Resumen: It was proved recently that a Banach space fails the Mazur intersection property if and only if the family of all closed, convex and bounded subsets which are intersections of balls is uniformly very porous. This paper deals with the geometrical implications of this result. It is shown that every equivalent norm on the space can be associated in a natural way with a
constant of porosity, whose interplay with the geometry of the space is then investigated. Among other things, we prove that this constant is closely related to the set of ε-differentiability points of the space and the set of r-denting points of the dual. We also obtain estimates for this constant in several classical spaces.
Palabras clave: Uniformly very porous; Set of weak denting points; Differentiability points; Constant of porosity; Mazur intersection property; Equivalent norm
Departamento: Fac. de CC. Matemáticas - Depto. de Análisis Matemático
ISSN: 0019-2082
CDU: 514.7
Notas: Supported in part by DGICYT Grant BMF-2000-0609.The authors wish to thank the C.E.C.M., the Department of Mathematics and Statistics at Simon Fraser University, and especially J. Borwein, for their hospitality during the preparation of this paper.
Resumen: In this paper we prove that the best constant in the Sobolev trace embedding H1() ,! Lq(@) in a bounded smooth domain can be obtained as the limit as " ! 0 of the best constant of the usual Sobolev embedding H1() ,! Lq(!", dx/") where !" = {x 2 : dist(x, @)
Resumen: It is known that any periodic orbit of a Lipschitz ordinary differential equation must have period at least 2π/L, where L is the Lipschitz constant of f. In this paper, we prove a similar result for the semilinear evolution equation du/dt=-Au+f(u): for each α with 0 α 1/2 there exists a constant Kα such that if L is the Lipschitz constant of f as a map from D(Aα) into
H then any periodic orbit has period at least KαL-1/(1-α). As a concrete application we recover a result of Kukavica giving a lower bound on the period for the 2d Navier–Stokes equations with periodic boundary conditions.
Resumen: We analyze the sensitivity of a climatological model with respect to small changes in one of the distinguished parameters: the solar constant. We start by proving the stabilization of solutions of the evolution model when time tends to infinity. Later, we study the stationary problem and obtain uniqueness or a multiplicity of
solutions for different Values of the solar constant.
Resumen: The Ordenes Complex, Galicia, NW Spain, preserves high-pressure, moderate-temperature metamorphism in continental
margin rocks subducted during closure of the Rheic Ocean in the Variscan orogeny. The exposures extend across c90 km
perpendicular to strike and include rocks that reached depths of 30 to 60 km. Estimates of P–T conditions of rocks found near
the boundary
between overriding and subducting plates range from 430 8C at 1.0 GPa to 520 8C at 1.65 GPa. Structural
reconstructions including these data indicate an angle of subduction between 15 and 308.
A mathematical solution and numerical models have been used to estimate shear heating experienced by this well-exposed
paleo-subduction zone. Best fit of model to thermobarometric results occurs if shear stress in the upper reaches of the fault
separating subducting and overriding slabs was c100 MPa (constant shear) or c10.0% of pressure (constant coefficient of
friction) assuming a convergence rate of 6 cm year1. At greater depths negative feedback between temperature and shear stress
caused the system to approach steady state with decreasing shear stress and with little increase in temperature. The decrease in
shear stress at temperatures above 400 8C occurs as the rheological properties of the rock at higher temperature and (or) pressure
allow more plastic behavior. This suggests that high-temperature metamorphism is unlikely to occur in subducting crust without
special circumstances. A comparison of these results with estimates of shear stress inferred from seismicity and heat flow at
active convergent boundaries in the Pacific indicates that shear stress is best described as a pressure-dependent variable not as a
constant shear stress.
Resumen: Aim: to study the effectiveness of an electronic apex locator (Justy II) in locating simulated horizontal and vertical fractures in single roots.
Methods: an electronic apex locator (EAL) (Justy II, Yoshida Dentcraft, Tokyo, Japan) was used to measure the distance within the canal of horizontal (n=31) and vertical (n=31) fractures, created
with a disk in single-rooted teeth. Accuracy of the EAL was evaluated by comparing the measurements with those made using a size 10 file. Data were analyzed with the non-parametric Passing and Bablok method.
Results: for simulated horizontal fractures the EAL measured exactly the same length as a size 10 file, without constant or proportional errors. In vertical simulated fractures the EAL measured (on average) with a constant error of 7.5 mm shorter than the size 10 file; the difference had a wide confidence interval (–72.3 to 2.6 mm).
Conclusion: in this laboratory study, the Justy II EAL was able to determine accurately the position of simulated horizontal fractures but was unreliable when measuring simulated vertical fractures.
Resumen: Abstract: Dentin permeability was measured alternatively with two methods: a 10-ul capillary
method with visual evaluation (PC) and a motorized automatic measuring device (Flodec, FD), both interposed in a simulated perfusion system. Eight human third molar coronal fragments were connected to systems, and their permeability to
distilled water
measured at 0, 5, 10, 15, 20, 25, and 29 cmH2O pressure. Resultant permeabilities (in ul/s) for
both techniques were interrelated with the use of the Passing and Bablok nonparametric method, which gives information about the range of constant and proportional errors and their 95% confidence intervals (95CI). The relationship between the methods is described by the regression formula: FD =-0.0003 + 0.945·PC, with 95CI for constant (-0.0015–0.0009) and for slope (0.738–1.168), indicating that both methods are interchangeable, although not
identical.
Resumen: In this article we examine the concentration and oscillation effects developed by high-frequency eigenfunctions of the Laplace operator in a compact Riemannian manifold. More precisely, we are interested in the structure of the possible invariant semiclassical measures obtained as limits of Wigner measures corresponding to eigenfunctions. These measures
describe simultaneously the concentration and oscillation effects developed by a sequence of eigenfunctions. We present some results showing how to obtain invariant semiclassical measures from eigenfunctions with prescribed symmetries. As an application of these results, we give a simple proof of the fact that in a manifold of constant positive sectional curvature, every measure which is invariant by the geodesic flow is an invariant semiclassical measure.
Palabras clave: Eigenfunctions of the Laplacian; Semiclassical measures; Wigner distributions; Manifolds of constant sectional curvature; Invariant measures
Resumen: We have cloned and expressed in Escherichia coli a 702-base pair gene coding for the dihydrofolate reductase (DHFR) domain of the bifunctional dihydrofolate reductase-thymidylate synthase (DHFR-TS) from Trypanosoma cruzi. The DHFR domain was purified to homogeneity by methotrexate-Sepharose chromatography followed by an anion-exchange
chromatography step in a mono Q column, and displayed a single 27-kDa band on SDS-PAGE. Gel filtration showed that the catalytic domain was expressed as a monomer. Kinetic parameters were similar to those reported for the wild-type bifunctional enzyme with Km values of 0.75 microM for dihydrofolate and 16 microM for NADPH and a kcat value of 16.5 s-1. T. cruzi DHFR is poorly inhibited by trimethoprim and pyrimethamine and the inhibition constants were always lower for the bifunctional enzyme. The binding of methotrexate was characteristic of a class of inhibitors that form an initial complex which isomerizes slowly to a tighter complex and are referred to as 'slow, tight-binding' inhibitors. While the slow-binding step of inhibition was apparently unaffected in the individually expressed DHFR domain, the overall inhibition constant was two-fold higher as a consequence of the superior inhibition constant value obtained for the initial inhibitory complex.
