Torsion theories are here extended to categories equipped with an ideal of 'null morphisms', or equivalently a full subcategory of 'null objects'. Instances of this extension include closure operators viewed as generalised torsion theories in a 'category of pairs', and factorization systems viewed as torsion theories in a category of morphisms. The first point has essentially been treated in [15].

The miombo woodland is the most extensive dry forest in the world, with the potential to store substantial amounts of biomass carbon. Efforts to obtain accurate estimates of carbon stocks in the miombo woodlands are limited by a general lack of biomass estimation models (BEMs). This study aimed to evaluate the accuracy of most commonly employed allometric models for estimating aboveground bioma...

We bring together time series data on trade, production, and input-use to compute the value added content of trade over the past four decades (1970-2009). Comparing the ratio of value added to gross exports, we measure changes in production fragmentation for the world as a whole, individual countries, and bilateral trade partners. For the world, the share of value added in trade falls by 10 to ...

Industrial evolution brings major new challenges due to increasing energy demands. This phenomenon encourages the improvement of control methodologies that reduce resource requirements. Lately, it has been observed that the building sector contributes considerably to final energy demand. Consequently, studies have been conducted on the technical systems and solutions applied in this sector to t...

Green’s functions are established tools for solving petroleum engineering flow problems. Their utility and rigor was extended to arbitrarily shaped reservoirs using the Boundary Element Method (BEM). Traditional BEMs are limited to single-phase flow in homogeneous reservoirs. Earlier authors have developed techniques to handle heterogeneity. These methods are perturbationbased and computation-i...

There has been considerable interest in recent years in the development of numerical methods for time-harmonic acoustic and electromagnetic wave scattering problems that can efficiently resolve the scattered field at high frequencies. Standard finite or boundary element methods (FEMs and BEMs), with piecewise polynomial approximation spaces, suffer from the restriction that a fixed number of de...

There are two approaches to lattices used in the Mizar Mathematical Library: on the one hand, these structures are based on the set with two binary operations (with an equational characterization as in [17]). On the other hand, we may look at them as at relational structures (posets – see [12]). As the main result of this article we can state that the Mizar formalization enables us to use both ...