Bicyclic units, Bass cyclic units and free groups

Let G be a finite group and ZG its integral group ring. We show that if alpha is a nontrivial bicyclic unit of ZG, then there are bicyclic units beta and gamma of different types, such that and are non-abelian free groups. In the case when G is non-abelian of order coprime to 6 we prove the existence of a bicyclic unit u and a Bass cyclic unit v in ZG, such that < u(m), v > is a free non-abelian group for all sufficiently large positive integers m.

BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS

Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass cyclic units of infinite order based on non-central elements as some of them have finite order modulo the center. We prove a theorem that suggests that this is the only limitation to obtain a non-abelian free group from a given Bass cyclic unit. More precisely, we prove that if u is a Bass cyclic unit of an integral group ring ZG of a solvable and finite group G, such that u has infinite order modulo the center of U(ZG) and it is based on an element of prime order, then there is a non-abelian free group generated by a power of u and a power of a unit in ZG which is either a Bass cyclic unit or a bicyclic unit.

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is nowhere vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.

Maslov index in semi-Riemannian submersions

We study focal points and Maslov index of a horizontal geodesic gamma : I -> M in the total space of a semi-Riemannian submersion pi : M -> B by determining an explicit relation with the corresponding objects along the projected geodesic pi omicron gamma : I -> B in the base space. We use this result to calculate the focal Maslov index of a (spacelike) geodesic in a stationary spacetime which is orthogonal to a timelike Killing vector field.

Pseudo Focal Points Along Lorentzian Geodesics and Morse Index

Given a Lorentzian manifold (M,g), a geodesic gamma in M and a timelike Jacobi field Y along gamma, we introduce a special class of instants along gamma that we call Y-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the Y-pseudo conjugate instants form a finite set, and their number equals the Morse index of (a suitable restriction of) the index form. This gives a Riemannian-like Morse index theorem. As special cases of the theory, we will consider geodesics in stationary and static Lorentzian manifolds, where the Jacobi field Y is obtained as the restriction of a globally defined timelike Killing vector field.

COMPARISON RESULTS FOR CONJUGATE AND FOCAL POINTS IN SEMI-RIEMANNIAN GEOMETRY VIA MASLOV INDEX

We prove an estimate on the difference of Maslov indices relative to the choice of two distinct reference Lagrangians of a continuous path in the Lagrangian Grassmannian of a symplectic space. We discuss some applications to the study of conjugate and focal points along a geodesic in a semi-Riemannian manifold.

Assessing the Design of the Library's Discovery Interface and Online resources: A Case Study at the University of Maryland

This presentation was offered as part of the CUNY Library Assessment Conference, Reinventing Libraries: Reinventing Assessment, held at the City University of New York in June 2014.

Evaluation of a micro PV-Wind hybrid system in Nordic climate conditions

A one year data analysis for a micro PV-Wind hybrid system (0.52 kW + 1 kW), installed in Borlänge/Sweden is presented in this paper. The system performance was evaluated according the guidelines of the IEC 61724 standard. The parameters obtained allow a comparison with similar systems. The measurement data are also used to evaluate the sizing and operation of the hybrid system. In addition, the system was modelled in HOMER to study sizing options.

Brytmånens utformning vid trädfällning - Jämförande studier av böjmotstånd och gångjärnseffekt : Designing felling hinge in tree felling - Comparative studies of bending resistance and hinge effect

Vid trädfällning med motorsåg sparar man en så kallad brytmån som skall fungera som ett gång¬järn när trädet fälls. Om brytmånen går av tidigt finns en risk att trädet faller okontrolle¬rat. De rekommendationer som finns säger att brytmånens bredd skall göras proportionell mot trädets diameter. Genom att teoretiskt och praktiskt undersöka vilka krafter brytmånen utsätts för och vad den håller för har det varit möjligt att dra vissa slutsatser om hur en bra brytmån skall se ut. Ett viktigt resultat är att en bred brytmån (över 30-40 mm) är mycket trög att böja och inte fungerar i det avseendet att den går av redan vid små böjningar. Teoretiska be¬räkningar och praktiska försök visar att en relativt smal brytmån håller för belastningen vid rakt motlut även på stora träd. Som ny rekommendationen föreslås att brytmånens bredd inte bör vara mer än 30 mm. Av försöken kan man också dra slutsatsen att frusen ved är stel och brister tidigt, varför svår¬fällda träd inte bör fällas när veden är fryst.A felling hinge is used when felling trees by help of chain saw. If the hinge breaks early in the fall of the tree there is a great risk that the tree will fall without control. Present recommenda¬tions in Sweden say that the thickness of the felling hinge shall be made in proportion to the stem diameter. By use of theoretical and practical examinations of the forces stressing the felling hinge, and the strength of the wood itself, it has been possible to draw conclusions regarding the correct design of a felling hinge. One important result is that a thick felling hinge (over 30-40 mm) is very hard to bend and does not work well as it looses most of its strength already at a small forward bending angel. Theoretical calculations and practical tests show that a relatively narrow felling hinge will manage very well the forces when felling trees with lean opposite to the felling direction even for large trees. Our new recommendation is that the thickness of the felling hinge in normal Swedish conditions should not exceed 30 mm. Through the studies it can also be seen that frozen, brittle wood breaks at small bending angels. For that reason particularly difficult trees not should be felled when the wood is frozen.

Dancing with Mr. Penrose and other stories

Stories: Fallen Angel The Inheritance Schlog's Dance The New World Dancing With Mr. Penrose