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.

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.

A multi-moment finite volume formulation for shallow water equations on unstructured mesh

A novel and accurate finite volume method has been presented to solve the shallow water equations on unstructured grid in plane geometry. In addition to the volume integrated average (VIA moment) for each mesh cell, the point values (PV moment) defined on cell boundary are also treated as the model variables. The volume integrated average is updated via a finite volume formulation, and thus is numerically conserved, while the point value is computed by a point-wise Riemann solver. The cell-wise local interpolation reconstruction is built based on both the VIA and the PV moments, which results in a scheme of almost third order accuracy. Efforts have also been made to formulate the source term of the bottom topography in a way to balance the numerical flux function to satisfy the so-called C-property. The proposed numerical model is validated by numerical tests in comparison with other methods reported in the literature. (C) 2010 Elsevier Inc. All rights reserved.

Cosmological equations and thermodynamics on apparent horizon in thick braneworld

We derive the generalized Friedmann equation governing the cosmological evolution inside the thick brane model in the presence of two curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. We find two effective four-dimensional reductions of the generalized Friedmann equation in some limits and demonstrate that the reductions but not the generalized Friedmann equation can be rewritten as the first law of equilibrium thermodynamics on the apparent horizon of thick braneworld.