Structure and finiteness properties of subdirect products of groups

We investigate the structure of subdirect products of groups, particularly their finiteness properties. We pay special attention to the subdirect products of free groups, surface groups and HNN extensions. We prove that a finitely presented subdirect product of free and surface groups virtually contains a term of the lower central series of the direct product or else fails to intersect one of the direct summands. This leads to a characterization of the finitely presented subgroups of the direct product of 3 free or surface groups, and to a solution to the conjugacy problem for arbitrary finitely presented subgroups of direct products of surface groups. We obtain a formula for the first homology of a subdirect product of two free groups and use it to show there is no algorithm to determine the first homology of a finitely generated subgroup.Comment: 29 pages, no figure

Subgroups of direct products of limit groups

If $G_1,...,G_n$ are limit groups and $S\subset G_1\times...\times G_n$ is of type \FP_n(\mathbb Q) then $S$ contains a subgroup of finite index that is itself a direct product of at most $n$ limit groups. This settles a question of Sela.Comment: 20 pages, no figures. Final version. Accepted by the Annals of Mathematic

On the finite presentation of subdirect products and the nature of residually free groups

We establish {\em{virtual surjection to pairs}} (VSP) as a general criterion for the finite presentability of subdirect products of groups: if $\Gamma_1,...,\Gamma_n$ are finitely presented and $S<\Gamma_1\times...\times\Gamma_n$ projects to a subgroup of finite index in each $\Gamma_i\times\Gamma_j$, then $S$ is finitely presentable, indeed there is an algorithm that will construct a finite presentation for $S$. We use the VSP criterion to characterise the finitely presented residually free groups. We prove that the class of such groups is recursively enumerable. We describe an algorithm that, given a finite presentation of a residually free group, constructs a canonical embedding into a direct product of finitely many limit groups. We solve the (multiple) conjugacy problem and membership problem for finitely presentable subgroups of residually free groups. We also prove that there is an algorithm that, given a finite generating set for such a subgroup, will construct a finite presentation. New families of subdirect products of free groups are constructed, including the first examples of finitely presented subgroups that are neither ${\rm{FP}}_\infty$ nor of Stallings-Bieri typeComment: 44 pages. To appear in American Journal of Mathematics. This is a substantial rewrite of our previous Arxiv article 0809.3704, taking into account subsequent developments, advice of colleagues and referee's comment

Finitely presented subgroups of automatic groups and their isoperimetric functions

We describe a general technique for embedding certain amalgamated products into direct products. This technique provides us with a way of constructing a host of finitely presented subgroups of automatic groups which are not even asynchronously automatic. We can also arrange that such subgroups satisfy, at best, an exponential isoperimetric inequality.Comment: DVI and Post-Script files only. To appear in J. London Math. So

Description and calibration of the Langley Hypersonic CF4 tunnel: A facility for simulating low gamma flow as occurs for a real gas

The Langley Hypersonic CF4 Tunnel is a Mach 6 facility which simulates an important aspect of dissociative real-gas phenomena associated with the reentry of blunt vehicles, i.e., the decrease in the ratio of specific heats (gamma) that occurs within the shock layer of the vehicle. A general description of this facility is presented along with a discussion of the basic components, instrumentation, and operating procedure. Pitot-pressure surveys were made at the nozzle exit and downstream of the exit for reservoir temperatures from 1020 to 1495 R and reservoir pressures from 1000 to 2550 psia. A uniform test core having a diameter of circa 11 in. (0.55 times the nozzle-exit diameter) exists at the maximum value of reservoir pressure and temperature. The corresponding free-stream Mach number is 5.9, the unit Reynolds number is 4 x 10 to the 5th power per foot, the ratio of specific heats immediately behind a normal shock is 1.10, and the normal-shock density ratio is 12.6. When the facility is operated at reservoir temperatures below 1440 R, irregularities occur in the pitot-pressure profile within a small region about the nozzle centerline. These variations in pitot pressure indicate the existence of flow distrubances originating in the upstream region of the nozzle. This necessitates testing models off centerline in the uniform flow between the centerline region and either the nozzle boundary layer or the lip shock originating at the nozzle exit. Samples of data obtained in this facility with various models are presented to illustrate the effect of gamma on flow conditions about the model and the importance of knowing the magnitude of this effect

A review of current knowledge concerning the breeding and summer distribution of the cordilleran flycatcher (\u3cem\u3eEmpidonax occidentalis\u3c/em\u3e) in Mexico

The Cordilleran Flycatcher (Empidonax occidentalis) is one of many North American birds whose distribution crosses the US–Mexican border and for which little is presently known about summer distribution and breeding biology south of this border. In addition, the Cordilleran Flycatcher presents ornithologists with a number of challenging questions surrounding its taxonomy, migration, distribution, population structure, and species limits. In particular, there remains a good deal of uncertainty concerning the species-level relationships, seasonal movements, and the wintering and breeding distributions of both recognized subspecies of Cordilleran Flycatcher in Mexico. Using field observations, a thorough review of the literature, and the examination of several distributional databases, we compile current knowledge on Mexican populations during the summer months and emphasize directions for future research. We document the northern limit of confirmed breeding Cordilleran Flycatchers in Mexico and point to gaps in our understanding of its summer range south of the US border. Currently available data point to a potential migratory divide in northern Mexico, which has implications for species limits and evolutionary dynamics within the Cordilleran Flycatcher. El mosquero barranqueño (Empidonax occidentalis) es una de varias especies de aves norteamericanas cuya distribución cruza la frontera entre México y los Estados Unidos, y de la cual se conoce poco acerca de su distribución durante el verano y su biología reproductiva al sur de esta frontera. Además, el mosquero barranqueño presenta a los ornitólogos una serie de preguntas acerca de su taxonomía, migración, distribución, estructura poblacional, y límites taxonómicas adentro de la especie. En particular, sigue bastante incierto nuestro conocimiento sobre las relaciones filogenéticas entre ambas subespecies del mosquero barranqueño, sus movimientos estacionales, sus distribuciones durante el verano, y su reproducción adentro de México. Usando observaciones de campo, una revisión exhaustiva de la literatura, y examinación de varias bases de datos distribucionales, recompilamos el conocimiento actual sobre las poblaciones mexicanas durante la temporada reproductiva y sugerimos direcciones para investigaciones futuras. Documentamos el límite norte de reproducción del mosquero barranqueño confirmado en México y señalamos vacíos en nuestra comprensión de su rango estival al sur de la frontera con los Estados Unidos. Los datos actualmente disponibles apuntan a la posibilidad de una brecha migratoria en el norte de México, la existencia de cual tiene implicaciones para los límites de las especies y la dinámica evolutiva dentro del mosquero barranqueño

How Have the Procedural Aspects of the Telecommunications Act of 1996 Worked?

Good morning. I am Clinton Miller. I\u27m one of the three members of the Virginia State Corporation Commission and charged with moderating this next panel. I will give you a brief overview before they begin because there may be some people in the room who are not deeply familiar with the procedural aspects of the Telecommunication Act of 1996

A Unified Operating System for Clouds and Manycore: fos

Single chip processors with thousands of cores will be available in the next ten years and clouds of multicore processors afford the operating system designer thousands of cores today. Constructing operating systems for manycore and cloud systems face similar challenges. This work identifies these shared challenges and introduces our solution: a factored operating system (fos) designed to meet the scalability, faultiness, variability of demand, and programming challenges of OSâ s for single-chip thousand-core manycore systems as well as current day cloud computers. Current monolithic operating systems are not well suited for manycores and clouds as they have taken an evolutionary approach to scaling such as adding fine grain locks and redesigning subsystems, however these approaches do not increase scalability quickly enough. fos addresses the OS scalability challenge by using a message passing design and is composed out of a collection of Internet inspired servers. Each operating system service is factored into a set of communicating servers which in aggregate implement a system service. These servers are designed much in the way that distributed Internet services are designed, but provide traditional kernel services instead of Internet services. Also, fos embraces the elasticity of cloud and manycore platforms by adapting resource utilization to match demand. fos facilitates writing applications across the cloud by providing a single system image across both future 1000+ core manycores and current day Infrastructure as a Service cloud computers. In contrast, current cloud environments do not provide a single system image and introduce complexity for the user by requiring different programming models for intra- vs inter-machine communication, and by requiring the use of non-OS standard management tools