Estimates for the Poisson kernel and Hardy spaces on compact manifolds

We study Hardy spaces on the boundary of a smooth open subset or R-n and prove that they can be defined either through the intrinsic maximal function or through Poisson integrals, yielding identical spaces. This extends to any smooth open subset of R-n results already known for the unit ball. As an application, a characterization of the weak boundary values of functions that belong to holomorphic Hardy spaces is given, which implies an F. and M. Riesz type theorem. (C) 2004 Elsevier B.V. All rights reserved.

Reversibility properties of semigroup actions on homogeneous spaces

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

Cauchy-Stieltjes Integral on Time Scales in Banach Spaces and Hysteresis Operators

The play operator has a fundamental importance in the theory of hysteresis. It was studied in various settings as shown by P. Krejci and Ph. Laurencot in 2002. In that work it was considered the Young integral in the frame of Hilbert spaces. Here we study the play in the frame of the regulated functions (that is: the ones having only discontinuities of the first kind) on a general time scale T (that is: with T being a nonempty closed set of real numbers) with values in a Banach space. We will be showing that the dual space in this case will be defined as the space of operators of bounded semivariation if we consider as the bilinearity pairing the Cauchy-Stieltjes integral on time scales.

Ectopic mineralization of articular cartilage in the bullfrog Rana catesbeiana and its possible involvement in bone closure

Mineralization of the articular cartilage is a pathological condition associated with age and certain joint diseases in humans and other mammals. In this work, we describe a physiological process of articular cartilage mineralization in bullfrogs. Articular cartilage of the proximal and distal ends of the femur and of the proximal end of the tibia-fibula was studied in animals of different ages. Mineralization of the articular cartilage was detected in animals at 1 month post-transformation. This mineralization, which appeared before the hypertrophic cartilage showed any calcium deposition, began at a restricted site in the lateral expansion of the cartilage and then progressed to other areas of the epiphyseal cartilage. Mineralized structures were identified by von Kossa's staining and by in vivo incorporation of calcein green. Element analysis showed that calcium crystals consisted of poorly crystalline hydroxyapatite. Mineralized matrix was initially spherical structures that generally coalesced after a certain size to occupy larger areas of the cartilage. Alkaline phosphatase activity was detected at the plasma membrane of nearby chondrocytes and in extracellular matrix. Apoptosis was detected by the TUNEL (TDT-mediated dUTP-biotin nick end-labeling) reaction in some articular chondrocytes from mineralized areas. The area occupied by calcium crystals increased significantly in older animals, especially in areas under compression. Ultrastructural analyses showed clusters of needle-like crystals in the extracellular matrix around the chondrocytes and large blocks of mineralized matrix. In 4-year-old animals, some lamellar bone (containing bone marrow) occurred in the same area as articular cartilage mineralization. These results show that the articular cartilage of R. catesbeiana undergoes precocious and progressive mineralization that is apparently stimulated by compressive forces. We suggest that this mineralization is involved in the closure of bone extremities, since mineralization appears to precede the formation of a rudimentary secondary center of ossification in older animals.

Integrable aspects of the scaling q-state Potts models I: bound states and bootstrap closure

We discuss the q-state Potts models for q less than or equal to 4, in the scaling regimes close to their critical or tricritical points. Starting from the kink S-matrix elements proposed by Chim and Zamolodchikov, the bootstrap is closed for the scaling regions of all critical points, and for the tricritical points when 4 > q greater than or equal to 2. We also note a curious appearance of the extended last line of Freudenthal's magic square in connection with the Potts models. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Quasiprobability distribution functions for periodic phase spaces: I. Theoretical aspects

An approach featuring s-parametrized quasiprobability distribution functions is developed for situations where a circular topology is observed. For such an approach, a suitable set of angle - angular momentum coherent states must be constructed in an appropriate fashion.

Schwinger and Pegg-Barnett approaches and a relationship between angular and Cartesian quantum descriptions: II. Phase spaces

Following the discussion-in state-space language-presented in a preceding paper, we work on the passage from the phase-space description of a degree of freedom described by a finite number of states (without classical counterpart) to one described by an infinite (and continuously labelled) number of states. With this it is possible to relate an original Schwinger idea to the Pegg-Barnett approach to the phase problem. In phase-space language, this discussion shows that one can obtain the Weyl-Wigner formalism, for both Cartesian and angular coordinates, as limiting elements of the discrete phase-space formalism.

Extended Cahill-Glauber formalism for finite-dimensional spaces. II. Applications in quantum tomography and quantum teleportation

By means of a mod(N)-invariant operator basis, s-parametrized phase-space functions associated with bounded operators in a finite-dimensional Hilbert space are introduced in the context of the extended Cahill-Glauber formalism, and their properties are discussed in details. The discrete Glauber-Sudarshan, Wigner, and Husimi functions emerge from this formalism as specific cases of s-parametrized phase-space functions where, in particular, a hierarchical process among them is promptly established. In addition, a phase-space description of quantum tomography and quantum teleportation is presented and new results are obtained.

Discrete squeezed states for finite-dimensional spaces

We show how discrete squeezed states in an N-2-dimensional phase space can be properly constructed out of the finite-dimensional context. Such discrete extensions are then applied to the framework of quantum tomography and quantum information theory with the aim of establishing an initial study on the interference effects between discrete variables in a finite phase space. Moreover, the interpretation of the squeezing effects is seen to be direct in the present approach, and has some potential applications in different branches of physics.

Extended Cahill-Glauber formalism for finite-dimensional spaces: I. Fundamentals

The Cahill-Glauber approach for quantum mechanics on phase space is extended to the finite-dimensional case through the use of discrete coherent states. All properties and features of the continuous formalism are appropriately generalized. The continuum results are promptly recovered as a limiting case. The Jacobi theta functions are shown to have a prominent role in the context.

Quasiprobability distribution functions for finite-dimensional discrete phase spaces: Spin-tunneling effects in a toy model

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Curves in homogeneous spaces and their contact with 1-dimensional orbits

Let alpha be a C(infinity) curve in a homogeneous space G/H. For each point x on the curve, we consider the subspace S(k)(alpha) of the Lie algebra G of G consisting of the vectors generating a one parameter subgroup whose orbit through x has contact of order k with alpha. In this paper, we give various important properties of the sequence of subspaces G superset of S(1)(alpha) superset of S(2)(alpha) superset of S(3)(alpha) superset of ... In particular, we give a stabilization property for certain well-behaved curves. We also describe its relationship to the isotropy subgroup with respect to the contact element of order k associated with alpha.

Lower bounds on blow up solutions of the three-dimensional Navier-Stokes equations in homogeneous Sobolev spaces

Suppose that u(t) is a solution of the three-dimensional Navier-Stokes equations, either on the whole space or with periodic boundary conditions, that has a singularity at time T. In this paper we show that the norm of u(T - t) in the homogeneous Sobolev space (H)over dot(s) must be bounded below by c(s)t(-(2s-1)/4) for 1/2 < s < 5/2 (s not equal 3/2), where c(s) is an absolute constant depending only on s; and by c(s)parallel to u(0)parallel to((5-2s)/5)(L2)t(-2s/5) for s > 5/2. (The result for 1/2 < s < 3/2 follows from well-known lower bounds on blowup in Lp spaces.) We show in particular that the local existence time in (H)over dot(s)(R-3) depends only on the (H)over dot(s)-norm for 1/2 < s < 5/2, s not equal 3/2. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4762841]

Oroantral communication closure using a pedicled buccal fat pad graft

OBJETIVO: O objetivo desde artigo foi relatar um caso clínico de fechamento de fístula buco-sinusal tardia utilizando rotação de enxerto de tecido adiposo pediculado do corpo adiposo da bochecha. DESCRIÇÃO do CASO: Paciente do sexo masculino, 66 anos, leucoderma, em boas condições de saúde geral, foi encaminhado para fechamento de extensa comunicação buco-sinusal. Ao exame clínico, observou-se uma fístula de aproximadamente 10 mm de diâmetro comunicando a cavidade oral com o seio maxilar. A cirurgia foi realizada em nível ambulatorial, sob anestesia local, para fechar a fístula buco-sinusal com um enxerto de tecido adiposo pediculado do corpo adiposo da bochecha. A reparação da ferida e o fechamento do defeito foram observados no pós-operatório de 30 dias, com completa epitelização. CONCLUSÃO: O enxerto pediculado de tecido do corpo adiposo da bochecha mostrou-se uma alternativa simples, eficaz e segura no fechamento mediato da fístula buco-sinusal apresentada neste caso clínico.

Radiographic study of distal radial physeal closure in thoroughbred horses

Monthly radiography was performed to study distal radial physeal closure in ten male and ten female Throughbred horses. The height, thoracic circumference and metacarpus circumference were also measured, Distal radial physeal closure time was sooner in females than males, and took 701 +/- 37 and 748 +/- 55 days respectively.