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

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

Invariant variational principle for Hamiltonian mechanics

It is shown that the action for Hamiltonian equations of motion can be brought into invariant symplectic form. In other words, it can be formulated directly in terms of the symplectic structure $\omega$ without any need to choose some 1-form $\gamma$, such that $\omega= d \gamma$, which is not unique and does not even generally exist in a global sense.Comment: final version; to appear in J.Phys.A; 17 pages, 2 figure

Appropriateness and efficacy of Spa therapy for musculoskeletal disorders. A Delphi method consensus initiative among experts in Italy.

OBJECTIVE: The aim of the study was to identify the main aspects concerning appropriateness and efficacy of Spa therapy for musculoskeletal pathologies. METHODS: A committee of 8 experts from Italian universities, public hospitals, territorial services, research institutes and patient associations was set up. Clinicians from Italian medical centers specialized in rheumatology, rehabilitation and thermal medicine took part in a Delphi process aimed at obtaining consensus statements among the participants. RESULTS: Large consensus was obtained for statements grouped under the following main themes: treatment indications; choice of treatment modality and treatment efficacy. CONCLUSIONS: The experts developed a number of consensus statements which may be used as a practical reference to guide the choice of physicians to treat musculoskeletal diseases with Spa therapy

CD40 ligand and MCP-1 as predictors of cardiovascular events in diabetic patients with stroke

Aim: Up-regulation of soluble CD40 ligand (sCD40L) and of monocyte chemoattractant protein-1 (MCP-1) has been found in diabetes and in patients with acute cerebral ischemia. We asked whether (i) the two molecules are similarly upregulated among non-lacunar and lacunar diabetic strokes and (ii) sCD40L and/or MCP-1 predict the risk of cardiovascular events in this setting.Methods: Ninety patients with type 2 diabetes mellitus presenting with an acute ischemic stroke (compared with 45 control subjects) were evaluated on admission and up to 36 months (median 24 months) after the event.Results: Diabetic patients with acute stroke had higher plasma CD40L and MCP-1 than controls (p<0.0001), with no significant differences among lacunar and non-lacunar strokes. On multiple regres-sion analysis, only higher sCD40L quartiles and older age were associated with higher MCP-1 quar-tiles. Forty-eight percent of patients experienced vascular events. Cox regression analysis showed that only the presence of higher sCD40L values independently predicted the recurrence of vascular events.Conclusion: Up-regulation of inflammatory molecules, such as CD40L and MCP-1, is involved in the advanced stage of atherosclerotic cerebro-vascular disease and is associated with increased risk of recurrence of cardiovascular events.AIM: Up-regulation of soluble CD40 ligand (sCD40L) and of monocyte chemoattractant protein-1 (MCP-1) has been found in diabetes and in patients with acute cerebral ischemia. We asked whether (i) the two molecules are similarly upregulated among non-lacunar and lacunar diabetic strokes and (ii) sCD40L and/or MCP-1 predict the risk of cardiovascular events in this setting. METHODS: Ninety patients with type 2 diabetes mellitus presenting with an acute ischemic stroke (compared with 45 control subjects) were evaluated on admission and up to 36 months (median 24 months) after the event. RESULTS: Diabetic patients with acute stroke had higher plasma CD40L and MCP-1 than controls (p<0.0001), with no significant differences among lacunar and non-lacunar strokes. On multiple regression analysis, only higher sCD40L quartiles and older age were associated with higher MCP-1 quartiles. Forty-eight percent of patients experienced vascular events. Cox regression analysis showed that only the presence of higher sCD40L values independently predicted the recurrence of vascular events. CONCLUSION: Up-regulation of inflammatory molecules, such as CD40L and MCP-1, is involved in the advanced stage of atherosclerotic cerebro-vascular disease and is associated with increased risk of recurrence of cardiovascular events

Longitudinal Analysis of Quality of Life, Clinical, Radiographic, Echocardiographic, and Laboratory Variables in Dogs with Preclinical Myxomatous Mitral Valve Disease Receiving Pimobendan or Placebo: The EPIC Study

Background: Changes in clinical variables associated with the administration of pimobendan to dogs with preclinical myxomatous mitral valve disease (MMVD) and cardiomegaly have not been described. Objectives: To investigate the effect of pimobendan on clinical variables and the relationship between a change in heart size and the time to congestive heart failure (CHF) or cardiac-related death (CRD) in dogs with MMVD and cardiomegaly. To determine whether pimobendan-treated dogs differ from dogs receiving placebo at onset of CHF. Animals: Three hundred and fifty-four dogs with MMVD and cardiomegaly. Materials and Methods: Prospective, blinded study with dogs randomized (ratio 1:1) to pimobendan (0.4-0.6 mg/kg/d) or placebo. Clinical, laboratory, and heart-size variables in both groups were measured and compared at different time points (day 35 and onset of CHF) and over the study duration. Relationships between short-term changes in echocardiographic variables and time to CHF or CRD were explored. Results: At day 35, heart size had reduced in the pimobendan group:median change in (Delta) LVIDDN -0.06 (IQR:-0.15 to + 0.02), P < 0.0001, and LA:Ao -0.08 (IQR:-0.23 to + 0.03), P < 0.0001. Reduction in heart size was associated with increased time to CHF or CRD. Hazard ratio for a 0.1 increase in Delta LVIDDN was 1.26, P = 0.0003. Hazard ratio for a 0.1 increase in Delta LA:Ao was 1.14, P = 0.0002. At onset of CHF, groups were similar. Conclusions and Clinical Importance: Pimobendan treatment reduces heart size. Reduced heart size is associated with improved outcome. At the onset of CHF, dogs treated with pimobendan were indistinguishable from those receiving placebo

Regularity of the distance function from arbitrary closed sets

We investigate the distance function delta(phi)(K) from an arbitrary closed subset K of a finite-dimensional Banach space (R-n, phi), equipped with a uniformly convex l(2)-norm phi. These spaces are known as Minkowski spaces and they are one of the fundamental spaces of Finslerian geometry (see Martini et al. in Expo Math 19:97-142, 2001, https://doi.org/10.1016/S0723-0869(01)80025-6) . We prove that the gradient of delta(phi)(K) satisfies a Lipschitz property on the complement of the phi-cut-locus of K (a.k.a. the medial axis of R-n similar to K) and we prove a structural result for the set of points outside K where delta(phi)(K) is pointwise twice differentiable, providing an answer to a question raised by Hiriart-Urruty (Am Math Mon 89:456-458, 1982, hups://doi.org/10.2307/2321379). Our results give sharp generalisations of some classical results in the theory of distance functions and they are motivated by critical low-regularity examples for which the available results gives no meaningful or very restricted informations. The results of this paper find natural applications in the theory of partial differential equations and in convex geometry

Canonical quantization of so-called non-Lagrangian systems

We present an approach to the canonical quantization of systems with equations of motion that are historically called non-Lagrangian equations. Our viewpoint of this problem is the following: despite the fact that a set of differential equations cannot be directly identified with a set of Euler-Lagrange equations, one can reformulate such a set in an equivalent first-order form which can always be treated as the Euler-Lagrange equations of a certain action. We construct such an action explicitly. It turns out that in the general case the hamiltonization and canonical quantization of such an action are non-trivial problems, since the theory involves time-dependent constraints. We adopt the general approach of hamiltonization and canonical quantization for such theories (Gitman, Tyutin, 1990) to the case under consideration. There exists an ambiguity (not reduced to a total time derivative) in associating a Lagrange function with a given set of equations. We present a complete description of this ambiguity. The proposed scheme is applied to the quantization of a general quadratic theory. In addition, we consider the quantization of a damped oscillator and of a radiating point-like charge.Comment: 13 page

Two Mathematically Equivalent Versions of Maxwell's Equations

This paper is a review of the canonical proper-time approach to relativistic mechanics and classical electrodynamics. The purpose is to provide a physically complete classical background for a new approach to relativistic quantum theory. Here, we first show that there are two versions of Maxwell's equations. The new version fixes the clock of the field source for all inertial observers. However now, the (natural definition of the effective) speed of light is no longer an invariant for all observers, but depends on the motion of the source. This approach allows us to account for radiation reaction without the Lorentz-Dirac equation, self-energy (divergence), advanced potentials or any assumptions about the structure of the source. The theory provides a new invariance group which, in general, is a nonlinear and nonlocal representation of the Lorentz group. This approach also provides a natural (and unique) definition of simultaneity for all observers. The corresponding particle theory is independent of particle number, noninvariant under time reversal (arrow of time), compatible with quantum mechanics and has a corresponding positive definite canonical Hamiltonian associated with the clock of the source. We also provide a brief review of our work on the foundational aspects of the corresponding relativistic quantum theory. Here, we show that the standard square-root and the Dirac equations are actually two distinct spin-$\tfrac{1}{2}$ particle equations.Comment: Appeared: Foundations of Physic