Invariant Lagrangians, mechanical connections and the Lagrange-Poincare equations

We deal with Lagrangian systems that are invariant under the action of a symmetry group. The mechanical connection is a principal connection that is associated to Lagrangians which have a kinetic energy function that is defined by a Riemannian metric. In this paper we extend this notion to arbitrary Lagrangians. We then derive the reduced Lagrange-Poincare equations in a new fashion and we show how solutions of the Euler-Lagrange equations can be reconstructed with the help of the mechanical connection. Illustrative examples confirm the theory.Comment: 22 pages, to appear in J. Phys. A: Math. Theor., D2HFest special issu

Pneumococcus meningitis varandossag soran.

Bacterial meningitis is a life-threatening disease. The incidence of meningitis is about 2.6-6 cases per 100.000 adults per year in developed countries. The most common causative microorganisms are Sreptococcus pneumoniae and Neisseria meningitidis. A 33-year-old multigravida, at 24 week of gestation was admitted to the hospital because of ear pain, haedache, fever and confusion. Lumbal puncture was performed and cerebrospinal fluid analysis showed signs of bacterial meningitis. Latex agglutination test was positive for S. pneumoniae, Gram-positive diplococci have seen under microscope and later cultivation verified S. pneumoniae as the causative agent. After ceftriaxon, dexamethasone administration and treatment in intensive care unit, left side mastoidectomy was performed since cranial computed tomography showed acut exacerbation of chronic mastoiditis on the left side. After extubation, mobilisation and 14 days antibiotic treatment the patient, who had residual hearing loss on the left side, was discharged from the hospital. During the treatment the foetal parameters were normal. The patient at 39 week of gestation gave birth to a healthy infant. Forty-eight case reports have been published in this topic around the world until April, 2012. The most common causative agents were S. pneumoniae and Listeria monocytogenes. Because of the little amount of data, it is hard to appreciate the actual incidence and prognosis of this life-threatening illness both for mother and infant. As far as we know this is the first published case report of meningitis during pregnancy in Hungary. By this article we would like to draw attention to the importance of teamwork, of prevention of brain abscess formation and of the removal of the infection's focus

Ion beam analysis of microcrystalline quartz artifacts from the Reed Mound Site, Delaware County, Oklahoma

Ion beam analysis (IBA) has been a powerful, non-destructive tool for archaeological research worldwide for over four decades, yet its full potential is seldom realized in North American archaeology. Herein the potential of particle induced X-ray emission spectrometry (PIXE) as a tool for future Ozarks chert provenance studies is evaluated based on its ability to facilitate (1) discrimination of Ozarks chert materials from different geological formations and (2) identification of discrete groups of artifacts from the same geological formation. In addition, PIXE was also used to evaluate the elemental heterogeneity of Ozarks chert materials. Thirty chert (microcrystalline quartz) artifacts were visually sorted and classified according to macroscopic features characteristic of certain chert resources from particular Ozarks geological formations. The elemental concentrations obtained from PIXE analysis underwent multivariate statistical analyses in order to gain insight from the data. The results indicate that PIXE could be a useful tool for assigning Ozarks chert materials to their respective geological formations, and possibly for determining regional or sub-regional provenance

Isometries, submetries and distance coordinates on Finsler manifolds

This paper considers fundamental issues related to Finslerian iso- metries, submetries, distance and geodesics. It is shown that at each point of a Finsler manifold there is a distance coordinate system. Us- ing distance coordinates, a simple proof is given for the Finslerian version of the Myers-Steenrod theorem and for the differentiability of Finslerian submetries

The Berwald-type linearisation of generalised connections

We study the existence of a natural `linearisation' process for generalised connections on an affine bundle. It is shown that this leads to an affine generalised connection over a prolonged bundle, which is the analogue of what is called a connection of Berwald type in the standard theory of connections. Various new insights are being obtained in the fine structure of affine bundles over an anchored vector bundle and affineness of generalised connections on such bundles.Comment: 25 page

A setting for higher order differential equations fields and higher order Lagrange and Finsler spaces

We use the Fr\"olicher-Nijenhuis formalism to reformulate the inverse problem of the calculus of variations for a system of differential equations of order 2k in terms of a semi-basic 1-form of order k. Within this general context, we use the homogeneity proposed by Crampin and Saunders in [14] to formulate and discuss the projective metrizability problem for higher order differential equation fields. We provide necessary and sufficient conditions for higher order projectivpre-e metrizability in terms of homogeneous semi-basic 1-forms. Such a semi-basic 1-form is the Poincar\'e-Cartan 1-form of a higher order Finsler function, while the potential of such semi-basic 1-form is a higher order Finsler function.Comment: final, pre-published versio

Prospects for K+→π+ννˉK^+ \to \pi^+ \nu \bar{ \nu } at CERN in NA62

The NA62 experiment will begin taking data in 2015. Its primary purpose is a 10% measurement of the branching ratio of the ultrarare kaon decay $K^+ \to \pi^+ \nu \bar{ \nu }$, using the decay in flight of kaons in an unseparated beam with momentum 75 GeV/c.The detector and analysis technique are described here.Comment: 8 pages for proceedings of 50 Years of CP