Eigenfunctions and fundamental solutions of the Caputo fractional Laplace and Dirac operators

In this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.

Solutions of Tikhonov functional equations and applications to multiplication operators on Szegö spaces

We consider a natural representation of solutions for Tikhonov functional equations. This will be done by applying the theory of reproducing kernels to the approximate solutions of general bounded linear operator equations (when defined from reproducing kernel Hilbert spaces into general Hilbert spaces), by using the Hilbert-Schmidt property and tensor product of Hilbert spaces. As a concrete case, we shall consider generalized fractional functions formed by the quotient of Bergman functions by Szegö functions considered from the multiplication operators on the Szegö spaces.

Invertibility characterization of Wiener-Hopf plus Hankel operators on variable exponent Lebesgue spaces via even asymmetric factorization

We obtain invertibility and Fredholm criteria for the Wiener-Hopf plus Hankel operators acting between variable exponent Lebesgue spaces on the real line. Such characterizations are obtained via the so-called even asymmetric factorization which is applied to the Fourier symbols of the operators under study.

Homogenization of the p-Laplacian with nonlinear boundary condition on critical size particles: Identifying the strange term for the some non smooth and multivalued operators

We extend previous papers in the literature concerning the homogenization of Robin type boundary conditions for quasilinear equations, in the case of microscopic obstacles of critical size: here we consider nonlinear boundary conditions involving some maximal monotone graphs which may correspond to discontinuous or non-Lipschitz functions arising in some catalysis problems.

Strictly singular operators in pairs of L (p) space

Let E and F be Banach spaces. A linear operator from E to F is said to be strictly singular if, for any subspace Q aS, E, the restriction of A to Q is not an isomorphism. A compactness criterion for any strictly singular operator from L (p) to L (q) is found. There exists a strictly singular but not superstrictly singular operator on L (p) , provided that p not equal 2.

Rota's universal operators and invariant subspaces in Hilbert spaces

A Hilbert space operator is called universal (in the sense of Rota) if every operator on the Hilbert space is similar to a multiple of the restriction of the universal operator to one of its invariant subspaces. We exhibit an analytic Toeplitz operator whose adjoint is universal in the sense of Rota and commutes with a quasi-nilpotent injective compact operator with dense range. In particular, this new universal operator invites an approach to the Invariant Subspace Problem that uses properties of operators that commute with the universal operator.

The significant role of third-party logistics (3pl) operators as fosterers of organizational performance in colombian companies

La eliminación de barreras entre países es una consecuencia que llega con la globalización y con los acuerdos de TLC firmados en los últimos años. Esto implica un crecimiento significativo del comercio exterior, lo cual se ve reflejado en un aumento de la complejidad de la cadena de suministro de las empresas. Debido a lo anterior, se hace necesaria la búsqueda de alternativas para obtener altos niveles de productividad y competitividad dentro de las empresas en Colombia, ya que el entorno se ha vuelto cada vez más complejo, saturado de competencia no sólo nacional, sino también internacional. Para mantenerse en una posición competitiva favorable, las compañías deben enfocarse en las actividades que le agregan valor a su negocio, por lo cual una de las alternativas que se están adoptando hoy en día es la tercerización de funciones logísticas a empresas especializadas en el manejo de estos servicios. Tales empresas son los Proveedores de servicios logísticos (LSP), quienes actúan como agentes externos a la organización al gestionar, controlar y proporcionar actividades logísticas en nombre de un contratante. Las actividades realizadas pueden incluir todas o parte de las actividades logísticas, pero como mínimo la gestión y ejecución del transporte y almacenamiento deben estar incluidos (Berglund, 2000). El propósito del documento es analizar el papel de los Operadores Logísticos de Tercer nivel (3PL) como promotores del desempeño organizacional en las empresas colombianas, con el fin de informar a las MIPYMES acerca de los beneficios que se obtienen al trabajar con LSP como un medio para mejorar la posición competitiva del país.

On Ordinal VC-Dimension and Some Notions of Complexity

We generalize the classical notion of Vapnik–Chernovenkis (VC) dimension to ordinal VC-dimension, in the context of logical learning paradigms. Logical learning paradigms encompass the numerical learning paradigms commonly studied in Inductive Inference. A logical learning paradigm is defined as a set W of structures over some vocabulary, and a set D of first-order formulas that represent data. The sets of models of ϕ in W, where ϕ varies over D, generate a natural topology W over W. We show that if D is closed under boolean operators, then the notion of ordinal VC-dimension offers a perfect characterization for the problem of predicting the truth of the members of D in a member of W, with an ordinal bound on the number of mistakes. This shows that the notion of VC-dimension has a natural interpretation in Inductive Inference, when cast into a logical setting. We also study the relationships between predictive complexity, selective complexity—a variation on predictive complexity—and mind change complexity. The assumptions that D is closed under boolean operators and that W is compact often play a crucial role to establish connections between these concepts. We then consider a computable setting with effective versions of the complexity measures, and show that the equivalence between ordinal VC-dimension and predictive complexity fails. More precisely, we prove that the effective ordinal VC-dimension of a paradigm can be defined when all other effective notions of complexity are undefined. On a better note, when W is compact, all effective notions of complexity are defined, though they are not related as in the noncomputable version of the framework.

Safer construction voluntary code of practice : implications for SMEs

The majority of Australian construction firms are small businesses, with 97% of general construction businesses employing less than 20 employees and 85% employing less than five employees (Lin and Mills, 2001; Lingard and Holmes, 2001). The Australian Bureau of Statistics’ definition of a small to medium enterprise was used for the purpose of this study (McLennan, 2000). This included small business employing less than twenty people and medium business employing less than 200 people. Although small to medium enterprises (SME) make up the major share of construction organisations in Australia, there is a paucity of published research in relation to occupational health and safety (OHS) issues for this group. Typically, SME organisations “are frequently undercapitalized and depend on continuous cash flow for their continued business” (Cole, 2003; 12). Research by Lin and Mills (2001) indicates that these factors influence the smaller operators’ ability and motivation to achieve high levels of OHS compared to larger firms which tend to integrate OHS into their management systems. According to Lin and Mills (2001; 137) small firms “do not feel the need to focus on OHS in their management systems, instead they often believe that the control of risk is the responsibility of employees”. This report documents findings from a qualitative research study that examined SME organisations’ views of a newly developed voluntary code of practice (VCOP), and ways in which they might implement the code in their businesses. The research also explored respondents’ awareness of current safety issues in industry in the context of their personal experiences.

Generalising unitary time evolution

In this third Quantum Interaction (QI) meeting it is time to examine our failures. One of the weakest elements of QI as a field, arises in its continuing lack of models displaying proper evolutionary dynamics. This paper presents an overview of the modern generalised approach to the derivation of time evolution equations in physics, showing how the notion of symmetry is essential to the extraction of operators in quantum theory. The form that symmetry might take in non-physical models is explored, with a number of viable avenues identified.

AITPM Email Newsletter Volume 0903, March 2009: Presidents Message

President’s Report Hello fellow AITPM members, First I would like on behalf of all AITPM members to send our condolences to all who have been affected by February’s tragic bushfires in regional Victoria, and deliver our best wishes to all of those involved in the rebuilding efforts. Over time I expect that the Victorian Government’s Royal Commission will analyse the circumstances and put forward a range of measures which will improve fire safety in vulnerable areas. As transport professionals it will be important for us to consider the findings and look to undertaking any recommendations that relate to the work we do. Not only in Victoria, but nationwide. In particular, the importance of logistics was highlighted following the fire events. Donors across Australia were this time requested to donate money rather than goods, presumably due in part to problems associated with the transport system coping with additional uncoordinated freight load, whilst being needed to support emergency management vehicle and managed freight movements. Notwithstanding, it was wonderful to see otherwise difficult to obtain goods, such as animal feed, being donated from far afield and transported in kind by trucking operators. As stated in last month’s Newsletter, AITPM made a direct cash donation to the Red Cross Bushfire Appeal immediately following the events, and a further donation to the Queensland Premier’s Disaster Relief Fund to support recovery after the North Queensland floods, which claimed seven lives. Again, we will need to monitor how the rebuilding effort unfolds particularly in regional Victoria and centres including Ingham in North Queensland, but I would urge all AITPM members who are in a position to support the restoration of the affected communities to play a part, particularly over time once the initial shock subsides and the steady job of rebuilding is underway. Onto lighter matters, AITPM’s flagship event, the 2009 AITPM National Conference, Traffic Beyond Tomorrow, being held in Adelaide from 5 to 7 August, is fast approaching. www.aitpm.com has all of the details about how to register, sponsor a booth, and so forth. We are looking forward to catching up with our conference “regulars” and meeting with new folks to AITPM, and Australian traffic and transport planning and management. Adelaide is one of my favourite places to visit and I’m looking forward to riding the light rail line extension through town and checking out progress on the road system development. Best regards all, Jon Bunker

Sewage disposal and wildlife health in Antarctica

Sewage and its microbiology, treatment and disposal are important to the topic of Antarctic wildlife health because disposal of untreated sewage effluent into the Antarctic marine environment is both allowed and commonplace. Human sewage contains enteric bacteria as normal flora, and has the potential to contain parasites, bacteria and viruses which may prove pathogenic to Antarctic wildlife. Treatment can reduce levels of micro-organisms in sewage effluent, but is not a requirement of the Environmental Protocol to the Antarctic Treaty (the Madrid Protocol). In contrast, the deliberate release of non-native organisms for any other reason is prohibited. Hence, disposal of sewage effluent to the marine environment is the only activity routinely undertaken in Antarctica knowing that it will likely result in the release of large numbers of potentially non-native species. When the Madrid Protocol was negotiated, the decision to allow release of untreated sewage effluent was considered the only pragmatic option, as a prohibition would have been costly, and may not have been achievable by many Antarctic operators. In addition, at that time the potential for transmission of pathogens to wildlife from sewage was not emphasised as a significant potential risk. Since then, the transmission of disease-causing agents between species is more widely recognised and it is now timely to consider the risks of continued discharge of sewage effluent in Antarctica and whether there are practical alternatives.

Improved detection and tracking of objects in surveillance video

Surveillance networks are typically monitored by a few people, viewing several monitors displaying the camera feeds. It is then very difficult for a human operator to effectively detect events as they happen. Recently, computer vision research has begun to address ways to automatically process some of this data, to assist human operators. Object tracking, event recognition, crowd analysis and human identification at a distance are being pursued as a means to aid human operators and improve the security of areas such as transport hubs. The task of object tracking is key to the effective use of more advanced technologies. To recognize an event people and objects must be tracked. Tracking also enhances the performance of tasks such as crowd analysis or human identification. Before an object can be tracked, it must be detected. Motion segmentation techniques, widely employed in tracking systems, produce a binary image in which objects can be located. However, these techniques are prone to errors caused by shadows and lighting changes. Detection routines often fail, either due to erroneous motion caused by noise and lighting effects, or due to the detection routines being unable to split occluded regions into their component objects. Particle filters can be used as a self contained tracking system, and make it unnecessary for the task of detection to be carried out separately except for an initial (often manual) detection to initialise the filter. Particle filters use one or more extracted features to evaluate the likelihood of an object existing at a given point each frame. Such systems however do not easily allow for multiple objects to be tracked robustly, and do not explicitly maintain the identity of tracked objects. This dissertation investigates improvements to the performance of object tracking algorithms through improved motion segmentation and the use of a particle filter. A novel hybrid motion segmentation / optical flow algorithm, capable of simultaneously extracting multiple layers of foreground and optical flow in surveillance video frames is proposed. The algorithm is shown to perform well in the presence of adverse lighting conditions, and the optical flow is capable of extracting a moving object. The proposed algorithm is integrated within a tracking system and evaluated using the ETISEO (Evaluation du Traitement et de lInterpretation de Sequences vidEO - Evaluation for video understanding) database, and significant improvement in detection and tracking performance is demonstrated when compared to a baseline system. A Scalable Condensation Filter (SCF), a particle filter designed to work within an existing tracking system, is also developed. The creation and deletion of modes and maintenance of identity is handled by the underlying tracking system; and the tracking system is able to benefit from the improved performance in uncertain conditions arising from occlusion and noise provided by a particle filter. The system is evaluated using the ETISEO database. The dissertation then investigates fusion schemes for multi-spectral tracking systems. Four fusion schemes for combining a thermal and visual colour modality are evaluated using the OTCBVS (Object Tracking and Classification in and Beyond the Visible Spectrum) database. It is shown that a middle fusion scheme yields the best results and demonstrates a significant improvement in performance when compared to a system using either mode individually. Findings from the thesis contribute to improve the performance of semi-automated video processing and therefore improve security in areas under surveillance.

Techniques for inserting additional trains into existing timetables

In this paper techniques for scheduling additional train services (SATS) are considered as is train scheduling involving general time window constraints, fixed operations, maintenance activities and periods of section unavailability. The SATS problem is important because additional services must often be given access to the railway and subsequently integrated into current timetables. The SATS problem therefore considers the competition for railway infrastructure between new services and existing services belonging to the same or different operators. The SATS problem is characterised as a hybrid job shop scheduling problem with time window constraints. To solve this problem constructive algorithm and metaheuristic scheduling techniques that operate upon a disjunctive graph model of train operations are utilised. From numerical investigations the proposed framework and associated techniques are tested and shown to be effective.

National guidelines for digital modelling

These National Guidelines and Case Studies for Digital Modelling are the outcomes from one of a number of Building Information Modelling (BIM)-related projects undertaken by the CRC for Construction Innovation. Since the CRC opened its doors in 2001, the industry has seen a rapid increase in interest in BIM, and widening adoption. These guidelines and case studies are thus very timely, as the industry moves to model-based working and starts to share models in a new context called integrated practice. Governments, both federal and state, and in New Zealand are starting to outline the role they might take, so that in contrast to the adoption of 2D CAD in the early 90s, we ensure that a national, industry-wide benefit results from this new paradigm of working. Section 1 of the guidelines give us an overview of BIM: how it affects our current mode of working, what we need to do to move to fully collaborative model-based facility development. The role of open standards such as IFC is described as a mechanism to support new processes, and make the extensive design and construction information available to asset operators and managers. Digital collaboration modes, types of models, levels of detail, object properties and model management complete this section. It will be relevant for owners, managers and project leaders as well as direct users of BIM. Section 2 provides recommendations and guides for key areas of model creation and development, and the move to simulation and performance measurement. These are the more practical parts of the guidelines developed for design professionals, BIM managers, technical staff and ‘in the field’ workers. The guidelines are supported by six case studies including a summary of lessons learnt about implementing BIM in Australian building projects. A key aspect of these publications is the identification of a number of important industry actions: the need for BIM-compatible product information and a national context for classifying product data; the need for an industry agreement and setting process-for-process definition; and finally, the need to ensure a national standard for sharing data between all of the participants in the facility-development process.