Extending Bauer's corollary to fractional derivatives

We comment on the method of Dreisigmeyer and Young [D. W. Dreisigmeyer and P. M. Young, J. Phys. A \textbf{36}, 8297, (2003)] to model nonconservative systems with fractional derivatives. It was previously hoped that using fractional derivatives in an action would allow us to derive a single retarded equation of motion using a variational principle. It is proven that, under certain reasonable assumptions, the method of Dreisigmeyer and Young fails.Comment: Accepted Journal of Physics A at www.iop.org/EJ/journal/JPhys

Improving keratoconus management with central corneal regularization and corneal collagen cross-linking protocol treatment

Purpose. To evaluate safety and efficacy of customized central corneal regularization (CCR), together with simultaneous accelerated corneal collagen cross-linking (A-CXL) - CCR-CXL protocol, to treat keratoconus-related corneal ectasia. Design. Retrospective, comparative observational case series. Methods. Patients that had undergone combined CCR-CXL protocol. Main inclusion criteria were keratoconus visual acuity deterioration and contact lens intolerance. All patients underwent complete ophthalmological evaluation, corrected distance visual acuity (CDVA) and Scheimpflug-corneal tomography. Central corneal regularization was performed by ablation using flying spot laser. Subsequently, the stroma was saturated with 0.17% riboflavin-5-phosphate added every 2 minutes, followed by A-CXL 9 mW/cm2 for 10 minutes. CDVA, medium keratometry value (Kmed), and total corneal morphological irregularity index (CMI) of patients were analyzed before surgery and after 1, 3 and 12 months. A P value of.05 or less was considered statistically significant. Results. 46 eyes of 39 keratoconus patients were treated. At 1 month, the mean CDVA (LogMar) increased from 0.19 ± 0.02 to 0.12 ± 0.02 (P < .05), and the difference remained stable at month 12. Kmax decrease was statistically significant from 57.02 ± 5.65 to 50.21 ± 4.48 (P < .05). CMI decreased significantly from 47.8 ± 2.84 to 30.1 ± 2.4 (P < .01). Conclusions. CCR-CXL protocol is safe and effective in arresting keratectasia progression and increasing corneal optic regularity in keratoconus. These findings showed a significant improvement in CDVA, keratometry values and corneal optical aberrations after being treated with the CCR-CXL protocol. Copyright © Società Editrice Universo (SEU

Nonconservative Lagrangian mechanics II: purely causal equations of motion

This work builds on the Volterra series formalism presented in [D. W. Dreisigmeyer and P. M. Young, J. Phys. A \textbf{36}, 8297, (2003)] to model nonconservative systems. Here we treat Lagrangians and actions as `time dependent' Volterra series. We present a new family of kernels to be used in these Volterra series that allow us to derive a single retarded equation of motion using a variational principle

Lagrangian multiform structure for the lattice Gel'fand-Dikii hierarchy

The lattice Gel'fand-Dikii hierarchy was introduced by Nijhoff, Papageorgiou, Capel and Quispel in 1992 as the family of partial difference equations generalizing to higher rank the lattice Korteweg-de Vries systems, and includes in particular the lattice Boussinesq system. We present a Lagrangian for the generic member of the lattice Gel'fand-Dikii hierarchy, and show that it can be considered as a Lagrangian 2-form when embedded in a higher dimensional lattice, obeying a closure relation. Thus the multiform structure proposed in arXiv:0903.4086v2 [nlin.SI] is extended to a multi-component system.Comment: 12 page

Ileal metastasis from thoracic melanoma disclosed by video capsule endoscopy: an unusual but not extraordinary source of obscure bleeding

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Intraventricular flow patterns during right ventricular apical pacing

Objectives To assess differences in blood flow momentum (BFM) and kinetic energy (KE) dissipation in a model of cardiac dyssynchrony induced by electrical right ventricular apical (RVA) stimulation compared with spontaneous sinus rhythm. Methods We cross-sectionally enrolled 12 consecutive patients (mean age 74\ub18 years, 60% male, mean left ventricular ejection fraction 58%\ub16 %), within 48 hours from pacemaker (PMK) implantation. Inclusion criteria were: age>18 years, no PMK-dependency, sinus rhythm with a spontaneous narrow QRS at the ECG, preserved ejection fraction (>50%) and a low percentage of PMKstimulation (<20%). All the participants underwent a complete echocardiographic evaluation, including left ventricular strain analysis and particle image velocimetry. Results Compared with sinus rhythm, BFM shifted from 27\ub13.3 to 34\ub17.6\ub0 (p=0.016), while RVA-pacing was characterised by a 35% of increment in KE dissipation, during diastole (p=0.043) and 32% during systole (p=0.016). In the same conditions, left ventricle global longitudinal strain (LV GLS) significantly decreased from 17\ub13.3 to 11%\ub12.8% (p=0.004) during RVA-stimulation. At the multivariable analysis, BFM and diastolic KE dissipation were significantly associated with LV GLS deterioration (Beta Coeff.=0.54, 95% CI 0.07 to 1.00, p=0.034 and Beta Coeff.=0.29, 95% CI 0.02 to 0.57, p=0.049, respectively). Conclusions In RVA-stimulation, BFM impairment and KE dissipation were found to be significantly associated with LV GLS deterioration, when controlling for potential confounders. Such changes may favour the onset of cardiac remodelling and sustain heart failure

A Variational Procedure for Time-Dependent Processes

A simple variational Lagrangian is proposed for the time development of an arbitrary density matrix, employing the "factorization" of the density. Only the "kinetic energy" appears in the Lagrangian. The formalism applies to pure and mixed state cases, the Navier-Stokes equations of hydrodynamics, transport theory, etc. It recaptures the Least Dissipation Function condition of Rayleigh-Onsager {\bf and in practical applications is flexible}. The variational proposal is tested on a two level system interacting that is subject, in one instance, to an interaction with a single oscillator and, in another, that evolves in a dissipative mode.Comment: 25 pages, 4 figure