Vector lattices with a Hausdorff uo-Lebesgue topology

We investigate the construction of a Hausdorff uo-Lebesgue topology on a vector lattice from a Hausdorff (o)-Lebesgue topology on an order dense ideal, and what the properties of the topologies thus obtained are. When the vector lattice has an order dense ideal with a separating order continuous dual, it is always possible to supply it with such a topology in this fashion, and the restriction of this topology to a regular sublattice is then also a Hausdorff uo-Lebesgue topology. A regular vector sublattice of $\mathrm{L}_0(X,\Sigma,\mu)$ for a semi-finite measure $\mu$ falls into this category, and the convergence of nets in its Hausdorff uo-Lebesgue topology is then the convergence in measure on subsets of finite measure. When a vector lattice not only has an order dense ideal with a separating order continuous dual, but also has the countable sup property, we show that every net in a regular vector sublattice that converges in its Hausdorff uo-Lebesgue topology always contains a sequence that is uo-convergent to the same limit. This enables us to give satisfactory answers to various topological questions about uo-convergence in this context.Comment: 37 pages. Minor changes; a few references added. Final version, to appear in J. Math. Anal. App

Unbounded order convergence in dual spaces

A net $(x_\alpha)$ in a vector lattice $X$ is said to be {unbounded order convergent} (or uo-convergent, for short) to $x\in X$ if the net (\abs{x_\alpha-x}\wedge y) converges to 0 in order for all $y\in X_+$. In this paper, we study unbounded order convergence in dual spaces of Banach lattices. Let $X$ be a Banach lattice. We prove that every norm bounded uo-convergent net in $X^*$ is $w^*$-convergent iff $X$ has order continuous norm, and that every $w^*$-convergent net in $X^*$ is uo-convergent iff $X$ is atomic with order continuous norm. We also characterize among $\sigma$-order complete Banach lattices the spaces in whose dual space every simultaneously uo- and $w^*$-convergent sequence converges weakly/in norm

Daylight adaptive optimal lighting system control strategies for energy savings and visual comfort in commercial buildings

Artificial lighting of commercial buildings in Malaysia consumes 21% of the total electrical energy. Therefore, reducing the energy is required to achieve sustainable buildings (i.e., higher energy efficiency and visual comfort), by implementing optimal light sensor placement method and optimisation-based control strategy. However, in recent works related to light sensor placement, energy performance and illuminance uniformity (Uo) are not considered, and the results did not provide the optimal number of sensors to be employed. To optimise power consumption (PC) and visual comfort simultaneously through the optimisation-based control strategy, the previous work developed a visual comfort model to represent Uo. However, the model did not consider daylight and the results of Uo need further improvement. This research proposes: (1) a new optimal light sensor placement method (OLSPM) by using combined particle swarm optimisation (PSO) and fuzzy logic controller (FLC) denoted as OLSPM-PSOFLC, and (2) a new visual comfort metric called illuminance uniformity deviation index (IUDI) and incorporated with multi-objective PSO (MOPSO) for solving energy consumption and visual comfort problem. The OLSPM�PSOFLC is developed to determine the optimal number and position of light sensors by considering PC while satisfying average illuminance level (Eav) and Uo. To ensure both PC and Uo in the room are always at the optimum levels, the IUDI with MOPSO is developed. Before the proposed methods are implemented, retrofitting lighting system is implemented first to determine the best lamp technology to be installed in terms of technical and economic metrics. An actual office room is considered for carrying out the proposed methods. The comparative results showed that the OLSPM�PSOFLC significantly reduced the number of sensors, energy consumption, carbon dioxide emission, payback period, and life cycle cost were 66%, 23%, 23%, and 30%, respectively, compared to the multi-sensor. Meanwhile, based on the comparative study of the IUDI and CVRMSE, the IUDI showed superior performance with 6% and 27% improvement of Uo and energy savings, respectively. Based on their superiority, the newly developed methods can be potentially implemented for all types of rooms and are very useful methodologies towards sustainable commercial buildings

Structural studies on silver(I) complexes containing phenylcyanamido ligands and uranyl(VI) complexes with beta-ketophenolates : a dissertation presented in partial fulfilment for the degree of Master of Science in Chemistry at Massey University

This thesis is divided into two parts. In Section One studies on the interaction of phenylcyanamides with silver(I) are reported. Section Two describes the results of studies on the complexes formed from β-ketophenol ligands and the uranyl ion. Section One Chapter 1 is a brief overview of the use of phenylcyanamides in forming coordination complexes with transition metals. In Chapter 2 the preparation of a series of silver complexes of the general formula [Ag(Ph₃P)₃(pcyd)], where pcyd is a phenylcyanamido anion, is described. The crystal structures of [Ag(Ph₃P)₃(4-Brpcyd)] and [Ag(Ph₃P)₃(4-MeOpcyd)] have been determined, in which the silver atom occupies a distorted tetrahedral environment, and the latter complex has a very short terminal C-N bond within the 4-methoxyphenylcyanamido ligand. Chapter 3 provides a comparison of all those transition metal complexes of phenylcyanamides that have been structurally characterised. Section Two Chapter 4 is a brief overview of the use of β-diketonate ligands in forming dinuclear complexes, especially those in which the uranyl ion (UO₂²+) is present. In Chapter 5 the preparation of the mononuclear complexes [UO₂(HL¹)₂(MeOH)], (UO₂(HL²)₂(EtOH)], the heterobinuclear complexes [U0₂Mn(L¹)₂(EtOH)]·1.5H₂O, and [UO₂Mn(L²)₂(EtOH)]·2H₂₂O and the oxo-ligand adducts [UO₂(HL¹)₂(Ph₃AsO)]·2H₂O, [U0₂(HL²)₂(Ph₃PO)] and [UO₂(HL²)₂(Ph₃AsO)] (H₂L¹ = 1-(2-hydroxyphenyl)-3- butanedione and H₂L² = 1-(2-hydroxyphenyl)-3-phenyl-l,3-propanedione) is described. The complexes have been characterized by a variety of physicochemical techniques and the crystal structures of [UO₂(HL¹)₂(EtOH)] and [UO₂(HL²)₂(EtOH)]·EtOH determined. Both complexes contain seven coordinate uranium(VI) in a pentagonal bipyramidal geometry in which the two bidentate β-diketonato ligands and the ethanol ligand make up the equatorial pentagonal plane. For the complex [UO₂(HL¹)₂(EtOH)] the HL¹ ligands are in a trans arrangement with respect to one another, whereas for the [UO₂(HL²)₂(EtOH)]·EtOH complex the HL² ligands adopt a cis arrangement. However, in solution variable temperature ¹H NMR spectra indicate that the cis and trans isomers are in equilibrium for both complexes

Relaxation measurements in the regime of the second magnetization peak in Nb films

We report on magnetic measurements as a function of field, temperature and time (relaxation) in superconducting Nb films of critical temperature Tc = 9.25 K. The magnetic measurements as a function of field exhibited a second magnetization peak (SMP) which in general is accompanied by thermomagnetic instabilities (TMIs). The lines where the SMP occurs and where the first flux jump in the virgin magnetization curves is observed, end at a characteristic point (To,Ho)=(7.2 K,80 Oe). Relaxation measurements showed that for T<To=7.2 K the activation energy Uo and the normalized relaxation rate S exhibit non-monotonic behavior as a function either of temperature or field. The extrema observed in Uo and S coincide with the onset and the maximum points of the SMP. In the regime T>To=7.2 K both Uo and S present a conventional monotonic behavior. These results indicate that the SMP behavior observed in our Nb films is promoted by the anomalous relaxation of the magnetization.Comment: To appear in Physica