Topological measures and quasi-linear functionals generalize linear functionals. We define study deficient topological on locally compact spaces. A measure a space is set function open closed sets which finitely additive sets, inner regular outer sets. Deficient measures. First we investigate positive, negative, total variation of signed that only assumed to be These variations turn out Then ex...

Nominal algebra is a logic of equality developed to reason algebraically in the presence of binding. In previous work it has been shown how nominal algebra can be used to specify and reason algebraically about systems with binding, such as first-order logic, the lambda-calculus, or process calculi. Nominal algebra has a semantics in nominal sets (sets with a finitely-supported permutation actio...

The paper presents the maximal set and three efficient sets in the decision-making systems with finitely many criteria. Here, we study some properties of these optimality sets maximal and efficient. In the end, it is proved that the efficient set is nonempty, pathconnected and compact, if the utility functions are continuous, concave and strictly quasiconcave.

For a number of locally finitely presentable categories K we describe the codensity monad full embedding all objects into K. We introduce concept D-ultrafilter on an object, where D is “nice” cogenerator prove that assigns to every object representing D-ultrafilters it. Our result covers e.g. sets, vector spaces, posets, semilattices, graphs and M-sets for finite commutative monoids M.

The paper examines the interrelationship between fiscal and monetary policy in a two-country monetary union. The worst scenario occurs when an independent central bank (CB) sets the nominal interest rate and responds to rising government debt/GDP ratios by monetisation. The result is high inflation, high debt/GDP ratios and a large public sector. Government debt and inflation are contained if t...

We discuss some basic geometry of sets definable in the Urysohn sphere using only finitely many parameters and briefly remark on the case of arbitrary definable sets. Then we discuss definable functions in the Urysohn sphere satisfying a special syntactic property.