Test ideals and flat base change problems in tight closure theory

Test ideals are an important concept in tight closure theory and their behavior via flat base change can be very difficult to understand. Our paper presents results regarding this behavior under flat maps with reasonably nice (but far from smooth) fibers. This involves analyzing, in depth, a special type of ideal of test elements, called the CS test ideal. Besides providing new results, the paper also contains extensions of a theorem by G. Lyubeznik and K. E. Smith on the completely stable test ideal and of theorems by F. Enescu and, independently, M. Hashimoto on the behavior of F-rationality under flat base change.Comment: 18 pages, to appear in Trans. Amer. Math. So

The Structure of F-Pure Rings

For a reduced F-finite ring R of characteristic p >0 and q=p^e one can write R^{1/q} = R^{a_q} \oplus M_q, where M_q has no free direct summands over R. We investigate the structure of F-finite, F-pure rings R by studying how the numbers a_q grow with respect to q. This growth is quantified by the splitting dimension and the splitting ratios of R which we study in detail. We also prove the existence of a special prime ideal P(R) of R, called the splitting prime, that has the property that R/P(R) is strongly F-regular. We show that this ideal captures significant information with regard to the F-purity of R.Comment: 15 page

Vascular neurocognitive disorders and the vascular risk factors

Dementias are clinical neurodegenerative diseases characterized by permanent and progressive transformation of cognitive functions such as memory, learning capacity, attention, thinking, language, passing judgments, calculation or orientation. Dementias represent a relatively frequent pathology, encountered at about 10% of the population of 65-year olds and 20% of the population of 80-year olds. This review presents the main etiological forms of dementia, which include Alzheimer form of dementia, vascular dementia, dementia associated with alpha-synucleionopathies, and mixed forms. Regarding vascular dementia, the risk factors are similar to those for an ischemic or hemorrhagic cerebrovascular accident: arterial hypertension, diabetes mellitus, dyslipidemia, smoking, obesity, age, alcohol consumption, cerebral atherosclerosis/ arteriosclerosis. Several studies show that efficient management of the vascular risk factors can prevent the expression and/ or progression of dementia. Thus, lifestyle changes such as stress reduction, regular physical exercise, decreasing dietary fat, multivitamin supplementation, adequate control of blood pressure and serum cholesterol, and social integration and mental stimulation in the elderly population are important factors in preventing or limiting the symptoms of dementia, a disease with significant individual, social, and economic implications

When does the F-signature exist?

This is a preprint of an article published in the Annales de la Faculte des Sciences de Toulouse, 15 (2006), 195-201.We show that the F-signature of an F-finite local ring R of characteristic p > 0 exists when R is either the localization of an N-graded ring at its irrelevant ideal or Q-Gorenstein on its punctured spectrum. This extends results by Huneke, Leuschke, Yao and Singh and proves the existence of the F-signature in the cases where weak F-regularity is known to be equivalent to strong F-regularity

Vascular neurocognitive disorders and the vascular risk factors

Dementias are clinical neurodegenerative diseases characterized by permanent and progressive transformation of cognitive functions such as memory, learning capacity, attention, thinking, language, passing judgments, calculation or orientation. Dementias represent a relatively frequent pathology, encountered at about 10% of the population of 65-year olds and 20% of the population of 80-year olds. This review presents the main etiological forms of dementia, which include Alzheimer form of dementia, vascular dementia, dementia associated with alpha-synucleionopathies, and mixed forms. Regarding vascular dementia, the risk factors are similar to those for an ischemic or hemorrhagic cerebrovascular accident: arterial hypertension, diabetes mellitus, dyslipidemia, smoking, obesity, age, alcohol consumption, cerebral atherosclerosis/ arteriosclerosis. Several studies show that efficient management of the vascular risk factors can prevent the expression and/ or progression of dementia. Thus, lifestyle changes such as stress reduction, regular physical exercise, decreasing dietary fat, multivitamin supplementation, adequate control of blood pressure and serum cholesterol, and social integration and mental stimulation in the elderly population are important factors in preventing or limiting the symptoms of dementia, a disease with significant individual, social, and economic implications

Generic dependence of the frequency-size distribution of earthquakes on depth and its relation to the strength profile of the crust

[1] We explore the idea that the relative size distribution of earthquakes, quantified using the so-called b-value, is negatively correlated with differential stress. Because the maximum possible differential stress increases linearly in the brittle upper crust, we expect to find a decrease of b with depth. We test this expectation for seven continental areas around the world, each of which is described by a regional earthquake catalog. We find a monotonic decrease in b-value between 5 and 15 km depth. The decrease stops near the brittle-ductile transition. We specifically focus on the high-quality catalogs of earthquakes in California to perform a sensitivity test with respect to depth uncertainty; we also estimate the probability-depth gradient for the occurrence of a target magnitude event and study the behavior of b with depth in near- and off-fault zones. We also translate the observed b-depth gradients into b-differential stress gradients. Our findings suggest that b-values are negatively correlated with differential stress and hus have the potential to act as stress meters in the Earth\u27s crust

Interaction with Nearly Environment and Old Structure for a Deep Excavation. Case History in Bucharest

The paper presents the influence of a deep excavation performed in Bucharest on the adjacent ground and on some old buildings around it; the damages and effects appeared during the excavation and the remedial measures are presented in detail, too. The excavation was designed to be 16.15 meters deep, sustained by a slurry wall enclosure of 60 cm thickness and pre-stressed anchors, and steel struts. Due to an accident that occured to the trench walls, a thorough monitoring by instrumentation started. The results of this monitoring are shown

Sensitivity study of forecasted aftershock seismicity based on Coulomb stress calculation and rate- and state-dependent frictional response

We use the Dieterich (1994) physics-based approach to simulate the spatio- temporal evolution of seismicity caused by stress changes applied to an infinite population of nucleating patches modeled through a rate- and state- dependent friction law. According to this model, seismicity rate changes depend on the amplitude of stress perturbation, the physical constitutive properties of faults (represented by the parameter Aσ), the stressing rate and the background seismicity rate of the study area. In order to apply this model in a predictive manner, we need to understand the impact of physical model parameters and the correlations between them. Firstly we discuss different definitions of the reference seismicity rate and show their impact on the computed rate of earthquake production for the 1992 Landers earthquake sequence as a case study. Furthermore, we demonstrate that all model parameters are strongly correlated for physical and statistical reasons. We discuss this correlation emphasizing that the estimations of the background seismicity rate, stressing rate and Aσ are strongly correlated to reproduce the observed aftershock productivity. Our analytically derived relation demonstrates the impact of these model parameters on the Omori-like aftershock decay: the c- value and the productivity of the Omori law, implying a p-value smaller or equal to 1. Finally, we discuss an optimal strategy to constrain model parameters for near-real time forecasts