Fuzzy automata as coalgebras

The coalgebraic method is of great significance to research in process algebra, modal logic, object-oriented design and component-based software engineering. In recent years, fuzzy control has been widely used in many fields, such as handwriting recognition and the control of robots or air conditioners. It is then an interesting topic to analyze the behavior of fuzzy automata from a coalgebraic point of view. This paper models different types of fuzzy automata as coalgebras with a monad structure capturing fuzzy behavior. Based on the coalgebraic models, we can define a notion of fuzzy language and consider several versions of bisimulation for fuzzy automata. A group of combinators is defined to compose fuzzy automata of two branches: state transition and output function. A case study illustrates the coalgebraic models proposed and their composition.This work has been supported by the Guangdong Science and Technology Department (Grant No. 2018B010107004) and the National Natural Science Foundation of China under grant No. 61772038, 61532019 and 61272160. L.S.B. was supported by the ERDF—European Regional Development Fund through the Operational Programme for Competitiveness and InternationalisationCOMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT, within project KLEE - POCI-01-0145-FEDER-030947

Current-induced Spin Polarization in Two-Dimensional Hole Gas

We investigate the current-induced spin polarization in the two-dimensional hole gas (2DHG) with the structure inversion asymmetry. By using the perturbation theory, we re-derive the effective $k$-cubic Rashba Hamiltonian for 2DHG and the generalized spin operators accordingly. Then based on the linear response theory we calculate the current-induced spin polarization both analytically and numerically with the disorder effect considered. We have found that, quite different from the two-dimensional electron gas, the spin polarization in 2DHG depends linearly on Fermi energy in the low doping regime, and with increasing Fermi energy, the spin polarization may be suppressed and even changes its sign. We predict a pronounced peak of the spin polarization in 2DHG once the Fermi level is somewhere between minimum points of two spin-split branches of the lowest light-hole subband. We discuss the possibility of measurements in experiments as regards the temperature and the width of quantum wells.Comment: 13 pages, 8 figures, submitted to PR

Irreducible Characters of General Linear Superalgebra and Super Duality

We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating the problem to the classical Kazhdan-Lusztig theory. We further verify a parabolic version of a conjecture of Brundan on the irreducible characters in the BGG category \mc{O} of the general linear superalgebra. We also prove the super duality conjecture

Spin-glass ground state in a triangular-lattice compound YbZnGaO4_4

We report on comprehensive results identifying the ground state of a triangular-lattice structured YbZnGaO$_4$ to be spin glass, including no long-range magnetic order, prominent broad excitation continua, and absence of magnetic thermal conductivity. More crucially, from the ultralow-temperature a.c. susceptibility measurements, we unambiguously observe frequency-dependent peaks around 0.1 K, indicating the spin-glass ground state. We suggest this conclusion to hold also for its sister compound YbMgGaO$_4$, which is confirmed by the observation of spin freezing at low temperatures. We consider disorder and frustration to be the main driving force for the spin-glass phase.Comment: Version as accepted to PR

Interfacial Tensions near Critical Endpoints: Experimental Checks of EdGF Theory

Predictions of the extended de Gennes-Fisher local-functional theory for the universal scaling functions of interfacial tensions near critical endpoints are compared with experimental data. Various observations of the binary mixture isobutyric acid $+$ water are correlated to facilitate an analysis of the experiments of Nagarajan, Webb and Widom who observed the vapor-liquid interfacial tension as a function of {\it both} temperature and density. Antonow's rule is confirmed and, with the aid of previously studied {\it universal amplitude ratios}, the crucial analytic ``background'' contribution to the surface tension near the endpoint is estimated. The residual singular behavior thus uncovered is consistent with the theoretical scaling predictions and confirms the expected lack of symmetry in $(T-T_c)$. A searching test of theory, however, demands more precise and extensive experiments; furthermore, the analysis highlights, a previously noted but surprising, three-fold discrepancy in the magnitude of the surface tension of isobutyric acid $+$ water relative to other systems.Comment: 6 figure

Nuclear Stopping as A Probe to In-medium Nucleon-nucleon Cross Section in Intermediate Energy Heavy Ion Collisions

Using an isospin-dependent quantum molecular dynamics, nuclear stopping in intermediate heavy ion collisions has been studied. The calculation has been done for colliding systems with different neutron-proton ratios in beam energy ranging from 15MeV/u to 150MeV/u. It is found that, in the energy region from above Fermi energy to 150MeV/u, nuclear stopping is very sensitive to the isospin dependence of in-medium nucleon-nucleon cross section, but insensitive to symmetry potential. From this investigation, we propose that nuclear stopping can be used as a new probe to extract the information on the isospin dependence of in-medium nucleon-nucleon cross section in intermediate energy heavy ion collisions