This paper describes the MLPQ constraint database system. The query language of MLPQ is SQL extended with linear arithmetic constraints. The input and output databases are Linear Constraint Databases (LCDBs). An important feature of the MLPQ system is that it can handle aggregate operators, Min, Max, Sum, Avg, etc. In MLPQ, these operators are evaluated for a series of linear programming (LP) p...

In the paper the equation of the form A+B = P , w h e r e A and B are binary aggregation operators, is investigated. A necessary and suu-cient condition for binary aggregation operators to be solutions of this equation, is proved. Already known solutions in some special classes of aggrega-tion operators, e.g., in the class of triangular norms and conorms, in the class of quasi{arithmetic means ...

We study multiply recurrent and hypercyclic operators as a special case of $\mathcal F$-hypercyclicity, where F$ is the family subsets natural numbers containing arbitrarily long arithmetic progressions. prove several properties operators, we characterize those which are weakly mixing recurrent, show that there but not mixing.

We give an extension of the refined Jensen’s operator inequality for n−tuples of self-adjoint operators, unital n−tuples of positive linear mappings and real valued continuous convex functions with conditions on the spectra of the operators. We also study the order among quasi-arithmetic means under similar conditions.

The ZM package is a collection of Fortran subroutines that performs floating point multiple precision evaluation of complex arithmetic and elementary functions. These routines use the FM package [7] for real multiple precision arithmetic, constants, and elementary functions. Brent’s MP package [4] did not support complex arithmetic, and Bailey’s more recent MP package [2,3] provides complex ari...

Averaging Operators on the Unit Interval Mai Gehrke, Carol Walker, Elbert Walker New Mexico State University, Las Cruces, New Mexico, USA In this paper we look at algebras consisting of the unit interval [0; 1] with the standard partial order together with an averaging operator. In working with negations and t-norms, it is not uncommon to call upon the arithmetic of the real numbers even though...

Let predicate P be converted from Boolean to numeric type by writing 〈P 〉, with 〈false〉 being 0 and 〈true〉 being 1, so that in a degenerate sense 〈P 〉 can be regarded as ‘the probability that P holds in the current state’. Then add explicit numbers and arithmetic operators, to give a richer language of arithmetic formulae into which predicates are embedded by 〈·〉. Abrial’s generalised substitut...