L^2 torsion without the determinant class condition and extended L^2 cohomology

We associate determinant lines to objects of the extended abelian category built out of a von Neumann category with a trace. Using this we suggest constructions of the combinatorial and the analytic L^2 torsions which, unlike the work of the previous authors, requires no additional assumptions; in particular we do not impose the determinant class condition. The resulting torsions are elements of the determinant line of the extended L^2 cohomology. Under the determinant class assumption the L^2 torsions of this paper specialize to the invariants studied in our previous work. Applying a recent theorem of D. Burghelea, L. Friedlander and T. Kappeler we obtain a Cheeger - Muller type theorem stating the equality between the combinatorial and the analytic L^2 torsions.Comment: 39 page

Davis-Beirut reaction: route to thiazolo-, thiazino-, and thiazepino-2H-indazoles.

Methods for the construction of thiazolo-, thiazino-, and thiazepino-2H-indazoles from o-nitrobenzaldehydes or o-nitrobenzyl bromides and S-trityl-protected 1°-aminothioalkanes are reported. The process consists of formation of the requisite N-(2-nitrobenzyl)(tritylthio)alkylamine, subsequent deprotection of the trityl moiety with TFA, and immediate treatment with aq. KOH in methanol under Davis-Beirut reaction conditions to deliver the target thiazolo-, thiazino-, or thiazepino-2H-indazole in good overall yield. Subsequent S-oxidation gives the corresponding sulfone

Lyapunov 1-forms for flows

In this paper we find conditions which guarantee that a given flow $\Phi$ on a compact metric space $X$ admits a Lyapunov one-form $\omega$ lying in a prescribed \v{C}ech cohomology class $\xi\in \check H^1(X;\R)$. These conditions are formulated in terms of the restriction of $\xi$ to the chain recurrent set of $\Phi$. The result of the paper may be viewed as a generalization of a well-known theorem of C. Conley about the existence of Lyapunov functions.Comment: 27 pages, 3 figures. This revised version incorporates a few minor improvement

Embedding right-angled Artin groups into graph braid groups

We construct an embedding of any right-angled Artin group $G(\Delta)$ defined by a graph $\Delta$ into a graph braid group. The number of strands required for the braid group is equal to the chromatic number of $\Delta$. This construction yields an example of a hyperbolic surface subgroup embedded in a two strand planar graph braid group.Comment: 8 pages. Final version, appears in Geometriae Dedicata

Evidence for a Bulk Complex Order-Parameter in Y0.9Ca0.1Ba2Cu3O7-delta Thin Films

We have measured the penetration depth of overdoped Y0.9Ca0.1Ba2Cu3O7-delta (Ca-YBCO) thin films using two different methods. The change of the penetration depth as a function of temperature has been measured using the parallel plate resonator (PPR), while its absolute value was obtained from a quasi-optical transmission measurements. Both sets of measurements are compatible with an order parameter of the form: Delta*dx2-y2+i*delta*dxy, with Delta=14.5 +- 1.5 meV and delta=1.8 meV, indicating a finite gap at low temperature. Below 15 K the drop of the scattering rate of uncondensed carriers becomes steeper in contrast to a flattening observed for optimally doped YBCO films. This decrease supports our results on the penetration depth temperature dependence. The findings are in agreement with tunneling measurements on similar Ca-YBCO thin films.Comment: 11 pages, 4 figure

Traffic Characteristics of a Distributed Memory System

We believe that many distributed computing systems of the future will use distributed shared memory as a technique for interprocess communication. Thus, traffic generated by memory requests will be a major component of the traffic for any networks which connect nodes in such a system. In this paper, we study memory reference strings gathered with a tracing program we devised. We study several models. First, we look at raw reference data, as would be seen if the network were a backplane. Second, we examine references in units of blocks , first using a one-block cache model and then with an infinite cache. Finally, we study the effect of predictive prepaging of these blocks on the traffic. We provide a novel representation of memory reference data which can be used to calculate interarrival distributions directly. Integrating communication with computation can be used to control both traffic and performance

Supersymmetry, homology with twisted coefficients and n-dimensional knots

Let $n$ be any natural number. Let $K$ be any $n$-dimensional knot in $S^{n+2}$. We define a supersymmetric quantum system for $K$ with the following properties. We firstly construct a set of functional spaces (spaces of fermionic \{resp. bosonic\} states) and a set of operators (supersymmetric infinitesimal transformations) in an explicit way. Thus we obtain a set of the Witten indexes for $K$. Our Witten indexes are topological invariants for $n$-dimensional knots. Our Witten indexes are not zero in general. If $K$ is equivalent to the trivial knot, all of our Witten indexes are zero. Our Witten indexes restrict the Alexander polynomials of $n$-knots. If one of our Witten indexes for an $n$-knot $K$ is nonzero, then one of the Alexander polynomials of $K$ is nontrivial. Our Witten indexes are connected with homology with twisted coefficients. Roughly speaking, our Witten indexes have path integral representation by using a usual manner of supersymmetric theory.Comment: 10pages, no figure

Consistency Management in the EROS Kernel

EROS is a persistent operating system targeted towards managing resources with great longevity. The system provides a persistent single level store supporting two fundamental object types: nodes and pages. All primary objects, including memory segments and protection domains, are constructed out of these fundamental objects, and inherit their persistence. EROS is a pure capability system: access to objects is provided exclusively through the invocation of kernel enforced, secure capabilities. This paper describes the EROS Abstract Machine and the mechanisms used to achieve efficient consistency management within the system. The implementation, including all primary objects, a low overhead checkpoint/migration subsystem, and an efficient interprocess communication mechanism, requires less than 64 Kbytes of supervisor code (prior to size tuning)