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.

Instability of nonminimally coupled scalar fields in the spacetime of slowly rotating compact objects

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Compact groups of galaxies selected by stellar mass: the 2MASS compact group catalogue

We present a photometric catalogue of compact groups of galaxies (p2MCGs) automatically extracted from the Two-Micron All Sky Survey (2MASS) extended source catalogue. A total of 262 p2MCGs are identified, following the criteria defined by Hickson, of which 230 survive visual inspection (given occasional galaxy fragmentation and blends in the 2MASS parent catalogue). Only one quarter of these 230 groups were previously known compact groups (CGs). Among the 144 p2MCGs that have all their galaxies with known redshifts, 85 (59?per cent) have four or more accordant galaxies. This v2MCG sample of velocity-filtered p2MCGs constitutes the largest sample of CGs (with N = 4) catalogued to date, with both well-defined selection criteria and velocity filtering, and is the first CG sample selected by stellar mass. It is fairly complete up to Kgroup similar to 9 and radial velocity of similar to 6000?km?s-1. We compared the properties of the 78 v2MCGs with median velocities greater than 3000?km?s-1 with the properties of other CG samples, as well as those (mvCGs) extracted from the semi-analytical model (SAM) of Guo et al. run on the high-resolution Millennium-II simulation. This mvCG sample is similar (i.e. with 2/3 of physically dense CGs) to those we had previously extracted on three other SAMs run on the Millennium simulation with 125 times worse spatial and mass resolutions. The space density of v2MCGs within 6000?km?s-1 is 8.0 X 10-5?h3?Mpc-3, i.e. four times that of the Hickson sample [Hickson Compact Group (HCG)] up to the same distance and with the same criteria used in this work, but still 40?per cent less than that of mvCGs. The v2MCG constitutes the first group catalogue to show a statistically large firstsecond ranked galaxy magnitude gap according to TremaineRichstone statistics, as expected if the first ranked group members tend to be the products of galaxy mergers, and as confirmed in the mvCGs. The v2MCG is also the first observed sample to show that first-ranked galaxies tend to be centrally located, again consistent with the predictions obtained from mvCGs. We found no significant correlation of group apparent elongation and velocity dispersion in the quartets among the v2MCGs, and the velocity dispersions of apparently round quartets are not significantly larger than those of chain-like ones, in contrast to what has been previously reported in HCGs. By virtue of its automatic selection with the popular Hickson criteria, its size, its selection on stellar mass, and its statistical signs of mergers and centrally located brightest galaxies, the v2MCG catalogue appears to be the laboratory of choice to study physically dense groups of four or more galaxies of comparable luminosity.

Transiting exoplanets from the CoRoT space mission XX. CoRoT-20b: A very high density, high eccentricity transiting giant planet

We report the discovery by the CoRoT space mission of a new giant planet, CoRoT-20b. The planet has a mass of 4.24 +/- 0.23 M-Jup and a radius of 0.84 +/- 0.04 R-Jup. With a mean density of 8.87 +/- 1.10 g cm(-3), it is among the most compact planets known so far. Evolutionary models for the planet suggest a mass of heavy elements of the order of 800 M-circle plus if embedded in a central core, requiring a revision either of the planet formation models or both planet evolution and structure models. We note however that smaller amounts of heavy elements are expected by more realistic models in which they are mixed throughout the envelope. The planet orbits a G-type star with an orbital period of 9.24 days and an eccentricity of 0.56. The star's projected rotational velocity is v sin i = 4.5 +/- 1.0 km s(-1), corresponding to a spin period of 11.5 +/- 3.1 days if its axis of rotation is perpendicular to the orbital plane. In the framework of Darwinian theories and neglecting stellar magnetic breaking, we calculate the tidal evolution of the system and show that CoRoT-20b is presently one of the very few Darwin-stable planets that is evolving toward a triple synchronous state with equality of the orbital, planetary and stellar spin periods.

Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.

An Efficient Hybrid GO-PWS Algorithm to Analyze Conformal Serrated-Edge Reflectors for Millimeter-Wave Compact Range

A method to analyze parabolic reflectors with arbitrary piecewise rim is presented in this communication. This kind of reflectors, when operating as collimators in compact range facilities, needs to be large in terms of wavelength. Their analysis is very inefficient, when it is carried out with fullwave/MoM techniques, and it is not very appropriate for designing with PO techniques. Also, fast GO formulations do not offer enough accuracy to reach performance results. The proposed algorithm is based on a GO-PWS hybrid scheme, using analytical as well as non-analytical formulations. On one side, an analytical treatment of the polygonal rim reflectors is carried out. On the other side, non-analytical calculi are based on efficient operations, such as M2 order 2-dimensional FFT. A combination of these two techniques in the algorithm ensures real ad-hoc design capabilities, reached through analysis speedup. The purpose of the algorithm is to obtain an optimal conformal serrated-edge reflector design through the analysis of the field quality within the quiet zone that it is able to generate in its forward half space.

CANDELS: The progenitors of compact quiescent galaxies at z ~ 2

We combine high-resolution Hubble Space Telescope/WFC3 images with multi-wavelength photometry to track the evolution of structure and activity of massive (M_*> 10^10 M_☉) galaxies at redshifts z = 1.4-3 in two fields of the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey. We detect compact, star-forming galaxies (cSFGs) whose number densities, masses, sizes, and star formation rates (SFRs) qualify them as likely progenitors of compact, quiescent, massive galaxies (cQGs) at z = 1.5-3. At z≲2, cSFGs present SFR = 100-200 M_☉ yr^–1, yet their specific star formation rates (sSFR ~ 10^–9 yr^–1) are typically half that of other massive SFGs at the same epoch, and host X-ray luminous active galactic nuclei (AGNs) 30 times (~30%) more frequently. These properties suggest that cSFGs are formed by gas-rich processes (mergers or disk-instabilities) that induce a compact starburst and feed an AGN, which, in turn, quench the star formation on dynamical timescales (few 10^8 yr). The cSFGs are continuously being formed at z = 2-3 and fade to cQGs down to z ~ 1.5. After this epoch, cSFGs are rare, thereby truncating the formation of new cQGs. Meanwhile, down to z = 1, existing cQGs continue to enlarge to match local QGs in size, while less-gas-rich mergers and other secular mechanisms shepherd (larger) SFGs as later arrivals to the red sequence. In summary, we propose two evolutionary tracks of QG formation: an early (z≲2), formation path of rapidly quenched cSFGs fading into cQGs that later enlarge within the quiescent phase, and a late-arrival (z≳2) path in which larger SFGs form extended QGs without passing through a compact state.

Lipschitz compact operators

We introduce the notion of Lipschitz compact (weakly compact, finite-rank, approximable) operators from a pointed metric space X into a Banach space E. We prove that every strongly Lipschitz p-nuclear operator is Lipschitz compact and every strongly Lipschitz p-integral operator is Lipschitz weakly compact. A theory of Lipschitz compact (weakly compact, finite-rank) operators which closely parallels the theory for linear operators is developed. In terms of the Lipschitz transpose map of a Lipschitz operator, we state Lipschitz versions of Schauder type theorems on the (weak) compactness of the adjoint of a (weakly) compact linear operator.

Fast algorithms for automatic mapping with space-limited covariance functions

In this paper we discuss a fast Bayesian extension to kriging algorithms which has been used successfully for fast, automatic mapping in emergency conditions in the Spatial Interpolation Comparison 2004 (SIC2004) exercise. The application of kriging to automatic mapping raises several issues such as robustness, scalability, speed and parameter estimation. Various ad-hoc solutions have been proposed and used extensively but they lack a sound theoretical basis. In this paper we show how observations can be projected onto a representative subset of the data, without losing significant information. This allows the complexity of the algorithm to grow as O(n m 2), where n is the total number of observations and m is the size of the subset of the observations retained for prediction. The main contribution of this paper is to further extend this projective method through the application of space-limited covariance functions, which can be used as an alternative to the commonly used covariance models. In many real world applications the correlation between observations essentially vanishes beyond a certain separation distance. Thus it makes sense to use a covariance model that encompasses this belief since this leads to sparse covariance matrices for which optimised sparse matrix techniques can be used. In the presence of extreme values we show that space-limited covariance functions offer an additional benefit, they maintain the smoothness locally but at the same time lead to a more robust, and compact, global model. We show the performance of this technique coupled with the sparse extension to the kriging algorithm on synthetic data and outline a number of computational benefits such an approach brings. To test the relevance to automatic mapping we apply the method to the data used in a recent comparison of interpolation techniques (SIC2004) to map the levels of background ambient gamma radiation. © Springer-Verlag 2007.

Sparse signal representation by adaptive non-uniform B-spline dictionaries on a compact interval

Non-uniform B-spline dictionaries on a compact interval are discussed in the context of sparse signal representation. For each given partition, dictionaries of B-spline functions for the corresponding spline space are built up by dividing the partition into subpartitions and joining together the bases for the concomitant subspaces. The resulting slightly redundant dictionaries are composed of B-spline functions of broader support than those corresponding to the B-spline basis for the identical space. Such dictionaries are meant to assist in the construction of adaptive sparse signal representation through a combination of stepwise optimal greedy techniques.