Thermodynamic properties and phase diagrams of spin-1 quantum Ising systems with three-spin interactions

The spin-1 quantum Ising systems with three-spin interactions on two-dimensional triangular lattices are studied by mean-field method. The thermal variations of order parameters and phase diagrams are investigated in detail. The stable, metastable and unstable branches of the order parameters are obtained. According to the stable conditions at critical point, we find that the systems exhibit tricritical points. With crystal field and biquadratic interactions, the system has rich phase diagrams with single reentrant or double reentrant phase transitions for appropriate ranges of the both parameters.Comment: 10 pages, 5 figure

Mixed principal eigenvalues in dimension one

This is one of a series of papers exploring the stability speed of one-dimensional stochastic processes. The present paper emphasizes on the principal eigenvalues of elliptic operators. The eigenvalue is just the best constant in the $L^{2}$-Poincar\'e inequality and describes the decay rate of the corresponding diffusion process. We present some variational formulas for the mixed principal eigenvalues of the operators. As applications of these formulas, we obtain case by case explicit estimates, a criterion for positivity, and an approximating procedure for the eigenvalue.Comment: 45 pages; Front. Math. China, 201

Computational Aspects of Optional P\'{o}lya Tree

Optional P\'{o}lya Tree (OPT) is a flexible non-parametric Bayesian model for density estimation. Despite its merits, the computation for OPT inference is challenging. In this paper we present time complexity analysis for OPT inference and propose two algorithmic improvements. The first improvement, named Limited-Lookahead Optional P\'{o}lya Tree (LL-OPT), aims at greatly accelerate the computation for OPT inference. The second improvement modifies the output of OPT or LL-OPT and produces a continuous piecewise linear density estimate. We demonstrate the performance of these two improvements using simulations

A single chemosensor for multiple analytes: fluorogenic and ratiometric absorbance detection of Zn²⁺, Mg²⁺ and F⁻, and its cell imaging

A simple coumarin based sensor 1 has been synthesized from the condensation reaction of 7-hydroxycoumarin and ethylenediamine via the intermediate 7-hydroxy-8-aldehyde-coumarin. As a multiple analysis sensor, 1 can monitor Zn²⁺ with the fluorescence enhanced at 457 nm, and ratiometric detection at 290 nm, 350 nm and 420 nm in DMF/H₂O (1/4, v/v) medium. Sensor 1 can also monitor Mg²⁺ with the fluorescence enhanced at 430 nm, and ratiometric detection at 290 nm, 370 nm and 430 nm in DMF medium through the interaction of chelation enhance fluorescence (CHEF) with metal ions. Furthermore, 1 also can monitor F⁻ with the fluorescence enhanced at 460 nm, and ratiometric detection at 290 nm and 390 nm in DMF medium simultaneously via hydrogen bonding and deprotonation with F− anion. Spectral titration, isothermal titration calorimetry and mass spectrometry revealed that the sensor formed a 1:1 complex with Mg²⁺, Zn²⁺ or F⁻, with stability constants of 4.5 × 10⁶, 3.4 × 10⁶, 8.0 × 10⁴ M⁻1 respectively. The complexation of the ions by 1 was an exothermic reaction driven by entropy processes. Furthermore, the sensor exhibits good membrane-permeability and was capable of monitoring at the intracellular Zn²⁺ level in living cells