Spectral analysis and the Aharonov-Bohm\~ effect on certain almost-Riemannian manifold

We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalised Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

Impact of a Fram Strait cyclone on ice edge, drift, divergence, and concentration: Possibilities and limits of an observational analysis

This study aims at the determination of a Fram Strait cyclone track and of the cyclone’s impact on ice edge, drift, divergence, and concentration. A 24 h period on 13–14 March 2002 framed by two RADARSAT images is analyzed. Data are included from autonomous ice buoys, a research vessel, Special Sensor Microwave Imager (SSM/I) and QuikSCAT satellite, and the operational European Centre for Medium-Range Weather Forecasts (ECMWF) model. During this 24 h period the cyclone moved northward along the western ice edge in the Fram Strait, crossed the northern ice edge, made a left-turn loop with 150 km diameter over the sea ice, and returned to the northern ice edge. The ECMWF analysis places the cyclone track 100 km too far west over the sea ice, a deviation which is too large for representative sea ice simulations. On the east side of the northward moving cyclone, the ice edge was pushed northward by 55 km because of strong winds. On the rear side, the ice edge advanced toward the open water but by a smaller distance because of weaker winds there. The ice drift pattern as calculated from the ice buoys and the two RADARSAT images is cyclonically curved around the center of the cyclone loop. Ice drift divergence shows a spatial pattern with divergence in the loop center and a zone of convergence around. Ice concentration changes as retrieved from SSM/I data follow the divergence pattern such that sea ice concentration increased in areas of divergence and decreased in areas of convergence.

Cloud information content analysis of multi-angular measurements in the oxygen A-band: application to 3MI and MSPI

The vertical distribution of cloud cover has a significant impact on a large number of meteorological and climatic processes. Cloud top altitude and cloud geometrical thickness are then essential. Previous studies established the possibility of retrieving those parameters from multi-angular oxygen A-band measurements. Here we perform a study and comparison of the performances of future instruments. The 3MI (Multi-angle, Multi-channel and Multi-polarization Imager) instrument developed by EUMETSAT, which is an extension of the POLDER/PARASOL instrument, and MSPI (Multi-angles Spectro-Polarimetric Imager) develoloped by NASA's Jet Propulsion Laboratory will measure total and polarized light reflected by the Earth's atmosphere–surface system in several spectral bands (from UV to SWIR) and several viewing geometries. Those instruments should provide opportunities to observe the links between the cloud structures and the anisotropy of the reflected solar radiation into space. Specific algorithms will need be developed in order to take advantage of the new capabilities of this instrument. However, prior to this effort, we need to understand, through a theoretical Shannon information content analysis, the limits and advantages of these new instruments for retrieving liquid and ice cloud properties, and especially, in this study, the amount of information coming from the A-Band channel on the cloud top altitude (CTOP) and geometrical thickness (CGT). We compare the information content of 3MI A-Band in two configurations and that of MSPI. Quantitative information content estimates show that the retrieval of CTOP with a high accuracy is possible in almost all cases investigated. The retrieval of CGT seems less easy but possible for optically thick clouds above a black surface, at least when CGT > 1–2 km.

ON THE NATURE OF THE PROTOTYPE LUMINOUS BLUE VARIABLE AG CARINAE. II. WITNESSING A MASSIVE STAR EVOLVING CLOSE TO THE EDDINGTON AND BISTABILITY LIMITS

We show that the significantly different effective temperatures (T(eff)) achieved by the luminous blue variable AG Carinae during the consecutive visual minima of 1985-1990 (T(eff) similar or equal to 22,800 K) and 2000-2001 (T(eff) similar or equal to 17,000 K) place the star on different sides of the bistability limit, which occurs in line-driven stellar winds around T(eff) similar to 21,000 K. Decisive evidence is provided by huge changes in the optical depth of the Lyman continuum in the inner wind as T(eff) changes during the S Dor cycle. These changes cause different Fe ionization structures in the inner wind. The bistability mechanism is also related to the different wind parameters during visual minima: the wind terminal velocity was 2-3 times higher and the mass-loss rate roughly two times smaller in 1985-1990 than in 2000-2003. We obtain a projected rotational velocity of 220 +/- 50 km s(-1) during 1985-1990 which, combined with the high luminosity (L(star) = 1.5 x 10(6) L(circle dot)), puts AG Car extremely close to the Eddington limit modified by rotation (Omega Gamma limit): for an inclination angle of 90 degrees, Gamma(Omega) greater than or similar to 1.0 for M(circle dot) less than or similar to 60. Based on evolutionary models and mass budget, we obtain an initial mass of similar to 100 M(circle dot) and a current mass of similar to 60-70 M(circle dot) for AG Car. Therefore, AG Car is close to, if not at, the Omega Gamma limit during visual minimum. Assuming M = 70 M(circle dot), we find that Gamma(Omega) decreases from 0.93 to 0.72 as AG Car expands toward visual maximum, suggesting that the star is not above the Eddington limit during maximum phases.

Phylogeny, species limits, and biogeography of the Brazilian lizards of the genus Eurolophosaurus (Squamata : Tropiduridae) as inferred from mitochondrial DNA sequences

Phylogenetic relationships and divergence times for 10 populations of the three recognized ""species"" of Brazilian lizards of genus Eurolophosaurus were estimated from 1229 bp of cyt b, COI, 12S, and 16S rRNA mitochondrial gene segments. Eurolophosaurus is monophyletic and the basal split within the genus separates E divaricatus from a clade comprising E amathites and E nanuzae. Three populations of E divaricatus, which occurs along the western bank of Rio S (a) over tildeo Francisco, were consistently grouped together. Oil the east bank of the river, E amathites and E nanuzae from state of Bahia were recovered as the sister group of E nanuzae populations from state of Minas Gerais. The paraphyly of E nanuzae and the high divergence levels among populations of E divaricatus strongly suggest that species limits in Eurolophosaurus should be revised. Even considering an extreme evolutionary rate of 2.8% sequence divergence per million years for the four gene segments analyzed together, E. divaricatus would have separated from the two other species by at least 5.5 my ago, and E. amathites from E nanuzae populations from Bahia and Minas Gerais, respectively, by 1.5 and 3.5 my. The paleolacustrine hypothesis and changes in the course of the river potentially explain faunal divergence in the area, but divergences are much older than previously admitted. (C) 2007 Elsevier Inc. All rights reserved.

Non-autonomous semilinear evolution equations with almost sectorial operators

Inspired by the theory of semigroups of growth a, we construct an evolution process of growth alpha. The abstract theory is applied to study semilinear singular non-autonomous parabolic problems. We prove that. under natural assumptions. a reasonable concept of solution can be given to Such semilinear singularly non-autonomous problems. Applications are considered to non-autonomous parabolic problems in space of Holder continuous functions and to a parabolic problem in a domain Omega subset of R(n) with a one dimensional handle.

Dynamics of a class of ODEs more general than almost periodic

A temporally global solution, if it exists, of a nonautonomous ordinary differential equation need not be periodic, almost periodic or almost automorphic when the forcing term is periodic, almost periodic or almost automorphic, respectively. An alternative class of functions extending periodic and almost periodic functions which has the property that a bounded temporally global solution solution of a nonautonomous ordinary differential equation belongs to this class when the forcing term does is introduced here. Specifically, the class of functions consists of uniformly continuous functions, defined on the real line and taking values in a Banach space, which have pre-compact ranges. Besides periodic and almost periodic functions, this class also includes many nonrecurrent functions. Assuming a hyperbolic structure for the unperturbed linear equation and certain properties for the linear and nonlinear parts, the existence of a special bounded entire solution, as well the existence of stable and unstable manifolds of this solution are established. Moreover, it is shown that this solution and these manifolds inherit the temporal behaviour of the vector field equation. In the stable case it is shown that this special solution is the pullback attractor of the system. A class of infinite dimensional examples involving a linear operator consisting of a time independent part which generates a C(0)-semigroup plus a small time dependent part is presented and applied to systems of coupled heat and beam equations. (C) 2010 Elsevier Ltd. All rights reserved.

Paper surfaces and dynamical limits

It is very common in mathematics to construct surfaces by identifying the sides of a polygon together in pairs: For example, identifying opposite sides of a square yields a torus. In this article the construction is considered in the case where infinitely many pairs of segments around the boundary of the polygon are identified. The topological, metric, and complex structures of the resulting surfaces are discussed: In particular, a condition is given under which the surface has a global complex structure (i.e., is a Riemann surface). In this case, a modulus of continuity for a uniformizing map is given. The motivation for considering this construction comes from dynamical systems theory: If the modulus of continuity is uniform across a family of such constructions, each with an iteration defined on it, then it is possible to take limits in the family and hence to complete it. Such an application is briefly discussed.

LIMITS OF TILTING MODULES

We study the problem of when a direct limit of tilting modules is still a tilting module.

On the composite of irreducible morphisms in almost sectional paths

We study here when the composite of it irreducible morphisms in almost sectional paths is non-zero and lies in Rn+1 (C) 2007 Elsevier B.V. All rights reserved.

The bar-radical of a class of almost alternative baric algebras

In this article we prove that, if (U, ) is a finite dimensional baric algebra of (gamma, delta) type over a field F of characteristic not equal 2,3,5 such that gamma(2) - delta(2) + delta = 1 and 0,1, then rad(U) = R(U)boolean AND(bar(U))(2), where R(U) is the nilradical (maximal nil ideal) of U.

Geodesics and Almost Geodesic Cycles in Random Regular Graphs

A geodesic in a graph G is a shortest path between two vertices of G. For a specific function e(n) of n, we define an almost geodesic cycle C in G to be a cycle in which for every two vertices u and v in C, the distance d(G)(u, v) is at least d(C)(u, v) - e(n). Let omega(n) be any function tending to infinity with n. We consider a random d-regular graph on n vertices. We show that almost all pairs of vertices belong to an almost geodesic cycle C with e(n)= log(d-1)log(d-1) n+omega(n) and vertical bar C vertical bar =2 log(d-1) n+O(omega(n)). Along the way, we obtain results on near-geodesic paths. We also give the limiting distribution of the number of geodesics between two random vertices in this random graph. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 66: 115-136, 2011

Applicatiion of Almost ideal demand system for a pharmaceutical

This thesis is an application of the Almost Ideal Demand System approach of Deaton and Muellbauer,1980, for a particular pharmaceutical, Citalopram, in which GORMAN´s (1971) multi-stage budgeting approach is applied basically since it is one of the most useful approach in estimating demand for differentiated products. Citalopram is an antidepressant drug that is used in the treatment of major depression. As for most other pharmaceuticals whose the patent has expired, there exist branded and generic versions of Citalopram. This paper is aimed to define its demand system with two stage models for the branded version and five generic versions, and to show whether generic versions are able to compete with the branded version. I calculated the own price elasticities, and it made me possible to compare and make a conclusion about the consumers’ choices over the brand and generic drugs. Even though the models need for being developed with some additional variables, estimation results of models and uncompensated price elasticities indicated that the branded version has still power in the market, and generics are able to compete with lower prices. One important point that has to be taken into consideration is that the Swedish pharmaceutical market faced a reform on October 1, 2002, that aims to make consumer better informed about the price and decrease the overall expenditures for pharmaceuticals. Since there were not significantly enough generic sales to take into calculation before the reform, my paper covers sales after the reform.

Limits to phase resolution in matter-wave interferometry

We study the quantum dynamics of a two-mode Bose-Einstein condensate in a time-dependent symmetric double-well potential using analytical and numerical methods. The effects of internal degrees of freedom on the visibility of interference fringes during a stage of ballistic expansion are investigated varying particle number, nonlinear interaction sign and strength, as well as tunneling coupling. Expressions for the phase resolution are derived and the possible enhancement due to squeezing is discussed. In particular, the role of the superfluid-Mott insulator crossover and its analog for attractive interactions is recognized.