title: Agreeable semigroups

authors: Jackson, Marcel

subjects: mathematics

abstract: This paper concerns the theory of partial maps under composition and more generally, the RC-semigroups introduced by Jackson and Stokes [Semigroup Forum 62 (2001) 279–310] (semigroups with a unary operation called (right) closure). Many of the motivating examples have a natural meet-semilattice structure; the inverse semigroup of all injective partial transformations of a set and the semigroup of all binary operations under composition are two examples. We here view the semilattice meet as an additional operation, thereby obtaining a variety of algebras with one unary and two binary operations. The two non-semigroup operations are then shown to be captured by a single binary operation, via the notion of an agreeable semigroup. We look at a number of properties of these structures including their congruences (which are uniquely determined by their restriction to certain idempotents), a relationship with so-called interior semigroups, and a natural category associated with a large variety of RC-semigroups (which includes all inverse semigroups). For example, we show that the existence of equalisers in this category is intimately connected with the existence of the natural meet-semilattice structure.

text: Agreeable semigroups This paper concerns the theory of partial maps under composition and more generally, the RC-semigroups introduced by Jackson and Stokes [Semigroup Forum 62 (2001) 279–310] (semigroups with a unary operation called (right) closure). Many of the motivating examples have a natural meet-semilattice structure; the inverse semigroup of all injective partial transformations of a set and the semigroup of all binary operations under composition are two examples. We here view the semilattice meet as an additional operation, thereby obtaining a variety of algebras with one unary and two binary operations. The two non-semigroup operations are then shown to be captured by a single binary operation, via the notion of an agreeable semigroup. We look at a number of properties of these structures including their congruences (which are uniquely determined by their restriction to certain idempotents), a relationship with so-called interior semigroups, and a natural category associated with a large variety of RC-semigroups (which includes all inverse semigroups). For example, we show that the existence of equalisers in this category is intimately connected with the existence of the natural meet-semilattice structure.

year: 2003

title: Characterization and adsorption performance of New Zealand biochar for the removal of paracetamol and ibuprofen from synthetic solutions in batch and column systems

authors: Shein, Shun Lei Shwe Yee

abstract: Pharmaceuticals are a significant class of emerging organic contaminants that have been increasingly detected in aquatic environments. Their persistence and limited removal by conventional treatment methods poses considerable risks to both flora and fauna. The study investigates the adsorption performance of New Zealand-sourced biochar both raw and surface-modified for the removal of two widely used pharmaceuticals, paracetamol and ibuprofen, from aqueous solutions. With its local availability and carbon-rich structure, biochar was evaluated as an innovative solution to address the growing challenge of emerging pharmaceutical pollutants in aquatic environments. The research aimed to characterize the physicochemical properties of biochar and evaluate its adsorption capacity under batch and column configurations, addressing removal efficiency, equilibrium behaviour, kinetic mechanisms, and dynamic breakthrough performance. The biochar was instrumentally analysed by BET surface area analysis, Fourier-transform infrared spectroscopy (FTIR) and scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM–EDX) to examine the biochar’s surface structure and functional groups. Premium Biochar demonstrated the highest BET surface area (308.3 m²/g), which further increased to 354 m²/g after 30% KOH activation, indicating enhanced porosity and improved availability of adsorption sites. Batch adsorption experiments revealed that paracetamol achieved higher removal efficiencies and adsorption capacities (up to 8.5 mg/g) compared to ibuprofen (maximum of 2.8 mg/g), largely due to its smaller molecular size and greater polarity. The non-linear technique using isotherm and kinetic model was used to validate the process efficiency of pharmaceuticals removal. Kinetic modelling indicated pseudo-second order and Elovich models best described the adsorption mechanisms (R² > 0.997), confirming chemisorption on heterogeneous surfaces as the dominant process. Isotherm analysis showed multilayer Freundlich adsorption for paracetamol and monolayer Langmuir adsorption for ibuprofen reflecting differences in multilayer versus monolayer adsorption behaviour. Column experiments were conducted under single-pass, closed-loop recirculation, and semi-continuous dosing modes. Single-pass continuous flow showed in rapid breakthrough at short empty bed contact times (1.6–4.5 minutes) due to hydraulic limitations. In contrast, closed-loop recirculation columns achieved up to 90% paracetamol removal and 58% ibuprofen removal under extended operation, specifically, the optimal condition when using 1 mm particle size KOH-activated biochar (1 mm KOH-modified biochar, 15 L/min flow, 500 min runtime). Semi-continuous dosing experiments demonstrated gradual adsorbent saturation with final adsorption capacities of approximately 0.43–0.57 mg/g, supporting the need for regeneration strategies in long-term applications.

text: Characterization and adsorption performance of New Zealand biochar for the removal of paracetamol and ibuprofen from synthetic solutions in batch and column systems Pharmaceuticals are a significant class of emerging organic contaminants that have been increasingly detected in aquatic environments. Their persistence and limited removal by conventional treatment methods poses considerable risks to both flora and fauna. The study investigates the adsorption performance of New Zealand-sourced biochar both raw and surface-modified for the removal of two widely used pharmaceuticals, paracetamol and ibuprofen, from aqueous solutions. With its local availability and carbon-rich structure, biochar was evaluated as an innovative solution to address the growing challenge of emerging pharmaceutical pollutants in aquatic environments. The research aimed to characterize the physicochemical properties of biochar and evaluate its adsorption capacity under batch and column configurations, addressing removal efficiency, equilibrium behaviour, kinetic mechanisms, and dynamic breakthrough performance. The biochar was instrumentally analysed by BET surface area analysis, Fourier-transform infrared spectroscopy (FTIR) and scanning electron microscopy with energy dispersive X-ray spectroscopy (SEM–EDX) to examine the biochar’s surface structure and functional groups. Premium Biochar demonstrated the highest BET surface area (308.3 m²/g), which further increased to 354 m²/g after 30% KOH activation, indicating enhanced porosity and improved availability of adsorption sites. Batch adsorption experiments revealed that paracetamol achieved higher removal efficiencies and adsorption capacities (up to 8.5 mg/g) compared to ibuprofen (maximum of 2.8 mg/g), largely due to its smaller molecular size and greater polarity. The non-linear technique using isotherm and kinetic model was used to validate the process efficiency of pharmaceuticals removal. Kinetic modelling indicated pseudo-second order and Elovich models best described the adsorption mechanisms (R² > 0.997), confirming chemisorption on heterogeneous surfaces as the dominant process. Isotherm analysis showed multilayer Freundlich adsorption for paracetamol and monolayer Langmuir adsorption for ibuprofen reflecting differences in multilayer versus monolayer adsorption behaviour. Column experiments were conducted under single-pass, closed-loop recirculation, and semi-continuous dosing modes. Single-pass continuous flow showed in rapid breakthrough at short empty bed contact times (1.6–4.5 minutes) due to hydraulic limitations. In contrast, closed-loop recirculation columns achieved up to 90% paracetamol removal and 58% ibuprofen removal under extended operation, specifically, the optimal condition when using 1 mm particle size KOH-activated biochar (1 mm KOH-modified biochar, 15 L/min flow, 500 min runtime). Semi-continuous dosing experiments demonstrated gradual adsorbent saturation with final adsorption capacities of approximately 0.43–0.57 mg/g, supporting the need for regeneration strategies in long-term applications.

year: 2025-07-06

title: Environmental performance outcomes and indicators for indigenous peoples: Review of literature

authors: Kennedy, Nathan

subjects: New Zealand

abstract: The literature review in this report was the starting point for developing a Māori research strand (2003-2009) within the Planning Under Co-operative Mandates (PUCM) research programme (1995-2009). An early task of the PUCM Māori team was to review the international literature on environmental outcomes and indicators for indigenous peoples. This was in order to gain an understanding of what had been written on the subject and to become familiar with approaches taken by others that might provide lessons for the development of our proposed kaupapa Māori outcomes and indicators framework and methodology, which was aimed at local government performance in Aotearoa/New Zealand. This current report is not intended to provide an exhaustive catalogue of writings on environmental performance outcomes and indicators for indigenous peoples, including Māori. Rather, some of the more obvious and important writings are noted as a ready reference for others interested in this topic. Before detailing the approach we took in carrying out the review, the key terms, outcomes and indicators, are defined.

text: Environmental performance outcomes and indicators for indigenous peoples: Review of literature The literature review in this report was the starting point for developing a Māori research strand (2003-2009) within the Planning Under Co-operative Mandates (PUCM) research programme (1995-2009). An early task of the PUCM Māori team was to review the international literature on environmental outcomes and indicators for indigenous peoples. This was in order to gain an understanding of what had been written on the subject and to become familiar with approaches taken by others that might provide lessons for the development of our proposed kaupapa Māori outcomes and indicators framework and methodology, which was aimed at local government performance in Aotearoa/New Zealand. This current report is not intended to provide an exhaustive catalogue of writings on environmental performance outcomes and indicators for indigenous peoples, including Māori. Rather, some of the more obvious and important writings are noted as a ready reference for others interested in this topic. Before detailing the approach we took in carrying out the review, the key terms, outcomes and indicators, are defined.

year: 2009-07-31