Hybrid Proximal Point Algorithm and Applications to Equilibrium Problems and Convex Programming

The problem of finding minima of weakly sequentially lower semicontinuous functions on reflexive Banach spaces is studied by means of convex and nonconvex subdifferentials. Finding a descent direction for a non-stationary point is a question of importance for many optimization algorithms. The existence or non-existence of such a direction is clarified through several theorems and a series of selective examples. For the general problem, a notion called radius of descent is proposed and shown to be useful for the analysis related to descent directions.     

Facile and Efficient Method for the Synthesis of 14-Substituted-14-H-dibenzo[a,j]xanthenes Catalyzed by Ruthenium Chloride Hydrate as a Homogeneous Catalyst

Synthesis of dibenzoxanthenes through condensation of β-naphthol with various aromatic and aliphatic aldehydes in ethanol as an ecofriendly solvent using Ru^III as catalyst is reported.

Probabilistic error bounds on constraint violation for empirical-analytical Lagrangian models of motion

Nonlinear Dynamics - In contrast to many systems studied in the field of classical mechanics, models of animal motion are often distinguished in that they are both highly uncertain and evolve in a...     

Preserving maximal monotonicity with applications in sum and composition rules

In this paper, we study maximal monotonicity preserving mappings on the Banach space X × X ^*. Indeed, for a maximal monotone set ${M \subset X\times X^*}$ and for a multifunction ${T: X \times X^* \multimap Y \times Y^*}$ , under some sufficient conditions on M and T we show that T(M) is maximal monotone. As two consequences of this result we get sum and composition rules for maximal monotone operators.     

Efficient RuIII-catalyzed synthesis of 9-aryl-9H-xanthene-3,6-diols as precursors to fluorones

Efficient condensation of resorcinol and various aromatic aldehydes in the presence of RuCl₃nH₂O as a homogeneous catalyst under reflux conditions was investigated.It was found that a very simple method afforded good to excellent yields of the desired products.     

Photoinitiated atom transfer radical polymerization: Current status and future perspectives

In macromolecular and material science, atom transfer radical polymerization (ATRP) has intensely influenced the research strategies facilitating fabrication of a wide range of polymers with well‐defined structures and functions and their conjugation with biomolecules. Recently, the required copper (I) catalyst for ATRP process is generated by photoinduced redox reactions involving the in situ reduction of Cu(II) to Cu(I). Photochemically initiated reactions provide several distinct advantages, including temporal and spatial controls, rapid and energy efficient activation. The process is based on photoredox reactions of copper catalysts under various radiation sources with or without various photoinitiators. This Highlight focuses on the historical development, mechanistic aspects, limitations, and opportunities of photoinitiated ATRP along with selected examples. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 2878–2888     

Phenacyl Ethyl Carbazolium as a Long Wavelength Photoinitiator for Free Radical Polymerization

A new phenacyl‐type photoinitiator based on ethyl carbazole as a long wavelength photo­initiator is developed for free radical polymerization. Phenacyl ethyl carbazolium hexafluoroantimonate (PECH) photoinitiator is synthesized in a two‐step, one‐pot manner by quaternizing ethyl carbazole with phenacyl bromide and subsequent ion exchange reaction with potassium hexafluoroantimonate. Under irradiation, PECH tends to undergo homolytic bond cleavage bringing about initiating free radicals. However, as evidenced by cyclic voltammetry and real‐time photobleaching studies, formation of initiating cationic species is highly unlikely as the photochemically formed charged carbazole units tend to couple.

     

Semiconductor nanoparticles for photoinitiation of free radical polymerization in aqueous and organic media

Photoinduced free radical polymerization of vinyl monomers by using semiconductor inorganic nanoparticles (NPs) is investigated. Zinc oxide and iron‐doped zinc oxide were used as photosensitive compounds to initiate the polymerization of acrylamide as a water‐soluble monomer in aqueous environment and methyl methacrylate as an oil‐soluble monomer in organic media under UV‐light irradiation. The method uses photochemically generated electrons and holes from the NPs to form initiating hydroxyl radicals in aqueous media, while tertiary amines and iodonium salt served as coinitiator in organic media. The initiation mechanism in organic media involves hydrogen abstraction or reduction processes via charge carriers, respectively. The kinetic of the polymerization in both environments was studied by means of a photo‐differential scanning calorimetry. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 1500–1507     

Convex sub-differential sum rule via convex semi-closed functions with applications in convex programming

This paper deals with some basic notions of convex analysis and convex optimization via convex semi-closed functions. A decoupling-type result and also a sandwich theorem are proved. As a consequence of the sandwich theorem, we get a convex sub-differential sum rule and two separation results. Finally, the derived convex sub-differential sum rule is applied to solving the convex programming problem.     

Application of maximum likelihood multivariate curve resolution to noisy data sets

In this work, two different maximum likelihood approaches for multivariate curve resolution based on maximum likelihood principal component analysis (MLPCA) and on weighted alternating least squares (WALS) are compared with the standard multivariate curve resolution alternating least squares (MCR‐ALS) method. To illustrate this comparison, three different experimental data sets are used: the first one is an environmental aerosol source apportionment; the second is a time‐course DNA microarray, and the third one is an ultrafast absorption spectroscopy. Error structures of the first two data sets were heteroscedastic and uncorrelated, and the difference between them was in the existence of missing values in the second case. In the third data set about ultrafast spectroscopy, error correlation between the values at different wavelengths is present. The obtained results confirmed that the resolved component profiles obtained by MLPCA‐MCR‐ALS are practically identical to those obtained by MCR‐WALS and that they can differ from those resolved by ordinary MCR‐ALS, especially in the case of high noise. It is shown that methods that incorporate uncertainty estimations (such as MLPCA‐ALS and MCR‐WALS) can provide more reliable results and better estimated parameters than unweighted approaches (such as MCR‐ALS) in the case of the presence of high amounts of noise. The possible advantage of using MLPCA‐MCR‐ALS over MCR‐WALS is then that the former does not require changing the traditional MCR‐ALS algorithm because MLPCA is only used as a preliminary data pretreatment before MCR analysis. Copyright © 2013 John Wiley & Sons, Ltd.