On moduli spaces for abelian categories

We show that if A is an abelian category satisfying certain mild conditions, then one can introduce the concept of a moduli space of (semi)stable objects which has the structure of a projective algebraic variety. This idea is applied to several important abelian categories in representation theory, like highest weight categories.

On the Relative Socle for Stratifying Systems

Let A be a finite dimensional k-algebra, (, ) be a stratifying system in mod(A) and F() be the class of -filtered A-modules. In this article, we give the definition and also study some of the properties of the relative socle in F(). We approach the relative socle in three ways. Namely, we view it as (1) a -semisimple subobject of M having the largest -length, (2) a maximal -semisimple subobject of M, and (3) a minimal -essential subobject of M.

Gaseous air pollution and emergency hospital visits for hypertension in Beijing, China : a time-stratified case-crossover study

Background: A number of epidemiological studies have been conducted to research the adverse effects of air pollution on mortality and morbidity. Hypertension is the most important risk factor for cardiovascular mortality. However, few previous studies have examined the relationship between gaseous air pollution and morbidity for hypertension. ---------- Methods: Daily data on emergency hospital visits (EHVs) for hypertension were collected from the Peking University Third Hospital. Daily data on gaseous air pollutants (sulfur dioxide (SO2) and nitrogen dioxide (NO2)) and particulate matter less than 10 μm in aerodynamic diameter (PM10) were collected from the Beijing Municipal Environmental Monitoring Center. A time-stratified case-crossover design was conducted to evaluate the relationship between urban gaseous air pollution and EHVs for hypertension. Temperature and relative humidity were controlled for. ---------- Results: In the single air pollutant models, a 10 μg/m3 increase in SO2 and NO2 were significantly associated with EHVs for hypertension. The odds ratios (ORs) were 1.037 (95% confidence interval (CI): 1.004-1.071) for SO2 at lag 0 day, and 1.101 (95% CI: 1.038-1.168) for NO2 at lag 3 day. After controlling for PM10, the ORs associated with SO2 and NO2 were 1.025 (95% CI: 0.987-1.065) and 1.114 (95% CI: 1.037-1.195), respectively.---------- Conclusion: Elevated urban gaseous air pollution was associated with increased EHVs for hypertension in Beijing, China.

Tissue engineering of stratified articular cartilage from chondrocyte subpopulations

Objective: To test if subpopulations of chondrocytes from different cartilage zones could be used to engineer cartilage constructs with features of normal stratification. Design: Chondrocytes from the superficial and middle zones of immature bovine cartilage were cultured in alginate, released, and seeded either separately or sequentially to form cartilage constructs. Constructs were cultured for 1 or 2 weeks and were assessed for growth, compressive properties, and deposition, and localization of matrix molecules and superficial zone protein (SZP). Results: The cartilaginous constructs formed from superficial zone chondrocytes exhibited less matrix growth and lower compressive properties than constructs from middle zone chondrocytes, with the stratified superficial-middle constructs exhibiting intermediate properties. Expression of SZP was highest at the construct surfaces, with the localization of SZP in superficial-middle constructs being concentrated at the superficial surface. Conclusions: Manipulation of subpopulations of chondrocytes can be useful in engineering cartilage tissue with a biomimetic approach, and in fabricating constructs that exhibit stratified features of normal articular cartilage. (C) 2003 OsteoArthritis Research Society International. Published by Elsevier Ltd. All rights reserved.

Short-term retention of labeled chondrocyte subpopulations in stratified tissue-engineered cartilaginous constructs implanted in vivo in mini-pigs

It is likely that effective application of cell-laden implants for cartilage defects depends on retention of implanted cells and interaction between implanted and host cells. The objectives of this study were to characterize stratified cartilaginous constructs seeded sequentially with superficial (S) and middle (M) chondrocyte subpopulations labelled with fluorescent cell tracking dye PKH26 (*) and determine the degree to which these stratified cartilaginous constructs maintain their architecture in vivo after implantation in mini-pigs for 1 week. Alginate-recovered cells were seeded sequentially to form stratified S*/M (only S cells labelled) and S*/M* (both S and M cells labelled) constructs. Full-thickness defects (4 mm diameter) were created in the patellofemoral groove of adult Yucatan mini-pigs and filled with portions of constructs or left empty. Constructs were characterized biochemically, histologically, and biomechanically, and stratification visualized and quantified, before and after implant. After 1 week, animals were sacrificed and implants retrieved. After 1 week in vivo, glycosaminoglycan and collagen content of constructs remained similar to that at implant, whereas DNA content increased. Histological analyses revealed features of an early repair response, with defects filled with tissues containing little matrix and abundant cells. Some implanted (PKH26-labeled) cells persisted in the defects, although constructs did not maintain a stratified organization. Of the labelled cells, 126 +/- 38% and 32 +/- 8% in S*/M and S*/M* constructs, respectively, were recovered. Distribution of labelled cells indicated interactions between implanted and host cells. Longer-term in vivo studies will be useful in determining whether implanted cells are sufficient to have a positive effect in repair.

Viscous dissipation effects on natural convection from a vertical plate with uniform surface heat flux placed in a thermally stratified media

In the present study we investigate the effect of viscous dissipation on natural convection from a vertical plate placed in a thermally stratified environment. The reduced equations are integrated by employing the implicit finite difference scheme of Keller box method and obtained the effect of heat due to viscous dissipation on the local skin friction and local Nusselt number at various stratification levels, for fluids having Prandtl numbers of 10, 50, and 100. Solutions are also obtained using the perturbation technique for small values of viscous dissipation parameters $\xi$ and compared to the finite difference solutions for 0 · $\xi$ · 1. Effect of viscous dissipation and temperature stratification are also shown on the velocity and temperature distributions in the boundary layer region.

Natural convection flow with combined buoyancy effects due to thermal and mass diffusion in a thermally stratified media

We present here a numerical study of laminar doubly diffusive free convection flows adjacent to a vertical surface in a stable thermally stratified medium. The governing equations of mass, momentum, energy and species are non-dimensionalized. These equations have been solved by using an implicit finite difference method and local non-similarity method. The results show many interesting aspects of complex interaction of the two buoyant mechanisms that have been shown in both the tabular as well as graphical form.

Spatially stratified sampling using auxiliary information for geostatistical mapping

This paper presents a method of spatial sampling based on stratification by Local Moran’s I i calculated using auxiliary information. The sampling technique is compared to other design-based approaches including simple random sampling, systematic sampling on a regular grid, conditional Latin Hypercube sampling and stratified sampling based on auxiliary information, and is illustrated using two different spatial data sets. Each of the samples for the two data sets is interpolated using regression kriging to form a geostatistical map for their respective areas. The proposed technique is shown to be competitive in reproducing specific areas of interest with high accuracy.

Natural convection from a vertical plate embedded in a stratified medium with uniform heat source

Natural convection flow from an isothermal vertical plate with uniform heat source embedded in a stratified medium has been discussed in this paper. The resulting momentum and energy equations of boundary layer approximation are made non-similar by introducing the usual non-similarity transformations. Numerical solutions of these equations are obtained by an implicit finite difference method for a wide range of the stratification parameter, X. The solutions are also obtained for different values of pertinent parameters, namely, the Prandtl number, Pr and the heat generation or absorption parameter, λ and are expressed in terms of the local skin-friction and local heat transfer, which are shown in the graphical form. Effect of heat generation or absorption on the streamlines and isotherms are also shown graphically for different values of λ.

"The Stratified Record upon Which We Set Our Feet" : The Spatial Turn and the Multilayering of History, Geography, and Geology

In Thomas Mann’s tetralogy of the 1930s and 1940s, Joseph and His Brothers, the narrator declares history is not only “that which has happened and that which goes on happening in time,” but it is also “the stratified record upon which we set our feet, the ground beneath us.” By opening up history to its spatial, geographical, and geological dimensions Mann both predicts and encapsulates the twentieth-century’s “spatial turn,” a critical shift that divested geography of its largely passive role as history’s “stage” and brought to the fore intersections between the humanities and the earth sciences. In this paper, I draw out the relationships between history, narrative, geography, and geology revealed by this spatial turn and the questions these pose for thinking about the disciplinary relationship between geography and the humanities. As Mann’s statement exemplifies, the spatial turn itself has often been captured most strikingly in fiction, and I would argue nowhere more so than in Graham Swift’s Waterland (1983) and Anne Michaels’s Fugitive Pieces (1996), both of which present space, place, and landscape as having a palpable influence on history and memory. The geographical/geological line that runs through both Waterland and Fugitive Pieces continues through Tim Robinson’s non-fictional, two-volume “topographical” history Stones of Aran. Robinson’s Stones of Aran—which is not history, not geography, and not literature, and yet is all three—constructs an imaginative geography that renders inseparable geography, geology, history, memory, and the act of writing.

Helmholtz Instability In Stratified Shear Flows With Magnetic-Fields

The stability characteristics of a Helmholtz velocity profile in a stratified Boussinesq fluid in the presence of a rigid boundary is studied, A jump in the magnetic field is introduced at a level different from the velocity discontinuity. New unstable modes in addition to the Kelvin-Helmhottz mode are found. The wavelengths of these unstable modes are close to the wavelengths of internal Alfv6n gravity waves in the atmospher.

Instabilities of a compressible stratified fluid in horizontal sheared motion

The stability characteristics of a Helmholtz velocity profile in a stably stratified, compressible atmosphere in the presence of a lower boundary are studied. A jump in the Brunt–Väisälä frequency is introduced and the level at which this jump occurs is assumed to be different from the shear zone, to simulate sharp temperature discontinuities in the atmosphere. The results are compared with those of Pellacani, Tebaldi, and Tosi and Lindzen and Rosenthal. In the present configuration, new unstable modes with larger growth rates are found. The wavelengths of the most unstable gravity waves for the parameters pertaining to observed cases of clear air turbulence agree quite closely with the experimental values. Physics of Fluids is copyrighted by The American Institute of Physics