Gradient Estimates For The CR Heat Equation On Complete noncompact Pseudo-Hermitian Manifolds

In this paper, we derive local and global Li-Yau type gradient estimates for the positive solutions of the CR heat equation on complete noncompact pseudo-Hermitian manifolds. As applications of the gradient estimates, we give a Harnack inequality for positive solutions of the CR heat equation, and then obtain an upper bound estimate for the corresponding heat kernel.Comment: All comments welcome

Morphology in the total electron content under geomagnetic disturbed conditions: results from global ionosphere maps

International audienceUsing 8-year global ionosphere maps (GIMs) of TEC products from the Jet Propulsion Laboratory (JPL), we make a statistical study on the morphology of the global ionospheric behaviors with respect to the geomagnetic disturbances. Results show that the behaviors of TEC during geomagnetic storm present clear seasonal and local time variations under geomagnetic control in a similar way as those of NmF2 (Field and Rishbeth, 1997). A negative phase of TEC occurs with high probability in the summer hemisphere and most prominent near the geomagnetic poles, while a positive phase is obvious in the winter hemisphere and in the far pole region. A negative storm effect toward lower latitudes tends to occur from post-midnight to the morning sector and recedes to high latitude in the afternoon. A positive storm effect is separated by geomagnetic latitudes and magnetic local time. Furthermore, ionospheric responses at different local time sectors with respect to the storm commencement shows very different developing processes corresponding to the evolution of the geomagnetic storm. A daytime positive storm effect is shown to be more prominent in the American region than those in the Asian and European regions, which may suggest a longitudinal effect of the ionospheric storm

Refractometer probe based on a reflective carbon nanotube-modified microfiber Bragg grating

A carbon nanotube (CNT)-modified microfiber Bragg grating (MFBG) is proposed to measure the refractive index with a strong enhancement of the sensitivity in the low refractive index region. The introduction of the CNT layer influences the evanescent field of the MFBG and causes modification of the reflection spectrum. With the increase of the surrounding refractive index (SRI), we observe significant attenuation to the peak of the Bragg resonance, while its wavelength remains almost unchanged. Our detailed experimental results disclose that the CNT-MFBG demonstrates strong sensitivity in the low refractive index range of 1.333-1.435, with peak intensity up to -53.4 dBm/refractive index unit, which is 15-folds higher than that of the uncoated MFBG. Therefore, taking advantage of the CNT-induced evanescent field enhancement, the reflective MFBG probe presents strong sensing capability in biochemical fields

Label-free glucose biosensor based on enzymatic graphene oxide-functionalized tilted fiber grating

A label-free biosensor based on graphene oxide (GO) and glucose oxidase (GOD) functionalized tilted fiber grating (TFG) with large tilted angle is proposed for low concentration glucose detection. Taking advantages of sufficient binding sites of the GO with oxygen-containing groups, the enzymes (GOD) are covalently immobilized onto GO-deposited TFG via 1-ethyl-3-(3-dimethylaminopropyl) carbodiimide and N-hydroxyl succinimide cross-liner. Surface characterizations with optical microscopy, scanning electron microscopy, Raman and infrared spectroscopy provide detailed assessments and evidences about the homogeneity of GO deposition and the effectiveness of enzyme modification. Through the specific catalysis reaction of GOD on the glucose, a considerable refractive index change in local microenvironment around the TFG results in the resonant wavelength shifts of cladding modes. The detection results of the low-concentration glucose demonstrate that the resonant wavelength has a linear response to the glucose concentration in the range of 0–8 mM with a response coefficient of ∼0.24 nm/mM, showing an enhanced sensitivity and bio-selectivity compared with the pristine TFG. The miniaturized size and remote label-free sensing capacity of the proposed device permit a multitude of opportunities for single-point measurement in harsh conditions and hard-to-reach spaces, presenting a promising candidate for label-free glucose detection for disease diagnosis, pharmaceutical research and bioengineering applications