Cocycle deformations for liftings of quantum linear spaces

Let $A$ be a Hopf algebra over a field $K$ of characteristic 0 and suppose there is a coalgebra projection $\pi$ from $A$ to a sub-Hopf algebra $H$ that splits the inclusion. If the projection is $H$-bilinear, then $A$ is isomorphic to a biproduct R #_{\xi}H where $(R,\xi)$ is called a pre-bialgebra with cocycle in the category $_{H}^{H}\mathcal{YD}$. The cocycle $\xi$ maps $R \otimes R$ to $H$. Examples of this situation include the liftings of pointed Hopf algebras with abelian group of points $\Gamma$ as classified by Andruskiewitsch and Schneider [AS1]. One asks when such an $A$ can be twisted by a cocycle $\gamma:A\otimes A\rightarrow K$ to obtain a Radford biproduct. By results of Masuoka [Ma1, Ma2], and Gr\"{u}nenfelder and Mastnak [GM], this can always be done for the pointed liftings mentioned above. In a previous paper [ABM1], we showed that a natural candidate for a twisting cocycle is {$\lambda \circ \xi$} where $\lambda\in H^{\ast}$ is a total integral for $H$ and $\xi$ is as above. We also computed the twisting cocycle explicitly for liftings of a quantum linear plane and found some examples where the twisting cocycle we computed was different from {$\lambda \circ \xi$}. In this note we show that in many cases this cocycle is exactly $\lambda\circ\xi$ and give some further examples where this is not the case. As well we extend the cocycle computation to quantum linear spaces; there is no restriction on the dimension

Use of Kriging Technique to Study Roundabout Performance

Road intersections are dangerous places because of the many conflicting points between motorized and nonmotorized vehicles. In the case of defined traffic volume, several research groups have proved that roundabouts reduced the number of injuries and fatal accident cases. In recent years, many countries have adopted roundabouts as a standard design solution for both urban and rural roads. Several recent studies have investigated the performance of roundabouts, including some with models that calculated the entering flow (Q sub e) as a function of the circulating flow (Q sub c). Most existing models have been constructed with the use of linear or exponential statistical regression. The interpolative techniques in classical statistics are based on the use of canonical forms (linear or polynomial) that completely ignore the correlation law between collected data. As such, the determined interpolation stems from the assumption that the data represent a random sample. In the research reported in this paper, a geostatistical approach was considered: the relationship Q sub e versus Q sub c is supposed to be a regionalized phenomenon. According to that supposition, collected data do not represent a random sample of values but are supposed to be related to each other with a defined law. This recognition allows the realization of interpolation on the basis of the real law of the phenomenon. This paper discusses the fundamental theories, the applied operating procedures, and the first results obtained in modeling the Q sub e versus Q sub c relationship with the application of geostatistics

Designing the venue logistics management operations for a World Exposition

World Expositions, due to their size and peculiar features, pose a number of logistics challenges. This paper aims at developing a design framework for the venue logistics management (VLM) operations to replenish food products to the event site, through a combination of qualitative and quantitative research approaches. First, an in-depth interview methodology, combined with the outcomes of a literature review, is adopted for defining the key variables for the tactical and operational set-up of the VLM system. Second, a quantitative approach is developed to define the necessary logistics resources. The framework is then applied to the case of Milan 2015 World Exposition. It is the first time that such a design framework for a World Exposition is presented: the originality of this research lies in the proposal of a systematic approach that adds to the experiential practices constituting the current body of knowledge on event logistics

Quasi-bialgebra Structures and Torsion-free Abelian Groups

We describe all the quasi-bialgebra structures of a group algebra over a torsion-free abelian group. They all come out to be triangular in a unique way. Moreover, up to an isomorphism, these quasi-bialgebra structures produce only one (braided) monoidal structure on the category of their representations. Applying these results to the algebra of Laurent polynomials, we recover two braided monoidal categories introduced in \cite{CG} by S. Caenepeel and I. Goyvaerts in connection with Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras)

Polynomial growth of discrete quantum groups, topological dimension of the dual and *-regularity of the Fourier algebra

Banica and Vergnioux have shown that the dual discrete quantum group of a compact simply connected Lie group has polynomial growth of order the real manifold dimension. We extend this result to a general compact group and its topological dimension, by connecting it with the Gelfand-Kirillov dimension of an algebra. Furthermore, we show that polynomial growth for a compact quantum group G of Kac type implies *-regularity of the Fourier algebra A(G), that is every closed ideal of C(G) has a dense intersection with A(G). In particular, A(G) has a unique C*-norm.Comment: to appear in Annales de l'Institut Fourie

Eco-efficient supply chain networks: Development of a design framework and application to a real case study

© 2015 Taylor & Francis. This paper presents a supply chain network design framework that is based on multi-objective mathematical programming and that can identify 'eco-efficient' configuration alternatives that are both efficient and ecologically sound. This work is original in that it encompasses the environmental impact of both transportation and warehousing activities. We apply the proposed framework to a real-life case study (i.e. Lindt & Sprüngli) for the distribution of chocolate products. The results show that cost-driven network optimisation may lead to beneficial effects for the environment and that a minor increase in distribution costs can be offset by a major improvement in environmental performance. This paper contributes to the body of knowledge on eco-efficient supply chain design and closes the missing link between model-based methods and empirical applied research. It also generates insights into the growing debate on the trade-off between the economic and environmental performance of supply chains, supporting organisations in the eco-efficient configuration of their supply chains