with fκ(s) as large as possible (resp. Fκ(s) as small as possible) given that the above inequality holds for all choices of A satisfying (1). Selberg [2] has shown (in a much more general context) that the functions fκ(s), Fκ(s) are continuous, monotone, and computable for s > 1, that they do not change if we replace (1) with (2), and that they tend to 1 exponentially as s goes to infinity. Mor...

The advantages of new types H2TiO3 lithium-ion sieves, including excellent adsorption performance, high-efficiency Li+-ion selectivity, reliable regeneration, environmental friendliness, and easy preparation, have attracted considerable attention. Currently, the prices lithium carbonate other related products are rapidly increasing, so use sieves to extract resources in salt lake brine has beco...

Recently, a paraxially individual far-field model was presented for the focusing and imaging analysis of pinhole photon sieves. By use of a local Taylor expansion of the integrated function of the Rayleigh-Sommerfeld diffraction formula, the small-size property of the individual pinholes, and the linear superposition principle, we extend this model to the nonparaxial case of high-numerical-aper...

Morphological scale-spaces have become an important tool for analysing greyscale images. However, their extension to colour images has proven elusive until recently. In this paper an original evaluation of two recently proposed colour sieves is presented, both algorithmically and in terms of their computational and segmentation performance. A new colour sieve structure is also proposed, motivat...

We describe our single-instruction multiple data (SIMD) implementation of the multiple polynomial quadratic sieve integer factoring algorithm. On a 16K MasPar massively parallel computer, our implementation can factor 100 digit integers in a few days. Its most notable success was the factorization of the 110-digit RSA-challenge number, which took about a month.

Zeolite and zeolite-like molecular sieves are being used in a large number of applications such as adsorption and catalysis. Achievement of the long-standing goal of creating a chiral, polycrystalline molecular sieve with bulk enantioenrichment would enable these materials to perform enantioselective functions. Here, we report the synthesis of enantiomerically enriched samples of a molecular si...

Organosilyl groups were successfully incorporated in AFI and VFI aluminophosphate frameworks using organoalkoxysilanes to modify hydrophobicity and acidity of the molecular sieves.