Note on the locally product and almost locally product structures

This paper is concerned with a study of some of the properties of locally product and almost locally product structures on a differentiable manifold X n of class C k . Every locally product space has certain almost locally product structures which transform the local tangent space to X n at an arbitrary point P in a set fashion: this is studied in Theorem (2.2). Theorem (2.3) considers the nature of transformations that exist between two co-ordinate systems at a point whenever an almost locally product structure has the same local representation in each of these co-ordinate systems. A necessary and sufficient condition for X n to be a locally product manifold is obtained in terms of the pseudo-group of co-ordinate transformations on X n and the subpseudo-groups [cf., Theoren (2.1)]. Section 3 is entirely devoted to the study of integrable almost locally product structures.

Industry Linkages and Audit Firms' Industry Portfolio Choice: Evidence from Product Language

Audit firms are organized along industry lines and industry specialization is a prominent feature of the audit market. Yet, we know little about how audit firms make their industry portfolio decisions, i.e., how audit firms decide which set of industries to specialize in. In this study, I examine how the linkages between industries in the product space affect audit firms’ industry portfolio choice. Using text-based product space measures to capture these industry linkages, I find that both Big 4 and small audit firms tend to specialize in industry-pairs that 1) are close to each other in the product space (i.e., have more similar product language) and 2) have a greater number of “between-industries” in the product space (i.e., have a greater number of industries with product language that is similar to both industries in the pair). Consistent with the basic tradeoff between specialization and coordination, these results suggest that specializing in industries that have more similar product language and more linkages to other industries in the product space allow audit firms greater flexibility to transfer industry-specific expertise across industries as well as greater mobility in the product space, hence enhancing its competitive advantage. Additional analysis using the collapse of Arthur Andersen as an exogenous supply shock in the audit market finds consistent results. Taken together, the findings suggest that industry linkages in the product space play an important role in shaping the audit market structure.

Ongoing Adaptation as a Feature of Complexity : Further Thoughts and Possible Ideas for Pedagogy in Physical Activity

This chapter takes as its central premise the human capacity to adapt to changing environments. It is an idea that is central to complexity theory but receives only modest attention in relation to learning. To do this we will draw from a range of fields and then consider some recent research in motor control that may extend the discussion in ways not yet considered, but that will build on advances already made within pedagogy and motor control synergies. Recent work in motor control indicates that humans have far greater capacity to adapt to the ‘product space’ than was previously thought, mainly through fast heuristics and on-line corrections. These are changes that can be made in real (movement) time and are facilitated by what are referred to as ‘feed-forward’ mechanisms that take advantage of ultra-fast ways of recognizing the likely outcomes of our movements and using this as a source of feedback. We conclude by discussing some possible ideas for pedagogy within the sport and physical activity domains, the implications of which would require a rethink on how motor skill learning opportunities might best be facilitated.

Tools for compositional data with a total

Compositional data analysis usually deals with relative information between parts where the total (abundances, mass, amount, etc.) is unknown or uninformative. This article addresses the question of what to do when the total is known and is of interest. Tools used in this case are reviewed and analysed, in particular the relationship between the positive orthant of D-dimensional real space, the product space of the real line times the D-part simplex, and their Euclidean space structures. The first alternative corresponds to data analysis taking logarithms on each component, and the second one to treat a log-transformed total jointly with a composition describing the distribution of component amounts. Real data about total abundances of phytoplankton in an Australian river motivated the present study and are used for illustration.

Variational principles in evolution

For a one-locus selection model, Svirezhev introduced an integral variational principle by defining a Lagrangian which remained stationary on the trajectory followed by the population undergoing selection. It is shown here (i) that this principle can be extended to multiple loci in some simple cases and (ii) that the Lagrangian is defined by a straightforward generalization of the one-locus case, but (iii) that in two-locus or more general models there is no straightforward extension of this principle if linkage and epistasis are present. The population trajectories can be constructed as trajectories of steepest ascent in a Riemannian metric space. A general method is formulated to find the metric tensor and the surface-in the metric space on which the trajectories, which characterize the variations in the gene structure of the population, lie. The local optimality principle holds good in such a space. In the special case when all possible linkage disequilibria are zero, the phase point of the n-locus genetic system moves on the surface of the product space of n higher dimensional unit spheres in a certain Riemannian metric space of gene frequencies so that the rate of change of mean fitness is maximum along the trajectory. In the two-locus case the corresponding surface is a hyper-torus.

Compositional data and Simpson's paradox

Simpson's paradox, also known as amalgamation or aggregation paradox, appears when dealing with proportions. Proportions are by construction parts of a whole, which can be interpreted as compositions assuming they only carry relative information. The Aitchison inner product space structure of the simplex, the sample space of compositions, explains the appearance of the paradox, given that amalgamation is a nonlinear operation within that structure. Here we propose to use balances, which are specific elements of this structure, to analyse situations where the paradox might appear. With the proposed approach we obtain that the centre of the tables analysed is a natural way to compare them, which avoids by construction the possibility of a paradox. Key words: Aitchison geometry, geometric mean, orthogonal projection

Information provision in procurement auctions

We analyze the optimal provision of information in a procurement auction with horizontally differentiated goods. The buyer has private information about her preferred location on the product space and has access to a costless communication device. A seller who pays the entry cost may submit a bid comprising a location and a minimum price. We characterize the optimal information structure and show that the buyer prefers to attract only two bids. Further, additional sellers are inefficient since they reduce total and consumer surplus, gross of entry costs. We show that the buyer will not find it optimal to send public information to all sellers. On the other hand, she may profit from setting a minimum price and that a severe hold-up problem arises if she lacks commitment to set up the rules of the auction ex-ante.

Bosonic D-branes at finite temperature with an external field

Bosonic boundary states at finite temperature are constructed as solutions of boundary conditions at T not equal0 for bosonic open strings with a constant gauge field F-ab coupled to the boundary. The construction is done in the framework of ther-mo field dynamics where a thermal Bogoliubov transformation maps states and operators to finite temperature. Boundary states are given in terms of states from the direct product space between the Fock space of the closed string and another identical copy of it. By analogy with zero temperature, the boundary states have the interpretation of Dp-branes at finite temperature. The boundary conditions admit two different solutions. The entropy of the closed string in a Dp-brane state is computed and analyzed. It is interpreted as the entropy of the Dp-brane at finite temperature.

International technological dynamics in production sectors: An empirical analysis

A new methodology is proposed for evaluating the economic development opportunities associated with the different industries making up a country’s economic structure. To this end, neo-Schumpeterian concepts are used to reinterpret the tools afforded by the “product space” literature in an attempt to assess the technological pervasiveness and sophistication of different production sectors. The ultimate objective is to develop a description of today’s techno-productive paradigm and the differential role that the various sectors play in it. An analysis of export data from 113 countries and territories for 2005-2009 indicates that the key sectors in the world economy are: industrial machinery, scientific and medical instruments, and pharmaceuticals. The strong performance of sectors based on mature technologies suggests that key sectors originating in different stages in history can survive and overlap one another, much like geological strata, owing to the persistence of older technological systems.

Desenvolvimento de um sensor virtual para processos não-lineares e variantes no tempo, com aplicação em planta de neutralização de PH

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Using an Outdoor Learning Space to Teach Sustainability and Material Processes in HE product Design.

The world is facing environmental changes that are increasingly affecting how we think about manufacturing, the consumption of products and use of resources. Within the HE product design community, thinking and designing sustainability’ has evolved to become a natural part of the curriculum. Paradoxical as the rise in awareness of sustainability increases there is growing concern within HE product design of the loss of workshop facilities and as a consequence a demise in teaching traditional object-making skills and material experimentation. We suggest the loss of workshops and tangible ‘learning by making skills’ also creates a lost opportunity for a rich learning resource to address sustainable thinking, design and manufacture ‘praxis’ within HE design education. Furthermore, as learning spaces are frequently discussed in design research, there seems to be little focus on how the use of an outdoor environment might influence learning outcomes particularly with regard to material teaching and sustainability. This 'case study' of two jewellery workshops, used outdoor learning spaces to explore both its impact on learning outcomes and to introduce some key principles of sustainable working methodologies and practices. Academics and students mainly from Norway and Scotland collaborated on this international research project. Participants made models from disposable packaging materials, which were cast in tin, in the sand on a local beach, using found timber to create a heat source for melting the metal. This approach of using traditional making skills, materials and nature was found to be a relevant contribution to a sustainable discourse.

A Product Twistor Space

∗Research supported in part by NSF grant INT-9903302.

A Coopetition Space for Complex Product Specification

Part 3: Product-Service Systems