Branes,Quantum Nambu Brackets and the Hydrogen Atom

The Nambu-bracket quantization of the hydrogen atom is worked out as an illustration of the general method. The dynamics of topological open branes is controlled classically by Nambu brackets. Such branes then may be quantized through the consistent quantization of the underlying Nambu brackets: properly defined, the quantum Nambu-brackets comprise an associative structure, although the naive derivation property is mooted through operator entwinement. For superintegrable systems, such as the hydrogen atom, the results coincide with those furnished by Hamiltonian quantization - but the method is not limited to Hamiltonian systems.     

直径不超过4的树的割宽

§ 1　IntroductionThe cutwidth problem for graphs,as well as a class of optimal labeling and embed-ding problems,have significant applications in VLSI designs,network communicationsand other areas (see [2 ] ) .We shall follow the graph-theoretic terminology and notation of [1 ] .Let G=(V,E)be a simple graph with vertex set V,| V| =n,and edge set E.A labeling of G is a bijec-tion f:V→ { 1 ,2 ,...,n} ,which can by regarded as an embedding of G into a path Pn.Fora given labeling f of G,th…     

Methodological reflections on a three-step-design combining observation,stimulated recall and interview

In this paper a tripartite qualitative design combining abservation, stimulated recall and interview is presented and discussed. This three-step-design makes it possible to get insight into the interaction of internal and external processes when solving mathematical tasks. The data analysis depends on the research question and the methodological approach. In the light of two research projects in mathematics education two different methods of data analysis are presented and methodologically reflected.     

A market-based computational approach to collaborative organizational learning

We draw upon the concepts of knowledge market, organizational tacit knowledge, credit assignment, and single-loop learning in proposing a market-based conceptual model for collaborative organizational learning. Our proposed model is characterized by the local competition among seller agents and the global collaboration among winner agents in forming a plan, through a chain of ‘upstream–downstream’ working relationship, for task accomplishment. This feature is achieved through three closely coupled processes: the expert selection process, the capital reallocation process, and the plan formation process. Our model is intended for multiple-step learning environment in which each task consists of a sequence of single-step learning tasks. Learning at the global level is the result of a sequence of nested single-loop learning at the local level.     

Generalized binomial and negative binomial distributions of order<Emphasis Type="Italic">k</Emphasis> by the<Emphasis Type="Italic">l</Emphasis>-overlapping enumeration scheme

In this paper, we investigate the exact distribution of the waiting time for ther-th ℓ-overlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials. The probability generating functions are derived explicitly, and as asymptotic results, relationships of a negative binomial distribution of orderk and an extended Poisson distribution of orderk are discussed. We provide further insights into the run-related problems from the viewpoint of the ℓ-overlapping enumeration scheme. We also study the exact distribution of the number of ℓ-overlapping occurrences of success-runs in a fixed number of trials and derive the probability generating functions. The present work extends several properties of distributions of orderk and leads us a new type of geneses of the discrete distributions.     

The stable forking conjecture and generic structures

 We prove that for any simple theory which is constructed via Fr?issé-Hrushovski method, if the forking independence is the same as the d-independence then the stable forking property holds. Received: 22 January 2001 / Published online: 19 December 2002 This article is part of the author's D-Phil thesis, written at the University of Oxford and supported by the Ministry of Higher Education of Iran. The author would like to thank the Institute for Studies in Theoretical Physics and Mathematics (IPM), Tehran, Iran, for its financial support whilst working on this article. Mathematics Subject Classification (2000): 03C45 Key words or phrases: Generic structures – Fr?issé-Hrushovski method – Predimension – Simple theories – Stable theories – Stable forking conjecture     

An EOQ model with process reliability considerations

The classical economic order quantity (EOQ) model assumes that items produced are of perfect quality and that the unit cost of production is independent of demand. However, in realistic situations, product quality is never perfect, but is directly affected by the reliability of the production process. In this paper, we consider an EOQ model with imperfect production process and the unit production cost is directly related to process reliability and inversely related to the demand rate. In addition, a numerical example is given to illustrate the developed model. Sensitivity analysis is also performed and discussed.     

Approaches to sharing knowledge in group problem structuring

Problem-structuring techniques are an integral aspect of ‘Soft-OR’. SSM, SAST, Strategic Choice, and JOURNEY Making, all depend for their success on a group developing a shared view of a problem through some form of explicit modelling. The negotiated problem structure becomes the basis for problem resolution. Implicit to this process is an assumption that members of the group share and build their knowledge about the problem domain. This paper explores the extent to which this assumption is reasonable. The research is based on detailed records from the use of JOURNEY Making, where it has used special purpose Group Support software to aid the group problem structuring. This software continuously tracks the contributions of each member of the group and thus the extent to which they appear to be ‘connecting’ and augmenting their own knowledge with that of other members of the group. Software records of problem resolution in real organisational settings are used to explore the sharing of knowledge among senior managers. These explorations suggest a typology of knowledge sharing. The implications of this typology for problem structuring and an agenda for future research are considered.