Asymptotic behavior in time periodic parabolic problems with unbounded coefficients

We study asymptotic behavior in a class of non-autonomous second order parabolic equations with time periodic unbounded coefficients in $\mathbb R\times \mathbb R^d$. Our results generalize and improve asymptotic behavior results for Markov semigroups having an invariant measure. We also study spectral properties of the realization of the parabolic operator $u\mapsto {\cal A}(t) u - u_t$ in suitable $L^p$ spaces

Diffraction Resistant Scalar Beams Generated by a Parabolic Reflector and a Source of Spherical Waves

In this work, we propose the generation of diffraction resistant beams by using a parabolic reflector and a source of spherical waves positioned at a point slightly displaced from its focus (away from the reflector). In our analysis, considering the reflector dimensions much greater than the wavelength, we describe the main characteristics of the resulting beams, showing their properties of resistance to the diffraction effects. Due to its simplicity, this method may be an interesting alternative for the generation of long range diffraction resistant waves.Comment: 22 pages, 9 figures, Applied Optics, 201

Dye diffusion during laparoscopic tubal patency tests may suggest a lymphatic contribution to dissemination in endometriosis: A prospective, observational study

Aim Women with adenomyosis are at higher risk of endometriosis recurrence after surgery. This study was to assess if the lymphatic vessel network drained from the uterus to near organs where endometriosis foci lied. Methods A prospective, observational study, Canadian Task Force Classification II-2, was conducted at Sacro Cuore Don Calabria Hospital, Negrar, Italy. 104 white women aged 18–43 years were enrolled consecutively for this study. All patients underwent laparoscopy for endometriosis and a tubal dye test was carried out. Results Evidence of dye dissemination through the uterine wall and outside the uterus was noted in 27 patients (26%) with adenomyosis as it permeated the uterine wall and a clear passage of the dye was shown in the pelvic lymphatic vessels regardless whether the tubes were unobstructed. Histological assessment of the uterine biopsies confirmed adenomyosis. Conclusion Adenomyosis is characterized by ectatic lymphatics that allow the drainage of intrauterine fluids (the dye and, perhaps, menstrual blood) at minimal intrauterine pressure from the uterine cavity though the lymphatic network to extrauterine organs. Certainly, this may not be the only explanation for endometriosis dissemination but the correlation between the routes of the dye drainage and location of endometriosis foci is highly suggestive