A Lower Bound for the Differences of Powers of Linear Operators

Let T be a bounded linear operator in a Banach space, with σ（T）={1}. In 1983, Esterle-Berkani＇ s conjecture was proposed for the decay of differences （I - T） T^n as follows： Eitheror lim inf （n→∞（n＋1）｜｜（I-T）T^n｜｜≥1/e or T = I. We prove this claim and discuss some of its consequences.     

Study of the peak effect phenomenon in single crystals of 2H-NbSe2

The weakly pinned single crystals of the hexagonal 2H-NbSe₂ compound have emerged as prototypes for determining and characterizing the phase boundaries of the possible order-disorder transformations in the vortex matter. We present here a status report based on the ac and dc magnetization measurements of the peak effect phenomenon in three crystals of 2H-NbSe₂, in which the critical current densities vary over two orders of magnitude. We sketch the generic vortex phase diagram of a weakly pinned superconductor, which also utilizes theoretical proposals. We also establish the connection between the metastability effects and pinning.     

Elementary-field modeling of surface-plasmon excitation with partially coherent light

We present a mathematical model and its numerical implementation for the analysis of the interaction of spatially partially coherent electromagnetic fields with micro- and nanostructured objects. The model is based on the decomposition of the incident field into a set of fully coherent but mutually uncorrelated elementary field modes, and the use of the Fourier Modal Method (FMM) with the S-matrix propagation algorithm. We apply the model to studies of the excitation of surface plasmons in thin metallic slabs, nanowires, and resonant structures. We demonstrate, e.g., that the plasmon excitation efficiency is not essentially affected by the degree of spatial coherence. However, certain plasmon interference effects can be efficiently smoothed out by using illumination with reduced coherence.     

Transverse laser-mode structure determination from spatial coherence measurements: Experimental results

We demonstrate experimentally the feasibility of a certain coherence-theoretic algorithm for determining the relative modal weights of a laser beam that consists of multiple Hermite-Gaussian transverse modes. A computer-controlled Young's two-pinhole interferometer with a linear CCD array is used for the coherence measurements. The required scaling parameter (beam width) is obtained iteratively by library routines. Numerical simulations on the stability of the algorithm in the presence of experimental noise are also presented.     

Hörmander Class of Pseudo-Differential Operators on Compact Lie Groups and Global Hypoellipticity

In this paper we give several global characterisations of the Hörmander class \(\Psi ^m(G)\) of pseudo-differential operators on compact Lie groups in terms of the representation theory of the group. The result is applied to give criteria for the ellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of the first and second order globally hypoelliptic differential operators are given, in particular of operators that are locally not invertible nor hypoelliptic but globally are. Where the global hypoelliptiticy fails, one can construct explicit examples based on the analysis of the global symbols.     

Shaping Solid-State Supramolecular Cavities: Chemically Induced Accordionlike Movement of gamma-Zirconium Phosphate Containing Polyethylenoxide Pillars

The hydrophilic oxygen atoms of polyethylenoxide chains inserted as pillars in gamma-zirconium phosphate form hydrogen bonds with the acid groups of the host. As a result the pillars are almost perpendicular to the gamma layers. Upon changing the pH level of the supernatant solution the hydrogen bonds are broken and the pillars become almost perpendicular to the layers (shown schematically). Thus there is a reversible enlargement-shortening of the interlayer space.