Isotopic liftings of Clifford algebras and applications in elementary particle mass matrices

Isotopic liftings of algebraic structures are investigated in the context of Clifford algebras, where it is defined a new product involving an arbitrary, but fixed, element of the Clifford algebra. This element acts as the unit with respect to the introduced product, and is called isounit. We construct isotopies in both associative and non-associative arbitrary algebras, and examples of these constructions are exhibited using Clifford algebras, which although associative, can generate the octonionic, non-associative, algebra. The whole formalism is developed in a Clifford algebraic arena, giving also the necessary pre-requisites to introduce isotopies of the exterior algebra. The flavor hadronic symmetry of the six u,d,s,c,b,t quarks is shown to be exact, when the generators of the isotopic Lie algebra su(6) are constructed, and the unit of the isotopic Clifford algebra is shown to be a function of the six quark masses. The limits constraining the parameters, that are entries of the representation of the isounit in the isotopic group SU(6), are based on the most recent limits imposed on quark masses.Comment: 19 page

Statistical Model for Schedule Prediction: Validation in a Housing-Cooperative Construction Database

There are often considerable differences between the planned schedule for a construction project and what later develops during actual construction. This paper introduces an innovativeapproach that uses MarkovChain models to support predictions during earned value analyses. A statistical model was developed to predict possible deviations in a project schedule and the future progress of a project. This model, based on Markov chains, uses data from the past to adjust future predictions. A case study was built from a database of 90 housing cooperative construction projects and was validated in 12 more projects. A cross validation of three interactions was also carried out, obtaininganerror of 2.38% inthe prediction offuture progressandanerror of 4.29% intheprediction of construction timing.Theinnovative prediction model presented in this paper contributes to the management body of knowledge by introducing a new tool for the management and control of construction timing. The method presented improves construction management because it predicts future deviations in scheduleswithreducederrorsanddeterminestotaldeviationfromaconstructionschedulewithgreatprecision.Thisallowsbettercontroloverwork timing and represents important input in determining strategies and future actions.Agencia Nacional de Investigación e Innovació

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 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

Progress in Classical and Quantum Variational Principles

We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original Maupertuis (Euler-Lagrange) principle constrains the energy at every point along the trajectory. The generalized Maupertuis principle is equivalent to Hamilton's principle. Reciprocal principles are also derived for both the generalized Maupertuis and the Hamilton principles. The Reciprocal Maupertuis Principle is the classical limit of Schr\"{o}dinger's variational principle of wave mechanics, and is also very useful to solve practical problems in both classical and semiclassical mechanics, in complete analogy with the quantum Rayleigh-Ritz method. Classical, semiclassical and quantum variational calculations are carried out for a number of systems, and the results are compared. Pedagogical as well as research problems are used as examples, which include nonconservative as well as relativistic systems