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.     

Role of FTFSI Anion Asymmetry on Physical Properties of AFTFSI (A=Li,Na and K) Based Electrolytes and Consequences on Supercapacitor Application

This study compares the physicochemical properties of six electrolytes comprising of three salts: LiFTFSI, NaFTFSI and KFTFSI in two solvent mixtures, the binary (3EC/7EMC) and the ternary (EC/PC/3DMC). The transport properties (conductivity, viscosity) as a function of temperature and concentration were modeled using the extended Jones-Dole-Kaminsky equation, the Arrhenius model, and the Eyring theory of transition state for activated complexes. Results are discussed in terms of ionicity, solvation shell, and cross-interactions between electrolyte components. The application of the six formulated electrolytes in symmetrical activated carbon (AC)//AC supercapacitors (SCs) was characterized by cyclic voltammetry (CV), galvanostatic cycling with potential limitation (GCPL), electrochemical impedance spectroscopy (EIS) and accelerated aging. Results revealed that the geometrical flexibility of the FTFSI anion allows it to access and diffuse easily in AC whereas its counter ions (Li⁺, Na⁺ or K⁺) can remain trapped in porosity. However, this drawback was partially resolved by mixing LiFTFSI and KFTFSI salts in the electrolyte.     

Immobilizing redox enzymes at mesoporous and nanostructured electrodes

Three key challenges are stimulating intensive research in the development of productive direct electron transfer mode enzyme electrodes: proper enzyme orientation, high enzyme loading, and full retention of enzyme activity. In this review, we summarize some significant advances that have been reported in the last years on the design of mesoporous and nanostructured electrodes as enzyme scaffolds and of innovative methodologies for wiring enzymes to electrodes. Particular attention is given to investigations on physical factors that determine a favorable enzyme immobilization, to provide rational guidelines for the design of productive enzymatic electrodes. Finally, some emerging trends focused on the spatial organization of either single enzymes or enzyme cascades are also briefly addressed.     

A survey of surface tension,molar volume and density for Sn–Ag–Cu–Bi–Sb quinary alloys as lead-free solders

ABSTRACT

By applying the geometric models and the theoretical equation, the surface tension, the molar volume and the density were studied. The empirical calculations were carried out in temperature range 623?K?≤?T?≤?1123?K. Only few thermophysical properties were estimated for eight quinary alloys: Sn3.55Ag0.5Cu3Bi3Sb, Sn3.48Ag0.5Cu3Bi5Sb, Sn3.48 Ag0.5Cu5Bi3Sb, Sn3.40 Ag0.5Cu5Bi5Sb, Sn3.53Ag1Cu3Bi3Sb, Sn3.46Ag1Cu3Bi5Sb, Sn3.46Ag1Cu5Bi3Sb, Sn3.38Ag1Cu5Bi5Sb. The results show that surface tension and density have a linear appearance for all temperatures. We have also studied the influence of the composition and temperature in the studied alloys. The obtained theoretical results are compared with the experimental ones and with the conventional Pb–Sn welds.     

On the redox reactions between allyl radicals and NOx

NO_x mitigation is a central focus of combustion technologies with increasingly stringent emission regulations. NO_x can also enhance the autoignition of hydrocarbon fuels and can promote soot oxidation. The reaction between allyl radical (C₃H₅) and NO_x plays an important role in the oxidation kinetics of propene. In this work, we measured the absolute rate coefficients for the redox reaction between C₃H₅ and NO_x over the temperature range of 1000–1252 K and pressure range of 1.5–5.0 bar using a shock tube and UV laser absorption technique. We produced C₃H₅ by shock heating of C₃H₅I behind reflected shock waves. Using a Ti:Sapphire laser system with frequency quadrupling, we monitored the kinetics of C₃H₅ at 220 nm. Unlike low-temperature chemistry, the two target reactions, C₃H₅ + NO → products (R1) and C₃H₅ + NO₂ → products (R2), exhibited a strong positive temperature dependence for this radical-radical type reaction. However, these reactions did not show any pressure dependence over the pressure range of 1.5–5.0 bar, indicating that the measured rate coefficients are close to the high-pressure limit. The measured values of the rate coefficients resulted in the following Arrhenius expressions (in unit of cm³/molecule/s):$k_1\left({\mathrm{C}}_3{\mathrm{H}}_5+\text{NO}\right)=1.49\times {10}^{?10}\exp \left(?6083.6\frac{\mathrm{K}}{T}\right)\left(1017?1252K\right)$$k_2\left({\mathrm{C}}_3{\mathrm{H}}_5+\mathrm{N}{\mathrm{O}}_2\right)=1.71\times {10}^{?10}\exp \left(?3675.7\frac{\mathrm{K}}{T}\right)\left(1062?1250K\right)$To our knowledge, these are the first high-temperature measurements of allyl + NO_x reactions. The reported data will be highly useful in understanding the interaction of NO_x with resonantly stabilized radicals as well as the mutual sensitization effect of NO_x on hydrocarbon fuels.     

Differential Graded Bocses and A ∞ $A_{\infty }$ -Modules

Algebras and Representation Theory - We introduce and study the category of twisted modules over a triangular differential graded bocs. We show that in this category idempotents split, that it...     

On Anomalous Dissipation in the Plasma of the Dusty Lunar Exosphere

JETP Letters - One of the main features of the dusty plasma compared to the conventional plasma (without charged dust particles is anomalous dissipation that is caused by the charging of dust...