Two-state-variable stochastic tree problems

This paper extends the one-state-variable stochastic tree problem to the two-state-variable case. (Considering, for example, a tree whose size and price evolve according to two different Wiener processes, we solve for the optimal cutting time. The optimization of the expected present discounted value of the tree is converted to a standard free-boundary problem. Analytical results are reported. In particular we find that more variance near the optimal free boundary will increase the value of the tree. Finally, a method is developed to find the numerical solution to the free boundary problem. A numerical example is presented.     

Mesoporous material grafted with luminescent molecules for the design of selective metal ion chemosensor

Luminescent Schiff-base groups have been successfully grafted on the surface of mesoporous material MCM-48. The grafted Schiff-base groups were employed to prepare luminescent Schiff-base-Zn complex that was covalently bound to the MCM-48 surface. These luminescent mesoporous materials were characterized with X-ray, UV-VIS and emission spectroscopic methods. Experimental results demonstrated that MCM-48 modified with functional groups exhibited novel luminescent property. The chemosensing property of modified MCM-48 sample was investigated. It was demonstrated that the fluorescence of MCM-48 solid with Schiff-base groups could be completely quenched by Cu²⁺ cation and this mesoporous material was suitable for sensing Cu²⁺ cation in aqueous media.     

Fast redox kinetics of a perovskite oxygen carrier measured using micro-fluidized bed thermogravimetric analysis

Redox kinetics of oxygen carrier in chemical looping combustion (CLC) is important for reactor design and its oxidation enthalpy is important in order to establish auto thermal demonstration. Most published redox kinetics of oxygen carrier has been measured by thermogravimetric analysis (TGA) which can include additional diffusion limitations and thus underestimate the overall kinetics. In this study, the redox kinetics of a new perovskite oxygen carrier (CaMn_0.375Ti_0.5Fe_0.125O_3-δ) was measured by a novel micro-fluidized bed thermogravimetric analysis (MFB-TGA) method which can achieve real-time weight measurement of oxygen carrier in a fluidizing state with similar mass and heat transfer characteristics as in a CLC reactor. The experimental data from MFB-TGA were analyzed with a reactor model. The redox kinetics was described by a two-stage model of gas-solid reaction. The effect of temperature, O₂ concentrations and reducing gas type (H₂ and CH₄) on the redox kinetics in MFB-TGA was investigated and compared with other oxygen carriers such as natural manganese ore and ilmenite. It is observed that the oxidation of both manganese ore and ilmenite can be divided into two stages, a fast initial stage followed by a second slower stage, resulting in slower total oxidation rates. A very interesting finding is that there is only the fast initial stage for the oxygen carrier of CaMn_0.375Ti_0.5Fe_0.125O_3-δ, and the full oxidation of CaMn_0.375Ti_0.5Fe_0.125O_3-δ can be finished within ～4 s which is ～7.5 and ～30 times faster than that of manganese ore and ilmenite. The reduction kinetics of CaMn_0.375Ti_0.5Fe_0.125O_3-δ by H₂ is also ～5 and ～2.2 times faster than that of manganese ore and ilmenite, respectively. The kinetic parameters of three oxygen carriers were compared and the redox mechanism of CaMn_0.375Ti_0.5Fe_0.125O_3-δ was discussed.     

A theoretical kinetics study on low-temperature oxidation of n-C4H9 radicals

The low-temperature oxidation mechanism of n?butyl radicals (n-C₄H₉) has been investigated by high level quantum chemical calculations coupled with the Rice–Ramsperger–Kassel–Marcus/Master Equation (RRKM/ME) theory. The potential energy surfaces (PES) were explored at the QCISD(T)/CBS//B3LYP/6-311++G(d,p) level. The temperature- and pressure-dependent rate constants were computed and fitted in modified Arrhenius parameters. The major reaction channels were discussed to more deeply understand the competing relationships between chain branching, chain propagation and termination reactions. The results show that the 1,5 H-shift reaction is more competitive than the 1,6 H-shift and 1,4 H-shift for isomerization reactions of n?butyl peroxy radicals, and the concerted HO₂ elimination channel to form butene becomes more important at high temperatures. Furthermore, based on our calculations, a revised kinetic model was developed to describe n-butane oxidation. Good consistency between model predictions and experimental data was shown. This study enhances our understanding of the combustion mechanism of n-butane and can be used as a reliable reference for mechanistic understanding of larger alkanes.     

Exact Recovery of Stochastic Block Model by Ising Model

In this paper, we study the phase transition property of an Ising model defined on a special random graph—the stochastic block model (SBM). Based on the Ising model, we propose a stochastic estimator to achieve the exact recovery for the SBM. The stochastic algorithm can be transformed into an optimization problem, which includes the special case of maximum likelihood and maximum modularity. Additionally, we give an unbiased convergent estimator for the model parameters of the SBM, which can be computed in constant time. Finally, we use metropolis sampling to realize the stochastic estimator and verify the phase transition phenomenon thfough experiments.     

Coherence and Quantum Phase Transition in Spin Models

Based on quantum renormalization group (QRG) method, we investigated quantum coherence and quantum phase transition (QPT) in XXZ chain and XY chain, respectively. The results show that both the geometric quantum coherence and entropic coherecne can accurately indicate the QPT at critical point after enough iteration steps. Moreover, the increasing anisotropy parameter destroys the coherence in the XXZ chain, while enhances it in the XY chain. In addition, focused on the XXZ chain we analyzed the nonanalytic phenomena and scaling behaviors with different theoretical exponents in detail.

     

Complementary relation between quantum entanglement and entropic uncertainty

Quantum entanglement is regarded as one of the core concepts,which is used to describe the nonclassical correlation between subsystems,and entropic uncertainty relation plays a vital role in quantum precision measurement.It is well known that entanglement of formation can be expressed by von Neumann entropy of subsystems for arbitrary pure states.An interesting question is naturally raised:is there any intrinsic correlation between the entropic uncertainty relation and quantum entanglement?Or if the relation can be applied to estimate the entanglement.In this work,we focus on exploring the complementary relation between quantum entanglement and the entropic uncertainty relation.The results show that there exists an inequality relation between both of them for an arbitrary two-qubit system,and specifically the larger uncertainty will induce the weaker entanglement of the probed system,and vice versa.Besides,we use randomly generated states as illustrations to verify our results.Therefore,we claim that our observations might offer and support the validity of using the entropy uncertainty relation to estimate quantum entanglement.     

Exploratory Purification of Compounds from Aqueous Extracts of <Emphasis Type="Italic">Pinus massoniana</Emphasis> Lamb. by Two-Dimensional Preparative Liquid Chromatography

An off-line orthogonal two-dimensional preparative liquid chromatography method was developed for isolation of high-purity compounds from aqueous extracts of Pinus massoniana Lamb., which has efficient therapeutic properties in recipes of traditional Chinese medicines. A polar-enhanced reversed-phase (RP) column, XAqua C18 was selected for the first-dimensional separation. A HILIC column and a hydrophobic RP column were both explored in the second dimension. The preparation results indicated hydrophilic RP × HILIC mode would provide better separation efficiency for polar complexes, i.e., the second-dimensional separation was finished in less than 30 min and high-purity compounds were obtained. In this work, 16 fractions were collected efficiently in the first dimension with a recovery up to 96%, and six compounds with high purity and enough quantity were identified by NMR and high resolution mass spectrometry, including epicatechin, betuloside, taxifolin-3-O-xyloside, cedrusin-4-O-glucoside, massonianoside C and massonianoside D, and five are glycosides, including flavonoid glycosides, lignanoid glycosides and an arylbutanoid glycoside. Betuloside was first reported in the preparation of Pinus massoniana Lamb. This work demonstrated a flexible strategy of compromise in between time and resolution for selecting solvent and column to enhance preparative efficiency of polar complex systems.     

Magnetic Solid-Phase Extraction and Ionic Liquid Dispersive Liquid–Liquid Microextraction Coupled with High-Performance Liquid Chromatography for the Determination of Hexachlorophene in Cosmetics

An efficient, simple, and fast method based on ionic liquid dispersive liquid–liquid microextraction (IL-DLLME) followed by magnetic solid-phase extraction (MSPE) was developed as a new technique for extracting and purifying hexachlorophene (HCP) in cosmetics prior to high-performance liquid chromatography (HPLC) determination. In this method based on IL-DLLME and MSPE, 1-hexyl-3-methylimidazolium hexafluorophosphate ([C₆MIM][PF₆]) is used as the extraction solvent and Fe₃O₄ nanoparticles are used to remove hydrophobic additives in the cosmetics by physical adsorption. The main parameters affecting the efficiency of the IL-DLLME and MSPE of HCP were investigated and optimized. Under the optimum conditions, the method was linear in the range 0.5–40 µg mL^?1 with a correlation coefficient (R ²) of 0.9976 and had a detection limit of 0.14 µg mL^?1 at a signal-to-noise ratio (S/N) of 3. The recoveries of HCP in three cosmetic samples using the proposed method were in the range 74.5–97.7%, and the relative standard deviations (RSD, n = 5) were in the range 3.8–6.7%. The developed method was successfully applied to the determination of HCP in cosmetics.