Representations of the cyclically symmetric q-deformed algebra soq(3)so_q(3)

An algebra homomorphism $\psi$ from the nonstandard q-deformed (cyclically symmetric) algebra $U_q(so_3)$ to the extension ${\hat U}_q(sl_2)$ of the Hopf algebra $U_q(sl_2)$ is constructed. Not all irreducible representations of $U_q(sl_2)$ can be extended to representations of ${\hat U}_q(sl_2)$. Composing the homomorphism $\psi$ with irreducible representations of ${\hat U}_q(sl_2)$ we obtain representations of $U_q(so_3)$. Not all of these representations of $U_q(so_3)$ are irreducible. Reducible representations of $U_q(so_3)$ are decomposed into irreducible components. In this way we obtain all irreducible representations of $U_q(so_3)$ when $q$ is not a root of unity. A part of these representations turns into irreducible representations of the Lie algebra so$_3$ when $q\to 1$. Representations of the other part have no classical analogue. Using the homomorphism $\psi$ it is shown how to construct tensor products of finite dimensional representations of $U_q(so_3)$. Irreducible representations of $U_q(so_3)$ when $q$ is a root of unity are constructed. Part of them are obtained from irreducible representations of ${\hat U}_q(sl_2)$ by means of the homomorphism $\psi$.Comment: 28 pages, LaTe

Motivation and commitment among adult learners enrolled in an adult basic education class : the life histories of five adult learners.

This research project emerged from the researcher\u27s work as an adult basic education instructor in a community learning center. With an inordinately high attrition rate (over seventy percent), the researcher\u27s attention was easily focused on the small number of students who remained in the Learning Center and attended classes consistently. This group of five learners became the self-selected participants in the study. The purpose of the study was to examine the life experience of the five learners to gain insight into the nature of their motivation and commitment to learn. A series of up to six, one hour interviews were conducted with each of the participants. During the interviews, participants reflected on both past and present experience. Although it varied from person to person, discussions included childhood and family experience, prior school and educational experiences. Conclusions drawn from the research are not easily categorized. Motivating factors were different for each learner; one was motivated by a life-altering illness and another by the realities of finding employment without a high school diploma. The most salient insight gained from the research, however, was the similarity of experience across participants with issues related to dysfunctional families, personal violence, and substance abuse

The Barthel index: italian translation, adaptation and validation

The Barthel Index (BI) is widely used to measure disability also in Italy, although a validated and culturally adapted Italian version of BI has not been produced yet. This article describes the translation and cultural adaptation into Italian of the original 10-item version of BI, and reports the procedures for testing its validity and reliability. The cultural adaptation and validation process was based on data from a cohort of disabled patients from two different Rehabilitation Centers in Rome, Italy. Forward and backward translation method was adopted by qualified linguist and independent native English official translators. The scale obtained was reviewed by 20 experts in psychometric sciences. The Italian adapted version of the BI was then produced and validated. A total number of 180 patients were submitted to the adapted scale for testing its acceptability and internal consistency. The total time of compilation was 5 ± 2,6 minutes (range 3-10). Validation of the scale was performed by 7 trained professional therapists that submitted both the translated and the adapted versions to a group of 62 clinically stable patients (T-test=-2.051 p=0.05). The internal consistency by Cronbach’s alpha resulted equal to 0.96. Test – retest intra – rater reliability was evaluated on 35 cases; at test-retest was ICC=0.983 (95%IC: 0.967-0.992). This is the first study that reports translation, adaptation and validation of the BI in Italian language. It provides a new tool for professionals to measure functional disability when appraising Italian speaking disable patients in health and social care settings along the continuum of care

Isotopic Grand Unification with the Inclusion of Gravity (revised version)

We introduce a dual lifting of unified gauge theories, the first characterized by the isotopies, which are axiom- preserving maps into broader structures with positive-definite generalized units used for the representation of matter under the isotopies of the Poincare' symmetry, and the second characterized by the isodualities, which are anti-isomorphic maps with negative-definite generalized units used for the representation of antimatter under the isodualities of the Poincare' symmetry. We then submit, apparently for the first time, a novel grand unification with the inclusion of gravity for matter embedded in the generalized positive-definite units of unified gauge theories while gravity for antimatter is embedded in the isodual isounit. We then show that the proposed grand unification provides realistic possibilities for a resolution of the axiomatic incompatibilities between gravitation and electroweak interactions due to curvature, antimatter and the fundamental space-time symmetries.Comment: 20 pages, Latex, revised in various details and with added reference

Dynamic Resilient Containment Control in Multirobot Systems

In this article, we study the dynamic resilient containment control problem for continuous-time multirobot systems (MRSs), i.e., the problem of designing a local interaction protocol that drives a set of robots, namely the followers, toward a region delimited by the positions of another set of robots, namely the leaders, under the presence of adversarial robots in the network. In our setting, all robots are anonymous, i.e., they do not recognize the identity or class of other robots. We consider as adversarial all those robots that intentionally or accidentally try to disrupt the objective of the MRS, e.g., robots that are being hijacked by a cyber–physical attack or have experienced a fault. Under specific topological conditions defined by the notion of (r,s)-robustness, our control strategy is proven to be successful in driving the followers toward the target region, namely a hypercube, in finite time. It is also proven that the followers cannot escape the moving containment area despite the persistent influence of anonymous adversarial robots. Numerical results with a team of 44 robots are provided to corroborate the theoretical findings

Further insights on predictors of environmental tobacco smoke exposure during the pediatric age

Background: The smoking ban in public places has reduced Environmental Tobacco Smoke (ETS) exposure for non-smokers, but despite this, domestic environments still remain places at high risk of exposure, and, today, about 40% of children worldwide are exposed to ETS at home. The aims of the study are to investigate the contribution of several factors on ETS exposure among a group of Italian children and to evaluate the changes in smoking precautions adopted at home when the smoker is the mother, the father, or both parents, respectively. Methods: A cross-sectional study was performed on a sample of 519 Italian schoolchildren. Information was collected via a questionnaire. Results: 41.4% of the participants lived with at least one smoker. Almost half of the children exposed to ETS lived with one or more smokers who do not observe any home smoking ban. Lower maternal or paternal educational levels significantly increase the risk of ETS exposure at home and the “worst case” is represented by both parents who smoke. Conclusions: More effective preventive interventions are needed to protect children from ETS exposure. Some interventions should be specifically dedicated to smokers with a low educational level and to mothers that smoke

Lagrangian versus Quantization

We discuss examples of systems which can be quantized consistently, although they do not admit a Lagrangian description.Comment: 8 pages, no figures; small corrections, references adde

Versal deformations of a Dirac type differential operator

If we are given a smooth differential operator in the variable $x\in {\mathbb R}/2\pi {\mathbb Z},$ its normal form, as is well known, is the simplest form obtainable by means of the \mbox{Diff}(S^1)-group action on the space of all such operators. A versal deformation of this operator is a normal form for some parametric infinitesimal family including the operator. Our study is devoted to analysis of versal deformations of a Dirac type differential operator using the theory of induced \mbox{Diff}(S^1)-actions endowed with centrally extended Lie-Poisson brackets. After constructing a general expression for tranversal deformations of a Dirac type differential operator, we interpret it via the Lie-algebraic theory of induced \mbox{Diff}(S^1)-actions on a special Poisson manifold and determine its generic moment mapping. Using a Marsden-Weinstein reduction with respect to certain Casimir generated distributions, we describe a wide class of versally deformed Dirac type differential operators depending on complex parameters