result by constructing an example to show that the said error bound could fail to hold without the regularity condition. We believe that our approach will find further applications in the study of error bounds for structured convex optimization problems.     

Electron spin resonance from annealed titania nanotubes

Titania nanotubes were prepared using a hydrothermal method. Hydrogen titanate nanotubes (H-TNTs) with an anatase phase changed to anatase nanocrystals at about 500 °C, and then a rutile structure at ∼800 °C. A sharp and symmetrical electron spin resonance (ESR) signal (g=2.003), attributed to a single-electron-trapped oxygen-vacancy (SETOV), was obtained at the annealed H-TNTs (T<500 °C). The SETOV signal increased and maximized remarkably at about 400–500 °C. Then, the nanotube structure appeared to be demolished. Yet, when the vacuum-heated H-TNTs were sealed in N₂ or Ar ambient, some additional ESR signals appeared besides the SETOV signal. The broad asymmetric ESR signal (g=1.98) was attributed to a surface oxygen vacancy related to the Ti³⁺ sites in a reduced TiO₂ matrix. The vacuum-heated sodium titanate nanotubes (Na-TNTs) showed only the SETOV signal (T<500 °C). PACS 61.46.Fg; 61.72.Ji; 76.30.-v     

Vibrational quasi-degenerate perturbation theory: applications to fermi resonance in CO2, H2CO, and C6H6

A quasi-degenerate perturbation method with vibrational self-consistent field (VSCF) reference wavefunction is developed. It simultaneously accounts for strong anharmonic mode-mode coupling among a few states (static correlation) by a configuration interaction theory and for weak coupling with a vast number of the other states (dynamic correlation) by a perturbation theory. A general formula is derived based on the van Vleck perturbation theory. An algorithm that selects a compact set of the most important VSCF configurations which contribute to the static correlation is proposed and a scheme to limit the number of configurations considered for dynamic correlation is also implemented. This method reproduces the vibrational frequencies of CO2 and H2CO that are subject to the strongest anharmonic mode-mode coupling within 10 cm(-1) of vibrational configuration interaction results in a computational expense reduced by a factor of one to two orders of magnitude. The method also reproduces the infrared absorption of C6H6 in the CH stretching (nu12) frequency region, in which combination tones nu13nu16 and nu2nu13nu18 appear on account of an intensity borrowing from nu12via the anharmonic coupling.     

Unexpected ring transformation to pyrrolo[3.2-b]pyridine derivatives. Fused azolium salts. 22

2-Arylsulfanyl and 2-benzylsulfanylpyridinium N-arylimides (2) easily prepared from 3-aryltetrazolopyridinium salts (1) with aryl and benzylthiolates, respectively, reacted with various dipolarophiles yielding cycloadducts that underwent transformation to give tetrahydropyrrolo[3,2-b]pyridines (5, 6, and 8) in good yields. A similar rearrangement (formation of 15) was also observed in the case of parent derivatives being unsubstituted in position 2 (12). The abscence of any significant solvent effect, comparison of the sulfur and non-sulfur analogues, as well as the stereoselective nature of the observed ring transformation seem to support a sigmatropic mechanism. Structure elucidation of the products has been carried out by single-crystal X-ray diffraction and (1)H NMR experiments.     

5‐Hydroxyl Hydantoins via One‐Pot Microwave‐Assisted Air Oxidation of Ugi Products

The novel and one‐pot synthesis of 5‐hydroxyl hydantoins from Ugi five‐component condensation procedures is reported. The transformation was promoted via a microwave heating method and provided 5‐hydroxyl hydantoins in workable yields, representing a direct approach to this synthetically challenging and biologically interesting pharmacophore.     

结构振动对湍流近尾迹的影响

研究了圆柱绕流中流体与结构的相互作用,侧重结构振动对湍流尾迹的影响,用激光测振仪测量圆柱在升力方向的位移;用热线和LDA（二维）测量湍流的近尾迹,通过变化自由流的速度和圆柱体直径（特征尺寸）来变化雷诺数,用两个振动特性不同的（一个相对刚性,一个相对弹）圆柱来产生尾迹,研究固体结构振动对湍流近尾迹的平均速度场和湍流场的影响,结果表明,结构自由振动对湍流近尾迹场影响明显,该影响随雷诺数的变化不明显。     

Investigation on the stress behavior of cellulose acetate and the development of highly moisture‐resistant optical films for display devices

An optical film with high optical anisotropy was prepared by the stretching of a cellulose acetate film and the consequential orienting of a retardation‐enhancing additive. The change in retardation in response to moisture absorption was explored and it was found that the degree of the retardation variation is strongly related to the stretching temperature. Stress generated by the stretching and its relaxation was systematically investigated to elucidate the effect of stretching temperature on the irreversible change in retardation upon moisture absorption. The results show that the magnitude of releasable stress plays an important role in controlling changes in optical properties. In addition, the difference in the deformation behavior between glassy and rubbery states should be taken into account in the development of a moisture‐resistant optical film. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1470–1478     

Thermal stability of ester linkage in the presence of 1,2,3‐Triazole moiety generated by click reaction

The copper(I)‐catalyzed alkyne‐azide cycloaddition (CuAAC), so‐called “click” reaction, is one of most useful synthetic strategies to connect two polymer chains. 1,2,3‐Triazole ring (TA) produced by the click reaction has good thermal and chemical stability. However, we observed that block copolymers synthesized by the click reaction showed thermal degradation to give homopolymers when they are thermally annealed at high temperature, which is required for obtaining equilibrium microdomain structure. To investigate the origin of thermal instability of block copolymers, we synthesized model polystyrenes (PSs) using systematically designed bi‐functional atom transfer radical polymerization (ATRP) initiators containing TA. PS including both ester and TA groups showed thermal decomposition at relatively low temperature (e.g., 140 °C). MALDI‐TOF analysis clearly demonstrated that the cleavage site is the ester group adjacent to TA. We also found that the bromine group located at the polymer chain end plays an important role in pyrolysis of ester groups at low temperature. The pyrolysis occurs by syn‐elimination of the ester group. This result implies that the phase behavior of block copolymer synthesized by click reaction should be carefully investigated when high temperature thermal annealing is required. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 427–436