6,341 research outputs found
Finiteness in derived categories of local rings
New homotopy invariant finiteness conditions on modules over commutative
rings are introduced, and their properties are studied systematically. A number
of finiteness results for classical homological invariants like flat dimension,
injective dimension, and Gorenstein dimension, are established. It is proved
that these specialize to give results concerning modules over complete
intersection local rings. A noteworthy feature is the use of techniques based
on thick subcategories of derived categories.Comment: 40 pages. Minor revisions. To appear in Commentarii Math. Helvetic
DG algebras with exterior homology
We study differential graded algebras whose homology is an exterior algebra
over a commutative ring R on a generator of degree n, and also certain types of
differential modules over these DGAs. We obtain a complete classification when
R is the integers, or the prime field of characteristic p>0, and n is greater
than or equal to -1. The examples are unexpectedly interesting.Comment: 15 page
Incremental Grid-like Layout Using Soft and Hard Constraints
We explore various techniques to incorporate grid-like layout conventions
into a force-directed, constraint-based graph layout framework. In doing so we
are able to provide high-quality layout---with predominantly axis-aligned
edges---that is more flexible than previous grid-like layout methods and which
can capture layout conventions in notations such as SBGN (Systems Biology
Graphical Notation). Furthermore, the layout is easily able to respect
user-defined constraints and adapt to interaction in online systems and diagram
editors such as Dunnart.Comment: Accepted to Graph Drawing 201
The application of ultrasonic NDT techniques in tribology
The use of ultrasonic reflection is emerging as a technique for studying tribological contacts. Ultrasonic waves can be transmitted non-destructively through machine components and their behaviour at an interface describes the characteristics of that contact. This paper is a review of the current state of understanding of the mechanisms of ultrasonic reflection at interfaces, and how this has been used to investigate the processes of dry rough surface contact and lubricated contact. The review extends to cover how ultrasound has been used to study the tribological function of certain engineering machine elements
Status of Outer Planet Global Reference Atmospheric Model (GRAM) Upgrades
The inability to test planetary spacecraft in the flight environment prior to a mission requires engineers to rely on ground-based testing and models of the vehicle and expected environments. One of the most widely used engineering models of the atmosphere is the Global Reference Atmospheric Model (GRAM) developed and maintained by the NASA Marshall Space Flight Center (MSFC). The NASA Science Mission Directorate (SMD) has provided funding support to upgrade the GRAMs
The homotopy theory of dg-categories and derived Morita theory
The main purpose of this work is the study of the homotopy theory of
dg-categories up to quasi-equivalences. Our main result provides a natural
description of the mapping spaces between two dg-categories and in
terms of the nerve of a certain category of -bimodules. We also prove
that the homotopy category is cartesian closed (i.e. possesses
internal Hom's relative to the tensor product). We use these two results in
order to prove a derived version of Morita theory, describing the morphisms
between dg-categories of modules over two dg-categories and as the
dg-category of -bi-modules. Finally, we give three applications of our
results. The first one expresses Hochschild cohomology as endomorphisms of the
identity functor, as well as higher homotopy groups of the \emph{classifying
space of dg-categories} (i.e. the nerve of the category of dg-categories and
quasi-equivalences between them). The second application is the existence of a
good theory of localization for dg-categories, defined in terms of a natural
universal property. Our last application states that the dg-category of
(continuous) morphisms between the dg-categories of quasi-coherent (resp.
perfect) complexes on two schemes (resp. smooth and proper schemes) is
quasi-equivalent to the dg-category of quasi-coherent complexes (resp. perfect)
on their product.Comment: 50 pages. Few mistakes corrected, and some references added. Thm.
8.15 is new. Minor corrections. Final version, to appear in Inventione
The measurement of lubricant-film thickness using ultrasound
Ultrasound is reflected from a liquid layer between two solid bodies. This reflection depends on the ultrasonic frequency, the acoustic properties of the liquid and solid, and the layer thickness. If the wavelength is much greater than the liquid-layer thickness, then the response is governed by the stiffness of the layer. If the wavelength and layer thickness are similar, then the interaction of ultrasound with the layer is controlled by its resonant behaviour. This stiffness governed response and resonant response can be used to determine the thickness of the liquid layer, if the other parameters are known.
In this paper, ultrasound has been developed as a method to determine the thickness of lubricating films in bearing systems. An ultrasonic transducer is positioned on the outside of a bearing shell such that the wave is focused on the lubricant-film layer. The transducer is used to both emit and receive wide-band ultrasonic pulses. For a particular lubricant film, the reflected pulse is processed to give a reflection-coefficient spectrum. The lubricant-film thickness is then obtained from either the layer stiffness or the resonant frequency.
The method has been validated using fluid wedges at ambient pressure between flat and curved surfaces. Experiments on the elastohydrodynamic film formed between a sliding ball and a flat surface were performed. Film-thickness values in the range 50-500 nm were recorded, which agreed well with theoretical film-formation predictions. Similar measurements have been made on the oil film between the balls and outer raceway of a deep-groove ball bearing
New collections of p-subgroups and homology decompositions for classifying spaces of finite groups
Let G be a finite group and p a prime dividing its order. We define new
collections of p-subgroups of G. We study the homotopy relations among them and
with the standard collections of p-subgroups. We determine their ampleness and
sharpness properties.Comment: 14 pages, some revisions made, final version to appear in
Communications in Algebr
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