Iteration of closed geodesics in stationary Lorentzian manifolds

Following the lines of Bott in (Commun Pure Appl Math 9:171-206, 1956), we study the Morse index of the iterates of a closed geodesic in stationary Lorentzian manifolds, or, more generally, of a closed Lorentzian geodesic that admits a timelike periodic Jacobi field. Given one such closed geodesic gamma, we prove the existence of a locally constant integer valued map Lambda(gamma) on the unit circle with the property that the Morse index of the iterated gamma(N) is equal, up to a correction term epsilon(gamma) is an element of {0,1}, to the sum of the values of Lambda(gamma) at the N-th roots of unity. The discontinuities of Lambda(gamma) occur at a finite number of points of the unit circle, that are special eigenvalues of the linearized Poincare map of gamma. We discuss some applications of the theory.

The smallest simple Moufang loop

We study the simple Moufang loop GLL(F(2)) and give a complete description of its lattice of subloops. (C) 2008 Elsevier Inc. All rights reserved.

On a Gromoll-Meyer type theorem in globally hyperbolic stationary spacetimes

Following the lines of the celebrated Riemannian result of Gromoll and Meyer, we use infinite dimensional equivariant Morse theory to establish the existence of infinitely many geometrically distinct closed geodesics in a class of globally hyperbolic stationary Lorentzian manifolds.

Some classes of semisimple group (and loop) algebras over finite fields

We determine the structure of the semisimple group algebra of certain groups over the rationals and over those finite fields where the Wedderburn decompositions have the least number of simple components We apply our work to obtain similar information about the loop algebras of mdecomposable RA loops and to produce negative answers to the isomorphism problem over various fields (C) 2010 Elsevier Inc All rights reserved

Contravariantly finite subcategories closed under predecessors

Let A be an Artin algebra and mod A be the category of finitely generated right A-modules. We prove that an additive full subcategory C of mod A closed under predecessors is contravariantly finite if and only if its right Ext-orthogonal is covariantly finite, or if and only if the Ext-injectives in C define a cotilting module (over the support algebra of C) or, equivalently, if and only if C is the support of the representable functors given by the Ext-injectives. (C) 2009 Elsevier Inc. All rights reserved.

Demonstration of Closed Circuit TV by filming Wiliam C. H. Meyer in an Automotive classroom at the New York Trade School

Depiction of closed circuit TV students at the New York Trade School filming a voltage regulator check performed by William C. H. Meyer. Original caption reads, "Closed-circuit TV takes a class at the New York Trade School into the Automotive Shop where William C. H. Meyer, head of the Automotive Department, demonstrates a voltage-regulator check. Students Robert Niefeld (left) and Denis Mahoney serve as cameramen." Black and white photograph part of series of four photographs accompanying a press release of the New York Trade School announcing the demonstration of a new technique in closed-circuit TV developed at the New York Trade School.

Student at work with closed-circuit TV

A student in the Closed-circuit TV Dept. at the New York Trade School is shown working. Black and white photograph.

Closed-circuit Television Student Working

A student is show working with closed-circuit television at the New York Trade School. Black and white photograph.

Monitoring results of combined pellet and solar heating system

In this study the monitoring results of prototype installation of a recently developed solar combisystem have been evaluated. The system, that uses a water jacketed pellet stove as auxiliary heater, was installed in a single family house in Borlänge/Sweden. In order to allow an evaluation under realistic conditions the system has been monitored for a time period of one year. From the measurements of the system it could be seen that it is important that the pellet stove has a sufficient buffer store volume to minimize cycling. The measurements showed also that the stove gives a lower share of the produced heat to the water loop than measured under stationary conditions. The solar system works as expected and covers the heat demand during the summer and a part of the heat demand during spring and autumn. Potential for optimization exists for the parasitic electricity demand. The system consumes 680 kWh per year for pumps, valves and controllers which is more than 4% of the total primary heating energy demand.

Classroom of students watching demonstration of closed-circuit TV

Students watch monitors that show a voltage meter being filmed in the Automotive Dept by department head William C. H. Meyer as part of a demonstration of a new technique in closed-circuit television. This is one of a series of photographs accompanying a press release about the development and demonstration of the new technique at the New York Trade School. Original caption reads, "In a classroom on another floor, students all have "front row" seats for the demonstration. Camera concentrates on close-up of a meter, where readings show the result of the voltage-regulator check. Instructor (standing at microphone) is Arthur Richards." Black and white photograph with accompanying caption.