249 research outputs found
Cluster structures for 2-Calabi-Yau categories and unipotent groups
We investigate cluster tilting objects (and subcategories) in triangulated
2-Calabi-Yau categories and related categories. In particular we construct a
new class of such categories related to preprojective algebras of non Dynkin
quivers associated with elements in the Coxeter group. This class of
2-Calabi-Yau categories contains the cluster categories and the stable
categories of preprojective algebras of Dynkin graphs as special cases. For
these 2-Calabi-Yau categories we construct cluster tilting objects associated
with each reduced expression. The associated quiver is described in terms of
the reduced expression. Motivated by the theory of cluster algebras, we
formulate the notions of (weak) cluster structure and substructure, and give
several illustrations of these concepts. We give applications to cluster
algebras and subcluster algebras related to unipotent groups, both in the
Dynkin and non Dynkin case.Comment: 49 pages. For the third version the presentation is revised,
especially Chapter III replaces the old Chapter III and I
Consumers Attention and Interactivity towards Online Visual Advertisements: The Graphic Designers’ Peremptory Challenges.
Although new media graphic design is relatively new in Nigeria, compared to advertising, their scale, scope and immediacy have increased substantially with the diffusion of new technologies like mobile network, cable television and the Internet. This rapid development of information and communication technologies has enabled easy and rapid interaction between the graphic designer, advertiser and consumer. As a result, designers and advertisers are increasingly relying on various modes of interactive technology in new media to advertise and promote their products and services in Nigeria, thus, forcing the traditional design and advertising practices into relative obsolesce. In studying new media graphic design and advertising, this paper appraises online ads in Nigeria to highlight how designers and advertisers can effectively deliver messages to targeted audience. The major new media ad formats and their peculiar advantages over the traditional media are equally highlighted in the context of current design and advertising trend in general. Keywords: New Media, Graphics Design Formats, Advertising Trend, Online Advertising
Mutation in triangulated categories and rigid Cohen-Macaulay modules
We introduce the notion of mutation of -cluster tilting subcategories in a
triangulated category with Auslander-Reiten-Serre duality. Using this idea, we
are able to obtain the complete classifications of rigid Cohen-Macaulay modules
over certain Veronese subrings.Comment: 52 pages. To appear in Invent. Mat
Activation of stress-activated protein kinase in osteoarthritic cartilage: evidence for nitric oxide dependence
AbstractObjective We have demonstrated in bovine chondrocytes that nitric oxide (NO) mediates IL1 dependent apoptosis under conditions of oxidant stress. This process is accompanied by activation of c-Jun NH2-terminal kinase (JNK; also called stress-activated protein kinase). In these studies we examined activation of JNK in explant cultures of human osteoarthritic cartilage obtained at joint replacement surgery and we characterized the role of peroxynitrite to act as an upstream trigger.Design A novel technique to isolate chondrocyte proteins (<10% of total cartilage protein) from cartilage specimens was developed. It was used to analyse JNK activation by a western blot technique. To examine the hypothesis that chondrocyte JNK activation is a result of increased peroxynitrite, in vitro experiments were performed in which cultured chondrocytes were incubated with this oxidant.Results Activated JNK was detected in the cytoplasm of osteoarthritis (OA) affected chondrocytes but not in that of controls. In vitro, chondrocytes produce NO and superoxide anion. IL-1 (48h), which induces nitric oxide synthase, resulted in an activation of JNK; this effect was reversed by N-monomethylarginine (NMA). TNFα treated chondrocytes at 48h produce superoxide anion (EPR method). Exposure of cells to peroxynitrite led to an accumulation of intracellular oxidants, in association with JNK activation and cell death by apoptosis.Conclusion We suggest that JNK activation is among the IL-1 elicited responses that injure articular chondrocytes and this activation of JNK is dependent on intracellular oxidant formation (including NO peroxynitrite). In addition, the extraction technique here described is a novel method that permits the quantitation and study of proteins such as JNK involved in the signaling pathways of chondrocytes within osteoarthritic cartilage
Categorification of skew-symmetrizable cluster algebras
We propose a new framework for categorifying skew-symmetrizable cluster
algebras. Starting from an exact stably 2-Calabi-Yau category C endowed with
the action of a finite group G, we construct a G-equivariant mutation on the
set of maximal rigid G-invariant objects of C. Using an appropriate cluster
character, we can then attach to these data an explicit skew-symmetrizable
cluster algebra. As an application we prove the linear independence of the
cluster monomials in this setting. Finally, we illustrate our construction with
examples associated with partial flag varieties and unipotent subgroups of
Kac-Moody groups, generalizing to the non simply-laced case several results of
Gei\ss-Leclerc-Schr\"oer.Comment: 64 page
Torsion pairs and rigid objects in tubes
We classify the torsion pairs in a tube category and show that they are in
bijection with maximal rigid objects in the extension of the tube category
containing the Pruefer and adic modules. We show that the annulus geometric
model for the tube category can be extended to the larger category and
interpret torsion pairs, maximal rigid objects and the bijection between them
geometrically. We also give a similar geometric description in the case of the
linear orientation of a Dynkin quiver of type A.Comment: 25 pages, 13 figures. Paper shortened. Minor errors correcte
Auslander-Buchweitz approximation theory for triangulated categories
We introduce and develop an analogous of the Auslander-Buchweitz
approximation theory (see \cite{AB}) in the context of triangulated categories,
by using a version of relative homology in this setting. We also prove several
results concerning relative homological algebra in a triangulated category
\T, which are based on the behavior of certain subcategories under finiteness
of resolutions and vanishing of Hom-spaces. For example: we establish the
existence of preenvelopes (and precovers) in certain triangulated subcategories
of \T. The results resemble various constructions and results of Auslander
and Buchweitz, and are concentrated in exploring the structure of a
triangulated category \T equipped with a pair (\X,\omega), where \X is
closed under extensions and is a weak-cogenerator in \X, usually
under additional conditions. This reduces, among other things, to the existence
of distinguished triangles enjoying special properties, and the behavior of
(suitably defined) (co)resolutions, projective or injective dimension of
objects of \T and the formation of orthogonal subcategories. Finally, some
relationships with the Rouquier's dimension in triangulated categories is
discussed.Comment: To appear at: Appl. Categor. Struct. (2011); 22 page
On Morita and derived equivalences for cohomological Mackey algebras
By results of the second author, a source algebra equivalence between two p-blocks of finite groups induces an equivalence between the categories of cohomological Mackey functors associated with these blocks, and a splendid derived equivalence between two blocks induces a derived equivalence between the corresponding categories ofcohomological Mackey functors. The main result of this paper proves a partial converse: an equivalence (resp. Rickard equivalence) between the categories of cohomological Mackey functors of two blocks of finite groups induces a permeable Morita (resp. derived) equivalence between the two block algebras
The GL(2, C) McKay correspondence
In this paper we show that for any affine complete rational surface singularity the quiver of the reconstruction algebra can be determined combinatorially from the dual graph of the minimal resolution. As a consequence the derived category of the minimal resolution is equivalent to the derived category of an algebra whose quiver is determined by the dual graph. Also, for any finite subgroup G of GL(2,C)GL(2,C), it means that the endomorphism ring of the special CM CC [[x, y]]G-modules can be used to build the dual graph of the minimal resolution of C2/GC2/G, extending McKay’s observation (McKay, Proc Symp Pure Math, 37:183–186, 1980) for finite subgroups of SL(2,C)SL(2,C) to all finite subgroups of GL(2,C)GL(2,C)
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Synthesis of accelerograms compatible with the Chinese GB 50011-2001 design spectrum via harmonic wavelets: artificial and historic records
A versatile approach is employed to generate artificial accelerograms which satisfy the compatibility criteria prescribed by the Chinese aseismic code provisions GB 50011-2001. In particular, a frequency dependent peak factor derived by means of appropriate Monte Carlo analyses is introduced to relate the GB 50011-2001 design spectrum to a parametrically defined evolutionary power spectrum (EPS). Special attention is given to the definition of the frequency content of the EPS in order to accommodate the mathematical form of the aforementioned design spectrum. Further, a one-to-one relationship is established between the parameter controlling the time-varying intensity of the EPS and the effective strong ground motion duration. Subsequently, an efficient auto-regressive moving-average (ARMA) filtering technique is utilized to generate ensembles of non-stationary artificial accelerograms whose average response spectrum is in a close agreement with the considered design spectrum. Furthermore, a harmonic wavelet based iterative scheme is adopted to modify these artificial signals so that a close matching of the signals’ response spectra with the GB 50011-2001 design spectrum is achieved on an individual basis. This is also done for field recorded accelerograms pertaining to the May, 2008 Wenchuan seismic event. In the process, zero-phase high-pass filtering is performed to accomplish proper baseline correction of the acquired spectrum compatible artificial and field accelerograms. Numerical results are given in a tabulated format to expedite their use in practice
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