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.

Compact stacked planar inverted-F antenna for passive deep brain stimulation implants

A compact meandered three-layer stacked circular planar inverted-F antenna is designed and simulated at the UHF band (902.75 – 927.25 MHz) for passive deep brain stimulation implants. The UHF band is used because it offers small antenna size, and high data rate. The top and middle radiating layers are meandered, and low cost substrate and superstrate materials are used to limit the radius and height of the antenna to 5 mm and 1.64 mm, respectively. A dielectric substrate of FR-4 of εr= 4.7 and δ= 0.018, and a biocompatible superstrate of silicone of er= 3.7 and d= 0.003 with thickness of 0.2 mm are used in the design. The resonance frequency of the proposed antenna is 918 MHz with a bandwidth of 24 MHz at return loss of −10 dB in free space. The antenna parameter such as 3D gain pattern of the designed antenna within a skin-tissue model is evaluated by using the finite element method. The compactness, wide bandwidth, round shape, and stable characteristics in skin make this antenna suitable for DBS. The feasibility of the wireless power transmission to the implant in the human head is also examined.

Spinoza/space/speed/sublime: Problems of philosophy and politics in the post-colonial fiction of Gerald Murnane

This article takes account of the ‘spontaneity’ of the post-colonial fiction of Gerald Murnane within the ‘dominating space’ of the philosophy of Spinoza. My use of Paul Carter’s terms here is strategic. The compact of fiction and philosophy in Murnane corresponds with the relationship of spontaneity to the dominating organization of desire in Carter’s rendering of an Aboriginal hunter. Carter’s phrase “‘a figure at once spontaneous and wholly dominated by the space of his desire’” worries Ken Gelder and Jane M. Jacobs, who suggest that it subjugates the formation of Aboriginal desire (incorporating spontaneity) to impulses of imperialism. The captivating immanence of Spinoza’s philosophy in Murnane’s fiction, which I will demonstrate with various examples, puts pressure on the fiction to occupy the same space as the space of the philosophy. Here is a clue to why Murnane’s post-colonial thematics have been little explored by critics with an interest in post-colonial politics. The desire of Spinoza’s philosophy creates a spatial textuality within which the spontaneity of Murnane’s fiction, to the degree that it maximizes or fills the philosophy, is minimized in its political effects. That is to say, the fiction shifts politics into an external space of what Roland Barthes calls “resistance or condemnation”. However, the different speeds (or timings) of Murnane and Spinoza, within the one space, mitigate this resistance of the outside, at least in respect of certain circumstances of post-coloniality. It is especially productive, I suggest, to engage Carter’s representation of an Aboriginal hunter through the compact of coincidental spaces and differential speeds created by Murnane’s fiction in Spinoza’s philosophy. This produces a ceaseless activation of desire and domination, evidenced in Murnane’s short story ‘Land Deal’, and indexed by a post-Romantic sublime. What limits the value of Murnane’s fiction in most contexts of post-colonial politics, is precisely what makes it useful in the matter of Carter’s Aboriginal hunter.

Development of a compact rectenna for wireless powering of a head-mountable deep brain stimulation device

Design of a rectangular spiral planar inverted-F antenna (PIFA) at 915 MHz for wireless power transmission applications is proposed. The antenna and rectifying circuitry form a rectenna, which can produce dc power from a distant radio frequency energy transmitter. The generated dc power is used to operate a low-power deep brain stimulation pulse generator. The proposed antenna has the dimensions of 10 mm × 12.5 mm × 1.5 mm and resonance frequency of 915 MHz with a measured bandwidth of 15 MHz at return loss of -10 dB. A dielectric substrate of FR-4 of εr = 4.8 and δ = 0.015 with thickness of 1.5 mm is used for both antenna and rectifier circuit simulation and fabrication because of its availability and low cost. An L-section impedance matching circuit is used between the PIFA and voltage doubler rectifier. The impedance matching circuit also works as a low-pass filter for elimination of higher order harmonics. Maximum dc voltage at the rectenna output is 7.5 V in free space and this rectenna can drive a deep brain stimulation pulse generator at a distance of 30 cm from a radio frequency energy transmitter, which transmits power of 26.77 dBm.

Distinct kinetics of molecular gelation in a confined space and its relation to the structure and property of thin gel films

Thin films of molecular gels formed in a confined space have potential applications in transdermal delivery, artificial skin, molecular electronics, etc. The microstructures and properties of thin gel films can be significantly different from those of their bulk counterparts. However, so far a comprehensive understanding of the effects of spatial confinement on the molecular gelation kinetics, fiber network structure and related mechanical properties is still lacking. In this work, using rheological techniques, we investigated the effect of one-dimensional confinement on the formation kinetics of fiber networks in the molecular gelation process. Fractal analyses of the kinetic information in terms of an extended Dickinson model enabled us to describe quantitatively the distinct kinetic signature of molecular gelation. The structural features derived from gelation kinetics support well the fractal patterns of the fiber networks acquired by optical and electron microscopy. With the kinetics-structure correlation, we can gain an in-depth understanding of the confinement-induced differences in the structure and consequently the mechanical properties of a model molecular gelling system. Particularly, the confinement induced structural transition, from a three-dimensional, dense and compact spherulitic network composed of highly branched fibers to a quasi-two-dimensional sparse spherulitic network composed of less branched fibers and entangled fibrils at the boundary areas, renders a gel film to become less stiff but more ductile. Our study suggests here a new strategy of engineering the fiber network microstructure to achieve functional gel films with unusual but useful properties.

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.