Solid Echo in Three-Spin Groups with Arbitrary Constants of Dipole–Dipole Interaction

Applied Magnetic Resonance - The suggested approach allowed us to derive analytical expressions for modeling the shape of solid-echo signal and its time evolution for a system of three-spin groups...     

Simulation of dependence of the cross section of deuterons beam fragmentation into cumulative pions and protons on the mass of the target nucleus

Physics of Atomic Nuclei - We have studied the mechanisms influencing production of cumulative pions and protons in the fragmentation of the incident deuterons into cumulative pions and protons...     

Role of method of synthesis on the size of flakes,dispersion stability and thermophysical properties of aqua based reduced graphene oxide nanofluids

Journal of Thermal Analysis and Calorimetry - The role of method of synthesis on the size of flakes, dispersion stability and thermophysical properties of aqua based reduced graphene oxide (rGO)...     

Hybrid (ND-Co3O4/EG) nanoliquid through a permeable cylinder under homogeneous-heterogeneous reactions and slip effects

Journal of Thermal Analysis and Calorimetry - Modeling and computations are performed to study the ND-Co3O4/EG hybrid nanoliquid mixed convective flow past a vertical porous cylinder. The flow...     

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.