Quotient triangulated categories

For a self-orthogonal module $T$, the relation between the quotient triangulated category $D^b(A)/K^b({\rm add} T)$ and the stable category of the Frobenius category of $T$-Cohen-Macaulay modules is investigated. In particular, for a Gorenstein algebra, we get a relative version of the description of the singularity category due to Happel. Also, the derived category of a Gorenstein algebra is explicitly given, inside the stable category of the graded module category of the corresponding trivial extension algebra, via Happel's functor $F: D^b(A) \longrightarrow T(A)^{\mathbb{Z}}{-}\underline{\rm mod}$.Comment: 14 pages. Manu. Math., to appea

Subsystem Rényi Entropy of Thermal Ensembles for SYK-like models

The Sachdev-Ye-Kitaev model is an N-modes fermionic model with infinite range random interactions. In this work, we study the thermal Rényi entropy for a subsystem of the SYK model using the path-integral formalism in the large-N limit. The results are consistent with exact diagonalization [1] and can be well approximated by thermal entropy with an effective temperature [2] when subsystem size M ≤ N/2. We also consider generalizations of the SYK model with quadratic random hopping term or U(1) charge conservation

The Wiener and Terminal Wiener indices of trees

Heydari \cite{heydari2013} presented very nice formulae for the Wiener and terminal Wiener indices of generalized Bethe trees. It is pity that there are some errors for the formulae. In this paper, we correct these errors and characterize all trees with the minimum terminal Wiener index among all the trees of order $n$ and with maximum degree $\Delta$.Comment: 13 page

Amphiphilic blockers punch through a mutant CLC-0 pore.

Intracellularly applied amphiphilic molecules, such as p-chlorophenoxy acetate (CPA) and octanoate, block various pore-open mutants of CLC-0. The voltage-dependent block of a particular pore-open mutant, E166G, was found to be multiphasic. In symmetrical 140 mM Cl(-), the apparent affinity of the blocker in this mutant increased with a negative membrane potential but, paradoxically, decreased when the negative membrane potential was greater than -80 mV, a phenomenon similar to the blocker "punch-through" shown in many blocker studies of cation channels. To provide further evidence of the punch-through of CPA and octanoate, we studied the dissociation rate of the blocker from the pore by measuring the time constant of relief from the block under various voltage and ionic conditions. Consistent with the voltage dependence of the effect on the steady-state current, the rate of CPA dissociation from the E166G pore reached a minimum at -80 mV in symmetrical 140 mM Cl(-), and the direction of current recovery suggested that the bound CPA in the pore can dissociate into both intracellular and extracellular solutions. Moreover, the CPA dissociation depends upon the Cl(-) reversal potential with a minimal dissociation rate at a voltage 80 mV more negative than the Cl(-) reversal potential. That the shift of the CPA-dissociation rate follows the Cl(-) gradient across the membrane argues that these blockers can indeed punch through the channel pore. Furthermore, a minimal CPA-dissociation rate at a voltage 80 mV more negative than the Cl(-) reversal potential suggests that the outward blocker movement through the CLC-0 pore is more difficult than the inward movement