Strict solutions to stochastic parabolic evolution equations in M-type 2 Banach spaces

We study a stochastic linear evolution equation $dX+A(t)Xdt=F(t)dt+ G(t)dw_t$ in a Banach space of M-type 2. We construct unique strict solutions to the equation on the basis of the theory of deterministic linear evolution equations. The abstract results are applied to stochastic diffusion equations.Comment: 27 pages, to appear in Funkcialaj Ekvacio

Critical Behavior in Doping-Driven Metal−-Insulator Transition on Single-Crystalline Organic Mott-FET

We present the carrier transport properties in the vicinity of a doping-driven Mott transition observed at a field-effect transistor (FET) channel using a single crystal of the typical two-dimensional organic Mott insulator $\kappa$-(BEDT-TTF)$_2$CuN(CN)$_2$Cl ($\kappa$-Cl).The FET shows a continuous metal$-$insulator transition (MIT) as electrostatic doping proceeds. The phase transition appears to involve two-step crossovers, one in Hall measurement and the other in conductivity measurement. The crossover in conductivity occurs around the conductance quantum $e^2/h$ , and hence is not associated with "bad metal" behavior, which is in stark contrast to the MIT in half-filled organic Mott insulators or that in doped inorganic Mott insulators. Through in-depth scaling analysis of the conductivity, it is found that the above carrier transport properties in the vicinity of the MIT can be described by a high-temperature Mott quantum critical crossover, which is theoretically argued to be a ubiquitous feature of various types of Mott transitions. [This document is the unedited Authors' version of a Submitted Work that was subsequently accepted for publication in Nano Letters, copyright \copyright American Chemical Society after peer review. To access the final edited and published work see http://dx.doi.org/10.1021/acs.nanolett.6b03817]Comment: 40 pages, 16 figures in Nano Letters, ASAP (2017

EXPONENTIAL ATTRACTORS FOR NON-AUTONOMOUS DISSIPATIVE SYSTEM

In this paper we will introduce a version of exponential attractor for non-autonomous equations as a time dependent set with uniformly bounded finite fractal dimension which is positively invariant and attracts every bounded set at an exponential rate. This is a natural generalization of the existent notion for autonomous equations. A generation theorem will be proved under the assumption that the evolution operator is a compact perturbation of a contraction. In the second half of the paper, these results will be applied to some non-autonomous chemotaxis system

Phospholipase A2 in skin biology : new insights from gene-manipulated mice and lipidomics

The skin represents one of the tissues that are most profoundly influenced by alterations in the quality of lipids (lipoquality). Lipids not only constitute cellular membranes, but also serve as bioactive lipid mediators and essential components of the skin barrier. Phospholipase A2 (PLA2) enzymes supply fatty acids and lysophospholipids from membrane phospholipids, thereby variably affecting cutaneous homeostasis. Accordingly, perturbation of particular PLA2-driven lipid pathways can be linked to various forms of skin disease. In this review article, we highlight the roles of several PLA2 subtypes in cutaneous pathophysiology, as revealed by transgenic/knockout studies in combination with comprehensive lipidomics. We focus mainly on secreted PLA2 group IIF (sPLA2-IIF), which is associated with epidermal hyperplasia through mobilization of a unique lipid metabolite. We also address the distinct roles of sPLA2-IIE in hair follicles and sPLA2-IID in lymphoid immune cells that secondarily affect cutaneous inflammation, and provide some insights into species differences in sPLA2s. Additionally, we briefly overview the patatin-like phospholipase PNPLA1, which belongs to the Ca2+-independent PLA2 (iPLA2) family, as a key regulator of skin barrier function through catalysis of a unique non-PLA2 reaction. These knowledges on lipid metabolism driven by various PLA2 subtypes will open novel opportunities for translated studies toward diagnosis and therapy of human skin diseases