Algebraic Theories over Nominal Sets

We investigate the foundations of a theory of algebraic data types with variable binding inside classical universal algebra. In the first part, a category-theoretic study of monads over the nominal sets of Gabbay and Pitts leads us to introduce new notions of finitary based monads and uniform monads. In a second part we spell out these notions in the language of universal algebra, show how to recover the logics of Gabbay-Mathijssen and Clouston-Pitts, and apply classical results from universal algebra.Comment: 16 page

Relation Liftings on Preorders and Posets

The category Rel(Set) of sets and relations can be described as a category of spans and as the Kleisli category for the powerset monad. A set-functor can be lifted to a functor on Rel(Set) iff it preserves weak pullbacks. We show that these results extend to the enriched setting, if we replace sets by posets or preorders. Preservation of weak pullbacks becomes preservation of exact lax squares. As an application we present Moss's coalgebraic over posets

Semantics of Higher-Order Recursion Schemes

Higher-order recursion schemes are recursive equations defining new operations from given ones called "terminals". Every such recursion scheme is proved to have a least interpreted semantics in every Scott's model of \lambda-calculus in which the terminals are interpreted as continuous operations. For the uninterpreted semantics based on infinite \lambda-terms we follow the idea of Fiore, Plotkin and Turi and work in the category of sets in context, which are presheaves on the category of finite sets. Fiore et al showed how to capture the type of variable binding in \lambda-calculus by an endofunctor H\lambda and they explained simultaneous substitution of \lambda-terms by proving that the presheaf of \lambda-terms is an initial H\lambda-monoid. Here we work with the presheaf of rational infinite \lambda-terms and prove that this is an initial iterative H\lambda-monoid. We conclude that every guarded higher-order recursion scheme has a unique uninterpreted solution in this monoid

Relation lifting, with an application to the many-valued cover modality

We introduce basic notions and results about relation liftings on categories enriched in a commutative quantale. We derive two necessary and sufficient conditions for a 2-functor T to admit a functorial relation lifting: one is the existence of a distributive law of T over the "powerset monad" on categories, one is the preservation by T of "exactness" of certain squares. Both characterisations are generalisations of the "classical" results known for set functors: the first characterisation generalises the existence of a distributive law over the genuine powerset monad, the second generalises preservation of weak pullbacks. The results presented in this paper enable us to compute predicate liftings of endofunctors of, for example, generalised (ultra)metric spaces. We illustrate this by studying the coalgebraic cover modality in this setting.Comment: 48 pages, accepted for publication in LMC

Hydrothermal carbonization and torrefaction of cabbage waste

ArticleIn recent years, waste biomass has been increasingly becoming an energy source. The utilization of biomass includes a number of potential treatments: thermochemical, physicochemical and biochemical. In the food industry, significant amounts of biodegradable wastes are produced which have to be quickly treated to not pose an environmental problem. In this work cabbage waste (Brassica oleracea var. capitata) was treated by hydrothermal carbonization and torrefaction. Hydrothermal carbonization experiments were carried out in a pressure reactor vessel Berghof BR-300 (inner volume 400 mL, temperature regulation by Berghof BTC 3000). The carbonization took place at target temperatures 180 °C and 225 °C. Torrefaction tests were carried out in a thermogravimetric programmable oven LECO TGA701 under nitrogen atmosphere at temperatures 225 °C, 250 °C and 275 °C. The residence time was 30 min for both processes. Proximate and elemental composition, as well as calorific value was analysed in all samples. To express the influence of the treatments on combustion behaviour, stoichiometric combustion calculations were performed. The analyses show a positive effect of both torrefaction and hydrothermal carbonization on fuel properties in the samples. Most obvious is the reduction in oxygen content which depends on the process temperature. After hydrothermal carbonization at 225 °C the oxygen content was lowered by 46.7%. The net calorific value increased proportionally with temperature in both processes. After hydrothermal carbonization at 225 °C the net calorific value increased on average by 3 MJ kg-1 to 20.89 MJ kg-1 . Both tested processes significantly increased the fuel value of this biodegradable waste

Specialty types of waste paper as an energetic commodity

ArticleThe collection and recycling rate of paper and paper packaging material has been on a rise. From 2010 to 2016 in Czech Republic, the recycled amount of all paper went up by 32%, while the share of energy use in waste paper utilization decreased f rom 5.5% to 3.8%. However, not every paper and cardboard product can be recycled, and some are rejected from the recycling stream. Recycling specialty types of paper with other grades of recyclable paper is often not possible and their production is not hi gh enough for their separate recycling to be feasible. If material utilization is not feasible then within the waste hierarchy the next best treatment is their energy utilization. Therefore, this article evaluates selected types of specialty paper for thei r energy content. They were silicone coated papers, polymer coated papers, and paper cores. For all samples proximate, elemental and calorimetric analyses were determined and based on them stoichiometric combustion calculations were performed. Silicon coat ed papers fared generally well having small to reasonable ash content 1 – 10% and net calorific value from 15.10 to 17.10 MJ kg - 1 on dry basis. Polymer coated papers had ash content around 6% and net calorific value from value from 16.29 to 22.98 MJ kg - 1 on dry basis. With the exception of paper cores and self - copying paper, all evaluated paper types could be recommended as a component in refuse derived fuels. The least suitable samples were paper cores with nearly 20% wt. of ash and net calorific value 12.45 MJ kg - 1 on dry basis

How Iterative are Iterative Algebras?

AbstractIterative algebras are defined by the property that every guarded system of recursive equations has a unique solution. We prove that they have a much stronger property: every system of recursive equations has a unique strict solution. And we characterize those systems that have a unique solution in every iterative algebra