131 research outputs found
The optimal form of the scanning near-field optical microscopy probe
A theoretical approach to determine the optimal form of the near-field
optical microscope probe is proposed. An analytical expression of the optimal
probe form with subwavelength aperture has been obtained. The advantages of the
probe with the optimal form are illustrated using numerical calculations. The
conducted calculations show 10 times greater light throughput and the reception
possibility of the more compactly localized light at the output probe aperture
which could indicate better spatial resolution of the optical images in
near-field optical technique using optimal probe.Comment: 12 pages, 6 figure
Arithmetic complexity via effective names for random sequences
We investigate enumerability properties for classes of sets which permit
recursive, lexicographically increasing approximations, or left-r.e. sets. In
addition to pinpointing the complexity of left-r.e. Martin-L\"{o}f, computably,
Schnorr, and Kurtz random sets, weakly 1-generics and their complementary
classes, we find that there exist characterizations of the third and fourth
levels of the arithmetic hierarchy purely in terms of these notions.
More generally, there exists an equivalence between arithmetic complexity and
existence of numberings for classes of left-r.e. sets with shift-persistent
elements. While some classes (such as Martin-L\"{o}f randoms and Kurtz
non-randoms) have left-r.e. numberings, there is no canonical, or acceptable,
left-r.e. numbering for any class of left-r.e. randoms.
Finally, we note some fundamental differences between left-r.e. numberings
for sets and reals
There is no low maximal d. c. e. degree - Corrigendum
We give a corrected proof of an extension of the Robinson Splitting Theorem for the d. c. e. degrees. © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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