On computational aspects of discrete Sobolev inner products on the unit circle

In this paper, we show how to compute in O(n2) steps the Fourier coefficients associated with the Gelfand-Levitan approach for discrete Sobolev orthogonal polynomials on the unit circle when the support of the discrete component involving derivatives is located outside the closed unit disk. As a consequence, we deduce the outer relative asymptotics of these polynomials in terms of those associated with the original orthogonality measure. Moreover, we show how to recover the discrete part of our Sobolev inner product. © 2013 Elsevier Inc. All rights reserved.

A Favard type theorem for orthogonal polynomials on the unit circle from a three term recurrence formula

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Basic hypergeometric polynomials with zeros on the unit circle

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Sieved para-orthogonal polynomials on the unit circle

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Szegö polynomials: quadrature rules on the unit circle and on [-1, 1]

We consider some of the relations that exist between real Szegö polynomials and certain para-orthogonal polynomials defined on the unit circle, which are again related to certain orthogonal polynomials on [-1, 1] through the transformation x = (z1/2+z1/2)/2. Using these relations we study the interpolatory quadrature rule based on the zeros of polynomials which are linear combinations of the orthogonal polynomials on [-1, 1]. In the case of any symmetric quadrature rule on [-1, 1], its associated quadrature rule on the unit circle is also given.

A further note on the college admission game

When a stable matching rule is used for a college admission market, questions on incentives facing agents of both sides of the market naturally emerge. This note states and proves four important results which fill a gap in the theory of incentives for the college admission model. Two of them have never been demonstrated but have been used along the years and are responsible for the success that this theory has had in explaining empirical economic phenomena.

Rigidity for piecewise smooth homeomorphisms on the circle

We find conditions for two piecewise 'C POT.2+V' homeomorphisms f and g of the circle to be 'C POT.1' conjugate. Besides the restrictions on the combinatorics of the maps (we assume that the maps have bounded combinatorics), and necessary conditions on the one-side derivatives of points where f and g are not differentiable, we also assume zero mean-nonlinearity for f and g.

A forgotten little chapter on isoperimetric inequalities. On the fraction of a convex and closed plane area lying outside a circle with which it shares a diameter

[EN]Often some interesting or simply curious points are left out when developing a theory. It seems that one of them is the existence of an upper bound for the fraction of area of a convex and closed plane area lying outside a circle with which it shares a diameter, a problem stemming from the theory of isoperimetric inequalities. In this paper such a bound is constructed and shown to be attained for a particular area. It is also shown that convexity is a necessary condition in order to avoid the whole area lying outside the circle

The influence of career histories on team perfomance in new product development: a study of the video game industry

The purpose of this research is to contribute to the literature on organizational demography and new product development by investigating how diverse individual career histories impact team performance. Moreover we highlighted the importance of considering also the institutional context and the specific labour market arrangements in which a team is embedded, in order to interpret correctly the effect of career-related diversity measures on performance. The empirical setting of the study is the videogame industry, and the teams in charge of the development of new game titles. Video games development teams are the ideal setting to investigate the influence of career histories on team performance, since the development of videogames is performed by multidisciplinary teams composed by specialists with a wide variety of technical and artistic backgrounds, who execute a significant amounts of creative thinking. We investigate our research question both with quantitative methods and with a case study on the Japanese videogame industry: one of the most innovative in this sector. Our results show how career histories in terms of occupational diversity, prior functional diversity and prior product diversity, usually have a positive influence on team performance. However, when the moderating effect of the institutional setting is taken in to account, career diversity has different or even opposite effect on team performance, according to the specific national context in which a team operates.

The role of language in tv shows and its impact on the audience: A linguistic analysis of Game of Thrones

Through the analysis of American TV show Game of Thrones, this dissertation will focus on the linguistic issues concerning the adaptation from books to television, the power of language over the audience, and the creation of two languages, with all the linguistic and cultural implications related to this phenomenon.

Game-theoretic view on intermediated exchange

Intermediaries permeate modern economic exchange. Most classical models on intermediated exchange are driven by information asymmetry and inventory management. These two factors are of reduced significance in modern economies. This makes it necessary to develop models that correspond more closely to modern financial marketplaces. The goal of this dissertation is to propose and examine such models in a game theoretical context. The proposed models are driven by asymmetries in the goals of different market participants. Hedging pressure as one of the most critical aspects in the behavior of commercial entities plays a crucial role. The first market model shows that no equilibrium solution can exist in a market consisting of a commercial buyer, a commercial seller and a non-commercial intermediary. This indicates a clear economic need for non-commercial trading intermediaries: a direct trade from seller to buyer does not result in an equilibrium solution. The second market model has two distinct intermediaries between buyer and seller: a spread trader/market maker and a risk-neutral intermediary. In this model a unique, natural equilibrium solution is identified in which the supply-demand surplus is traded by the risk-neutral intermediary, whilst the market maker trades the remainder from seller to buyer. Since the market maker’s payoff for trading at the identified equilibrium price is zero, this second model does not provide any motivation for the market maker to enter the market. The third market model introduces an explicit transaction fee that enables the market maker to secure a positive payoff. Under certain assumptions on this transaction fee the equilibrium solution of the previous model applies and now also provides a financial motivation for the market maker to enter the market. If the transaction fee violates an upper bound that depends on supply, demand and riskaversity of buyer and seller, the market will be in disequilibrium.

On the comparison of a novel serious game and electroencephalography biomarkers for early dementia screening

Patients with amnestic mild cognitive impairment are at high risk for developing Alzheimer's disease. Besides episodic memory dysfunction they show deficits in accessing contextual knowledge that further specifies a general spatial navigation task or an executive function (EF) virtual action planning. Virtual reality (VR) environments have already been successfully used in cognitive rehabilitation and show increased potential for use in neuropsychological evaluation allowing for greater ecological validity while being more engaging and user friendly. In our study we employed the in-house platform of virtual action planning museum (VAP-M) and a sample of 25 MCI and 25 controls, in order to investigate deficits in spatial navigation, prospective memory, and executive function. In addition, we used the morphology of late components in event-related potential (ERP) responses, as a marker for cognitive dysfunction. The related measurements were fed to a common classification scheme facilitating the direct comparison of both approaches. Our results indicate that both the VAP-M and ERP averages were able to differentiate between healthy elders and patients with amnestic mild cognitive impairment and agree with the findings of the virtual action planning supermarket (VAP-S). The sensitivity (specificity) was 100% (98%) for the VAP-M data and 87% (90%) for the ERP responses. Considering that ERPs have proven to advance the early detection and diagnosis of "presymptomatic AD," the suggested VAP-M platform appears as an appealing alternative.