Decompositions of factor codes and embeddings between shift spaces with unequal entropies

Given a factor code between sofic shifts X and Y, there is a family of decompositions of the original code into factor codes such that the entropies of the intermediate subshifts arising from the decompositions are dense in the interval from the entropy of Y to that of X. Furthermore, if X is of finite type, we can choose those intermediate subshifts as shifts of finite type. In the second part of the paper, given an embedding from a shift space to an irreducible sofic shift, we characterize the set of the entropies of the intermediate subshifts arising from the decompositions of the given embedding into embeddings.Comment: 14pages, 2 figures; v2) minor revision. to appear in Ergodic Theory Dynamical System

Dust, Ice, and Gas in Time (DIGIT) Herschel Observations of GSS30-IRS1 in Ophiuchus

As a part of the "Dust, Ice, and Gas In Time" (DIGIT) key program on Herschel, we observed GSS30-IRS1, a Class I protostar located in Ophiuchus (d = 120 pc), with Herschel/Photodetector Array Camera and Spectrometer. More than 70 lines were detected within a wavelength range from 50 to 200 mu m, including CO, H2O, OH, and two atomic [O I] lines at 63 and 145 mu m. The [C II] line, known as a tracer of externally heated gas by the interstellar radiation field (ISRF), is also detected at 158 mu m. All lines, except [O I] and [C II], are detected only at the central spaxel of 9 ''.4 x 9 ''.4. The [O I] emissions are extended along a NE-SW orientation, and the [C II] line is detected over all spaxels, indicative of an external photodissociation region. The total [C II] intensity around GSS30 reveals that the far-ultraviolet radiation field is in the range of 3 to 20 G(0), where G(0) is in units of the Habing Field, 1.6 x 10(-3) erg cm(-2) s(-1). This enhanced external radiation field heats the envelope of GSS30-IRS1, causing the continuum emission to be extended, unlike the molecular emission. The best-fit continuum model of GSS30-IRS1 with the physical structure including flared disk, envelope, and outflow shows that the internal luminosity is 10 L-circle dot, and the region is externally heated by a radiation field enhanced by a factor of 130 compared to the standard local ISRF.NASANational Research Foundation of Korea (NRF) - Ministry of Education of the Korean government NRF-2012R1A1A2044689National Research Foundation (NRF) - Ministry of Education of KoreaAstronom

COMPUTER-GENERATED HOLOGRAM ETCHED IN GAAS FOR OPTICAL INTERCONNECTION OF VLSI CIRCUITS

By integrating, on a wafer plane, GaAs semiconductor optoelectronic modulators and detectors with computer-generated holograms between then, the potential for in-plane interconnections is proposed. We report the fabrication and characterisation of a binary-phase relief hologram etched in a GaAs wafer using an averaged Fresnel zone plate design to focus light to 2 x 2 spots for array interconnection. Efficiencies of 28% for this design of binary CGH etched in GaAs have been achieved, close to the theoretical maximum