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.     

Computational design of new organic (D–π–A) dyes based on benzothiadiazole for photovoltaic applications,especially dye-sensitized solar cells

Research on Chemical Intermediates - A theoretical study on four organic dyes based on bis(4-hexyloxy)triphenylamine as donor and electron acceptor cyanoacrylic acid with a...     

Epidemiological models with quadratic equation for endemic equilibria—A bifurcation atlas

The existence and occurrence, especially by a backward bifurcation, of endemic equilibria is of utmost importance in determining the spread and persistence of a disease. In many epidemiological models, the equation for the endemic equilibria is quadratic, with the coefficients determined by the parameters of the model. Despite its apparent simplicity, such an equation can describe an amazing number of dynamical behaviors. In this paper, we shall provide a comprehensive survey of possible bifurcation patterns, deriving explicit conditions on the equation's parameters for the occurrence of each of them, and discuss illustrative examples.     

A thermodynamic approach with internal variables using Lagrange formalism. Part I: General framework

We present some reflections on the application of the Lagrangian formalism for continuous media locally uniform subjected to internal irreversible evolutions. The Lagrangian density, defined as the time derivative of a non-equilibrium thermodynamic potential, [Thermodynamics of Relaxation Processes using Internal variables within a Lagrange-formalism. P. Germain’s Anniversary Volume 2000. Contiuum Thermomechanics: the Art and Science of Modeling Matter’s Behaviour, 2000], contains all the symmetry properties of the system. The generalised Lagrange co-ordinates correspond to the state and internal variables of the time derivative of the generalised Gibbs potential. The latter being used within the framework of the De Donder’s method, must also account for the memory effect of the physical medium.This first part is devoted to the thermodynamic framework called the distribution of non-linear relaxations approach (DNLR) developed by C. Cunat on the basis of the generalised Gibbs’ relation.     

ZnTe6O13, a new ZnO–TeO2 phase

Our investigations into the ZnO–TeO₂ system have produced a new phase, zinc(II) hexatellurium(IV) tridecaoxide, ZnTe₆O₁₃, with trigonal (R) symmetry, synthesized by repeated heating and cooling to a maximum temperature of 1053 K. The asymmetric unit consists of a Zn atom coordinated in a distorted octahedral fashion by two unique tellurium(IV) oxide units that form trigonal–bipyramidal TeO₄ and TeO₃₊₁ corner‐ and edge‐shared polyhedra. Except for the Zn and an O atom, which occupy 6c positions, all atoms occupy 18f general positions.     

Stabilité du fibré tangent des surfaces de Del Pezzo

Sans résumé     

A short and efficient synthesis of 2′-deoxybenzo- and pyridoimidazole C-nucleosides

A short route to a series of 2′-deoxy-C-nucleosides featuring substituted nucleobases has been developed. The key step is the formation of the cyclized products following Mukaiyama's type amide coupling and a simple dehydration, starting from readily accessible synthons. The epimerization of the C1′-stereogenic center was avoided under mild and controlled conditions.     

A short and highly stereoselective synthesis of α-(2-aminothiazolyl)-C-nucleosides

A short route to novel α-(2-aminothiazolyl)-C-nucleosides has been developed. The key step was the high diastereoselective reduction of the hemiacetal intermediates using L-Selectride, which afforded the corresponding R-diols in quantitative yields. These diols were converted, after C4-C1 ring closure and protecting groups cleavage, to their corresponding free α-C-nucleosides.     

Influence of moisture on the viscoelastic relaxations in long aliphatic chain contained semiaromatic polyamide, (PA9‐T) fiber

The effect of moisture on the mechanical relaxation processes of semiaromatic semicrystalline polyamides synthesized by a long‐chain aliphatic diamine and terephthalic acid was investigated by dynamic viscoelastic analysis (DVA) and differential scanning calorimetry (DSC). Moreover, the implication of moisture with the amorphous and crystalline domains was also examined by temperature‐dependent wide‐angle X‐ray diffraction and Fourier transform infrared spectra. The characteristics of the relaxations such as α, β, γ, and the pronounced peak shoulder appeared at 25–100 °C in DVA tan δ curves were found to be strongly susceptible to the presence of moisture. With moisture evaporation, the peak shoulder of 25–100 °C and the β‐relaxation disappeared. The former is anticipated to originate from to the side group motion of hydrogen‐bonded water, whereas the later one is from the motions of the amide–water complex units. With the disappearance of the β‐relaxation, the γ‐relaxation appeared simultaneously in much lower temperatures and ultimately coupled with the δ‐relaxation. The γ‐relaxation is attributed to be associated with the molecular motion of the amide group and δ‐relaxation with for the motion of the methylene units. The existence of two types of water was identified in the polymer, namely, tightly bound and loosely bound. The tightly bound water is believed to be directly connected by hydrogen bonding with the strong polar groups and the loosely bound water weakly links with those connected water making hydrogen bridges. The moisture acts as a plasticizer in the polymer matrix, which causes quite a large depression in its glass transition temperature (T_g). WAXD and FTIR studies corroborated the existence of water solely in amorphous regions, i.e., no rapport of water with the crystalline parts. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2878–2891, 2003