On the Proximal Point Algorithm

Let A be a maximal monotone operator in a real Hilbert space H and let {u _n } be the sequence in H given by the proximal point algorithm, defined by u _n =(I+c _n A)⁻¹(u _n−1−f _n ), ∀ n≥1, with u ₀=z, where c _n >0 and f _n ∈H. We show, among other things, that under suitable conditions, u _n converges weakly or strongly to a zero of A if and only if lim inf  _n→+∞|w _n |<+∞, where w _n =(∑ _k=1 ⁿ c _k )⁻¹∑ _k=1 ⁿ c _k u _k . Our results extend previous results by several authors who obtained similar results by assuming A ⁻¹(0)≠φ.     

Properties of nuclear matter using the velocity-dependent effective potential ofs-wave interaction

Two forms of a velocity-dependent effective potential are used. The binding energy and the incompressibility of the nuclear matter are calculated. These are found to be in a good agreement with those obtained by others and with the experimental results. The single-particle potential, the effective massM ^* and the nuclear surface energy are also discussed and compared with those obtained by the others.     

An analytical model for evaluating the metal-metal surface energy

Metal-metal surface energies are calculated as a function of the electron density at the interface. Their contribution to the adhesion energy is shown to be small.     

Suitability of Liquid Crystal Polymer substrates for high frequency acoustic devices

Polymer substrates are widely seen as a low-cost route to flexible circuits for systems incorporating displays, sensing functions and transistors. To date most polymer-based devices have involved passive components such as humidity sensors, constructed using metals and additional organic layers. The starting point of the study described here, is whether more advanced components incorporating functional materials can be integrated into devices on polymer substrates. An understanding will be required of the material factors that limit performance and, if possible, techniques developed to circumvent them so that their performance can be compared to that of standard silicon-based components.     

Conformal curves on the WO3 surface

We have studied the isoheight lines on the WO3 surface as a physical candidate for conformally invariant curves. We have shown that these lines are conformally invariant with the same statistics of domain walls in the critical Ising model. They belong to the family of conformal invariant curves called Schramm-Loewner evolution (or SLE(kappa)), with diffusivity of kappa approximately 3. This can be regarded as the first experimental observation of SLE curves. We have also argued that Ballistic Deposition (BD) can serve as a growth model giving rise to contours with similar statistics at large scales.     

A strong convergence theorem for solutions to a nonhomogeneous second order evolution equation

In this paper, we establish the strong convergence of possible solutions to the following nonhomogeneous second order evolution system

     

News item

It is shown within a simple Thomas-Fermi approximation including exchange and correlation that the main contribution to the surface energy comes from an excess positive charge near the surface.     

Dual Ligand‐Enabled Nondirected C−H Olefination of Arenes

The application of the Pd‐catalyzed oxidative C?H olefination of arenes, also known as the Fujiwara–Moritani reaction, has traditionally been limited by the requirement for directing groups on the substrate or the need to use the arene in large excess, typically as a (co)solvent. Herein the development of a catalytic system is described that, through the combined action of two complementary ligands, makes it possible to use directing‐group‐free arenes as limiting reagents for the first time. The reactions proceed under a combination of both steric and electronic control and enable the application of this powerful reaction to valuable arenes, which cannot be utilized in excess.