Harnack and pointwise estimates for degenerate or singular parabolic equations

In this paper we give both an historical and technical overview of the theory of Harnack inequalities for nonlinear parabolic equations in divergence form. We start reviewing the elliptic case with some of its variants and geometrical consequences. The linear parabolic Harnack inequality of Moser is discussed extensively, together with its link to two-sided kernel estimates and to the Li-Yau differential Harnack inequality. Then we overview the more recent developements of the theory for nonlinear degenerate/singular equations, highlighting the differences with the quadratic case and introducing the so-called intrinsic Harnack inequalities. Finally, we provide complete proofs of the Harnack inequalities in some paramount case to introduce the reader to the expansion of positivity method.Comment: Survey paper, 50 pages, 5 figures. Comments welcom

Fizik öğrencileri, algoritmik problem çözücüler midir yoksa kavramsal düşünürler mi?

Bu çalışmada, Atatürk Üniversitesi, Kazım Karabekir Eğitim Fakültesi, Fizik Eğitimi Anabilim Dalı, 8. Yarıyıl öğrencilerinden seksen kişilik bir öğrenci grubuna, ilk yedi yarıyılda okutulan derslerden seçilmiş beş konu ile ilgili olarak, beş çift problem sorulmuş ve önceden kendilerine verilmiş olan yöntemlerden birisini kullanarak problemlerin çözümü istenmiştir. Bu öğrencilerden “yetenekli, zeki”olanların, fiziğin nasılından daha çok niçinini arzu ederek, algoritmik problem çözmekten ziyade, kavramlarla ilgilenerek problemleri çözmeye çalıştıkları gözlenmiştir

Online Εvaluation of Earth Observation Derived Indicators for Urban Planning and Management

Extensive urbanization and growth of population density have acquired a paramount interest towards a sustainable urban development. Earth Observation (EO) is an important source of information required for urban planning and management. The availability of EO data provides the immense opportunity for urban environmental indicators development easily derived by remote sensors. In this study, the state of the art methods were employed to develop urban planning and management relevant indicators that can be evaluated by using EO data. The importance of this approach lies on providing alternatives for improving urban planning and management, without consuming time and resources in collecting field or archived data. The evaluated urban indicators were integrated into a Web‐based Information System that was developed for online exploitation. The results for three case studies are therefore available online and can be used by urban planners and stakeholders in supporting their planning decisions

Solid-state reference electrodes based on carbon nanotubes and polyacrylate membranes

A novel potentiometric solid-state reference electrode containing single-walled carbon nanotubes as the transducer layer between a polyacrylate membrane and the conductor is reported here. Single-walled carbon nanotubes act as an efficient transducer of the constant potentiometric signal originating from the reference membrane containing the Ag/AgCl/Cl− ions system, and they are needed to obtain a stable reference potentiometric signal. Furthermore, we have taken advantage of the light insensitivity of single-walled carbon nanotubes to improve the analytical performance characteristics of previously reported solid-state reference electrodes. Four different polyacrylate polymers have been selected in order to identify the most efficient reservoir for the Ag/AgCl system. Finally, two different arrangements have been assessed: (1) a solid-state reference electrode using photo-polymerised n-butyl acrylate polymer and (2) a thermo-polymerised methyl methacrylate:n-butyl acrylate (1:10) polymer. The sensitivity to various salts, pH and light, as well as time of response and stability, has been tested: the best results were obtained using single-walled carbon nanotubes and photo-polymerised n-butyl acrylate polymer. Water transport plays an important role in the potentiometric performance of acrylate membranes, so a new screening test method has been developed to qualitatively assess the difference in water percolation between the polyacrylic membranes studied. The results presented here open the way for the true miniaturisation of potentiometric systems using the excellent properties of single-walled carbon nanotubes

Abstracts from the 20th International Symposium on Signal Transduction at the Blood-Brain Barriers

https://deepblue.lib.umich.edu/bitstream/2027.42/138963/1/12987_2017_Article_71.pd

AC losses in a commercial Bi: 2223/Ag tape

We have investigated the effect of temperature, field amplitude, frequency and orientation of the field on AC losses in a commercial Bi:2223/Ag tape. The measurements were performed using an AC susceptometer. The experimental results show that the losses depend on field amplitude, temperature, and strongly on frequency. Due to the strong dependence of AC losses on frequency, measurements were pursued at several frequencies between 20 Hz and 10 kHz, at both 20 and 30 K. The strong frequency dependence at these low temperatures is attributed to eddy current losses or/and inter-filamentary coupling losses. At higher temperatures and low frequencies, the main contribution to AC losses comes from hysteresis losses due to the flux entry into and exit from the superconducting tape during the up and down swings of the magnetic field. We have calculated the hysteresis losses in the critical state framework, as a function of AC field amplitudes and temperature, for planar geometry. Experimental data are analyzed by comparing them with the calculated curves. © 2009 IOP Publishing Ltd.107T015This work was supported by TUBITAK-TBAG under the grant contract number: 107T015 and Research Fund of Karadeniz Technical University

Irreversibility line and flux relaxation in Bi:2223/Ag tape prepared by CTFF technique: H//c axis

We have studied flux dynamics in Bi:2223/Ag tape prepared by the CTFF technique in the orientation of H//c axis. Irreversibility line (IL) of a Bi:2223/Ag tape has been determined from AC susceptibility and the DC magnetization technique based on FC and ZFC curves. We have observed that the irreversibility temperature determined from the AC susceptibility method locates at a higher temperature than that was determined from the DC magnetization method. This shift could be attributed to the viscous dissipation generated by the oscillation of flux lines. FC magnetization at 20 K and 30 K for the field range from 500 to 2500 Oe are the same and show a plateau implying the same amount of reversible magnetization due to the Meissner current. Remanent magnetization versus temperature curves, which give us information on the flux pinning mechanism of the vortices, are also presented. © 2010 Springer Science+Business Media, LLC.Karadeniz Teknik Üniversitesi: 2006.111.001.1 107T015Acknowledgements This work was supported by TUBITAK-TBAG under the grant contract number 107T015 and the Research Fund of Karadeniz Technical University under the grant contract number 2006.111.001.1