Acyclic Edge Coloring of Graphs with Maximum Degree 4

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a'(G). It was conjectured by Alon, Sudakov, and Zaks that for any simple and finite graph G, a'(G) <= Delta+2, where Delta=Delta(G) denotes the maximum degree of G. We prove the conjecture for connected graphs with Delta(G)<= 4, with the additional restriction that m <= 2n-1, where n is the number of vertices and m is the number of edges in G. Note that for any graph G, m <= 2n, when Delta(G)<= 4. It follows that for any graph G if Delta(G)<= 4, then a'(G) <= 7.

On the Arrangement of Cliques in Chordal Graphs with respect to the Cuts

A cut (A, B) (where B = V - A) in a graph G = (V, E) is called internal if and only if there exists a vertex x in A that is not adjacent to any vertex in B and there exists a vertex y is an element of B such that it is not adjacent to any vertex in A. In this paper, we present a theorem regarding the arrangement of cliques in a chordal graph with respect to its internal cuts. Our main result is that given any internal cut (A, B) in a chordal graph G, there exists a clique with kappa(G) + vertices (where kappa(G) is the vertex connectivity of G) such that it is (approximately) bisected by the cut (A, B). In fact we give a stronger result: For any internal cut (A, B) of a chordal graph, and for each i, 0 <= i <= kappa(G) + 1 such that vertical bar K-i vertical bar = kappa(G) + 1, vertical bar A boolean AND K-i vertical bar = i and vertical bar B boolean AND K-i vertical bar = kappa(G) + 1 - i. An immediate corollary of the above result is that the number of edges in any internal cut (of a chordal graph) should be Omega(k(2)), where kappa(G) = k. Prompted by this observation, we investigate the size of internal cuts in terms of the vertex connectivity of the chordal graphs. As a corollary, we show that in chordal graphs, if the edge connectivity is strictly less than the minimum degree, then the size of the mincut is at least kappa(G)(kappa(G)+1)/2 where kappa(G) denotes the vertex connectivity. In contrast, in a general graph the size of the mincut can be equal to kappa(G). This result is tight.

Shaping (reflexive) professional identities across an undergraduate degree programme: A longitudinal case study

In our complex and incongruous professional worlds, where there is no blueprint for dealing with unpredictable people and events, it is imperative that individuals develop reflexive approaches to professional identity building. Notwithstanding the importance of disciplinary knowledge and skills, higher education has a crucial role to play in guiding students to examine and mediate self in relation to context for effective decision-making and action. This paper reports on a small-scale longitudinal project that investigated the ways in which ten undergraduate students over the course of a three-year Radiation Therapy degree shaped their professional identities. Theories of reflexivity and methods of discourse analysis are utilised to understand the ways in which individuals accounted for their professional identity projects at university. The findings suggest that, across time, the participants negotiated professional ‘becoming’ through four distinct kinds of reflexive modalities. These findings have implications for teaching strategies and curriculum design in undergraduate programs.

Closo versus Hypercloso Metallaboranes: A DFT Study

The structures and electronic relationship of 9-, 10-, 11-, and 12-vertex closo and hypercloso (isocloso) etallaboranes are explored using OFT calculations. The role of the transition metal in stabilizing the hypercloso borane structures is explained using the concept of orbital compatibility. The hypercloso structures, C6H6MBn-1Hn-1 (n = 9-12; M = Fe, Ru, and Os) are taken as model complexes. Calculations on metal free polyhedral borane BnHn suggest that n vertex hypercloso structures need only n skeleton electron pairs (SEPs), but the structure will have one or more six-degree vertices, whereas the corresponding closo structures with n + 1 SEPs have only four- and five-degree vertices. This high-degree vertex of hypercloso structures can be effectively occupied by transition metal fragments with their highly diffused orbitals. Calculations further show that a heavy transition metal with more diffused orbitals prefers over a light transition metal to form hypercloso geometry, This is in accordance with the fact that there are more experimentally characterized hypercloso structures with the heavy transition metals. The size of the exohedral ligands attached to the metal atom also plays a role in deciding the stability of the hypercloso structure. The interaction between the borane and the metal fragments in the hypercloso geometry is analyzed using the fragment molecular orbital approach. The interconversion of the closo and hypercloso structures by the addition and removal of the electrons is also discussed in terms of the correlation diagrams.

Optimum design of a Lanchester damper for a viscously damped single degree of freedom system subjected to inertial excitation

The problem of designing an optimum Lanchester damper for a viscously damped single degree of freedom system subjected to inertial harmonic excitation is investigated. Two criteria are used for optimizing the performance of the damper: (i) minimum motion transmissibility; (ii) minimum force transmissibility. Explicit expressions are developed for determining the absorber parameters.

Variation in the walking time to bus stop by the degree of transit captivity

Measures of transit accessibility are important in evaluating transit services, planning for future services and investment on land use development. Existing tools measure transit accessibility using averaged walking distance or walking time to public transit. Although the mode captivity may have significant implications on one’s willingness to walk to use public transit, this has not been addressed in the literature to date. Failed to distinguish transit captive users may lead to overestimated ridership and spatial coverage of transit services. The aim of this research is to integrate the concept of transit captivity into the analysis of walking access to public transit. The conventional way of defining “captive” and “choice” transit users showed no significant difference in their walking times according to a preliminary analysis. A cluster analysis technique is used to further divide “choice” users by three main factors, namely age group, labour force status and personal income. After eliminating “true captive” users, defined as those without driver’s licence or without a car in respective household, “non-true captive” users were classified into a total of eight groups having similar socio-economic characteristics. The analysis revealed significant differences in the walking times and patterns by their level of captivity to public transit. This paper challenges the rule-of-thumb of 400m walking distance to bus stops. In average, people’s willingness to walk dropped drastically at 268m and continued to drop constantly until it reached the mark of 670m, where there was another drastic drop of 17%, which left with only 10% of the total bus riders willing to walk 670m or more. This research found that mothers working part time were the ones with lowest transit captivity and thus most sensitive to the walking time, followed by high-income earners and the elderly. The level of captivity increases when public transit users earned lesser income, such as students and students working part time.

A note on synthesis of the general, two-degree-of-freedom linkage

A graphical method is presented for synthesis of the general, seven-link, two-degree-of-freedom plane linkage to generate functions of two variables. The method is based on point position reduction and permits synthesis of the linkage to satisfy upto six arbitrarily selected precision positions.

Optimum design of Lanchester damper for a viscously damped single degree of freedom system by using minimum force transmissibility criterion

The problem of optimum design of a Lanchester damper for minimum force transmission from a viscously damped single degree of freedom system subjected to harmonic excitation is investigated. Explicit expressions are developed for determining the optimum absorber parameters. It is shown that for the particular case of the undamped single degree of freedom system the results reduce to the classical ones obtained by using the concept of a fixed point on the transmissibility curves.

A closed-form optimal tuning of mass dampers for one degree-of-freedom systems under rotating unbalance forcing

This paper is focused on the study of a vibrating system forced by a rotating unbalance and coupled to a tuned mass damper (TMD). The analysis of the dynamic response of the entire system is used to define the parameters of such device in order to achieve optimal damping properties. The inertial forcing due to the rotating unbalance depends quadratically on the forcing frequency and it leads to optimal tuning parameters that differ from classical values obtained for pure harmonic forcing. Analytical results demonstrate that frequency and damping ratios, as a function of the mass parameter, should be higher than classical optimal parameters. The analytical study is carried out for the undamped primary system, and numerically investigated for the damped primary system. We show that, for practical applications, proper TMD tuning allows to achieve a reduction in the steady-state response of about 20% with respect to the response achieved with a classically tuned damper. Copyright © 2015 by ASME.

Reproducibility of scratch assays is affected by the initial degree of confluence: Experiments, modelling and model selection

Scratch assays are difficult to reproduce. Here we identify a previously overlooked source of variability which could partially explain this difficulty. We analyse a suite of scratch assays in which we vary the initial degree of confluence (initial cell density). Our results indicate that the rate of re-colonisation is very sensitive to the initial density. To quantify the relative roles of cell migration and proliferation, we calibrate the solution of the Fisher–Kolmogorov model to cell density profiles to provide estimates of the cell diffusivity, D, and the cell proliferation rate, λ. This procedure indicates that the estimates of D and λ are very sensitive to the initial density. This dependence suggests that the Fisher–Kolmogorov model does not accurately represent the details of the collective cell spreading process, since this model assumes that D and λ are constants that ought to be independent of the initial density. Since higher initial cell density leads to enhanced spreading, we also calibrate the solution of the Porous–Fisher model to the data as this model assumes that the cell flux is an increasing function of the cell density. Estimates of D and λ associated with the Porous–Fisher model are less sensitive to the initial density, suggesting that the Porous–Fisher model provides a better description of the experiments.

Semi-active vibration isolation using a near-zero-spring-rate device:steady state analysis of a single-degree-of-freedom model

A vibration isolator is described which incorporates a near-zero-spring-rate device within its operating range. The device is an assembly of a vertical spring in parallel with two inclined springs. A low spring rate is achieved by combining the equivalent stiffness in the vertical direction of the inclined springs with the stiffness of the vertical central spring. It is shown that there is a relation between the geometry and the stiffness of the individual springs that results in a low spring rate. Computer simulation studies of a single-degree-of-freedom model for harmonic base input show that the performance of the proposed scheme is superior to that of the passive schemes with linear springs and skyhook damping configuration. The response curves show that, for small to large amplitudes of base disturbance, the system goes into resonance at low frequencies of excitation. Thus, it is possible to achieve very good isolation over a wide low-frequency band. Also, the damper force requirements for the proposed scheme are much lower than for the damper force of a skyhook configuration or a conventional linear spring with a semi-active damper.

Looking out of the void : Scaffolds to assist drama higher research degree students on the path to artist–scholar

In recent years, a number of Australian and international universities have offered the ability to complete postgraduate qualifications using the research frame known as creative practice as research. This has been particularly prevalent in the Drama discipline in the Creative Industries Faculty at Queensland University of Technology (QUT). There has been a noticeable shift away from students undertaking a traditional research Master of Arts (Research) or Doctor of Philosophy to a higher proportion of research higher degree students undertaking research through their creative work. The somewhat ephemeral nature of the theatre and performance practice can generate anxieties for students about how to best represent, analyse and discuss the creative practice within a theoretical frame. The argument in this paper is situated in the experience of two artist-scholars who undertook their studies at QUT while under principal supervision of the author and explores the research scaffolds that supervisors in Drama at QUT have developed to assist research higher degree students to navigate the tricky persona of artist–scholar.

Vertex-Fused Metallaborane Clusters: Synthesis, Characterization and Electronic Structure of [(eta(5)-C5Me5Mo)(3)MoB9H18]

The reaction of the [(eta(5)-C5Me5)MoCl4] complex with [LiBH4 - TH F] in toluene at - 70 degrees C, followed by pyrolysis at 110 degrees C, afforded dark brown [(eta(5)-C5Me5Mo)(3)MoB9H18], 2, in parallel with the known [(eta(5)-C5Me5Mo)(2)B5H9], 1. Compound 2 has been characterized in solution by H-1, B-11, and C-13 NMR spectroscopy and elemental analysis, and the structural types were unequivocally established by crystallographic studies. The title compound represents a novel class of vertex-fused clusters in which a Mo atom has been fused in a perpendicular fashion between two molybdaborane clusters. Electronic structure calculations employing density functional theory yield geometries in agreement with the structure determinations, and on grounds of density functional theory calculations, we have analyzed the bonding patterns in the structure,

Enhancing learning for research higher degree students

Universities’ push toward the production of high quality research is not limited to academic staff and experienced researchers. In this environment of research rich agendas, Higher Degree Research (HDR) students are increasingly expected to engage in the publishing of good quality papers in high impact journals. IFN001: Advanced Information Research Skills (AIRS) is a credit bearing mandatory coursework requirement for Queensland University of Technology (QUT) doctorates. Since its inception in 1989, this unique blended learning program has provided the foundations for new researchers to produce original and innovative research. AIRS was redeveloped in 2012, and has now been evaluated with reference to the university’s strategic research priorities. Our research is the first comprehensive evaluation of the program from the learner perspective. We measured whether the program develops essential transferrable skills and graduate capabilities to ensure best practice in the areas of publishing and data management. In particular, we explored whether AIRS prepares students to be agile researchers with the skills to adapt to different research contexts both within and outside academia. The target group for our study consisted of HDR students and supervisors at QUT. Both quantitative and qualitative research methods were used for data collection. Gathering data was by survey and focus groups with qualitative responses analyzed using NVivo. The results of the survey show that 82% of students surveyed believe that AIRS assisted their research process and helped them learn skills they need as a researcher. The 18% of respondents who expressed reservation about the benefits of AIRS were also examined to determine the key areas of concern. These included trends related to the timing of the program early in the candidature and a belief among some students that their previous research experience was sufficient for postgraduate study. New insights have been gained into how to better support HDR learners in partnership with supervisors and how to enhance learning experiences of specific cohorts, including international students and mature learners.

Boxicity and maximum degree

A d-dimensional box is a Cartesian product of d closed intervals on the real line. The boxicity of a graph is the minimum dimension d such that it is representable as the intersection graph of d-dimensional boxes. We give a short constructive proof that every graph with maximum degree D has boxicity at most 2D2. We also conjecture that the best upper bound is linear in D.