A variable coefficient nonlinear Schr\"{o}dinger equation with a four-dimensional symmetry group and blow-up of its solutions

A canonical variable coefficient nonlinear Schr\"{o}dinger equation with a four dimensional symmetry group containing \SL(2,\mathbb{R}) group as a subgroup is considered. This typical invariance is then used to transform by a symmetry transformation a known solution that can be derived by truncating its Painlev\'e expansion and study blow-ups of these solutions in the $L_p$-norm for $p>2$, $L_\infty$-norm and in the sense of distributions.Comment: 10 page

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

Management of Cervical Root Fracture Using Orthodontic Extrusion and Crown Reattachment: A Case Report

Root fractures involve damage to pulp, cementum, dentin, and periodontal ligaments. These injuries affect 0.5% to 7% of permanent teeth. Cervical root fractures are less frequently seen and have a worse prognosis compared with the fractures in the apical or middle third of the root. This case report describes the treatment of a cervical root fracture in a maxillary central incisor. After removal of the coronal fragment, the root was filled temporarily with calcium hydroxide and orthodontic extrusion was initiated. The remaining root portion was elevated above the epithelial attachment and a successful coronal restoration was made using the natural crown of the traumatized tooth

Buccal and Palatal Talon Cusps with Pulp Extensions on a Supernumerary Primary Tooth

This paper reports an unusual occurrence of talon cusp on a supernumerary primary incisor, presenting on both labial and palatal sides. The tooth was scheduled for extraction due to its interference with the occlusion. Morphometric analysis of the taloned cusps was performed on digitized replicas of the tooth crown using open-source image analysis toolkit (ImageJ). Further non-destructive investigation of the taloned crown under cone-beam X-ray computed tomography revealed pulpal extensions in both talon cusps

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

Unusual Ectopic Eruption of a Permanent Central Incisor Following an Intrusion Injury to the Primary Tooth

Intrusive luxation of primary teeth carries a high risk of damage to underlying permanent tooth germs. Ectopic eruption of permanent incisors is an unusual outcome of traumatic injury to their predecessors. In this case report, we describe the multidisciplinary management of the consequences of a primary tooth intrusion that led to severe ectopic eruption of the permanent left central incisor in a horizontal position at the level of the labial sulcus

Functional use change in green spaces: a case study of Kırklareli province

Green spaces which are one of the most important public spaces in urban design have an important role on qualified daily urban life. People escape from intense work pressure and traffic jam of metropoles to those urban green areas to take a breath even they cover a small size. In time, people's expectations from green spaces as functional and quantitative needs are changing. This change occurs due to increasing population and as the character of the urban life. This study examines the functional use and quantitative change of urban green spaces of Kirklareli Province from past to present. Kirklareli is a border city to Bulgaria which is located in north-west part of Turkey and this gives a transitional and a multicultural character to the city. The population is about 67360. In the course of time; green space needs have increased by the increasing population. In addition to this, green spaces' functional use change has been identified. According to the results of the study; from the aspect of the green space standards, Kirklareli found above standards with 17.5 m(2) per capita, but on the other hand, sport and playground areas found insufficient. The Oldest and the newest city plans of Kirklareli (1940s and 2012s cadastral plans) have been compared and site surveys implemented as the methodology. In site survey, current green spaces' functional uses as sport or playground are observed and determined and also current quantitative measure of the green spaces are verified. Urban green spaces in Kirklareli Province evaluated through considering world's most populated urban green space standards and Turkey's standards. This study utilizes to compose a substructure of the urban green space. Determined deficiencies and inadequacies of green spaces and functional needs in this study, can guide to further studies and implementations of Kirklareli Municipality.Publisher versio