The relationship between knowledge and the use of nutrition information on food package

Nutrition labelling, soon obligatory for all food circulating on the EU market, is a topic of interest since being an important tool that shapes consumers’ conscious food choices. The study tested the influence of nutrition knowledge on the use of labelled nutrition information on 200 Croatian consumers. A comprehensive three-section questionnaire comprising demographic data, a nutrition knowledge test, and questions about the use of nutrition information provided on food labels was employed. Cluster analysis identified three participating clusters (having good, medium, or poor nutrition knowledge). Answers to 70% of the questionnaire items were correct, but the application of nutrition knowledge in an everyday food selection scored low. Best knowledgeable participants (middle-aged with university degree) tend to browse the nutrition label per se, information on sugar content, fat content, the list of ingredients, and the list of additives. The same group of consumers consider nutrition labelling policy helpful and find the information provided on nutrition labels understandable and useful in conscious food choices. Multivariate logistic regression confirmed the use of labelled nutrition information to be significantly influenced by education and nutrition knowledge. Bottom-line, consumers consider nutrition labelling important, but do not pay close attention to information on certain nutrients

Heisenberg double versus deformed derivatives

Two approaches to the tangent space of a noncommutative space whose coordinate algebra is the enveloping algebra of a Lie algebra are known: the Heisenberg double construction and the approach via deformed derivatives, usually defined by procedures involving orderings among noncommutative coordinates or equivalently involving realizations via formal differential operators. In an earlier work, we rephrased the deformed derivative approach introducing certain smash product algebra twisting a semicompleted Weyl algebra. We show here that the Heisenberg double in the Lie algebra case, is isomorphic to that product in a nontrivial way, involving a datum $\phi$ parametrizing the orderings or realizations in other approaches. This way, we show that the two different formalisms, used by different communities, for introducing the noncommutative phase space for the Lie algebra type noncommutative spaces are mathematically equivalent

Differential structure on kappa-Minkowski space, and kappa-Poincare algebra

We construct realizations of the generators of the $\kappa$-Minkowski space and $\kappa$-Poincar\'{e} algebra as formal power series in the $h$-adic extension of the Weyl algebra. The Hopf algebra structure of the $\kappa$-Poincar\'{e} algebra related to different realizations is given. We construct realizations of the exterior derivative and one-forms, and define a differential calculus on $\kappa$-Minkowski space which is compatible with the action of the Lorentz algebra. In contrast to the conventional bicovariant calculus, the space of one-forms has the same dimension as the $\kappa$-Minkowski space.Comment: 20 pages. Accepted for publication in International Journal of Modern Physics

Gauge transformations and symmetries of integrable systems

We analyze several integrable systems in zero-curvature form within the framework of $SL(2,\R)$ invariant gauge theory. In the Drienfeld-Sokolov gauge we derive a two-parameter family of nonlinear evolution equations which as special cases include the Kortweg-de Vries (KdV) and Harry Dym equations. We find residual gauge transformations which lead to infinintesimal symmetries of this family of equations. For KdV and Harry Dym equations we find an infinite hierarchy of such symmetry transformations, and we investigate their relation with local conservation laws, constants of the motion and the bi-Hamiltonian structure of the equations. Applying successive gauge transformatinos of Miura type we obtain a sequence of gauge equivalent integrable systems, among them the modified KdV and Calogero KdV equations.Comment: 18pages, no figure Journal versio

Noncommutative Differential Forms on the kappa-deformed Space

We construct a differential algebra of forms on the kappa-deformed space. For a given realization of the noncommutative coordinates as formal power series in the Weyl algebra we find an infinite family of one-forms and nilpotent exterior derivatives. We derive explicit expressions for the exterior derivative and one-forms in covariant and noncovariant realizations. We also introduce higher-order forms and show that the exterior derivative satisfies the graded Leibniz rule. The differential forms are generally not graded-commutative, but they satisfy the graded Jacobi identity. We also consider the star-product of classical differential forms. The star-product is well-defined if the commutator between the noncommutative coordinates and one-forms is closed in the space of one-forms alone. In addition, we show that in certain realizations the exterior derivative acting on the star-product satisfies the undeformed Leibniz rule.Comment: to appear in J. Phys. A: Math. Theo

Covariant realizations of kappa-deformed space

We study a Lie algebra type $\kappa$-deformed space with undeformed rotation algebra and commutative vector-like Dirac derivatives in a covariant way. Space deformation depends on an arbitrary vector. Infinitely many covariant realizations in terms of commuting coordinates of undeformed space and their derivatives are constructed. The corresponding coproducts and star products are found and related in a new way. All covariant realizations are physically equivalent. Specially, a few simple realizations are found and discussed. The scalar fields, invariants and the notion of invariant integration is discussed in the natural realization.Comment: 31 pages, no figures, LaTe

Generalized kappa-deformed spaces, star-products, and their realizations

In this work we investigate generalized kappa-deformed spaces. We develop a systematic method for constructing realizations of noncommutative (NC) coordinates as formal power series in the Weyl algebra. All realizations are related by a group of similarity transformations, and to each realization we associate a unique ordering prescription. Generalized derivatives, the Leibniz rule and coproduct, as well as the star-product are found in all realizations. The star-product and Drinfel'd twist operator are given in terms of the coproduct, and the twist operator is derived explicitly in special realizations. The theory is applied to a Nappi-Witten type of NC space