The ℓs\ell^s-boundedness of a family of integral operators on UMD Banach function spaces

We prove the $\ell^s$-boundedness of a family of integral operators with an operator-valued kernel on UMD Banach function spaces. This generalizes and simplifies earlier work by Gallarati, Veraar and the author, where the $\ell^s$-boundedness of this family of integral operators was shown on Lebesgue spaces. The proof is based on a characterization of $\ell^s$-boundedness as weighted boundedness by Rubio de Francia.Comment: 13 pages. Generalization of arXiv:1410.665

Assessment of endometrial and ovarian characteristics using three dimensional power Doppler ultrasound to predict response in frozen embryo transfer cycles

<p>Abstract</p> <p>Objective</p> <p>To evaluate whether endometrial or ovarian parameters as measured using 3D power Doppler ultrasound would predict the outcome in frozen embryo transfer (FET) cycles.</p> <p>Methods</p> <p>Thirty women with no known gynecological pathology undergoing FET were recruited. The FET was carried out in the natural menstrual cycle 3-4 days after the first positive LH test result. Blood samples for hormonal analysis were collected, and three-dimensional (3D) ultrasonographic examination was performed on the day of the FET and repeated with analysis of the total hCG one week later.</p> <p>Results</p> <p>The demographic, clinical, and embryological characteristics were similar between the pregnant (15/30) and nonpregnant groups (15/30). There were no differences between the groups in endometrial/subendometrial thickness, volume, or vascularization index (VI). The endometrial triple-line pattern was more often present in the pregnant group on the day of the FET (93.3% vs. 40.0%, 95% CI 25.5-81.2%). No differences in the ovaries were observed on the day of the FET. At the second visit, the triple-line pattern was still more often present in those patients who had conceived (91.7% vs. 42.9%, 95% CI 18.5-79.1%), and their corpus luteum was more active as judged by the rise in 17-hydroxyprogesterone and estradiol levels. No differences were observed in the dominant ovarian vasculature.</p> <p>Conclusions</p> <p>According to our results, measurement of power Doppler indices using 3D ultrasound on the day of the FET does not provide any additional information concerning the outcome of the cycle. The existence of the triple-line pattern on the day of the FET seems to be a prognostic sign of a prosperous outcome after FET. The dominant ovary in the pregnant group seems to be already activated one week after the FET.</p

On the well-posedness of the periodic KdV equation in high regularity classes

We prove well-posedness results for the initial value problem of the periodic KdV equation in classes of high regularity solutions. More precisely, we consider the problem in weighted Sobolev spaces, which comprise classical Sobolev spaces, Gevrey spaces, and analytic spaces. We show that the initial value problem is well posed in all spaces with subexponential growth of Fourier coefficients, and ‘almost well posed’ in spaces with exponential growth of Fourier coefficients

Is proximal airway pressure a good reflection of peripheral airspace pressure in infants and children models under HFJV?

This experimental study was carried out to determine if an alveolar positive end-expiratory pressure (PEEP) could occur during high frequency jet ventilation (HFJV) in infants, and if tracheal pressure is a good estimation of alveolar pressure. We used physical models simulating a 1.5 kg premature (P), a 3 kg newborn (N) and a 6 kg child (C) with normal compliance and normal resistance. Moreover, in the N model, we used two different resistances and lung compliance heterogeneity was studied in the P model. Pressure was measured simultaneously in the tube simulating trachea (Paw) and in the bottle simulating the lung (Palv). HFJV was performed either via an endotracheal tube (ETT) or via a long catheter as in laryngoscopy. The ratio of injection time upon cycle duration (Ti/Ttot) was 20% or 30%, jet frequency was altered from 150 to 300 min-1 and the driving pressure was set as in clinical practice (0.5 and 0.6 bar). PEEP occurred mainly in N (1.1 to 3.2 cm H2O) and C models (0 to 3.5 cm H2O). It was inversely related to expiratory time (Te). The end-expiratory pressure drop between Palv and Paw (delta EEP) was higher in N and increased from 0.5 to 2 cm H2O with the shortening of Te and with airway resistances, i.e. the presence of ETT. In the heterogeneous model, PEEP and delta EEP were greater in the higher compliance alveolus. This study shows that the end-expiratory Palv is underestimated by end-expiratory Paw.(ABSTRACT TRUNCATED AT 250 WORDS