Regularity properties for general HJB equations. A BSDE method

In this work we investigate regularity properties of a large class of Hamilton-Jacobi-Bellman (HJB) equations with or without obstacles, which can be stochastically interpreted in form of a stochastic control system which nonlinear cost functional is defined with the help of a backward stochastic differential equation (BSDE) or a reflected BSDE (RBSDE). More precisely, we prove that, firstly, the unique viscosity solution $V(t,x)$ of such a HJB equation over the time interval $[0,T],$ with or without an obstacle, and with terminal condition at time $T$, is jointly Lipschitz in $(t,x)$, for $t$ running any compact subinterval of $[0,T)$. Secondly, for the case that $V$ solves a HJB equation without an obstacle or with an upper obstacle it is shown under appropriate assumptions that $V(t,x)$ is jointly semiconcave in $(t,x)$. These results extend earlier ones by Buckdahn, Cannarsa and Quincampoix [1]. Our approach embeds their idea of time change into a BSDE analysis. We also provide an elementary counter-example which shows that, in general, for the case that $V$ solves a HJB equation with a lower obstacle the semi-concavity doesn't hold true.Comment: 30 page

Possible link of a structurally driven spin flip transition and the insulator-metal transition in the perovskite La1−x_{1-x}Bax_{x}CoO3_{3}

The complex nature of the magnetic ground state in La$_{1-x}$A$_{x}$CoO$_{3}$ (A = Ca, Sr, Ba) has been investigated via neutron scattering. It was previously observed that ferromagnetic (FM) as well as antiferromagnetic (AFM) correlations can coexist prior to the insulator-metal transition (IMT). We focused on a unique region in the Ba phase diagram, from x = 0.17 - 0.22, in which a commensurate AFM phase appears first with a propagation vector, k = (0, -0.5, 0.5), and the Co moment in the (001)$_{R}$ plane of the rhombohedral lattice. With increasing x, the AFM component weakens while an FM order appears with the FM Co moment directed along the (001)$_{R}$ (=(111)$_{C}$) axis. By x = 0.22, a spin flip to new FM component appears as the crystal fully transforms to an orthorhombic (Pnma) structure, with the Co moments pointing along a new direction, (001)$_{O}$ (=(110)$_{C}$). It is the emergence of the magnetic Pnma phase that leads to IMT.Comment: 5 page

TRPV4, TRPC1, and TRPP2 assemble to form a flow-sensitive heteromeric channel

Transient receptor potential (TRP) channels, a superfamily of ion channels, can be divided into 7 subfamilies, including TRPV, TRPC, TRPP, and 4 others. Functional TRP channels are tetrameric complexes consisting of 4 pore-forming subunits. The purpose of this study was to explore the heteromerization of TRP subunits crossing different TRP subfamilies. Two-step coimmunoprecipitation (co-IP) and fluorescence resonance energy transfer (FRET) were used to determine the interaction of the different TRP subunits. Patch-clamp and cytosolic Ca2+ measurements were used to determine the functional role of the ion channels in flow conditions. The analysis demonstrated the formation of a heteromeric TRPV4-C1-P2 complex in primary cultured rat mesenteric artery endothelial cells (MAECs) and HEK293 cells that were cotransfected with TRPV4, TRPC1, and TRPP2. In functional experiments, pore-dead mutants for each of these 3 TRP isoforms nearly abolished the flow-induced cation currents and Ca2+ increase, suggesting that all 3 TRPs contribute to the ion permeation pore of the channels. We identified the first heteromeric TRP channels composed of subunits from 3 different TRP subfamilies. Functionally, this heteromeric TRPV4- C1-P2 channel mediates the flow-induced Ca2+ increase in native vascular endothelial cells.-Du, J., Ma, X., Shen, B., Huang, Y., Birnbaumer, L., Yao, X. TRPV4, TRPC1, and TRPP2 assemble to form a flowsensitive heteromeric channel.Fil: Du, Juan. Chinese University Of Hong Kong; Hong Kong. Anhui Medical University; ChinaFil: Ma, Xin. Chinese University Of Hong Kong; Hong KongFil: Shen, Bing. Chinese University Of Hong Kong; Hong Kong. Anhui Medical University; ChinaFil: Huang, Yu. Chinese University Of Hong Kong; Hong KongFil: Birnbaumer, Lutz. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. National Institutes of Health; Estados UnidosFil: Yao, Xiaoqiang. Chinese University Of Hong Kong; Hong Kon