Loop Groups and Discrete KdV Equations

A study is presented of fully discretized lattice equations associated with the KdV hierarchy. Loop group methods give a systematic way of constructing discretizations of the equations in the hierarchy. The lattice KdV system of Nijhoff et al. arises from the lowest order discretization of the trivial, lowest order equation in the hierarchy, b_t=b_x. Two new discretizations are also given, the lowest order discretization of the first nontrivial equation in the hierarchy, and a "second order" discretization of b_t=b_x. The former, which is given the name "full lattice KdV" has the (potential) KdV equation as a standard continuum limit. For each discretization a Backlund transformation is given and soliton content analyzed. The full lattice KdV system has, like KdV itself, solitons of all speeds, whereas both other discretizations studied have a limited range of speeds, being discretizations of an equation with solutions only of a fixed speed.Comment: LaTeX, 23 pages, 1 figur

WKB formalism and a lower limit for the energy eigenstates of bound states for some potentials

In the present work the conditions appearing in the WKB approximation formalism of quantum mechanics are analyzed. It is shown that, in general, a careful definition of an approximation method requires the introduction of two length parameters, one of them always considered in the text books on quantum mechanics, whereas the second one is usually neglected. Afterwards we define a particular family of potentials and prove, resorting to the aforementioned length parameters, that we may find an energy which is a lower bound to the ground energy of the system. The idea is applied to the case of a harmonic oscillator and also to a particle freely falling in a homogeneous gravitational field, and in both cases the consistency of our method is corroborated. This approach, together with the Rayleigh--Ritz formalism, allows us to define an energy interval in which the ground energy of any potential, belonging to our family, must lie.Comment: Accepted in Modern Physics Letters

On Dirac theory in the space with deformed Heisenberg algebra. Exact solutions

The Dirac equation has been studied in which the Dirac matrices \hat{\boldmath\alpha}, \hat\beta have space factors, respectively $f$ and $f_1$, dependent on the particle's space coordinates. The $f$ function deforms Heisenberg algebra for the coordinates and momenta operators, the function $f_1$ being treated as a dependence of the particle mass on its position. The properties of these functions in the transition to the Schr\"odinger equation are discussed. The exact solution of the Dirac equation for the particle motion in the Coulomnb field with a linear dependence of the $f$ function on the distance $r$ to the force centre and the inverse dependence on $r$ for the $f_1$ function has been found.Comment: 13 page

Polynomial Solutions of Shcrodinger Equation with the Generalized Woods Saxon Potential

The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods Saxon potential are obtained in terms of the Jacobi polynomials. Nikiforov Uvarov method is used in the calculations. It is shown that the results are in a good agreement with the ones obtained before.Comment: 14 pages, 2 figures, submitted to Physical Review

Mathematical Structure of Relativistic Coulomb Integrals

We show that the diagonal matrix elements $,$ where $O$ $={1,\beta,i\mathbf{\alpha n}\beta}$ are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, may be considered as difference analogs of the radial wave functions. Such structure provides an independent way of obtaining closed forms of these matrix elements by elementary methods of the theory of difference equations without explicit evaluation of the integrals. Three-term recurrence relations for each of these expectation values are derived as a by-product. Transformation formulas for the corresponding generalized hypergeometric series are discussed.Comment: 13 pages, no figure

Anomalous diffusion in quantum Brownian motion with colored noise

Anomalous diffusion is discussed in the context of quantum Brownian motion with colored noise. It is shown that earlier results follow simply and directly from the fluctuation-dissipation theorem. The limits on the long-time dependence of anomalous diffusion are shown to be a consequence of the second law of thermodynamics. The special case of an electron interacting with the radiation field is discussed in detail. We apply our results to wave-packet spreading

Control of cellular automata

We study the problem of master-slave synchronization and control of totalistic cellular automata (CA) by putting a fraction of sites of the slave equal to those of the master and finding the distance between both as a function of this fraction. We present three control strategies that exploit local information about the CA, mainly, the number of nonzero Boolean derivatives. When no local information is used, we speak of synchronization. We find the critical properties of control and discuss the best control strategy compared with synchronization

Connection between type B (or C) and F factorizations and construction of algebras

In a recent paper (Del Sol Mesa A and Quesne C 2000 J. Phys. A: Math. Gen. 33 4059), we started a systematic study of the connections among different factorization types, suggested by Infeld and Hull, and of their consequences for the construction of algebras. We devised a general procedure for constructing satellite algebras for all the Hamiltonians admitting a type E factorization by using the relationship between type A and E factorizations. Here we complete our analysis by showing that for Hamiltonians admitting a type F factorization, a similar method, starting from either type B or type C ones, leads to other types of algebras. We therefore conclude that the existence of satellite algebras is a characteristic property of type E factorizable Hamiltonians. Our results are illustrated with the detailed discussion of the Coulomb problem.Comment: minor changes, 1 additional reference, final form to be published in JP

Recovery in cognitive motor dissociation after severe brain injury: A cohort study.

To investigate the functional and cognitive outcomes during early intensive neurorehabilitation and to compare the recovery patterns of patients presenting with cognitive motor dissociation (CMD), disorders of consciousness (DOC) and non-DOC. We conducted a single center observational cohort study of 141 patients with severe acquired brain injury, consecutively admitted to an acute neurorehabilitation unit. We divided patients into three groups according to initial neurobehavioral diagnosis at admission using the Coma Recovery Scale-Revised (CRS-R) and the Motor Behavior Tool (MBT): potential clinical CMD, [N = 105]; DOC [N = 19]; non-DOC [N = 17]). Functional and cognitive outcomes were assessed at admission and discharge using the Glasgow Outcome Scale, the Early Rehabilitation Barthel Index, the Disability Rating Scale, the Rancho Los Amigos Levels of Cognitive Functioning, the Functional Ambulation Classification Scale and the modified Rankin Scale. Confirmed recovery of conscious awareness was based on CRS-R criteria. CMD patients were significantly associated with better functional outcomes and potential for improvement than DOC. Furthermore, outcomes of CMD patients did not differ significantly from those of non-DOC. Using the CRS-R scale only; approximatively 30% of CMD patients did not recover consciousness at discharge. Our findings support the fact that patients presenting with CMD condition constitute a separate category, with different potential for improvement and functional outcomes than patients suffering from DOC. This reinforces the need for CMD to be urgently recognized, as it may directly affect patient care, influencing life-or-death decisions

Incidence and public health burden of sunburn among beachgoers in the United States.

The beach environment creates many barriers to effective sun protection, putting beachgoers at risk for sunburn, a well-established risk factor for skin cancer. Our objective was to estimate incidence of sunburn among beachgoers and evaluate the relationship between sunburn incidence and sun-protective behaviors. A secondary analysis, of prospective cohorts at 12 locations within the U.S. from 2003 to 2009 (n = 75,614), were pooled to evaluate sunburn incidence 10-12 days after the beach visit. Behavioral and environmental conditions were cross-tabulated with sunburn incidence. Multivariable logistic regression was used to estimate the association between new sunburn and sun-protective behaviors. Overall, 13.1% of beachgoers reported sunburn. Those aged 13-18 years (16.5%), whites (16.0%), and those at beach locations along the Eastern Seaboard (16.1%), had the highest incidence of sunburn. For those spending ≥5 h in the sun, the use of multiple types of sun protection reduced odds of sunburn by 55% relative to those who used no sun protection (Odds Ratio = 0.45 (95% Confidence Interval:0.27-0.77)) after adjusting for skin type, age, and race. Acute health effects of sunburn tend to be mild and self-limiting, but potential long-term health consequences are more serious and costly. Efforts to encourage and support proper sun-protective behaviors, and increase access to shade, protective clothing, and sunscreen, can help prevent sunburn and reduce skin cancer risk among beachgoers