On an Extremal Problem concerning Bernstein Operators

* The second author is supported by the Alexander-von-Humboldt Foundation. He is on leave from: Institute of Mathematics, Academia Sinica, Beijing 100080, People’s Republic of China.

Direct and Converse Theorems for Generalized Bernstein-Type Operators

2000 Mathematics Subject Classification: 41A25, 41A27, 41A36.

Weighted Approximation by a Class of Bernstein-Type Operators

AMS classification: 41A36, 41A10, 41A25, 41Al7.

Neurofuzzy network model construction using Bézier-Bernstein polynomial functions

Neurofuzzy modelling systems combine fuzzy logic with quantitative artificial neural networks via a concept of fuzzification by using a fuzzy membership function usually based on B-splines and algebraic operators for inference, etc. The paper introduces a neurofuzzy model construction algorithm using Bezier-Bernstein polynomial functions as basis functions. The new network maintains most of the properties of the B-spline expansion based neurofuzzy system, such as the non-negativity of the basis functions, and unity of support but with the additional advantages of structural parsimony and Delaunay input space partitioning, avoiding the inherent computational problems of lattice networks. This new modelling network is based on the idea that an input vector can be mapped into barycentric co-ordinates with respect to a set of predetermined knots as vertices of a polygon (a set of tiled Delaunay triangles) over the input space. The network is expressed as the Bezier-Bernstein polynomial function of barycentric co-ordinates of the input vector. An inverse de Casteljau procedure using backpropagation is developed to obtain the input vector's barycentric co-ordinates that form the basis functions. Extension of the Bezier-Bernstein neurofuzzy algorithm to n-dimensional inputs is discussed followed by numerical examples to demonstrate the effectiveness of this new data based modelling approach.

Reconciling community and commerce? Collaboration between produsage communities and commercial operators

Collaborative user-led content creation by online communities, or produsage (Bruns 2008), has generated a variety of useful and important resources and other valuable outcomes, from open source software through the Wikipedia to a variety of smaller-scale, specialist projects. These are often seen as standing in an inherent opposition to commercial interests, and attempts to develop collaborations between community content creators and commercial partners have had mixed success rates to date. However, such tension between community and commerce is not inevitable, and there is substantial potential for more fruitful exchanges and collaboration. This article contributes to the development of this understanding by outlining the key underlying principles of such participatory community processes and exploring the potential tensions which could arise between these communities and their potential external partners. It also sketches out potential approaches to resolving them.

Acceptability of the distress thermometer and problem list to community-based telephone cancer helpline operators, and to cancer patients and carers

Background Cancer can be a distressing experience for cancer patients and carers, impacting on psychological, social, physical and spiritual functioning. However, health professionals often fail to detect distress in their patients due to time constraints and a lack of experience. Also, with the focus on the patient, carer needs are often overlooked. This study investigated the acceptability of brief distress screening with the Distress Thermometer (DT) and Problem List (PL) to operators of a community-based telephone helpline, as well as to cancer patients and carers calling the service. Methods Operators (n = 18) monitored usage of the DT and PL with callers (cancer patients/carers, >18 years, and English-speaking) from September-December 2006 (n = 666). The DT is a single item, 11-point scale to rate level of distress. The associated PL identifies the cause of distress. Results The DT and PL were used on 90% of eligible callers, most providing valid responses. Benefits included having an objective, structured and consistent means for distress screening and triage to supportive care services. Reported challenges included apparent inappropriateness of the tools due to the nature of the call or level of caller distress, the DT numeric scale, and the level of operator training. Conclusions We observed positive outcomes to using the DT and PL, although operators reported some challenges. Overcoming these challenges may improve distress screening particularly by less experienced clinicians, and further development of the PL items and DT scale may assist with administration. The DT and PL allow clinicians to direct/prioritise interventions or referrals, although ongoing training and support is critical in distress screening.

The construction of social identity in new nuclear operators : a longitudinal study

Countless studies have stressed the importance of social identity, particularly its role in various organizational outcomes, yet questions remain as to how identities initially develop, shift and change based on the configuration of multiple, pluralistic relationships grounded in an organizational setting. The interactive model of social identity formation has been proposed recently to explain the internalization of shared norms and values – critical in identity formation – has not received empirical examination. We analyzed multiple sources of data from nine nuclear professionals over three years to understand the construction of social identity in new entrants entering an organization. Informed by our data analyses, we found support for the interactive model and that age and level of experience influenced whether they undertook an inductive or deductive route of the group norm and value internalization. This study represents an important contribution to the study of social identity and the process by which identities are formed, particularly under conditions of duress or significant organizational disruption.

PAC-Bayes-empirical-Bernstein inequality

We present PAC-Bayes-Empirical-Bernstein inequality. The inequality is based on combination of PAC-Bayesian bounding technique with Empirical Bernstein bound. It allows to take advantage of small empirical variance and is especially useful in regression. We show that when the empirical variance is significantly smaller than the empirical loss PAC-Bayes-Empirical-Bernstein inequality is significantly tighter than PAC-Bayes-kl inequality of Seeger (2002) and otherwise it is comparable. PAC-Bayes-Empirical-Bernstein inequality is an interesting example of application of PAC-Bayesian bounding technique to self-bounding functions. We provide empirical comparison of PAC-Bayes-Empirical-Bernstein inequality with PAC-Bayes-kl inequality on a synthetic example and several UCI datasets.

SOTrain: A new program for training supervisors and operators in Australian sugar factories

The provision of effective training of supervisors and operators is essential if sugar factories are to operate profitably and in an environmentally sustainable and safe manner. The benefits of having supervisor and operator staff with a high level of operational skills are reduced stoppages, increased recovery, improved sugar quality, reduced damage to equipment, and reduced OH&S and environmental impacts. Training of new operators and supervisors in factories has traditionally relied on on-the-job training of the new or inexperienced staff by experienced supervisors and operators, supplemented by courses conducted by contractors such as Sugar Research Institute (SRI). However there is clearly a need for staff to be able to undertake training at any time, drawing on the content of online courses as required. An improved methodology for the training of factory supervisors and operators has been developed by QUT on behalf of a syndicate of mills. The new methodology provides ‘at factory’ learning via self-paced modules. Importantly, the training resources for each module are designed to support the training programs within sugar factories, thereby establishing a benchmark for training across the sugar industry. The modules include notes, training guides and session plans, guidelines for walkthrough tours of the stations, learning activities, resources such as videos, animations, job aids and competency assessments. The materials are available on the web for registered users in Australian Mills and many activities are best undertaken online. Apart from a few interactive online resources, the materials for each module can also be downloaded. The acronym SOTrain (Supervisor and Operator Training) has been applied to the new training program.

A Classification of Homogeneous Operators in the Cowen-Douglas Class

A complete list of homogeneous operators in the Cowen-Douglas class B-n(D) is given. This classification is obtained from an explicit realization of all the homogeneous Hermitian holomorphic vector bundles on the unit disc under the action of the universal covering group of the bi-holomorphic automorphism group of the unit disc.

On the eigenvalues and eigenfunctions of some integral operators

Some properties of the eigenvalues of the integral operator Kgt defined as Kτf(x) = ∫0τK(x − y) f (y) dy were studied by [1.], 554–566), with some assumptions on the kernel K(x). In this paper the eigenfunctions of the operator Kτ are shown to be continuous functions of τ under certain circumstances. Also, the results of Vittal Rao and the continuity of eigenfunctions are shown to hold for a larger class of kernels.

Quaternary unary operators

Unary operators are functions of a single variable. Realization of quaternary unary operators (QUOs) using quaternary multiplexer (QMUX) is presented in this paper. QUOs are divided into eight groups on the basis of the number of change overs in the output for an input sequence of 0, 1, 2, 3. This grouping reduces the hardware required to realize them. QMUX with two, three, and four input lines are proposed for the realization of QUOs belonging to the eight groups. A systematic procedure for the selection of QMUX and the implementation of the QUOs are given. The QMUXs are designed using CMOS ICs. The hardware required for their implementation is also discussed.

Representations and properties of para-Bose oscillator operators. I. Energy position and momentum eigenstates

Para-Bose commutation relations are related to the SL(2,R) Lie algebra. The irreducible representation [script D]alpha of the para-Bose system is obtained as the direct sum Dbeta[direct-sum]Dbeta+1/2 of the representations of the SL(2,R) Lie algebra. The position and momentum eigenstates are then obtained in this representation [script D]alpha, using the matrix mechanical method. The orthogonality, completeness, and the overlap of these eigenstates are derived. The momentum eigenstates are also derived using the wave mechanical method by specifying the domain of the definition of the momentum operator in addition to giving it a formal differential expression. By a careful consideration in this manner we find that the two apparently different solutions obtained by Ohnuki and Kamefuchi in this context are actually unitarily equivalent. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Judge Max Frankenbach of Berlin hiking with his wife Grete Frankenbach nee Bernstein; Sassal-Massone Portraits Couples

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