Diameter of orientations of graphs with given order and number of blocks

A strong orientation of a graph $G$ is an assignment of a direction to each edge such that $G$ is strongly connected. The oriented diameter of $G$ is the smallest diameter among all strong orientations of $G$. A block of $G$ is a maximal connected subgraph of $G$ that has no cut vertex. A block graph is a graph in which every block is a clique. We show that every bridgeless graph of order $n$ containing $p$ blocks has an oriented diameter of at most $n-\lfloor \frac{p}{2} \rfloor$. This bound is sharp for all $n$ and $p$ with $p \geq 2$. As a corollary, we obtain a sharp upper bound on the oriented diameter in terms of order and number of cut vertices. We also show that the oriented diameter of a bridgeless block graph of order $n$ is bounded above by $\lfloor \frac{3n}{4} \rfloor$ if $n$ is even and $\lfloor \frac{3(n+1)}{4} \rfloor$ if $n$ is odd.Comment: 15 pages, 2 figure

Architecture, persistence and dissolution of a 20 to 45 year old trichloroethene DNAPL source zone

AbstractA detailed field-scale investigation of processes controlling the architecture, persistence and dissolution of a 20 to 45year old trichloroethene (TCE) dense non-aqueous phase liquid (DNAPL) source zone located within a heterogeneous sand/gravel aquifer at a UK industrial site is presented. The source zone was partially enclosed by a 3-sided cell that allowed detailed longitudinal/fence transect monitoring along/across a controlled streamtube of flow induced by an extraction well positioned at the cell closed end. Integrated analysis of high-resolution DNAPL saturation (Sn) (from cores), dissolved-phase plume concentration (from multilevel samplers), tracer test and permeability datasets was undertaken. DNAPL architecture was determined from soil concentration data using partitioning calculations. DNAPL threshold soil concentrations and low Sn values calculated were sensitive to sorption assumptions. An outcome of this was the uncertainty in demarcation of secondary source zone diffused and sorbed mass that is distinct from trace amounts of low Sn DNAPL mass. The majority of source mass occurred within discrete lenses or pools of DNAPL associated with low permeability geological units. High residual saturation (Sn>10–20%) and pools (Sn>20%) together accounted for almost 40% of the DNAPL mass, but only 3% of the sampled source volume. High-saturation DNAPL lenses/pools were supported by lower permeability layers, but with DNAPL still primarily present within slightly more permeable overlying units. These lenses/pools exhibited approximately linearly declining Sn profiles with increasing elevation ascribed to preferential dissolution of the uppermost DNAPL. Bi-component partitioning calculations on soil samples confirmed that the dechlorination product cDCE (cis-dichloroethene) was accumulating in the TCE DNAPL. Estimated cDCE mole fractions in the DNAPL increased towards the DNAPL interface with the uppermost mole fraction of 0.04 comparable to literature laboratory data. DNAPL dissolution yielded heterogeneous dissolved-phase plumes of TCE and its dechlorination products that exhibited orders of magnitude local concentration variation. TCE solubility concentrations were relatively localised, but coincident with high saturation DNAPL lens source areas. Biotic dechlorination in the source zone area, however, caused cDCE to be the dominant dissolved-phase plume. The conservative tracer test usefully confirmed the continuity of a permeable gravel unit at depth through the source zone. Although this unit offered significant opportunity for DNAPL bypassing and decreased timeframes for dechlorination, it still transmitted a significant proportion of the contaminant flux. This was attributed to dissolution of DNAPL–mudstone aquitard associated sources at the base of the continuous gravel as well as contaminated groundwater from surrounding less permeable sand and gravel horizons draining into this permeable conduit. The cell extraction well provided an integrated metric of source zone dissolution yielding a mean concentration of around 45% TCE solubility (taking into account dechlorination) that was equivalent to a DNAPL mass removal rate of 0.4tonnes per annum over a 16m2 cell cross sectional area of flow. This is a significant flux considering the source age and observed occurrence of much of the source mass within discrete lenses/pools. We advocate the need for further detailed field-scale studies on old DNAPL source zones that better resolve persistent pool/lens features and are of prolonged duration to assess the ageing of source zones. Such studies would further underpin the application of more surgical remediation technologies

A qualitative evaluation of healthy weight services in a local authority in England

Objective The purpose of this study was to evaluate the healthy weight services in one local authority in England, where obesity levels have been above the national average since 2006. Design We conducted process and outcome evaluation using a qualitative methodology. Data were generated in focus group discussions and semi-structured interviews with clients, practitioners, healthcare professionals and volunteers. Results Ninety-one individuals from six services participated in the evaluation. Staff competencies and empowerment outcomes were identified as areas of strength. However, despite examples of excellent practice and enthusiastic recommendations from clients, access and referral processes were areas of weakness. Conclusion In England, local authorities have an important role to play in tackling obesity. It is crucial that they are provided with the tools to be able to implement healthy weight interventions effectively. A whole-systems approach presents a real opportunity for staff in local authorities and public health to work collaboratively and innovatively towards the same goal of continuous improvement in obesity management

4-Hydr­oxy-4,4-diphenyl­butan-2-one

The mol­ecules of the title compound, C16H16O2, display an intra­molecular O—H⋯O hydrogen bond between the hydroxyl donor and the ketone acceptor. Inter­molecular C—H⋯π inter­actions connect adjacent mol­ecules into chains that propagate parallel to the ac diagonal. The chains are arranged in sheets, and mol­ecules in adjacent sheets inter­act via inter­molecular O—H⋯O hydrogen bonds

Monitoring well utility in a heterogeneous DNAPL source zone area : Insights from proximal multilevel sampler wells and sampling capture-zone modelling

Groundwater-quality assessment at contaminated sites often involves the use of short-screen (1.5 to 3 m) monitoring wells. However, even over these intervals considerable variation may occur in contaminant concentrations in groundwater adjacent to the well screen. This is especially true in heterogeneous dense non-aqueous phase liquid (DNAPL) source zones, where cm-scale contamination variability may call into question the effectiveness of monitoring wells to deliver representative data. The utility of monitoring wells in such settings is evaluated by reference to high-resolution multilevel sampler (MLS) wells located proximally to short-screen wells, together with sampling capture-zone modelling to explore controls upon well sample provenance and sensitivity to monitoring protocols. Field data are analysed from the highly instrumented SABRE research site that contained an old trichloroethene source zone within a shallow alluvial aquifer at a UK industrial facility. With increased purging, monitoring-well samples tend to a flow-weighted average concentration but may exhibit sensitivity to the implemented protocol and degree of purging. Formation heterogeneity adjacent to the well-screen particularly, alongside pump-intake position and water level, influence this sensitivity. Purging of low volumes is vulnerable to poor reproducibility arising from concentration variability predicted over the initial 1 to 2 screen volumes purged. Marked heterogeneity may also result in limited long-term sample concentration stabilization. Development of bespoke monitoring protocols, that consider screen volumes purged, alongside water-quality indicator parameter stabilization, is recommended to validate and reduce uncertainty when interpreting monitoring-well data within source zone areas. Generalised recommendations on monitoring well based protocols are also developed. A key monitoring well utility is their proportionately greater sample draw from permeable horizons constituting a significant contaminant flux pathway and hence representative fraction of source mass flux. Acquisition of complementary, high-resolution, site monitoring data, however, vitally underpins optimal interpretation of monitoring-well datasets and appropriate advancement of a site conceptual model and remedial implementation

Waste-derived inosilicate carrier for antimicrobial Zn2+ and Ag+ ions

Recent research by the authors has demonstrated that the inosilicate, lithium metasilicate (Li2SiO3), can be prepared by hydrothermal synthesis from waste green container glass (GCG) [1,2]. This study investigated the potential of this material to be ion-exchanged with antimicrobial Zn2+ or Ag+ ions for use as a filler in polymer composites. Antimicrobial polymer composites are an advantage in applications where the communication of pathogenic bacteria poses a problem, such as hospitals, abattoirs and food-processing factories. The naturally-occurring biodegradable mucopolysaccharide derivative, chitosan, was used as a model polymer in this study. The lithium metasilicate product was synthesised from GCG in LiOH(aq) and ion-exchanged with either Zn2+ or Ag+ ions via batch sorption. The in vitro antibacterial properties of solvent-cast metasilicate-chitosan composite membranes were then evaluated by zone of inhibition against Escherichia coli, Pseudomonas aeruginosa and Staphylococcus aureus

100 years of chemistry at Rhodes University

The history of Grahamstown is well documented and two books deal with the history of Rhodes University.1,2 Although the Chemistry Department was one of the founding departments, coverage in the official histories is minimal and sometimes inaccurate or misleading. The Rhodes University Centenary is an appropriate time to look back on some of the achievements of the department and some of its graduates over the past 100 years

Architecture, persistence and dissolution of 20 to 45 old trichlorethene DNAPL source zone

A detailed field-scale investigation of processes controlling the architecture, persistence and dissolution of a 20 to 45 year old trichloroethene (TCE) dense non-aqueous phase liquid (DNAPL) source zone located within a heterogeneous sand/gravel aquifer at a UK industrial site is presented. The source zone was partially enclosed by a 3-sided cell that allowed detailed longitudinal/fence transect monitoring along/across a controlled streamtube of flow induced by an extraction well positioned at the cell closed end. Integrated analysis of high-resolution DNAPL saturation (Sn) (from cores), dissolved-phase plume concentration (from multilevel samplers), tracer test and permeability datasets was undertaken. DNAPL architecture was determined from soil concentration data using partitioning calculations. DNAPL threshold soil concentrations and low Sn values calculated were sensitive to sorption assumptions. An outcome of this was the uncertainty in demarcation of secondary source zone diffused and sorbed mass that is distinct from trace amounts of low Sn DNAPL mass. The majority of source mass occurred within discrete lenses or pools of DNAPL associated with low permeability geological units. High residual saturation (Sn > 10–20%) and pools (Sn > 20%) together accounted for almost 40% of the DNAPL mass, but only 3% of the sampled source volume. High-saturation DNAPL lenses/pools were supported by lower permeability layers, but with DNAPL still primarily present within slightly more permeable overlying units. These lenses/pools exhibited approximately linearly declining Sn profiles with increasing elevation ascribed to preferential dissolution of the uppermost DNAPL. Bi-component partitioning calculations on soil samples confirmed that the dechlorination product cDCE (cis-dichloroethene) was accumulating in the TCE DNAPL. Estimated cDCE mole fractions in the DNAPL increased towards the DNAPL interface with the uppermost mole fraction of 0.04 comparable to literature laboratory data. DNAPL dissolution yielded heterogeneous dissolved-phase plumes of TCE and its dechlorination products that exhibited orders of magnitude local concentration variation. TCE solubility concentrations were relatively localised, but coincident with high saturation DNAPL lens source areas. Biotic dechlorination in the source zone area, however, caused cDCE to be the dominant dissolved-phase plume. The conservative tracer test usefully confirmed the continuity of a permeable gravel unit at depth through the source zone. Although this unit offered significant opportunity for DNAPL bypassing and decreased timeframes for dechlorination, it still transmitted a significant proportion of the contaminant flux. This was attributed to dissolution of DNAPL–mudstone aquitard associated sources at the base of the continuous gravel as well as contaminated groundwater from surrounding less permeable sand and gravel horizons draining into this permeable conduit. The cell extraction well provided an integrated metric of source zone dissolution yielding a mean concentration of around 45% TCE solubility (taking into account dechlorination) that was equivalent to a DNAPL mass removal rate of 0.4 tonnes per annum over a 16 m2 cell cross sectional area of flow. This is a significant flux considering the source age and observed occurrence of much of the source mass within discrete lenses/pools. We advocate the need for further detailed field-scale studies on old DNAPL source zones that better resolve persistent pool/lens features and are of prolonged duration to assess the ageing of source zones. Such studies would further underpin the application of more surgical remediation technologies