Exact Solutions of a (2+1)-Dimensional Nonlinear Klein-Gordon Equation

The purpose of this paper is to present a class of particular solutions of a C(2,1) conformally invariant nonlinear Klein-Gordon equation by symmetry reduction. Using the subgroups of similitude group reduced ordinary differential equations of second order and their solutions by a singularity analysis are classified. In particular, it has been shown that whenever they have the Painlev\'e property, they can be transformed to standard forms by Moebius transformations of dependent variable and arbitrary smooth transformations of independent variable whose solutions, depending on the values of parameters, are expressible in terms of either elementary functions or Jacobi elliptic functions.Comment: 16 pages, no figures, revised versio

Neutron stars in a perturbative f(R)f(R) gravity model with strong magnetic fields

We investigate the effect of a strong magnetic field on the structure of neutron stars in a model with perturbative $f(R)$ gravity. The effect of an interior strong magnetic field of about $10^{17 \sim 18}$ G on the equation of state is derived in the context of a quantum hadrodynamics (QHD) model. We solve the modified spherically symmetric hydrostatic equilibrium equations derived for a gravity model with $f(R)=R+\alpha R^2$. Effects of both the finite magnetic field and the modified gravity are detailed for various values of the magnetic field and the perturbation parameter $\alpha$ along with a discussion of their physical implications. We show that there exists a parameter space of the modified gravity and the magnetic field strength, in which even a soft equation of state can accommodate a large ($> 2$ M$_\odot$) maximum neutron star mass through the modified mass-radius relation

Hippocrates is alive and weaning in Brazil

In a group of postoperative patients, Taniguchi and coworkers compared the effect of a computerized system for weaning against 'manual care'. The computerized system involved automatic adjustments to the level of pressure support to achieve a target respiratory rate. Manual care involved adjustments to the level of pressure support to keep the ratio of respiratory frequency to tidal volume below 80. The duration of ventilator weaning was equivalent with the two approaches. The level of pressure support, however, was lower with manual care than with computerized ventilation. The study adds support to the notion that ventilator duration is shortened when weaning is contemplated at the earliest possible time. The findings also emphasize the importance of the Hippocratic dictum that patient outcome is improved when care is individualized rather than delivered according to a protocol

Palaeotethys-related sediments of the Karaburun Peninsula, western Turkey: constraints on provenance and stratigraphy from detrital zircon geochronology

Detrital zircon U–Pb geochronology of 15 Late Palaeozoic to Early Mesozoic siliciclastic sandstones from the Karaburun Peninsula in western Turkey determines maximum sedimentation ages, identifies possible source areas, and anchors the study area within the Palaeotethyan realm. Siliciclastic sandstones yielded ages from Triassic to Archean with major input from Palaeozoic to Neoproterozoic sources and very few Mesoproterozoic zircons. The youngest age groups set the new limit of the maximum depositional ages to Late Carboniferous–Early Permian for the Küçükbahçe and Dikendağı formations. Detrital zircons from Triassic sandstones are mainly Neoproterozoic and Palaeozoic in age. Zircons from the Scythian–Anisian Gerence Formation are predominantly Devonian and Carboniferous in age, while also Permian and Triassic zircon grains occur in the Carnian–Rhaetian Güvercinlik Formation. According to the zircon age populations and the data available from possible source regions, the Karaburun siliciclastic sediments, with the exception of two samples from the Dikendağı Formation, record sediment supply from units located at the southern margin of Eurasia during Late Palaeozoic and Early Mesozoic times. This interpretation is in agreement with palaeotectonic reconstructions for the closely related Greek islands of Chios and Inousses. The presence of Devonian accompanied by Carboniferous zircons in some of the Karaburun samples reveals similarities with Karakaya Complex sandstones of the Sakarya Zone in NW Turkey

Nonlinear Evolution Equations Invariant Under Schroedinger Group in three-dimensional Space-time

A classification of all possible realizations of the Galilei, Galilei-similitude and Schroedinger Lie algebras in three-dimensional space-time in terms of vector fields under the action of the group of local diffeomorphisms of the space \R^3\times\C is presented. Using this result a variety of general second order evolution equations invariant under the corresponding groups are constructed and their physical significance are discussed

Group-invariant solutions of a nonlinear acoustics model

Based on a recent classification of subalgebras of the symmetry algebra of the Zabolotskaya-Khokhlov equation, all similarity reductions of this equation into ordinary differential equations are obtained. Large classes of group-invariant solutions of the equation are also determined, and some properties of the reduced equations and exact solutions are discussed.Comment: 14 page