Equações de diferenças: aplicações no ensino médio

Pós-graduação em Matemática em Rede Nacional - IBILCE

Alternate treatments of jacobian singularities in polar coordinates within finite-difference schemes

Jacobian singularities of differential operators in curvilinear coordinates occur when the Jacobian determinant of the curvilinear-to-Cartesian mapping vanishes, thus leading to unbounded coefficients in partial differential equations. Within a finite-difference scheme, we treat the singularity at the pole of polar coordinates by setting up complementary equations. Such equations are obtained by either integral or smoothness conditions. They are assessed by application to analytically solvable steady-state heat-conduction problems.

Amostragem de terra para fins de fertilidade em função da ferramenta de amostragem

Embora existam indicações de que a pá de corte proporcione melhor qualidade de amostragem de terra para fins de análise de fertilidade, seu manuseio demanda muito tempo. No presente trabalho foram comparados os resultados da análise química de terra proveniente de 15 áreas distintas, cujas amostras foram obtidas com cinco tipos de trado e com pá de corte. Também foram comparados o tempo demandado para a realização do trabalho e o volume de terra coletado com as diferentes ferramentas, em dois solos de texturas distintas. O tempo médio de amostragem foi estimado, avaliando-se o tempo gasto por seis pessoas para tomar dez amostras. Para o estudo de qualidade de resultados foram amostradas 15 áreas, com solos, manejos e níveis de fertilidade distintos, de modo a se obter grande variação entre os valores das características avaliadas. As amostragens constaram da estratificação por profundidades e amostras de 0 a 20 cm de profundidade no teste de tempo. A amostragem com a pá de corte demora de 1,3 a 2,3 vezes mais do que com os trados. Para os valores de pH, matéria orgânica, acidez do solo, Al trocável e P disponível, os resultados foram equivalentes para todas as ferramentas empregadas. Entretanto, para as bases do solo (Ca, Mg e K), as ferramentas empregadas resultaram, na maioria das vezes, em resultados diferentes dos obtidos pela pá de corte.

Sparse 1D discrete Dirac operators I: Quantum transport

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Sparse one-dimensional discrete Dirac operators II: Spectral properties

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

BOUND HYDROGENIC STATES IN A MAGNETIC FIELD: A FINITE-DIFFERENCE APPROACH

A finite-difference scheme is used to calculate bound electronic states of an electron in a hydrogen atom subject to a magnetic field. The numerical results are in good agreement with exact results, in the absence of the magnetic field, and with a two-parameters variational calculation, when the magnetic field is applied.

Assessment of a high-order finite difference upwind scheme for the simulation of convection-diffusion problems

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.

Predictors of health status do not change over three-year periods and exacerbation makes difference in chronic obstructive pulmonary disease

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

Electroacupuncture analgesia in dogs: is there a difference between uni- and bi-lateral stimulation?

Objective To compare the analgesic effect of uni- and bi-lateral electroacupuncture (EA) in response to thermal and mechanical nociceptive stimuli and to investigate the cardiorespiratory, endocrine, and behavioral changes in dogs submitted to EA.Study design Prospective, randomized cross-over experimental study.Animals Eight adult, clinically healthy, cross-breed dogs, weighing 13 +/- 4 kg.Methods Dogs underwent electrostimulation at false acupoints (T-false); bilateral EA at acupoints, stomach 36, gall bladder 34 and spleen 6 (T-EA/bil); unilateral EA at the same points (T-EA/uni) or were untreated (T-control). All animals received acepromazine (0.05 mg kg(-1)) IV; and heart rate, pulse oximetry, indirect arterial blood pressure, respiratory rate, PECO2, rectal temperature, and plasma cortisol concentration were measured before, during, and after EA. Analgesia was tested using thoracic and abdominal cutaneous thermal and mechanical stimuli, and an interdigital thermal stimulus. Behavior was classified as calm or restless. Analysis of variance for repeated measures followed by Tukey's test was used for analysis of the data.Results There were no cardiorespiratory differences among the treatments. The cutaneous pain threshold was higher after EA, compared with false points. The latency period was shorter and analgesia was more intense in T-EA/bil than T-EA/uni, when both were compared with T-false and T-control. Six out of eight animals treated with EA were calm during treatment, and 5/8 and 4/8 of the T-false and T-control animals, respectively, were restless. Latency to interdigital thermal stimulation increased in T-EA/bil compared with the others. There was no difference in plasma cortisol concentrations among the treatments.Conclusions Bilateral EA produced a shorter latency period, a greater intensity, and longer duration of analgesia than unilateral stimulation, without stimulating a stress response.Clinical relevance Bilateral EA produces a better analgesic effect than unilateral EA.

Unconstrained variables of non-commutative open strings

The boundary conditions of the bosonic string theory in non-zero B-field background are equivalent to the second class constraints of a discretized version of the theory. By projecting the original canonical coordinates onto the constraint surface we derive a set of coordinates of string that are unconstrained. These coordinates represent a natural framework for the quantization of the theory.

Multitrace operators and the generalized AdS/CFT prescription

We show that multitrace interactions can be consistently incorporated into an extended AdS conformal field theory (CFT) prescription involving the inclusion of generalized boundary conditions and a modified Legendre transform prescription. We find new and consistent results by considering a self-contained formulation which relates the quantization of the bulk theory to the AdS/CFT correspondence and the perturbation at the boundary by double-trace interactions. We show that there exist particular double-trace perturbations for which irregular modes are allowed to propagate as well as the regular ones. We perform a detailed analysis of many different possible situations, for both minimally and nonminimally coupled cases. In all situations, we make use of a new constraint which is found by requiring consistency. In the particular nonminimally coupled case, the natural extension of the Gibbons-Hawking surface term is generated.

Duality between non-commutative Yang-Mills-Chem-Simons and non-Abelian self-dual models

By introducing an appropriate parent action and considering a perturbative approach, we establish, up to fourth order terms in the field and for the full range of the coupling constant, the equivalence between the non-commutative Yang-Mills-ChernSimons theory and the non-commutative, non-Abelian self-dual model. In doing this, we consider two different approaches by using both the Moyal star-product and the Seiberg-Witten map. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods

We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross-Pitaevskii (GP) equation, and use it to study the resonance dynamics of a trapped Bose-Einstein condensate induced by a periodic variation in the atomic scattering length. When the frequency of oscillation of the scattering length is an even multiple of one of the trapping frequencies along the x, y or z direction, the corresponding size of the condensate executes resonant oscillation. Using the concept of the differentiation matrix, the partial-differential GP equation is reduced to a set of coupled ordinary differential equations, which is solved by a fourth-order adaptive step-size control Runge-Kutta method. The pseudospectral method is contrasted with the finite-difference method for the same problem, where the time evolution is performed by the Crank-Nicholson algorithm. The latter method is illustrated to be more suitable for a three-dimensional standing-wave optical-lattice trapping potential.

Combined D0 measurements constraining the CP-violating phase and width difference in the B-s(0) system

We combine the D0 measurement of the width difference between the light and heavy B-s(0) mass eigenstates and of the CP-violating mixing phase determined from the time-dependent angular distributions in the B-s(0)-> J/psi phi decays along with the charge asymmetry in semileptonic decays also measured with the D0 detector. With the additional constraint from the world average of the flavor-specific B-s(0) lifetime, we obtain Delta Gamma(s)equivalent to(Gamma(L)-Gamma(H))=0.13 +/- 0.09 ps(-1) and vertical bar phi(s)vertical bar=0.70(-0.47)(+0.39) or Delta Gamma(s)=-0.13 +/- 0.09 ps(-1) and vertical bar phi(s)vertical bar=2.44(-0.39)(+0.47). The data sample corresponds to an integrated luminosity of 1.1 fb(-1) accumulated with the D0 detector at the Fermilab Tevatron Collider.