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

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

The Moyal-Lie Theory of Phase Space Quantum Mechanics

A Lie algebraic approach to the unitary transformations in Weyl quantization is discussed. This approach, being formally equivalent to the $\star$-quantization, is an extension of the classical Poisson-Lie formalism which can be used as an efficient tool in the quantum phase space transformation theory.Comment: 15 pages, no figures, to appear in J. Phys. A (2001

Analytic Controllability of Time-Dependent Quantum Control Systems

The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation in which the state moves in an infinite-dimensional Hilbert space, a drift term is present, and the operators driving the state evolution may be unbounded. However, considerations are restricted by the assumption that there exists an analytic domain, dense in the state space, on which solutions of the controlled Schrodinger equation may be expressed globally in exponential form. The issue of controllability then naturally focuses on the ability to steer the quantum state on a finite-dimensional submanifold of the unit sphere in Hilbert space -- and thus on analytic controllability. A relatively straightforward strategy allows the extension of Lie-algebraic conditions for strong analytic controllability derived earlier for the simpler, time-independent system in which the drift Hamiltonian and the interaction Hamiltonia have no intrinsic time dependence. Enlarging the state space by one dimension corresponding to the time variable, we construct an augmented control system that can be treated as time-independent. Methods developed by Kunita can then be implemented to establish controllability conditions for the one-dimension-reduced system defined by the original time-dependent Schrodinger control problem. The applicability of the resulting theorem is illustrated with selected examples.Comment: 13 page

The Inverse Variational Problem for Autoparallels

We study the problem of the existence of a local quantum scalar field theory in a general affine metric space that in the semiclassical approximation would lead to the autoparallel motion of wave packets, thus providing a deviation of the spinless particle trajectory from the geodesics in the presence of torsion. The problem is shown to be equivalent to the inverse problem of the calculus of variations for the autoparallel motion with additional conditions that the action (if it exists) has to be invariant under time reparametrizations and general coordinate transformations, while depending analytically on the torsion tensor. The problem is proved to have no solution for a generic torsion in four-dimensional spacetime. A solution exists only if the contracted torsion tensor is a gradient of a scalar field. The corresponding field theory describes coupling of matter to the dilaton field.Comment: 13 pages, plain Latex, no figure

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

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

Effect of Pimobendan in Dogs with Preclinical Myxomatous Mitral Valve Disease and Cardiomegaly: The EPIC Study - A Randomized Clinical Trial

Background: Pimobendan is effective in treatment of dogs with congestive heart failure (CHF) secondary to myxomatous mitral valve disease (MMVD). Its effect on dogs before the onset of CHF is unknown. Hypothesis/Objectives: Administration of pimobendan (0.4-0.6 mg/kg/d in divided doses) to dogs with increased heart size secondary to preclinical MMVD, not receiving other cardiovascular medications, will delay the onset of signs of CHF, cardiac-related death, or euthanasia. Animals: 360 client-owned dogs with MMVD with left atrial-to-aortic ratio >= 1.6, normalized left ventricular internal diameter in diastole >= 1.7, and vertebral heart sum >10.5. Methods: Prospective, randomized, placebo-controlled, blinded, multicenter clinical trial. Primary outcome variable was time to a composite of the onset of CHF, cardiac-related death, or euthanasia. Results: Median time to primary endpoint was 1228 days (95% CI: 856-NA) in the pimobendan group and 766 days (95% CI: 667-875) in the placebo group (P = .0038). Hazard ratio for the pimobendan group was 0.64 (95% CI: 0.47-0.87) compared with the placebo group. The benefit persisted after adjustment for other variables. Adverse events were not different between treatment groups. Dogs in the pimobendan group lived longer (median survival time was 1059 days (95% CI: 952-NA) in the pimobendan group and 902 days (95% CI: 747-1061) in the placebo group) (P = .012). Conclusions and Clinical Importance: Administration of pimobendan to dogs with MMVD and echocardiographic and radiographic evidence of cardiomegaly results in prolongation of preclinical period and is safe and well tolerated. Prolongation of preclinical period by approximately 15 months represents substantial clinical benefit

Raising awareness of non-hodgkin lymphoma in HIV-infected adolescents: Report of 2 cases in the HAART era

Human immunodeficiency virus (HIV) chronically infected patients are at increased risk of developing non-Hodgkin lymphoma compared with the general population. Highly active antiretroviral therapy has had a dramatic effect on the natural history of HIV infection, reducing the incidence of acquired immunodeficiency syndrome-related non-Hodgkin lymphoma and improving overall survival. However, problems related to adherence to treatment, frequently experienced during adolescence, may increase the risk of acquired immunodeficiency syndrome-related cancers. Optimizing highly active antiretroviral therapy and monitoring noncompliant patients with persisting HIV replication should be considered by physicians who take care of these patients. We herein report 2 cases of relapsed/progressive Burkitt lymphoma in HIV vertically infected adolescents