Density and viscosity of 1-butyl-3-methylimidazolium nitrate with ethanol, 1-propanol, or 1-butanol at several temperatures

Densities and viscosities of 1-butyl-3-methylimidazolium nitrate [Bmim][NO₃], and its binaries with alcohol (ethanol, 1-propanol, or 1-butanol) were measured at different temperatures. The densities and viscosities of pure ionic liquid were correlated successfully by empirical equations. The Vogel–Fulcher–Tammann equations can fit the experimental data of viscosities for pure IL. Excess molar volume and viscosity deviations were calculated for the binaries. The excess molar volumes have negative deviations from the ideal solution.     

Diffusion of the S isotope in soda-lime-silica and sodium trisilicate glass melts

The diffusivity of sulphur in nominal 10 Na₂O-16 CaO-74 SiO₂ (NCS) and 26 Na₂O-74 SiO₂ (NS3) melts was investigated in the temperature range 1273-1473 K using the ³⁵S radioactive isotope in a sandwich setup. Samples were sealed in platinum capsules and run with vertical alignment at 100 MPa confining pressure in an internally heated gas pressure vessel. Using the lowest diffusion coefficient D (m² s^− 1) for each temperature the Arrhenian relations logD = −(4.6 ± 0.3) − (216 ± 7) kJ mol^− 1/RT for NCS and logD = −(6.3 ± 0.6) − (167 ± 17) kJ mol^− 1/RT for NS3 were determined. Viscosity of the melts was used to test the applicability of the Stokes-Einstein (SE) and the Eyring (EY) equations to sulphur diffusion. The SE equation yields unrealistically low radii of the diffusing particles, a consequent of the non-molecular structure of the silicate melts. On the other hand, the Eyring relation yields reasonable jump distances of 550 pm (NCS) and 750 pm (NS3) by fitting the diffusion data to the EY equation. These large values imply that sulphate ions (ionic diameter = 290 pm) migrate as large entities through the silicate network.     

Vibration testing for anomaly detection

In this paper we propose an efficient method to reconstruct a small inclusion buried inside a body using the perturbation of modal parameters measured on the boundary of the body. We design a reconstruction algorithm based on the asymptotic expansions of the eigenvalue perturbations obtained by Ammari and Moskow (Math. Meth. Appl. Sci. 2003; 26 :67–75). We then implement this algorithm and demonstrate its viability and limitations. Copyright © 2008 John Wiley & Sons, Ltd.     

A Coupled System of Integrodifferential Equations Arising in Liquidity Risk Model

We study the mathematical aspects of the portfolio/consumption choice problem in a market model with liquidity risk introduced in (Pham and Tankov, Math. Finance, 2006, to appear). In this model, the investor can trade and observe stock prices only at exogenous Poisson arrival times. He may also consume continuously from his cash holdings, and his goal is to maximize his expected utility from consumption. This is a mixed discrete/continuous time stochastic control problem, nonstandard in the literature. We show how the dynamic programming principle leads to a coupled system of Integro-Differential Equations (IDE), and we prove an analytic characterization of this control problem by adapting the concept of viscosity solutions. This coupled system of IDE may be numerically solved by a decoupling algorithm, and this is the topic of a companion paper (Pham and Tankov, Math. Finance, 2006, to appear).     

Strong convergence of composite iterative methods for equilibrium problems and fixed point problems

We introduce a new composite iterative scheme by viscosity approximation method for finding a common point of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping. Our results substantially improve the corresponding results of Takahashi and Takahashi [A. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506-515]. Essentially a new approach for finding solutions of equilibrium problems and the fixed points of nonexpansive mappings is provided.     

Uniqueness results for nonlocal Hamilton-Jacobi equations

We are interested in nonlocal eikonal equations describing the evolution of interfaces moving with a nonlocal, non-monotone velocity. For these equations, only the existence of global-in-time weak solutions is available in some particular cases. In this paper, we propose a new approach for proving uniqueness of the solution when the front is expanding. This approach simplifies and extends existing results for dislocation dynamics. It also provides the first uniqueness result for a Fitzhugh-Nagumo system. The key ingredients are some new perimeter estimates for the evolving fronts as well as some uniform interior cone property for these fronts.     

Infinite horizon BSDEs with dissipative coefficients in Hilbert spaces and applications

In this paper we study a class of infinite horizon backward stochastic differential equations (BSDEs) of the form

     

A remark on regularity of 1D compressible isentropic Navier-Stokes equations with density-dependent viscosity

In this paper, we consider one-dimensional compressible isentropic Navier-Stokes equations with the viscosity depending on density and with the free boundary. The viscosity coefficient μ is proportional to ρθ with θ>0, where ρ is the density. The existence, uniqueness, regularity of global weak solutions in H¹([0,1]) have been established by Xin and Yao in [Z. Xin, Z. Yao, The existence, uniqueness and regularity for one-dimensional compressible Navier-Stokes equations, preprint]. Furthermore, under certain assumptions imposed on the initial data, we improve the regularity result obtained in [Z. Xin, Z. Yao, The existence, uniqueness and regularity for one-dimensional compressible Navier-Stokes equations, preprint] by driving some new a priori estimates.     

关于弱压缩算子的变分不等式解的粘滞逼近算法

在严格凸且具有一致Gâteaux可微范数的Banach空间$E$框架内, 该文借助于两种粘滞逼近算法去近似逼近关于弱压缩算子的变分不等式解并且也获得了相应的收敛率估计.     

Synthesis and properties of poly(bisphenol A acryloxyethyl phosphate) as a UV curable flame retardant oligomer

Poly(bisphenol A acryloxyethyl phosphate) (BPAAEP) being used for UV curable flame retardant coatings and adhesives, was synthesized from phosphorus oxychloride, hydroxylethyl acrylate and bisphenol A as raw materials, and characterized using ¹³C NMR, ³¹P NMR, FTIR, MS and GPC measurements. A series of formulations with different ratios of BPAAEP to urethane acrylate, EB220, were prepared to obtain flame retardant resins. The flame retardancy of the UV cured films was investigated by the limiting oxygen index (LOI). A synergistic effect between phosphorus and nitrogen was observed when 1.5 wt% phosphorus was presented in the resin. Their maximum photopolymerization rates and final unsaturation conversion (P^f) in the cured films at the presence of a 3 wt% photofragmenting initiator were investigated. The results showed that the P^f increased with increasing EB220 content photo-DSC analysis. The data from dynamic mechanical thermal analysis showed that BPAAEP has good miscibility with EB220. Moreover, the crosslink density and T_g of the cured film decreased along with the content of BPAAEP in the blend.