Abstract kinetic equations with positive collision operators

We consider "forward-backward" parabolic equations in the abstract form $Jd \psi / d x + L \psi = 0$, $0< x < \tau \leq \infty$, where $J$ and $L$ are operators in a Hilbert space $H$ such that $J=J^*=J^{-1}$, $L=L^* \geq 0$, and $\ker L = 0$. The following theorem is proved: if the operator $B=JL$ is similar to a self-adjoint operator, then associated half-range boundary problems have unique solutions. We apply this theorem to corresponding nonhomogeneous equations, to the time-independent Fokker-Plank equation $\mu \frac {\partial \psi}{\partial x} (x,\mu) = b(\mu) \frac {\partial^2 \psi}{\partial \mu^2} (x, \mu)$, $0<x<\tau$, $\mu \in \R$, as well as to other parabolic equations of the "forward-backward" type. The abstract kinetic equation $T d \psi/dx = - A \psi (x) + f(x)$, where $T=T^*$ is injective and $A$ satisfies a certain positivity assumption, is considered also.Comment: 20 pages, LaTeX2e, version 2, references have been added, changes in the introductio

SUMO-2 and PIAS1 modulate insoluble mutant Huntingtin protein accumulation

A key feature in Huntington disease (HD) is the accumulation of mutant Huntingtin (HTT) protein, which may be regulated by posttranslational modifications. Here, we define the primary sites of SUMO modification in the amino-terminal domain of HTT, show modification downstream of this domain, and demonstrate that HTT is modified by the stress-inducible SUMO-2. A systematic study of E3 SUMO ligases demonstrates that PIAS1 is an E3 SUMO ligase for both HTT SUMO-1 and SUMO-2 modification and that reduction of dPIAS in a mutant HTT Drosophila model is protective. SUMO-2 modification regulates accumulation of insoluble HTT in HeLa cells in a manner that mimics proteasome inhibition and can be modulated by overexpression and acute knockdown of PIAS1. Finally, the accumulation of SUMO-2-modified proteins in the insoluble fraction of HD postmortem striata implicates SUMO-2 modification in the age-related pathogenic accumulation of mutant HTT and other cellular proteins that occurs during HD progression

Management History: Issues and Ideas for Teaching and Research

This review examines the study of management history and discusses its role in management education. Management history provides a theoretical baseline, a historical perspective, and aframework for building and integrating knowledge. After examining issues in teaching and research, future needs and directions for management history are indicated.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline