Grabbing the gold

Imagine a tree with some integer amount of gold at each vertex. Two players can play a game by taking turns removing leaves one by one and taking the gold from those leaves. We prove a recent conjecture of Micek and Walczak that says that if a tree has an even number of vertices, the first player can always secure at least half of the gold.     

Numerical analysis of a synthetic jet using an automated adaptive method

An automated adaptive remeshing methodology is applied to a synthetic jet. A set of two‐dimensional, axisymmetric, time‐dependent Computational Fluid Dynamics analyses are performed. Grid independence is achieved via successive levels of adaptive refinement using a novel methodology. The method employs adaptive remeshing, performed in an automated fashion. Adaptation criteria are based upon the undivided differences in select field variables. Sensors are placed at strategic locations within the flow field, which are used to aid in judging grid independence. The resulting analytical predictions are compared to an experimental dataset. The automated methodology yields both a verified and validated set of analysis results for the synthetic jet. Copyright © 2011 John Wiley & Sons, Ltd.     

From vicious to virtuous circles: problem structuring for quantified decision making in operationalization of corporate social responsibility

There is no formalised approach for problem structuring and quantitative decision support to operationalise corporate social responsibility (CSR) implementation. In this paper, techniques for considering criteria relationships are outlined and a holistic, systematic framework combining a qualitative and quantitative method for practical CSR integration is provided. Cognitive mapping (CM) is applied to structure the problem picture, and the cause–effect relationships between decision elements. Soft CM methodology is employed to assess the cross-criteria interactions, at both an individual and a collective level. The interactions of criteria can have a significant impact upon CSR implementation. Such impacts can be direct or indirect through their close linkages to other criteria. The causal strategic map serves as an input to the analytic network process (ANP) to carry out the multi-criteria decision analysis. Then, CM and ANP are applied in a comparative analysis to verify whether the measures of criteria significance do correspond. The key criteria in networks are identified using centrality in CM and single limited priorities in ANP. This study demonstrates that using criteria without considering their interactions will result in shortcomings in the evaluation and assessment of CSR programmes. The holistic framework, combining CM and ANP proposed in this work, enhances the process of problem structuring and supports preference-based evaluation of decision alternatives. The results of our study yield that the mapping procedure has an influence on the criteria significance in networks. The correspondence between CM and ANP is stronger when cause relationships are rigidly interpreted. More unambiguous interpretations of causal relations can be achieved if methods are used jointly and common peaks of importance in both CM and ANP could potentially serve as indications of key decision elements.     

Spatially resolved wall temperature measurements during flow boiling in microchannels

Spatial and temporal variations of channel wall temperature during flow boiling microchannel flows using infrared thermography are presented and analyzed. In particular, the top channel wall temperature in a branching microchannel silicon heat sink is measured non-intrusively. Using this technique, time-averaged temperature measurements, with a spatial resolution of 10 μm, are presented over an 18 mm × 18 mm area of the heat sink. Also presented, within a specific sub-region of the heat sink, are intensity maps that are recorded at a rate of 120 frames per second. Time series data at selected point locations in this sub-region are analyzed for their frequency content, and dominant temperature fluctuations are extracted using proper orthogonal decomposition.Results at low-vapor-quality boiling condition indicate that temperatures can be determined from recorded radiation intensities with a temperature uncertainty varying from 0.9 °C at 25 °C to 1.0 °C at 125 °C. The time series data indicate periodic wall temperature fluctuations of approximately 2 °C that are attributed to the passage of vapor slugs. A dominant band of frequencies around 2–4 Hz is suggested by the frequency analysis. Proper orthogonal decomposition results indicate that first six orthogonal modes account for approximately 90% of the variance in temperature. The first mode reconstruction accounts for temporal variations in the dataset in the sub-region analyzed; however the magnitude of fluctuations and spatial variations in temperature are not accurately captured. A reconstruction using the first 25 modes is considered sufficient to capture both the temporal and spatial variations in the data.     

Numerical simulation of free‐surface flow using the level‐set method with global mass correction

A new numerical method that couples the incompressible Navier–Stokes equations with the global mass correction level‐set method for simulating fluid problems with free surfaces and interfaces is presented in this paper. The finite volume method is used to discretize Navier–Stokes equations with the two‐step projection method on a staggered Cartesian grid. The free‐surface flow problem is solved on a fixed grid in which the free surface is captured by the zero level set. Mass conservation is improved significantly by applying a global mass correction scheme, in a novel combination with third‐order essentially non‐oscillatory schemes and a five stage Runge–Kutta method, to accomplish advection and re‐distancing of the level‐set function. The coupled solver is applied to simulate interface change and flow field in four benchmark test cases: (1) shear flow; (2) dam break; (3) travelling and reflection of solitary wave and (4) solitary wave over a submerged object. The computational results are in excellent agreement with theoretical predictions, experimental data and previous numerical simulations using a RANS‐VOF method. The simulations reveal some interesting free‐surface phenomena such as the free‐surface vortices, air entrapment and wave deformation over a submerged object. Copyright © 2009 John Wiley & Sons, Ltd.     

A hybrid multiple-criteria decision analysis framework for corporate social responsibility implementation applied to an extractive industry case study

Integration of corporate social responsibility (CSR) into a company’s mainstream strategy is a complex task. Practical implementation of CSR requires analysis of both the external and internal environments to determine the prospects and challenges significantly influencing integration of sustainability into business strategy. In order to overcome limitations of single multiple-criteria decision analysis models, this paper proposes a hybrid integrated framework combining cognitive mapping and analytic networks process (ANP) to determine, prioritise and select CSR programmes for implementation. The strategic cognitive map serves as a foundation to build the ANP network and identify the importance of CSR programmes. A knapsack optimisation method is then used to optimally assign resources to CSR alternatives. We demonstrate the usefulness of the framework through a case study in the extractive sector. The framework was empirically tested with 61 respondents using postal and online surveys, MBA workshops, and conference networking.     

Connected‐Homomorphism‐Homogeneous Graphs

A relational structure is (connected‐) homogeneous if every isomorphism between finite (connected) substructures extends to an automorphism of the structure. We investigate notions that generalise (connected‐) homogeneity, where ‘isomorphism’ may be replaced by ‘homomorphism’ or ‘monomorphism’ in the definition. In particular, we study the classes of finite connected‐homomorphism‐homogeneous graphs, with the aim of producing classifications. The main result is a classification of the finite graphs, where a graph G is if every homomorphism from a finite connected induced subgraph of G into G extends to an endomorphism of G. The finite (connected‐homogeneous) graphs were classified by Gardiner in 1976, and from this we obtain classifications of the finite and finite graphs. Although not all the classes of finite connected‐homomorphism‐homogeneous graphs are completely characterised, we may still obtain the final hierarchy picture for these classes.     

Simultaneous Determination of Testosterone and Testosterone Enanthate in Equine Plasma by UHPLC-MS-MS

Testosterone and testosterone enanthate are performance-enhancing substances that are banned in racehorses competing in the State of Pennsylvania (PA). A tolerance concentration of 2,000 pg mL^?1 plasma has been established for testosterone in intact colts and stallions at the time they are competing in PA. Testosterone enanthate is a precursor of testosterone and can be used to boost plasma testosterone concentration above natural, age and seasonally variable plasma concentration. To control abuse, a verifiable method for rapid determination of both substances in equine plasma was needed. For this reason, an ultra high performance liquid chromatography-tandem mass spectrometry method for high-throughput analysis of both analytes in equine plasma was developed. Analytes were recovered from plasma by liquid–liquid extraction using mixture of methyl tert-butyl ether and ethyl acetate (50:50, v/v), separated on a C₁₈ sub-2 μm column and detected on a triple quadrupole mass spectrometer using positive electrospray ionization mode with selected reaction monitoring scan. SRM ion transitions of m/z 289 → m/z 97, m/z 289 → m/z 109, m/z 289 → m/z 79 were used for testosterone identification while m/z 401 → m/z 253, m/z 401 → m/z 271, m/z 401 → m/z 97 were employed for testosterone enanthate. Retention time and product ion intensity ratio were used as confirmation criteria to ascertain the presence of both analytes in equine plasma. The limits of detection, quantification and confirmation were 50 pg 0.5 mL^?1, 100 pg 0.5 mL^?1 and 250 pg 0.5 mL^?1, respectively for both analytes. The method was validated for recovery efficiency, sensitivity, matrix effect, linearity, precision and accuracy. This method is routinely used in the PA program for androgenic anabolic steroids doping control in racehorses and in the on-going testosterone enanthate pharmacokinetics study. The method is defensible, fast, selective, specific and reproducibly reliable.     

Bridging the Gap between Coordination and Cluster Compounds: Unusual Bonding Modes for Zinc

Inner virtue : The reaction of [Mo⁰(GaCp*)₆] with ZnMe₂ yields the novel multinuclear zinc system [MoZn₁₂Me₉Cp*₃] which geometrically resembles a classical Wade–Mingos cluster (with an interstitial molybdenum atom, see picture). In reality, its electronic structure features little direct Zn? Zn bonding, relying instead on Mo? Zn three‐center, two‐electron bonds spanning the body diagonals of the approximately icosahedral framework.