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

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

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

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

Long-term Intrinsic Rhythm Evaluation in Dogs with Atrioventricular Block

Background: Atrioventricular block (AVB) is a conduction abnormality along the atrioventricular node that, depending on etiology, may lead to different outcomes. Objectives: To evaluate variations of intrinsic rhythm (IR) in dogs that underwent pacemaker implantation (PMI). Animals: Medical records of 92 dogs affected by 3rd degree atrioventricular block (3AVB), advanced 2nd degree AVB (2AVB), paroxysmal 3AVB, 2:1 2AVB, or 3AVB with atrial fibrillation (AF) were retrospectively reviewed. Method: The patient IR was documented with telemetry on the day of 1 - (95% CI, 1-2), 33 - (95% CI, 28-35), 105 - (95%CI, 98-156), and 275 days (95%CI, 221-380) after PMI. According to AVB grade at different examinations, AVB was defined as progressed, regressed, or unchanged. Results: In 48 dogs, 3AVB remained unchanged, whereas in 7 it regressed. Eight cases of 2AVB progressed, 3 regressed and 2 remained unchanged. Eight cases of paroxysmal 3AVB progressed and 3 remained unchanged. Four dogs affected by 2:1 2AVB progressed, 2 regressed, and 1 remained unchanged. All cases with 3AVB with AF remained unchanged. Regression occurred within 30 days after PMI, whereas progression was documented at any time. Variations in IR were associated with type of AVB (P <03) and time of follow-up (P <0001). Conclusions and clinical importance: The degree of AVB assessed at the time of PMI should not be considered definitive because more than one-third of the cases in this study either progressed or regressed. Additional studies would be necessary to elucidate possible causes for transient AVB in dogs

Nonlocal, noncommutative picture in quantum mechanics and distinguished canonical maps

Classical nonlinear canonical (Poisson) maps have a distinguished role in quantum mechanics. They act unitarily on the quantum phase space and generate $\hbar$-independent quantum canonical maps. It is shown that such maps act in the noncommutative phase space as dictated by the classical covariance. A crucial observation made is that under the classical covariance the local quantum mechanical picture can become nonlocal in the Hilbert space. This nonlocal picture is made equivalent by the Weyl map to a noncommutative picture in the phase space formulation of the theory. The connection between the entanglement and nonlocality of the representation is explored and specific examples of the generation of entanglement are provided by using such concepts as the generalized Bell states. That the results have direct application in generating vacuum soliton configurations in the recently popular scalar field theories of noncommutative coordinates is also demonstrated.Comment: 14 pages, one figur

Idiopathic facial palsy: umbrella review of systematic reviews and meta-analyses

Idiopathic facial palsy is the most common disease of the VII cranial nerve. There are many treatments to facilitate recovery from this condition: pharmacological, surgical, rehabilitative, but the effectiveness of some of these treatments, especially the latter, is still under discussion. The purpose of this umbrella review of systematic reviews is to analyse the literature in order to investigate the different rehabilitation interventions in patients suffering from idiopathic facial palsy. A scientific literature search was carried out from January 2009 until August 2019, using Mesh the terms "facial palsy", "Bell's Palsy", "idiopathic facial nerve palsy", combined with "rehabilitation" and "therapy". Initially all the systematic reviews and meta-analyses of the last 10 years concerning rehabilitation treatments for the recovery of injured functions in facial palsy were included. Given the heterogeneity of the studies in the literature, which do not differentiate the different causes of facial palsy, all the causes of idiopathic facial palsy were included in the review. The research resulted in 94 published systematic reviews but only 6 were considered in respect to the inclusion criteria. All studies agree on the lack of high-quality scientific work to be able to say that Bell's physiotherapy treatments for facial palsy are effective, in particular with regard to recovery times during the rehabilitation process. Future studies are needed, in order to highlight the therapeutic implications of the different rehabilitation methods, with standardized protocols, in patients suffering from facial palsy of different aetiology

Integration of focal vibration and intra-articular oxygen–ozone therapy in rehabilitation of painful knee osteoarthritis

Objective: To examine the pain-reducing effects of intra-articular oxygen–ozone (O2O3) injections and mechanical focal vibration (mFV) versus O2O3 injections alone in patients with knee osteoarthritis. Methods: Patients with chronic pain (&gt;6 weeks) due to knee osteoarthritis (II–III on the Kellgren–Lawrence scale) were consecutively enrolled and divided into two groups: O2O3 (n = 25) and O2O3-mFV (n = 24). The visual analog scale (VAS), Knee Injury and Osteoarthritis Outcome Score (KOOS), and Medical Research Council (MRC) Manual Muscle Testing scale were administered at baseline (before treatment), after 3 weeks of treatment, and 1 month after the end of treatment. Patients received three once-weekly intra-articular injections of O2O3 into the knee (20 mL O3, 20 μg/mL). The O2O3-mFV group also underwent nine sessions of mFV (three sessions per week). Results: The VAS score, KOOS, and MRC score were significantly better in the O2O3-mFV than O2O3 group. The within-group analysis showed that all scores improved over time compared with baseline and were maintained even 1 month after treatment. No adverse events occurred. Conclusion: An integrated rehabilitation protocol involving O2O3 injections and mFV for 3 weeks reduces pain, increases autonomy in daily life activities, and strengthens the quadriceps femoris