On the convergence of double integrals and a generalized version of Fubini's theorem on successive integration

Let the function f: \bar{\R}^2_+ \to \C be such that f\in L^1_{\loc} (\bar{\R}^2_+). We investigate the convergence behavior of the double integral \int^A_0 \int^B_0 f(u,v) du dv \quad {\rm as} \quad A,B \to \infty,\leqno(*) where $A$ and $B$ tend to infinity independently of one another; while using two notions of convergence: that in Pringsheim's sense and that in the regular sense. Our main result is the following Theorem 3: If the double integral (*) converges in the regular sense, or briefly: converges regularly, then the finite limits $$\lim_{y\to \infty} \int^A_0 \Big(\int^y_0 f(u,v) dv\Big) du =: I_1 (A)$$ and $$\lim_{x\to \infty} \int^B_0 \Big(\int^x_0 f(u,v) du) dv = : I_2 (B)$$ exist uniformly in $0<A, B <\infty$, respectively; and $$\lim_{A\to \infty} I_1(A) = \lim_{B\to \infty} I_2 (B) = \lim_{A, B \to \infty} \int^A_0 \int^B_0 f(u,v) du dv.$$ This can be considered as a generalized version of Fubini's theorem on successive integration when f\in L^1_{\loc} (\bar{\R}^2_+), but $f\not\in L^1 (\bar{\R}^2_+)$

Application of different drying techniques in Diospyros kaki fruit Var. ‘Fuyu’

El objetivo fue evaluar el efecto de las condiciones de deshidratación sobre la pérdida de agua y los cambios de color en Dyospiros kaki var. 'Fuyu'. Las condiciones fueron: i) Secado con aire a velocidad (1,1 m/s) y temperatura (45, 60 y 75 ºC) constantes (SAC), ii) Secado intermitente con ciclos de flujo de aire/reposo de 45/45 minutos (SAC INT), a las mismas temperaturas, iii) Deshidratación osmótica en solución de sacarosa a 50 y 60º Brix y secado con aire a 60ºC (DO+SAC). El modelo de Page fue utilizado para describir la pérdida de agua. Los valores de n para SAC a 45 y 60 ºC, SAC INT y DO+SAC no presentaron diferencias significativas (p>0,05). Los valores de k aumentaron con la temperatura en SAC y SAC INT. Los parámetros L* y b* disminuyeron durante el secado. El ΔE no fue afectado por el SAC INT.The aim of this study was to evaluate the effect of drying conditions on water loss and color changes of Diospyros kaki var Fuyu fruit. The conditions were: i) drying with constant air flow rate (1,1 m/s) and temperature (45, 60 and 75 °C) (SAC), ii) intermittent drying with cicles of heat application/tempering time for 45/45 min (SAC INT), at the same temperatures, iii) Osmotic dehydration in sucrose solution at 50 and 60 °Brix before drying at 60 °C (DO + SAC). In order to describe the water loss the Page model was used. The n parameter values of SAC at 45 and 60 °C,SAC INT and DO + SAC were not significantly different (p> 0.05). The k values increased with temperature in SAC and SAC INT. L* and b* color parameters decreased during drying. The color difference ∆E was not affected by INT SAC.Fil: Borsini, Ariel Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Materiales de Misiones. Universidad Nacional de Misiones. Facultad de Ciencias Exactas Químicas y Naturales. Instituto de Materiales de Misiones; ArgentinaFil: Albani, Oscar Alfredo. Universidad Nacional de Misiones. Facultad de Ciencias Exactas, Químicas y Naturales; ArgentinaFil: Ramallo, Laura Ana. Universidad Nacional de Misiones. Facultad de Ciencias Exactas, Químicas y Naturales; Argentin

Upsilon suppression in PbPb collisions at the LHC

The Compact Muon Solenoid (CMS) has measured the suppression of the bottomonium states Y(1S), Y(2S), and Y(3S) in PbPb collisions at sqrt(s_NN) = 2.76 TeV relative to pp collisions, scaled by the number of inelastic nucleon-nucleon collisions. CMS observed a stronger suppression for the weaker bound Y(2S) and Y(3S) states than for the ground state Y(1S). Such "sequential melting" has been predicted to be a clear signature for the creation of a quark-gluon plasma. The suppression of the Y(1S) and Y(2S) has been measured as a function of collision centrality for Y in the rapidity interval |y| < 2.4 and with transverse momentum (p_T) down to 0. Furthermore, the p_T and rapidity dependence of the Y(1S) suppression are presented.Comment: 7 pages, 3 figures. To appear in Proc. 14th Int. Conf. on B-Physics at Hadron Machines (Beauty 2013), Bologna, Italy, April 8-12, 201

On the first-passage time of an integrated Gauss-Markov process

It is considered the integrated process $X(t)= x + \int _0^t Y(s) ds ,$ where $Y(t)$ is a Gauss-Markov process starting from $y.$ The first-passage time (FPT) of $X$ through a constant boundary and the first-exit time of $X$ from an interval $(a,b)$ are investigated, generalizing some results on FPT of integrated Brownian motion. An essential role is played by a useful representation of $X,$ in terms of Brownian motion which allows to reduces the FPT of $X$ to that of a time-changed Brownian motion. Some explicit examples are reported; when theoretical calculation is not available, the quantities of interest are estimated by numerical computation.Comment: 4 figure