Congruence lattices ofp-algebras

T. Kartriák proved the following theorem:Every finite distributive lattice is the congruence lattice of a finite p-algebra. We provide a short proof, and a generalization, of this result.Presented by J. Berman.The research of the first author was supported by the NSERC of Canada.The research of the second author was supported by the Hungarian National Foundation for Scientific Research, under Grant No. 1903.     

On isotone functions with the Substitution Property in distributive lattices

A universal algebra isaffine complete if all functions satisfying the Substitution Property are polynomials (composed of the basic operations and the elements of the algebra). In 1962, the first author proved that a bounded distributive lattice is affine complete if and only if it does not contain a proper Boolean interval. Recently, M. Ploica generalized this result to arbitrary distributive lattices.In this paper, we introduce a class of functions on a latticeL, we call themID-polynomials, that derive from polynomials on the ideal lattice (resp., dual ideal lattice) ofL; they are isotone functions and satisfy the Substitution Property. We prove that for a distributive latticeL, all unary functions with the Substitution Property are ID-polynomials if and only ifL contains no proper Boolean interval.The research of the first author was supported by the NSERC of Canada. The research of the second author was supported by the Hungarian National Foundation for Scientific Research, under Grant No. 1903.     

Operation of KrF and ArF tunable excimer lasers without Cassegrain optics

A commercial tunable excimer laser consists of an oscillator-amplifier combination. The oscillator produces high-quality light that is sent to the amplifier and is distributed throughout the amplifier cavity via Cassegrain optics. We describe here two alternative approaches, a single-pass configuration for use with KrF and a triple-pass configuration with ArF, both of which do away with the Cassegrain optics. In each approach, the beam energy is the same as with Cassegrain optics. For KrF, the changes provide better locking, a higher degree of linear polarization, and a better spatial beam homogeneity, but a poorer beam divergence. For ArF, there is also better beam homogeneity, but the locking efficiency and divergence are not as good as with Cassegrain optics.     

Second-order subdifferentials of C1,1 functions and optimality conditions

We present second-order subdifferentials of Clarke's type of C ^1,1 functions, defined in Banach spaces with separable duals. One of them is an extension of the generalized Hessian matrix of such functions in ⁿ , considered by J. B. H.-Urruty, J. J. Strodiot and V. H. Nguyen. Various properties of these subdifferentials are proved. Second-order optimality conditions (necessary, sufficient) for constrained minimization problems with C ^1,1 data are obtained.This work was partially supported by the National Foundation for Scientific Investigations in Bulgaria under contract No. MM-406/1994.     

Complexometric titrations controlled by anodic-stripping methods-I Voltammetric stripping

Anodic-stripping voltammetry is used to perform automatic complexometric titrations of metal ions, with high precision. The stripping peaks are converted into corresponding titrant volume increments which are added consecutively during stripping. In analysis of samples containing about 1 mmole, each of lead, indium and gallium, relative standard deviations of 0.008-0.03% were attained.