On the asymptotic minimum number of monochromatic 3-term arithmetic progressions

Let V(n) be the minimum number of monochromatic 3-term arithmetic progressions in any 2-coloring of {1,2,...,n}. We show that (1675/32768) n^2 (1+o(1)) <= V(n) <= (117/2192) n^2(1+o(1)). As a consequence, we find that V(n) is strictly greater than the corresponding number for Schur triples (which is (1/22) n^2 (1+o(1)). Additionally, we disprove the conjecture that V(n) = (1/16) n^2(1+o(1)), as well as a more general conjecture.Comment: 9 pages. Revised version fixes formatting errors (same text

An urban school for District Six

Why an urban school for District Six? The inspiration for this thesis was stimulated by various factors, the roots of which stem from the first term of 1965, when I was involved in a Redevelopment Scheme for District Six. As a student of Architecture, this exercise had a profound affect on me. It introduced to me vital considerations concerning Architecture of which, up until that time, I had only been superficially aware. It was necessary to study the anatomy of the city, to understand its complexity, before attempting to perform such a sensitive operation as a Redevelopment Scheme. To be one of a thousand designers in "a city of a thousand designers", it is just as necessary to be equipped with this understanding when involved with the design of an individual structure. This valuable exercise produced results of sufficient substance and merit to warrant it being carried a step further. The object of this thesis is to develop a school which will take its place in the proposed Redevelopment Scheme. The role of a school is an urban area such as District Six can be vitally important in cultivating a community within a slum and at the same time transforming it into a new world. A virtue must be made of increasing populations. Outdated suburban standards must be discarded - they have no place in a city. A new set of standards must be created to satisfy the needs of a rapidly expanding Twentieth Century urban environment. This is the challenge I have set myself

Studies of transition metal phosphine complexes relevant to catalysis

Methoxycarbonyl compounds of the type [Pd(X)(CO(_2)Me)(L(_2))] (1) and [Pd(X)(CO(_2)Me)(L)(_2)] (2) were used as models in the work related to hydroesterification using methyl formate instead of CO and MeOH. The behaviour of the complexes (1) and (2) in solution was examined, as was their behaviour in the presence of alkenes and nucleophiles. Many of these derivatives were too unstable to isolate, forming the corresponding dichloride complexes [Pd(X)(_2)(L(_2))] (3) and [Pd(X)(_2)(L)(_2)] (4). Several crystal structures of such complexes were obtained. The cationic complex [Pd(CO(_2)Me)(MeCN)(PPh(_3))(_2)](BF(_4)) (5) was synthesised from (2) by removal of the chloride ligand with silver tetrafluoroborate. This is the first isolated cationic methoxycarbonyl complex of palladium. A crystal structure of (5) was obtained. Some of the factors which affected the stability of methoxycarbonyl complexes were examined. Some of these systems were used as precursors for catalytic studies of hydroesterification. The second part of the work involved the chemistry of an unusual phosphine ligand and sohie of its analogues. The bidentate ligand dppn (6) has been reacted with some first row transition metal halides to give novel complexes such as [NiCl(_2)(dppn)] (7) and [CoCl(_2)(dppno)] (8). The ligand (6) also reacted with [Pd(MeCN)(_4)](BF(_4))(_2) (9) to give [Pd(MeCN)(_2)(dppn)](BF(_4))(_2) (10). Upon addition of dppe to (10), the acetonitrile and dppn ligands were entirely replaced by dppe to give the complex [Pd(dppe)(_2)](BF(_4))(_2) (11). When dppe was added to the nickel complex (7), the dppe displaced the chelating dppn ligand to give [NiCl(_2)(dppe)] (12) and free dppn. The cyclohexyl analogue of dppn, called dcpn (13) was synthesised. The complexes [PdCl(_2)dcpn)] (14) and [Pd(MeCN)(_2)(dcpn)](BF(_4))(_2) were made using the ligand (13). The phosphine oxides of (6) and (13) were made by exposure to air in solution. These compounds are called dpno (15) and dcno (16) respectively. Preliminary catalytic work using the ligand (6) was carried out

Application of clustering techniques to multispectral optical data over the ocean

MERIS, on Envisat, provides high-resolution radiometric data at nine discrete channels in the visible band. This paper looks at the potential of an unsupervised classification technique for utilizing these multi-spectral data to provide better discrimination between water masses according to their optical properties, and in particular whether phytoplankton groups can be distinguished. Although the majority of data do show a spectral peak associated with chlorophyll's red fluorescence line, clustering using only the red bands was found to separate out coastal waters according to their sediment content. Red-end classification also appeared to identify sub-pixel cloud, and demonstrate that the smile correction had not removed all the striping from the data. Classification using bands from the blue-green end showed a response to changes in chlorophyll concentration, but also indicated other variations. However, without in situ data no firm conclusions can be drawn on which phytoplankton groupings are present

Robust identification of local adaptation from allele frequencies

Comparing allele frequencies among populations that differ in environment has long been a tool for detecting loci involved in local adaptation. However, such analyses are complicated by an imperfect knowledge of population allele frequencies and neutral correlations of allele frequencies among populations due to shared population history and gene flow. Here we develop a set of methods to robustly test for unusual allele frequency patterns, and correlations between environmental variables and allele frequencies while accounting for these complications based on a Bayesian model previously implemented in the software Bayenv. Using this model, we calculate a set of `standardized allele frequencies' that allows investigators to apply tests of their choice to multiple populations, while accounting for sampling and covariance due to population history. We illustrate this first by showing that these standardized frequencies can be used to calculate powerful tests to detect non-parametric correlations with environmental variables, which are also less prone to spurious results due to outlier populations. We then demonstrate how these standardized allele frequencies can be used to construct a test to detect SNPs that deviate strongly from neutral population structure. This test is conceptually related to FST but should be more powerful as we account for population history. We also extend the model to next-generation sequencing of population pools, which is a cost-efficient way to estimate population allele frequencies, but it implies an additional level of sampling noise. The utility of these methods is demonstrated in simulations and by re-analyzing human SNP data from the HGDP populations. An implementation of our method will be available from http://gcbias.org.Comment: 27 pages, 7 figure

Meeting optimally the environmental challenge: A methodology for the lead industry

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Does the lead industry have a future, in the face of the developing environmental challenge? This thesis addresses this question and concludes, it should have for the foreseeable future, providing it adopts the changes detailed. These changes are posited within a framework, which consists of a strategy, approaches and tools. The changes are both technical and philosophical. They are technical, in the sense that the tools and approaches provide practical means whereby the environmental `risks' may be identified, assessed and managed. They are philosophical, because they set out and identify the features of a new conceptual paradigm, whose basis is in the concept of the `risk society'. The paradigm is significantly more holistic, multi-dimensional, inherently flexible, and is intended to be reflexive. Adoption of the elements of the framework, will facilitate a more effective establishment, and management of environmental `risk' credentials, which will help encourage better environmental decision making. Hence, it will facilitate, the balancing of resource consumption and environmental impact costs, versus social and economic benefits, in an improved manner. The modelling approaches, and selected inventory and environmental impact assessment tools, enclosed within this thesis, have been designed to facilitate the development of, and to function within, the new paradigm. These have been developed for BRM and MIM case studies, and function at the site-specific and the cradle-to-gate scales. The former consider the company site of Britannia Refined Metals (BRM) Ltd., where refining to produce primary and secondary refined lead products takes place, whilst the latter consider the life-cycle of the refined primary lead products of MIM Ltd. The modelling approaches have also been designed so, that they may be re-aggregated into models able to operate at many different scales, as required. The framework, and its elements, are applicable for all industries facing similar challenges.Britannia Refined Metals Ltd. (BRM

The M-Sigma Relation Derived from Sphere of Influence Arguments

The observed relation between supermassive black hole (SMBH) mass (M) and bulge stellar velocity dispersion (Sigma) is described by log(M) = alpha + beta*log(Sigma/200 km/s). As this relation has important implications for models of galaxy and SMBH formation and evolution, there continues to be great interest in adding to the M catalog. The "sphere of influence" (r) argument uses spatial resolution to exclude some M estimates and pre-select additional galaxies for further SMBH studies. This Letter quantifies the effects of applying the r argument to a population of galaxies and SMBHs that do not follow the M-Sigma relation. All galaxies with known values of Sigma, closer than 100 Mpc, are given a random M and selected when r is spatially resolved. These random SMBHs produce an M-Sigma relation of alpha=8.3, beta=4.0, consistent with observed values. Consequently, future proposed M estimates should not be justified solely on the basis of resolving r. This Letter shows the observed M-Sigma relation may simply be a result of available spatial resolution. However, it also implies the observed M-Sigma relation defines an upper limit. This potentially provides valuable new insight into the processes of galaxy and SMBH formation and evolution.Comment: ApJ Letters, accepte

Honesty, social presence, and self-service in retail

Retail self-service checkouts (SCOs) can benefit consumers and retailers, providing control and autonomy to shoppers independent from staff. Recent research indicates that the lack of presence of staff may provide the opportunity for consumers to behave dishonestly. This study examined whether a social presence in the form of visual, humanlike SCO interface agents had an effect on dishonest user behaviour. Using a simulated SCO scenario, participants experienced various dilemmas in which they could financially benefit themselves undeservedly. We hypothesised that a humanlike social presence integrated within the checkout screen would receive more attention and result in fewer instances of dishonesty compared to a less humanlike agent. Our hypotheses were partially supported by the results. We conclude that companies adopting self-service technology may consider the implementation of social presence to support ethical consumer behaviour, but that more research is required to explore the mixed findings in the current study

Generating symmetry-adapted bases for non-Abelian point groups to be used in vibronic coupling Hamiltonians

AbstractThe vibronic coupling Hamiltonian is a standard model used to describe the potential energy surfaces of systems in which non-adiabatic coupling is a key feature. This includes Jahn–Teller and Renner–Teller systems. The model approximates diabatic potential energy functions as polynomials expanded about a point of high symmetry. One must ensure the model Hamiltonian belongs to the totally symmetric irreducible representation of this point group. Here, a simple approach is presented to generate functions that form a basis for totally symmetric irreducible representations of non-Abelian groups and apply it to D∞h (2D) and O (3D). For the O group, the use of a well known basis-generating operator is also required. The functions generated for D∞h are then used to construct a ten state, four coordinate model of acetylene. The calculated absorption spectrum is compared to the experimental spectrum to serve as a validation of the approach