Microcalcification Border Characterization Using Wavelets on Digital Mammograms

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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)

Contrasting fluvial styles of the Paraguay River in the northwestern border of the Pantanal wetland, Brazil

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

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]

On the hardy space H¹ on products of half-spaces

We show that the Hardy space H¹ anal (R2+ x R2+) can be identified with the class of functions f such that f and all its double and partial Hubert transforms Hk f belong to L¹ (R2). A basic tool used in the proof is the bisubharmonicity of |F|q, where F is a vector field that satisfies a generalized conjugate system of Cauchy-Riemann type.

Mesoproterozoic rapakivi granites of the Rondonia Tin Province, southwestern border of the Amazonian craton, Brazil - I. Reconnaissance U-Pb geochronology and regional implications

Rapakivi granites and associated mafic and ultramafic rocks in the Rondonia Tin Province, southwestern Amazonian craton, Brazil were emplaced during six discrete episodes of magmatism between ca 1600 and 970 Ma. The seven rapakivi granite suites emplaced at this time were the Serra da Providencia Intrusive Suite (U-Pb ages between 1606 and 1532 Ma); Santo Antonio Intrusive Suite(U-Pb age 1406 Ma), Teotonio Intrusive Suite (U-Pb age 1387 Ma); Alto Candeias Intrusive Suite (U-Pb ages between 1346 and 1338 Ma); Sao Lourenco-Caripunas Intrusive Suite (U-Pb ages between 1314 and 1309 Ma); Santa Clara Intrusive Suite (U-Pb ages between 1082 and 1074 Ma); and Younger Granites of Rondonia (U-Pb ages between 998 and 974 Ma). The Serra da Providencia Intrusive Suite intruded the Paleoproterozoic (1.80 to 1.70 Ga) Rio Negro-Juruena crust whereas the other suites were emplaced into the 1.50 to 1.30 Ga Rondonia-San Ignacio crust. Their intrusion was contemporaneous with orogenic activity in other parts of the southwestern Amazonian craton, except for the oldest, Serra da Providencia Intrusive Suite. Orogenic events coeval with emplacement of the Serra da Providencia Intrusive Suite are not clearly recognized in the region. The Santo Antonio, Teotonio, Alto Candeias and Sao Lourenco-Caripunas Intrusive Suites are interpreted to represent extensional anorogenic magmatism associated with the terminal stages of the Rondonian-San Ignacio orogeny. At least the Sao Lourenco-Caripunas rapakivi granites and coeval intra-continental rift sedimentary rocks may, in contrast, represent the products of extensional tectonics and rifting preceding the Sunsas/Aguapei orogeny (1.25 to 1.0 Ga). The two youngest rapakivi suites, the Santa Clara Intrusive Suite and Younger Granites of Rondonia, seemingly represent inboard magmatism in the Rondonian-San Ignacio Province during a younger episode of reworking in the Rio Negro-Juruena Province during the waning stages of the collisional 1.1 to 1.0 Ga Sunsas/Aguapei orogeny. The six intra-plate rapakivi granite episodes in the southwestern part of the Amazonian craton form three broad periods of anorogenic magmatism that have age-correlative events composed of similar rocks and geologic environments in eastern Laurentia and Baltica, although the exact timing of magmatism appears slightly different. Recognition of lithologic and chronological correlations between various cratons provide important constraints to models explaining the interplay between rapakivi granite magmatism and deep crustal evolution of an early Mesoproterozoic supercontinent. They are, furthermore, important to plate tectonic models for the assembly, dispersal and reassembly of Amazonia, Laurentia and Baltica in the Mesoproterozoic and Neoproterozoic. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Discrete coherent states and probability distributions in finite-dimensional spaces

Operator bases are discussed in connection with the construction of phase space representatives of operators in finite-dimensional spaces, and their properties are presented. It is also shown how these operator bases allow for the construction of a finite harmonic oscillator-like coherent state. Creation and annihilation operators for the Fock finite-dimensional space are discussed and their expressions in terms of the operator bases are explicitly written. The relevant finite-dimensional probability distributions are obtained and their limiting behavior for an infinite-dimensional space are calculated which agree with the well known results. (C) 1996 Academic Press, Inc.

Dynamics in discrete phase spaces and time interval operators

The von Neumann-Liouville time evolution equation is represented in a discrete quantum phase space. The mapped Liouville operator and the corresponding Wigner function are explicitly written for the problem of a magnetic moment interacting with a magnetic field and the precessing solution is found. The propagator is also discussed and a time interval operator, associated to a unitary operator which shifts the energy levels in the Zeeman spectrum, is introduced. This operator is associated to the particular dynamical process and is not the continuous parameter describing the time evolution. The pair of unitary operators which shifts the time and energy is shown to obey the Weyl-Schwinger algebra. (C) 1999 Elsevier B.V. B.V. All rights reserved.