Calculation of isotope shifts and relativistic shifts in CI, CII, CIII and CIV

We present an accurate ab initio method of calculating isotope shifts and relativistic shifts in atomic spectra. We test the method on neutral carbon and three carbon ions. The relativistic shift of carbon lines may allow them to be included in analyses of quasar absorption spectra that seek to measure possible variations in the fine structure constant, alpha, over the lifetime of the Universe. Carbon isotope shifts can be used to measure isotope abundances in gas clouds: isotope abundances are potentially an important source of systematic error in the alpha-variation studies. These abundances are also needed to study nuclear reactions in stars and supernovae, and test models of chemical evolution of the Universe

Strength of inserts in titanium alloy machining

In this paper, a stressed state of a non-worn cutting wedge in a machined titanium alloy (Ti[6]Al[2]Mo[2]Cr) is analyzed. The distribution of contact loads on the face of a cutting tool was obtained experimentally with the use of a 'split cutting tool'. Calculation of internal stresses in the indexable insert made from cemented carbide (WC8Co) was carried out with the help of ANSYS 14.0 software. Investigations showed that a small thickness of the cutting insert leads to extremely high compressive stresses near the cutting edge, stresses that exceed the ultimate compressive strength of cemented carbide. The face and the base of the insert experience high tensile stresses, which approach the ultimate tensile strength of cemented carbide and increase a probability of cutting insert destruction. If the thickness of the cutting insert is bigger than 5 mm, compressive stresses near the cutting edge decrease, and tensile stresses on the face and base decrease to zero. The dependences of the greatest normal and tangential stresses on thickness of the cutting insert were found

Moths and butterflies (Lepidoptera) of the continental part of the Nenets Autonomous Okrug, Russia

Until very recently, Nenets Autonomous Okrug (NAO), located in the northeastern part of European Russia, was the least studied region of Russia in terms of itsmoth fauna. Intensive sampling in the surroundings of Naryan-Mar, combined with critical revision of earlier publications and evaluation of museum collections, resulted in the discovery of a relatively rich fauna of Lepidoptera. The first regional checklist of moths and butterflies of the continental part of NAO includes 324 species (169 species of microlepidoptera and 155 species of macrolepidoptera), 178 of which are reported fromNAOfor the first time.We estimate that 40 to 180 species remain to be found in the study region. The recorded speciesmostly belong to residents of northern boreal forests and bogs. The fauna of moths and butterflies of NAO clearly differs from the fauna of Fennoscandia, due to the relatively higher proportion ofEast Palaearctic andBeringian species

Theory of lossless polarization attraction in telecommunication fibers

In this work, polarization attraction is meant to be the conservative nonlinear effect that transforms any arbitrary input state of polarization (SOP) of an intense optical signal beam fed to a nonlinear medium into approximately one and the same SOP at the output, provided that the medium is driven by a relatively stronger counterpropagating pump beam. Essentially, the combination of the nonlinear medium and the pump beam serves as a lossless polarizer for the signal beam. The degree of polarization of the outcoming signal beam can be close to 100% (90% in our present simulations). With an eye toward the development of such lossless polarizers for fiber optics applications, we theoretically study the polarization attraction effect in the optical fibers that are used in telecommunication links; i.e., randomly birefringent fibers. A generic model for the fiber-based lossless polarizers is derived, and a statistical scheme for the quantification of their performance is proposed

A Necessary Condition for existence of Lie Symmetries in Quasihomogeneous Systems of Ordinary Differential Equations

Lie symmetries for ordinary differential equations are studied. In systems of ordinary differential equations, there do not always exist non-trivial Lie symmetries around equilibrium points. We present a necessary condition for existence of Lie symmetries analytic in the neighbourhood of an equilibrium point. In addition, this result can be applied to a necessary condition for existence of a Lie symmetry in quasihomogeneous systems of ordinary differential equations. With the help of our main theorem, it is proved that several systems do not possess any analytic Lie symmetries.Comment: 15 pages, no figures, AMSLaTe

Theory of lossless polarization attraction in telecommunication fibers: erratum

An erroneous procedure of averaging the components of the Stokes vector of a polarization scrambled beam over the Poincare sphere introduced in our earlier paper [J. Opt. Soc. Am. B 28, 100-108 (2011)] has been corrected

Classification of symmetric periodic trajectories in ellipsoidal billiards

We classify nonsingular symmetric periodic trajectories (SPTs) of billiards inside ellipsoids of R^{n+1} without any symmetry of revolution. SPTs are defined as periodic trajectories passing through some symmetry set. We prove that there are exactly 2^{2n}(2^{n+1}-1) classes of such trajectories. We have implemented an algorithm to find minimal SPTs of each of the 12 classes in the 2D case (R^2) and each of the 112 classes in the 3D case (R^3). They have periods 3, 4 or 6 in the 2D case; and 4, 5, 6, 8 or 10 in the 3D case. We display a selection of 3D minimal SPTs. Some of them have properties that cannot take place in the 2D case.Comment: 26 pages, 77 figures, 17 table