Non-principal ultrafilters, program extraction and higher order reverse mathematics

We investigate the strength of the existence of a non-principal ultrafilter over fragments of higher order arithmetic. Let U be the statement that a non-principal ultrafilter exists and let ACA_0^{\omega} be the higher order extension of ACA_0. We show that ACA_0^{\omega}+U is \Pi^1_2-conservative over ACA_0^{\omega} and thus that ACA_0^{\omega}+\U is conservative over PA. Moreover, we provide a program extraction method and show that from a proof of a strictly \Pi^1_2 statement \forall f \exists g A(f,g) in ACA_0^{\omega}+U a realizing term in G\"odel's system T can be extracted. This means that one can extract a term t, such that A(f,t(f))

An algorithmic approach to the existence of ideal objects in commutative algebra

The existence of ideal objects, such as maximal ideals in nonzero rings, plays a crucial role in commutative algebra. These are typically justified using Zorn's lemma, and thus pose a challenge from a computational point of view. Giving a constructive meaning to ideal objects is a problem which dates back to Hilbert's program, and today is still a central theme in the area of dynamical algebra, which focuses on the elimination of ideal objects via syntactic methods. In this paper, we take an alternative approach based on Kreisel's no counterexample interpretation and sequential algorithms. We first give a computational interpretation to an abstract maximality principle in the countable setting via an intuitive, state based algorithm. We then carry out a concrete case study, in which we give an algorithmic account of the result that in any commutative ring, the intersection of all prime ideals is contained in its nilradical

The Design and Installation of a Combined Concentrating Power Station, Solar Cooling System and Domestic Hot Water System

AbstractThe University of Technology, Sydney (UTS) has built a unique tri-generation system that provides chilled water, hot water, and electricity to their new Faculty of Engineering and Information Technology (FEIT) building. It integrates parabolic trough collectors, flat plate collectors, photovoltaic panels, and wind power as generators with thermal and chemical energy storage. The heat from the parabolic trough collectors is used to run a small-scale Organic Rankine Cycle (ORC) unit as well as a small-scale ammonia/water absorption chiller to provide either electricity or chilled water, respectively. The condenser heat from both units is fed into the domestic hot water (DHW) supply of the building in addition to the solar heat from the flat plate and the parabolic trough collectors. The design concept including the main system components and the system control strategy are described in detail. Further, the lessons learned during the installation and commissioning of the complex tri-generation system are given. As a novelty in this area, the tri-generation system has been specifically designed to allow students and researchers to work with it, hence this paper also describes the wide range of teaching opportunities for undergraduate and graduate engineering students as well as post-doc researchers

An alginate-layer technique for culture of Brassica oleracea L. protoplasts

Ten accessions belonging to the Brassica oleracea subspecies alba and rubra, and to B. oleracea var. sabauda were used in this study. Protoplasts were isolated from leaves and hypocotyls of in vitro grown plants. The influence of selected factors on the yield, viability, and mitotic activity of protoplasts immobilized in calcium alginate layers was investigated. The efficiency of protoplast isolation from hypocotyls was lower (0.7 ± 0.1 × 106 ml−1) than for protoplasts isolated from leaf mesophyll tissue (2 ± 0.1 × 106 ml−1). High (70–90%) viabilities of immobilized protoplasts were recorded, independent of the explant sources. The highest proportion of protoplasts undergoing divisions was noted for cv. Reball F1, both from mesophyll (29.8 ± 2.2%) and hypocotyl (17.5 ± 0.3%) tissues. Developed colonies of callus tissue were subjected to regeneration and as a result plants from six accessions were obtained

An Algorithmic Approach to the Existence of Ideal Objects in Commutative Algebra

The existence of ideal objects, such as maximal ideals in nonzero rings, plays a crucial role in commutative algebra. These are typically justified using Zorn\u2019s lemma, and thus pose a challenge from a computational point of view. Giving a constructive meaning to ideal objects is a problem which dates back to Hilbert\u2019s program, and today is still a central theme in the area of dynamical algebra, which focuses on the elimination of ideal objects via syntactic methods. In this paper, we take an alternative approach based on Kreisel\u2019s no counterexample interpretation and sequential algorithms. We first give a computational interpretation to an abstract maximality principle in the countable setting via an intuitive, state based algorithm. We then carry out a concrete case study, in which we give an algorithmic account of the result that in any commutative ring, the intersection of all prime ideals is contained in its nilradical