On equations for regular languages, finite automata, and sequential networks

We consider systems of equations of the form where A is the underlying alphabet, the Xi are variables, the Pi,a are boolean functions in the variables Xi, and each δi is either the empty word or the empty set. The symbols υ and denote concatenation and union of languages over A. We show that any such system has a unique solution which, moreover, is regular. These equations correspond to a type of automation, called boolean automation, which is a generalization of a nondeterministic automation. The equations are then used to determine the language accepted by a sequential network; they are obtainable directly from the network.

The Category-Theoretic Solution of Recursive Domain Equations

Recursive specifications of domains plays a crucial role in denotational semantics as developed by Scott and Strachey and their followers. The purpose of the present paper is to set up a categorical framework in which the known techniques for solving these equations find a natural place. The idea is to follow the well-known analogy between partial orders and categories, generalizing from least fixed-points of continuous functions over cpos to initial ones of continuous functors over $\omega $-categories. To apply these general ideas we introduce Wand's ${\bf O}$-categories where the morphism-sets have a partial order structure and which include almost all the categories occurring in semantics. The idea is to find solutions in a derived category of embeddings and we give order-theoretic conditions which are easy to verify and which imply the needed categorical ones. The main tool is a very general form of the limit-colimit coincidence remarked by Scott. In the concluding section we outline how compatibility considerations are to be included in the framework. A future paper will show how Scott's universal domain method can be included too.

Simultaneous multiwavelength observations of sagittarius A

We observed Sgr A* using the Very Large Array (VLA) and the Giant Metrewave Radio Telescope (GMRT) at multiple centimeter and millimeter wavelengths on 2003 June 17. The measured flux densities of Sgr A*, together with those obtained from the Submillimeter Array (SMA) and the Keck II 10 m telescope on the same date, are used to construct a simultaneous spectrum of Sgr A* from 90 cm to 3.8 mu m. The simultaneous spectrum shows a spectral break at about 3.6 cm, a possible signature of synchrotron self-absorption of the strong radio outburst that occurred near epoch 2003 July 17. At 90 cm, the flux density of Sgr A* is 0.22 +/- 0.06 Jy, suggesting a sharp decrease in flux density at wavelengths longer than 47 cm. The spectrum at long cm wavelengths appears to be consistent with free-free absorption by a screen of ionized gas with a cutoff similar to 100 cm. This cutoff wavelength appears to be three times longer than that of similar to 30 cm suggested by Davies, Walsh, & Booth based on observations in 1974 and 1975. Our analysis suggests that the flux densities of Sgr A* at wavelengths longer than 30 cm could be attenuated and modulated by stellar winds from massive stars close to Sgr A*.

ON THE RATE-EQUATIONS OF SEMICONDUCTOR-LASERS FOR MEASURING SPONTANEOUS EMISSION FACTOR

The rate equations used for measuring spontaneous emission factor beta is examined through the comparison of numerical results, The results show that beta obtained by using total spontaneous emission rate R(sp) = N/tau sp is about double of that using R(sp) = BN2, The magnitude difference between the measured beta and that predicted by classical theory [8] will disappear by using more reasonable R(sp) = BN2. The results also show that the magnitude of beta may be underestimated by ignoring the nonradiative recombination rates.

Choice of calibration equations of the TSM method

For the reciprocal-test fixtures, there are six independent S-parameters to. be determined, and the thru-short-match (TSM) calibration can provide eight calibration equations. In this paper, the relation of calibration equations is investigated. It has been shown that the four equations obtained from the measurement with a transmission standard can be used simultaneously in the calibration. Experimental results show that the different choice of equations will lead to quite different solution, and the calibration accuracy can be improved by taking advantages of the established relation among the calibration equations and properly choosing calibration equations.