Epimorphisms are not surjective, even in simple algebras
Using techniques developed by Comer on sheaf-theoretic duality for cylindric algebras, we refine a result of Judit Madarasz by showing that epimorphisms are not surjective even in the class of simple infinite dimensional cylindric algebras.
Galois theory for cylindric algebras and its applications
A Galois correspondence between cylindric set algebras and permutation groups is presented in this paper. Moreover, the Galois connection is used to help establish two important algebraic properties for certain classes of finite-dimensional cylindric algebras, namely the amalgamation property and the property that epimorphisms are surjective. The importance of the amalgamation property (AP for short) in algebraic logic has been recognized for a long time. In [16] the connection with the interpolation property of first-order logic is discussed. The positive amalgamation results from the author's thesis [2] and their extensions announced in [31 are cited in ?2.4 of [16]. These results are established, with a slight improvement, in ?4 below. The key to this study is a lattice anti-isomorphism between subgroups of the symmetric group S, and subalgebras of the full set algebra % (a, ,t) when 0 ,u > a + 1. In particular, this applies to Theorems 2.2, 2.8, 2.9, 3.7, 3.8(2), Corollaries 3.10, 5.5 and Lemma 5.2(2). Essentially the only result where the value of ,u is not known to be the best possible is in Theorem 2.5. Received by the editors July 6, 1983. Some of the contents of this paper were presented at the 74th Annual meeting of the American Mathematical Society in San Francisco, California, January 23-27, 1968. 1980 Mathematics Subject Classification. Primary 03G15; Secondary 06A15, 08B25.
Robust solutions of inverse problems in electromagnetic non-destructive evaluation
Non-destructive testing (NDT) is the application of physical measurement technology based on energy interaction with the material and its nonconformities. The material's response is sensed by transducers and sensors which?in most cases?scan the component and document the results in inspection images. However, NDT measures a physically defined quantity or even an intrinsic property. The difference between non-destructive evaluation (NDE) and NDT is in the interpretation of the inspection data. NDE has to discuss the inspection results in terms of quality elements and characteristics which are relevant to describe the fitness of the material for use. In the case of macroscopic defects these are the kind of defect (cracklike, globular) and its size and orientation to the main stress directions; in the case of material property determination the parameters are mainly mechanical properties. Therefore, in NDE one has to solve inverse problems. The solution of inverse problems based on mathematical procedures such as integral equations is a strong developing discipline and most of the articles prepared for this special issue of the journal have the objective of discussing the latest state of the art in that field. However, practical NDE needs robust and quick solutions which are to be applied mainly online. Therefore, we present here inversion procedures based on multiple linear regression algorithms applied to inspection data. We describe the calibration procedure to fit the free parameters of the model functions and give examples of practical applications in industry.