An improved finite element space for discontinuous pressures

We consider incompressible Stokes flow with an internal interface at which the pressure is discontinuous, as happens for example in problems involving surface tension. We assume that the mesh does not follow the interface, which makes classical interpolation spaces to yield suboptimal convergence rates (typically, the interpolation error in the L(2)(Omega)-norm is of order h(1/2)). We propose a modification of the P(1)-conforming space that accommodates discontinuities at the interface without introducing additional degrees of freedom or modifying the sparsity pattern of the linear system. The unknowns are the pressure values at the vertices of the mesh and the basis functions are computed locally at each element, so that the implementation of the proposed space into existing codes is straightforward. With this modification, numerical tests show that the interpolation order improves to O(h(3/2)). The new pressure space is implemented for the stable P(1)(+)/P(1) mini-element discretization, and for the stabilized equal-order P(1)/P(1) discretization. Assessment is carried out for Poiseuille flow with a forcing surface and for a static bubble. In all cases the proposed pressure space leads to improved convergence orders and to more accurate results than the standard P(1) space. In addition, two Navier-Stokes simulations with moving interfaces (Rayleigh-Taylor instability and merging bubbles) are reported to show that the proposed space is robust enough to carry out realistic simulations. (c) 2009 Elsevier B.V. All rights reserved.

On the extent of star countable spaces

For a topological property P, we say that a space X is star Pif for every open cover Uof the space X there exists Y aS, X such that St(Y,U) = X and Y has P. We consider star countable and star Lindelof spaces establishing, among other things, that there exists first countable pseudocompact spaces which are not star Lindelof. We also describe some classes of spaces in which star countability is equivalent to countable extent and show that a star countable space with a dense sigma-compact subspace can have arbitrary extent. It is proved that for any omega (1)-monolithic compact space X, if C (p) (X)is star countable then it is Lindelof.

Examples from trees, related to discrete subsets, pseudo-radiality and omega-boundedness

We construct some examples using trees. Some of them are consistent counterexamples for the discrete reflection of certain topological properties. All the properties dealt with here were already known to be non-discretely reflexive if we assume CH and we show that the same is true assuming the existence of a Suslin tree. In some cases we actually get some ZFC results. We construct also, using a Suslin tree, a compact space that is pseudo-radial but it is not discretely generated. With a similar construction, but using an Aronszajn tree, we present a ZFC space that is first countable, omega-bounded but is not strongly w-bounded, answering a question of Peter Nyikos. (C) 2008 Elsevier B.V. All rights reserved.

Structure and thermal reactivity of Zn(II) salts of isocinchomeronic acid (2,5-pyridinedicarboxylic acid)

The synthesis, an improved refined crystal and molecular structure re-determination, and the thermal decomposition behavior of two Zn(II) derivatives of isocinchomeronic acid (2,5-pyridinedicarboxylic acid or H(2)2,5-pydc) are presented. [Zn(2,5-pydc)(H(2)O)(3)Zn(2,5-pydc)(H(2)O)(2)](2) (1) crystallizes in the triclinic P-1 space group with a = 7.106(2), b = 11.450(2), c = 11.869(1) angstrom, alpha = 107.29(1), beta = 104.08(1), gamma = 90.32(2)degrees, and Z = 2. [Zn(2,5-pydc)(H(2)O)(2)] center dot H(2)O (2) is orthorhombic (P2(1)2(1)2(1) space group), with a = 7.342(1), b = 9.430(1), c = 13.834(2) angstrom, and Z = 4. The structures were refined to agreement R(1)-factors of 0.0315 (1) and 0.0336 (2). Complex (1) is arranged as molecular Zn(4)(2,5-pydc)(4)(H(2)O)(10) tetramers, the cages of which define channels that remain unblocked by anions. Compound (2) is polymeric with Zn(2,5-pydc)(H(2)O)(2) and Zn(2,5-pydc)(H(2)O)(3) units linked through bridging ligands. Both compounds were synthesized under mild conditions in aqueous media, without need to resort to hydrothermal media. Changing the pH from 4.51 to 5.75 suffices to direct the chemical processes toward the orthorhombic compound rather than to the triclinic one.

Slicing the metric space to provide quick indexing of complex data in the main memory

Searching in a dataset for elements that are similar to a given query element is a core problem in applications that manage complex data, and has been aided by metric access methods (MAMs). A growing number of applications require indices that must be built faster and repeatedly, also providing faster response for similarity queries. The increase in the main memory capacity and its lowering costs also motivate using memory-based MAMs. In this paper. we propose the Onion-tree, a new and robust dynamic memory-based MAM that slices the metric space into disjoint subspaces to provide quick indexing of complex data. It introduces three major characteristics: (i) a partitioning method that controls the number of disjoint subspaces generated at each node; (ii) a replacement technique that can change the leaf node pivots in insertion operations; and (iii) range and k-NN extended query algorithms to support the new partitioning method, including a new visit order of the subspaces in k-NN queries. Performance tests with both real-world and synthetic datasets showed that the Onion-tree is very compact. Comparisons of the Onion-tree with the MM-tree and a memory-based version of the Slim-tree showed that the Onion-tree was always faster to build the index. The experiments also showed that the Onion-tree significantly improved range and k-NN query processing performance and was the most efficient MAM, followed by the MM-tree, which in turn outperformed the Slim-tree in almost all the tests. (C) 2010 Elsevier B.V. All rights reserved.

On maximizing measures of homeomorphisms on compact manifolds

We prove that given a compact n-dimensional connected Riemannian manifold X and a continuous function g : X -> R, there exists a dense subset of the space of homeomorphisms of X such that for all T in this subset, the integral integral(X) g d mu, considered as a function on the space of all T-invariant Borel probability measures mu, attains its maximum on a measure supported on a periodic orbit.

The C(K, X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

In this paper, we prove that if a Banach space X contains some uniformly convex subspace in certain geometric position, then the C(K, X) spaces of all X-valued continuous functions defined on the compact metric spaces K have exactly the same isomorphism classes that the C(K) spaces. This provides a vector-valued extension of classical results of Bessaga and Pelczynski (1960) [2] and Milutin (1966) [13] on the isomorphic classification of the separable C(K) spaces. As a consequence, we show that if 1 < p < q < infinity then for every infinite countable compact metric spaces K(1), K(2), K(3) and K(4) are equivalent: (a) C(K(1), l(p)) circle plus C(K(2), l(q)) is isomorphic to C(K(3), l(p)) circle plus (K(4), l(q)). (b) C(K(1)) is isomorphic to C(K(3)) and C(K(2)) is isomorphic to C(K(4)). (C) 2011 Elsevier Inc. All rights reserved.

NEW CHARACTERIZATIONS OF COMPLETE SPACELIKE SUBMANIFOLDS IN SEMI-RIEMANNIAN SPACE FORMS

In this paper we study n-dimensional complete spacelike submanifolds with constant normalized scalar curvature immersed in semi-Riemannian space forms. By extending Cheng-Yau`s technique to these ambients, we obtain results to such submanifolds satisfying certain conditions on both the squared norm of the second fundamental form and the mean curvature. We also characterize compact non-negatively curved submanifolds in De Sitter space of index p.

An indecomposable Banach space of continuous functions which has small density

Using the method of forcing we construct a model for ZFC where CH does not hold and where there exists a connected compact topological space K of weight omega(1) < 2(omega) such that every operator on the Banach space of continuous functions on K is multiplication by a continuous function plus a weakly compact operator. In particular, the Banach space of continuous functions on K is indecomposable.

TAUT REPRESENTATIONS OF COMPACT SIMPLE LIE GROUPS

The concept of taut submanifold of Euclidean space is due to Carter and West, and can be traced back to the work of Chern and Lashof on immersions with minimal total absolute curvature and the subsequent reformulation of that work by Kuiper in terms of critical point theory. In this paper, we classify the reducible representations of compact simple Lie groups, all of whose orbits are tautly embedded in Euclidean space, with respect to Z(2)-coefficients.

A FREE BOUNDARY ISOPERIMETRIC PROBLEM IN HYPERBOLIC 3-SPACE BETWEEN PARALLEL HOROSPHERES

We investigate the isoperimetric problem of finding the regions of prescribed volume with minimal boundary area between two parallel horospheres in hyperbolic 3-space (the part of the boundary contained in the horospheres is not included). We reduce the problem to the study of rotationally invariant regions and obtain the possible isoperimetric solutions by studying the behavior of the profile curves of the rotational surfaces with constant mean curvature in hyperbolic 3-space. We also classify all the connected compact rotational surfaces M of constant mean curvature that are contained in the region between two horospheres, have boundary partial derivative M either empty or lying on the horospheres, and meet the horospheres perpendicularly along their boundary.

Spherical space forms - Homotopy self-equivalences and homotopy types, the case of the groups Z/a x (Z/b x TL(2)(F(p)))

Let G = Z/a x(mu) (Z/b x TL(2)(F(p))) and X(n) be an n-dimensional CW-complex with the homotopy type of the n-sphere. We determine the automorphism group Aut(G) and then compute the number of distinct homotopy types of spherical space forms with respect to free and cellular G-actions on all CW-complexes X(2dn - 1), where 2d is a period of G. Next, the group E(X(2dn - 1)/alpha) of homotopy self-equivalences of spherical space forms X(2dn - 1)/alpha, associated with such G-actions alpha on X(2dn - 1) are studied. Similar results for the rest of finite periodic groups have been obtained recently and they are described in the introduction. (C) 2009 Elsevier B.V. All rights reserved.

Histological Outcomes on the Development of New Space-making Devices for Maxillary Sinus Floor Augmentation

Background: Previous studies have pointed out that the mere elevation of the maxillary sinus membrane promotes bone formation without the use of augmentation materials. Purpose: This experimental study aimed at evaluating if the two-stage procedure for sinus floor augmentation could benefit from the use of a space-making device in order to increase the bone volume to enable later implant installation with good primary stability. Materials and Methods: Six male tufted capuchin primates (Cebus apella) were subjected to extraction of the three premolars and the first molar on both sides of the maxilla to create an edentulous area. The sinuses were opened using the lateral bone-wall window technique, and the membrane was elevated. One resorbable space-making device was inserted in each maxillary sinus, and the bone window was returned in place. The animals were euthanatized after 6 months, and biopsy blocks containing the whole maxillary sinus and surrounding soft tissues were prepared for ground sections. Results: The histological examination of the specimens showed bone formation in contact with both the schneiderian membrane and the device in most cases even when the device was displaced. The process of bone formation indicates that this technique is potentially useful for two-stage sinus floor augmentation. The lack of stabilization of the device within the sinus demands further improvement of space-makers for predictable bone augmentation. Conclusions: It is concluded that (1) the device used in this study did not trigger any important inflammatory reaction; (2) when the sinus membrane was elevated, bone formation was a constant finding; and (3) an ideal space-making device should be stable and elevate the membrane to ensure a maintained connection between the membrane and the secluded space.

Unilateral Correction of Space Loss in the Mixed Dentition

Distalization of maxillary molars is indicated for correction of Class II dental malocclusion and for space gain in cases of space deficiency. The ideal treatment with an intraoral fixed appliance for molar distalization should fulfill the following requirements: patient compliance; acceptable esthetics; comfort; minimum anterior anchor loss (as evidenced by inclination of incisors); bodily movement of the molars to avoid undesirable effects and unstable outcomes; and minimum time required during sessions for placement and activations. The purpose of this paper was to present an alternative treatment for space recovery in the area of the maxillary right second premolar when there has been significant mesial movement of the permanent maxillary right first molar. We used a modified appliance that allows unilateral molar distalization in cases of unilateral tooth/arch size discrepancy using the opposite side as anchor, thus reducing the mesialization of the anterior teeth. (Pediatr Dent 2008;30:334-41) Received August 17, 2006 / Last Revision October 17, 2007 / Revision Accepted October 17, 2007

Contribution to the ground-based follow-up of the Gaia space mission

The Gaia Space Mission [Mignard, F., 2005. The three-dimensional universe with Gaia. ESA/SP-576; Perryman, M., 2005. The three-dimensional universe with Gaia. ESA/SP-576] will observe several transient events as supernovae, microlensing, gamma ray bursts and new Solar System objects. The satellite, due to its scanning law, will detect these events but will not be able to monitor them. So, to take these events into consideration and to perform further studies it is necessary to follow them with Earth-based observations. These observations could be efficiently done by a ground-based network of well-equipped telescopes scattered in both hemispheres. Here we focus our attention at the new Solar System objects to be discovered and observed by the Gaia satellite [Mignard, F., 2002. Observations of Solar System objects by Gaia I. Detection of NEOS. Astron. Astrophys. 393, 727] mainly asteroids, NEOs and comets. A dedicated ground-based network of telescopes as proposed by Thuillot [2005. The three-dimensional universe with Gaia. ESA/SP-576] will allow to monitor those events, to avoid losing them and to perform a quick characterization of some physical properties which will be important for the identification of these objects in further measurements by Gaia. We present in this paper, the beginning of the organization of a Latin-American ground-based network of telescopes and observers joining several institutions in Argentina, Bolivia, Brazil and other Latin-American countries aiming to contribute to the follow-up of Gaia science alerts for Solar System objects. (C) 2008 Elsevier Ltd. All rights reserved.