Dois teoremas sôbre a função gama

This paper proves the following theorems on the gamma function: Theorem I The integral ∫O∞ t u e-t dt = Γ ( u + 1 ) , where u, real or complex, is such that R (u) > -1, will not change its value if we substitute z = Q (cos φ + i sen φ) for the real variable t, being jconstant and such that - Π/2 < φ < Π/2 , Theorem II The integral ∫-∞∞ w2u + 1 e -w² dw = Γ ( u + 1 ) , where 2u + 1 is supposed to be a non negative even integer, will not change its value if we substitute z = w + fi, f being a real constant, for the real variable w. The proof of both theorems is obtained by means of the well known Cauchy theorem on contour integrals on the complex plane, as suggested by CRAMÉR (1, p. 126) and LEVY (3, p. 178).

Vectorial capacity, basic reproduction number, force of infection and all that: formal notation to complete and adjust their classical concepts and equations

A dimensional analysis of the classical equations related to the dynamics of vector-borne infections is presented. It is provided a formal notation to complete the expressions for the Ross' Threshold Theorem, the Macdonald's basic reproduction "rate" and sporozoite "rate", Garret-Jones' vectorial capacity and Dietz-Molineaux-Thomas' force of infection. The analysis was intended to provide a formal notation that complete the classical equations proposed by these authors.

Parametric sensitivity analysis for the helium dimers on a model potential

Potential parameters sensitivity analysis for helium unlike molecules, HeNe, HeAr, HeKr and HeXe is the subject of this work. Number of bound states these rare gas dimers can support, for different angular momentum, will be presented and discussed. The variable phase method, together with the Levinson's theorem, is used to explore the quantum scattering process at very low collision energy using the Tang and Toennies potential. These diatomic dimers can support a bound state even for relative angular momentum equal to five, as in HeXe. Vibrational excited states, with zero angular momentum, are also possible for HeKr and HeXe. Results from sensitive analysis will give acceptable order of magnitude on potentials parameters.

Expressiveness and definability in circumscription

We investigate expressiveness and definability issues with respect to minimal models, particularly in the scope of Circumscription. First, we give a proof of the failure of the Löwenheim-Skolem Theorem for Circumscription. Then we show that, if the class of P; Z-minimal models of a first-order sentence is Δ-elementary, then it is elementary. That is, whenever the circumscription of a first-order sentence is equivalent to a first-order theory, then it is equivalent to a finitely axiomatizable one. This means that classes of models of circumscribed theories are either elementary or not Δ-elementary. Finally, using the previous result, we prove that, whenever a relation Pi is defined in the class of P; Z-minimal models of a first-order sentence Φ and whenever such class of P; Z-minimal models is Δ-elementary, then there is an explicit definition ψ for Pi such that the class of P; Z-minimal models of Φ is the class of models of Φ ∧ ψ. In order words, the circumscription of P in Φ with Z varied can be replaced by Φ plus this explicit definition ψ for Pi.

Development and validation of a genotype 3 recombinant protein-based immunoassay for hepatitis E virus serology in swine

Hepatitis E virus (HEV) is classified within the family Hepeviridae, genus Hepevirus. HEV genotype 3 (Gt3) infections are endemic in pigs in Western Europe and in North and South America and cause zoonotic infections in humans. Several serological assays to detect HEV antibodies in pigs have been developed, at first mainly based on HEV genotype 1 (Gt1) antigens. To develop a sensitive HEV Gt3 ELISA, a recombinant baculovirus expression product of HEV Gt3 open reading frame-2 was produced and coated onto polystyrene ELISA plates. After incubation of porcine sera, bound HEV antibodies were detected with anti-porcine anti-IgG and anti-IgM conjugates. For primary estimation of sensitivity and specificity of the assay, sets of sera were used from pigs experimentally infected with HEV Gt3. For further validation of the assay and to set the cutoff value, a batch of 1100 pig sera was used. All pig sera were tested using the developed HEV Gt3 assay and two other serologic assays based on HEV Gt1 antigens. Since there is no gold standard available for HEV antibody testing, further validation and a definite setting of the cutoff of the developed HEV Gt3 assay were performed using a statistical approach based on Bayes' theorem. The developed and validated HEV antibody assay showed effective detection of HEV-specific antibodies. This assay can contribute to an improved detection of HEV antibodies and enable more reliable estimates of the prevalence of HEV Gt3 in swine in different regions.

Uma avaliação das contribuições de Stiglitz à teoria dos mercados financeiros

The objective and originality of this paper lie in identifying Stiglitz's main theoretical contributions to Financial Economics and in briefly portraying the contemporary economic thought out of which these contributions emerged as well as in suggesting their connections with the subsequent economic thought. Grounded on a detailed analysis of Stiglitz's works on finance, his most important theoretical findings are singled out and gathered into four issues: (1) the conditions under which the Modigliani-Miller theorem is valid; (2) the inconsistency inherent to the efficient market hypothesis; (3) the microeconomic effects of asymmetrical information in financial markets; and (4) its real macroeconomic effects. In all of these topics, the focal point of Stiglitz's theoretical research is the unrealistic underpinnings on which the Arrow-Debreu competitive equilibrium model relies. It is also emphasised that this same perspective he coherently followed to construct a fully-fledged theoretical framework would be preserved in his empirical investigations, notably about developing countries, on which he has concentrated effort since the beginnings of the nineties.

The political role of the State in Cambridge theories of growth and distribution

In this paper we extend Kaldor’s Neo-Pasinetti theorem to the scope of budgetary interventions based on political orientations. First, we take into account a system of taxes and expenditures. Second, we introduce different reaction functions for public spending showing the political role of the State in Cambridge theory of distribution. It turns out that the validity of Kaldorian results depends on the political orientation adopted by government, which diminishes the range of application of the Neo-Pasinetti theorem.