We review recent results which relate spectral theory of discrete one-dimensional Schrödinger operators over strictly ergodic systems to uniform existence of the Lyapunov exponent. In combination with suitable ergodic theorems this allows one to establish Cantor spectrum of Lebesgue measure zero for a large class of quasicrystal Schrödinger operators. The results can also be used to study non-u...

(t,m, s)-nets are point sets in Euclidean s-space satisfying certain uniformity conditions, for use in numerical integration. They can be equivalently described in terms of ordered orthogonal arrays, a class of finite geometrical structures generalizing orthogonal arrays. This establishes a link between quasi-Monte Carlo methods and coding theory. In the present paper we prove an asymptotic Gil...

in this paper, we investigate the l-fuzzy proximities and the relationships betweenl-fuzzy topologies, l-fuzzy topogenous order and l-fuzzy uniformity. first, we show that the category of-fuzzy topological spaces can be embedded in the category of l-fuzzy quasi-proximity spaces as a coreective full subcategory. second, we show that the category of l -fuzzy proximity spaces is isomorphic to the ...

The second-harmonic interferometric spectroscopy (SHIS) which combines both amplitude (intensity) and phase spectra of the second-harmonic (SH) radiation is proposed as a new spectroscopic technique being sensitive to the type of critical points (CP's) of combined density of states at semiconductor surfaces. The increased sensitivity of SHIS technique is demonstrated for the buried Si(111)-SiO ...

The Malin Shelf, off north-west Ireland, was an important zone of confluence for marine-based ice streams the former British–Irish Ice Sheet (BIIS). Legacy geophysical datasets are used to construct models seismic character, relative age and distribution shelf sediments landforms. Buried surface landform assemblages provide evidence that during deglaciation Late Devensian BIIS, region occupied ...

Whole genome amplification (WGA) plays an important role in sample preparation of low-input templates for high-throughput sequencing. Multiple displacement amplification (MDA), a popular isothermal WGA methods, suffers a major hurdle of highly uneven amplification. Optimizations have been made in the past by separating the reagents into numbers of tiny chambers or droplets in microfluidic devic...

In this article, we propose a Partition ofUnity Refinement (PUR)method to improve the local approximations of elliptic boundary value problems in regions of interest. The PUR method only needs to refine the local meshes and hanging nodes generate no difficulty. The mesh qualities such as uniformity or quasi-uniformity are kept. The advantages of the PUR include its effectiveness and relatively ...