BackgroundDiphtheria has a big mortality rate. Vaccination practically eradicated it in industrialized countries. A decrease in vaccine coverage and public health deterioration cause a reemergence in the Soviet Union in 1990. These... more
BackgroundDiphtheria has a big mortality rate. Vaccination practically eradicated it in industrialized countries. A decrease in vaccine coverage and public health deterioration cause a reemergence in the Soviet Union in 1990. These circumstances seem to be being reproduced in refugee camps with a potential risk of new outbreak.MethodsWe constructed a mathematical model that describes the evolution of the Soviet Union epidemic outbreak. We use it to evaluate how the epidemic would be modified by changing the rate of vaccination, and improving public health conditions.ResultsWe observe that a small decrease of 15% in vaccine coverage, translates an ascent of 47% in infected people. A coverage increase of 15% and 25% decreases a 44% and 66% respectively of infected people. Just improving health care measures a 5%, infected people decreases a 11.31%. Combining high coverage with public health measures produces a bigger reduction in the amount of infected people compare to amelioration o...
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Research Interests: Adolescent, Biological Sciences, Hepatitis B, Humans, Child, and 15 moreCost Effectiveness Analysis, Infant, Immunization, Decision Tree, Cost effectiveness, Aged, Adult, Cost Benefit Analysis, Differential equation, Hepatitis B virus, Elsevier, Hepatitis B Vaccines, HBsAg, Markov model, and Child preschool
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Page 1. Carlos Segovia Fernández Roberto A. Macıas1 and José L. Torrea2 1 Instituto de Matemática Aplicada del Litoral (CONICET - Universidad Nacional del Litoral), Güemes 3450, 3000 Santa Fe, Argentina roberto.a.macias@gmail.com 2... more
Page 1. Carlos Segovia Fernández Roberto A. Macıas1 and José L. Torrea2 1 Instituto de Matemática Aplicada del Litoral (CONICET - Universidad Nacional del Litoral), Güemes 3450, 3000 Santa Fe, Argentina roberto.a.macias@gmail.com 2 Departamento de Matemáticas. ...
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ABSTRACT. Given an n×n matrix B, positive definite and symmetric, let LB be the differential operator in Rn given by LB = 1 2 − Bx · gradx . A class of higher Riesz transforms associated with LB is defined by means of higher gradients of... more
ABSTRACT. Given an n×n matrix B, positive definite and symmetric, let LB be the differential operator in Rn given by LB = 1 2 − Bx · gradx . A class of higher Riesz transforms associated with LB is defined by means of higher gradients of order k. It is shown that these ...
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Let T be an invertible measure-preserving transformation on a σ-finite measure space (X, μ) and let 1 < p < ∞. This paper uses an abstract method developed by José Luis Rubio de Francia which allows us to give a unified approach to... more
Let T be an invertible measure-preserving transformation on a σ-finite measure space (X, μ) and let 1 < p < ∞. This paper uses an abstract method developed by José Luis Rubio de Francia which allows us to give a unified approach to the problems of characterizing the positive measurable functions v such that the limit of the ergodic averages or the ergodic Hilbert transform exist for all f ∈ Lp (νdμ). As a corollary, we obtain that both problems are equivalent, extending to this setting some results of R. Jajte, I. Berkson, J. Bourgain and A. Gillespie. We do not assume the boundedness of the operator Tf(x) = f(Tx) on Lp (νdμ). However, the method of Rubio de Francia shows that the problems of convergence are equivalent to the existence of some measurable positive function u such that the ergodic maximal operator and the ergodic Hilbert transform are bounded from LP (νdμ) into LP (udμ). We also study and solve the dual problem.
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Let Β1, Β2 be a pair of Banach spaces and T be a vector valued martingale transform (with respect to general filtration) which maps Β1-valued martingales into Β2-valued martingales. Then, the following statements are equivalent: T is... more
Let Β1, Β2 be a pair of Banach spaces and T be a vector valued martingale transform (with respect to general filtration) which maps Β1-valued martingales into Β2-valued martingales. Then, the following statements are equivalent: T is bounded from into for some p (or equivalently for every p) in the range 1 < p < ∞; T is bounded from into BMOB2; T is bounded from BMOB1 into BMOB2; T is bounded from into . Applications to UMD and martingale cotype properties are given. We also prove that the Hardy space defined in the case of a general filtration has nice dense sets and nice atomic decompositions if and only if Β has the Radon-Nikodým property.
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Let Β1, Β2 be a pair of Banach spaces and T be a vector valued martingale transform (with respect to general filtration) which maps Β1-valued martingales into Β2-valued martingales. Then, the following statements are equivalent: T is... more
Let Β1, Β2 be a pair of Banach spaces and T be a vector valued martingale transform (with respect to general filtration) which maps Β1-valued martingales into Β2-valued martingales. Then, the following statements are equivalent: T is bounded from into for some p (or equivalently for every p) in the range 1 < p < ∞; T is bounded from into BMOB2; T is bounded from BMOB1 into BMOB2; T is bounded from into . Applications to UMD and martingale cotype properties are given. We also prove that the Hardy space defined in the case of a general filtration has nice dense sets and nice atomic decompositions if and only if Β has the Radon-Nikodým property.
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In this note we focus on the discrete fractional integrals as a natural continuation of our previous work about nonlocal fractional derivatives, discrete and continuous. We define the discrete fractional integrals by using the semigroup... more
In this note we focus on the discrete fractional integrals as a natural continuation of our previous work about nonlocal fractional derivatives, discrete and continuous. We define the discrete fractional integrals by using the semigroup theory and we study the regularity of {discrete fractional integrals} on the discrete H\"older spaces, which it is known in the differential equations field as the discrete Schauder estimates.
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This book was first published in 2001. It provides an introduction to Fourier analysis and partial differential equations and is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take... more
This book was first published in 2001. It provides an introduction to Fourier analysis and partial differential equations and is intended to be used with courses for beginning graduate students. With minimal prerequisites the authors take the reader from fundamentals to research topics in the area of nonlinear evolution equations. The first part of the book consists of some very classical material, followed by a discussion of the theory of periodic distributions and the periodic Sobolev spaces. The authors then turn to the study of linear and nonlinear equations in the setting provided by periodic distributions. They assume only some familiarity with Banach and Hilbert spaces and the elementary properties of bounded linear operators. After presenting a fairly complete discussion of local and global well-posedness for the nonlinear Schrödinger and the Korteweg-de Vries equations, they turn their attention, in the two final chapters, to the non-periodic setting, concentrating on probl...
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Let X be a Banach space. It is proved that an analogue of the Rubio de Francia square function estimate for partial sums of the Fourier series of X-valued functions holds true for all disjoint collections of subintervals of the set of... more
Let X be a Banach space. It is proved that an analogue of the Rubio de Francia square function estimate for partial sums of the Fourier series of X-valued functions holds true for all disjoint collections of subintervals of the set of integers of equal length and for all exponents p ≥ 2 if and only if the space X is a UMD space of type 2. The same criterion is obtained for the case of subintervals of the real line and Fourier integrals instead of Fourier series.
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Let$\mathcal{V}_\rho(\re^{-tH})$, ρ > 2, be the ρ-variation of the heat semigroup associated to the harmonic oscillatorH= ½(−Δ + |x|2). We show that iff∈L∞(ℝ), the$\mathcal{V}_\rho(\re^{-tH})$(f)(x) < ∞, a.e.x∈ ℝ. However, we find a... more
Let$\mathcal{V}_\rho(\re^{-tH})$, ρ > 2, be the ρ-variation of the heat semigroup associated to the harmonic oscillatorH= ½(−Δ + |x|2). We show that iff∈L∞(ℝ), the$\mathcal{V}_\rho(\re^{-tH})$(f)(x) < ∞, a.e.x∈ ℝ. However, we find a functionG∈L∞(ℝ), such that$\mathcal{V}_\rho(\re^{-tH})$(G)(x) ∉L∞(ℝ). We also analyse the local behaviour inL∞of the operator$\mathcal{V}_\rho(\re^{-tH})$. We find that its growth is smaller than that of a standard singular integral operator. As a by-product of our work we obtain anL∞(ℝ) functionF, such that the square functiona.e.x∈ ℝ, whereis the classical Poisson kernal in ℝ.
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We investigate the behaviour of the classical (non-smooth) Hardy-Littlewood maximal operator in the context of Banach lattices. We are mainly concerned with end-point results for p = ∞. Naturally, the main role is played by the space BMO.... more
We investigate the behaviour of the classical (non-smooth) Hardy-Littlewood maximal operator in the context of Banach lattices. We are mainly concerned with end-point results for p = ∞. Naturally, the main role is played by the space BMO. We analyze the range of the maximal operator in BMOx. This turns out to depend strongly on the convexity of the Banach lattice . We apply these results to study the behaviour of the commutators associated to the maximal operator. We also consider the parallel results for the maximal fractional integral operator.