Effective dynamics for a spin-1/2 particle constrained to a curved layer with inhomogeneous thickness

We derive an effective Hamiltonian for a spin-1/2 particle confined within a curved thin layer with non-uniform thickness using the confining potential approach.Our analysis reveals the presence of a pseudo-magnetic field and effective spin–orbit interaction(SOI)arising from the curvature,as well as an effective scalar potential resulting from variations in thickness.Importantly,we demonstrate that the physical effect of additional SOI from thickness fluctuations vanishes in low-dimensional systems,thus guaranteeing the robustness of spin interference measurements to thickness imperfection.Furthermore,we establish the applicability of the effective Hamiltonian in both symmetric and asymmetric confinement scenarios,which is crucial for its utilization in one-side etching systems.

The Mixed Spin-1/2 and Spin-1 Ising–Heisenberg Model in the Mean-Field Approximation: a New Approach

Thermodynamic properties of the mixed spin-1 and spin-1/2 Ising-Heisenberg model are studied on a honeycomb lattice using a new approach in the mean-field approximation to analyze the effects of longitudinal Dz and transverse Dx crystal fields. The phase diagrams are calculated in detail by studying the thermal variations of the order parameters, i.e., magnetizations and quadrupole moments, and compared with the literature to assess the reliability of the new approach. It is found that the model yields both second- and first-order phase transitions, and tricritical points. The compensation behavior of the model is also investigated for the sublattice magnetizations, and longitudinal and transverse quadrupolar moments. The latter type of compensation is observed in the literature but its possible importance is overlooked.

Effect of TS-1 Treatment by Mixed Alkaline on Propylene Epoxidation

Titanium silicate-1(TS-1) was treated with a mixed alkaline of tetrapropyl ammonium hydroxide(TPAOH) and NaOH. It was characterized by XRD, nitrogen physical adsorption, SEM, FT-IR, UV-Vis and ICPOES, and studied in propylene epoxidation. The mixed alkaline treatment with TPAOH/NaOH solution did not destroy the MFI structure of TS-1. With increasing NaOH concentrations, the relative crystallinity and the framework titanium decreased to some extent while the mesopore volume, mesopore diameter, and extra-framework titanium increased appreciably. When NaOH concentration was 0.0333 mol L^(-1), the best catalytic performance was obtained.

Error estimates of H^1-Galerkin mixed finite element method for Schrdinger equation

An H^1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition.

Nonlinear modes coupling of trapped spin-orbit coupled spin-1 Bose-Einstein condensates

We study analytically and numerically the nonlinear collective dynamics of quasi-one-dimensional spin-orbit coupled spin-1 Bose-Einstein condensates trapped in harmonic potential.The ground state of the system is determined by minimizing the Lagrange density,and the coupled equations of motions for the center-of-mass coordinate of the condensate and its width are derived.Then,two low energy excitation modes in breathing dynamics and dipole dynamics are obtained analytically,and the mechanism of exciting the anharmonic collective dynamics is revealed explicitly.The coupling among spin-orbit coupling,Raman coupling and spin-dependent interaction results in multiple external collective modes,which leads to the anharmonic collective dynamics.The cooperative effect of spin momentum locking and spin-dependent interaction results in coupling of dipolar and breathing dynamics,which strongly depends on spin-dependent interaction and behaves distinct characters in different phases.Interestingly,in the absence of spin-dependent interaction,the breathing dynamics is decoupled from spin dynamics and the breathing dynamics is harmonic.Our results provide theoretical evidence for deep understanding of the ground sate phase transition and the nonlinear collective dynamics of the system.

Highly efficient H^1-Galerkin mixed finite element method (MFEM) for parabolic integro-differential equation

A highly efficient H1-Galerkin mixed finite element method （MFEM） is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O（h^2） for both the original variable u in H1 （Ω） norm and the flux p = u in H（div, Ω） norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O（h^3） are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.

Ce_xTi_(1-x)O_2 Mixed Oxides Supported CuO Catalyst for NO Reduction by CO

Ce x Ti 1- x O 2 mixed oxides of different mole ratios ( x =0, 0.1, 0.2～0.9, 1.0) were prepared by co precipitation of TiCl 4 with Ce(NO 3) 3 and then loaded with different amounts of CuO. The effects of CuO on NO+CO reaction were investigated, and the structure and reductive properties of various CuO/Ce x Ti 1- x O 2 were characterized by the methodologies of BET, TPR and XRD. The results show that different Ce/Ti mole ratios and calcination temperatures induce changes of structure and reductive properties of the Ce x Ti 1- x O 2 mixed oxides. When x =0.1～0.5, amorphous CeTi 2O 6 phase mainly forms at 650 ℃ compared to the formation of CeTi 2O 6 which crystallizes at 800 ℃. When x >0.6, some TiO 2 enters the CeO 2 lattice and a CeO 2 TiO 2 solid solution is formed. The activity of 6%CuO/Ce x Ti 1- x O 2 calcined at 650 ℃ is largely affected by the x values, which is the highest when x =0.3, 0.4 and 0.9. The NO conversion reaches 70% at a reaction temperature of 150 ℃. By comparison, the x values have little effect on the activity of 6%CuO/Ce x Ti 1- x O 2 calcined at 800 ℃ . There are strong interactions between CuO and CeTi 2O 6, i.e., formation of the CeTi 2O 6 phase shifts the CuO reduction peak temperature from 380 to 200 ℃, and CuO, in turn, shifts the CeTi 2O 6 reduction peak temperature from 600 to 300 ℃.

An H^1-Galerkin Expanded Mixed Element Method for Semi-linear Hyperbolic Wave Equation

An H1-Galerkin expanded mixed finite element method is discussed for a class of second order semi-linear hyperbolic wave equations. By using the mixed formulation, we can get the optimal approximation for three variables: the scalar unknown, its gradient and its flux(coefficient times the gradient), simultaneously. We also prove the existence and uniqueness of semi-discrete solution. Finally, we obtain some numerical results to illustrate the efficiency of the method.

Phase diagrams in mixed spin-3/2 and spin-2 Ising system with two alternative layers within the effective-field theory

The phase diagrams in the mixed spin-3/2 and spin-2 Ising system with two alternative layers on a honeycomb lattice are investigated and discussed by the use of the effective-field theory with correlations. The interaction of the nearest-neighbour spins of each layer is taken to be positive （ferromagnetic interaction） and the interaction of the adjacent spins of the nearest-neighbour layers is considered to be either positive or negative （ferromagnetic or antiferromagnetic interaction）. The temperature dependence of the layer magnetizations of the system is examined to characterize the nature （continuous or discontinuous） of the phase transitions and obtain the phase transition temperatures. The system exhibits both second- and first-order phase transitions besides triple point （TP）, critical end point （E）, multicritical point （A）, isolated critical point （C） and reentrant behaviour depending on the interaction parameters. We have also studied the temperature dependence of the total magnetization to find the compensation points, as well as to determine the type of behaviour, and N-type behaviour in Neel classification nomenclature existing in the system. The phase diagrams are constructed in eight different planes and it is found that the system also presents the compensation phenomena depending on the sign of the bilinear exchange interactions.

Mixed L_1/H-infinity control for uncertain linear singular systems

The mixed L1/H-infinity control problem for a class of uncertain linear singular systems is considered using a matrix inequality approach. The purpose is to design a state feedback control law such that the resultant closed-loop system is regular, impulse-free, stable and satisfies some given mixed L1/H-infinity performance. A sufficient condition for the existence of such control law is given in terms of a set of matrix inequalities by the introduction of inescapable set and ＊-norm. When these matrix inequalities are feasible, an explicit expression of the desired state feedback control law is given. A numerical example is used to demonstrate the applicability of the proposed approach.

Approximation methods of mixed l_1/H_2 optimization problems for MIMO discrete-time systems

The mixed l1/H2 optimization problem for MIMO (multiple input-multiple output) discrete-time systems is considered. This problem is formulated as minimizing the l1-norm of a closed-loop transfer matrix while maintaining the H2-norm of another closed-loop transfer matrix at prescribed level. The continuity property of the optimal value in respect to changes in the H2-norm constraint is studied. The existence of the optimal solutions of mixed l1/H2 problem is proved. Because the solution of the mixed l1/H2 problem is based on the scaled-Q method, it avoids the zero interpolation difficulties. The convergent upper and lower bounds can be obtained by solving a sequence of finite dimensional nonlinear programming for which many efficient numerical optimization algorithms exist.

On the Dual of a Mixed H_2/l_1 Optimisation Problem

The general discrete-time Single-Input Single-Output （SISO） mixed H2/l1 control problem is considered in this paper. It is found that the existing results of duality theory cannot be directly applied to this infinite dimension optimisation problem. By means of two finite dimension approximate problems, to which duality theory can be applied, the dual of the mixed H2/l1 control problem is verified to be the limit of the duals of these two approximate problems.

Effect of Calcination Temperature on Structure and O_2 Desorption Properties of Ce_xPr_(1-x)O_(2-δ) Mixed Oxides

A series of CexPr1-xO2-δ (x=0, 0.5, 0.9, 1.0) mixed oxide calcined at different temperatures were synthesized by sol-gel method and characterized by Raman, XRD and O2-TPD techniques. When x=0.9, only a cubic phase CeO2 is observed. When x=0.5, the compound was combined by Pr6O11 and CeO2 mixed oxides. For CexPr1-xO2-δ (x=0.5, 0.9)samples 465 cm-1 Raman peak is attributed to the Raman active F2g mode of CeO2. The broad peak at about 570 cm-1 can be linked to lattice defects resulting in oxygen vacancies. The crystallite size of the samples increased as increasing the calcined temperature. But the increased value of Ce0.9Pr0.1O2-δ and Ce0.5Pr0.5O2-δ is smaller than single CeO2 and Pr6O11 obviously. It reveals that the insertion of Pr atom into the ceria lattice could enhance the sintering resistance and thermal stability of the mixed oxides. Calcination temperatures had great effect on the peak intensity for CeO2 but less effect on Ce0.8Pr0.2O2-δ in Raman spectra, and it may be caused by the colors transformation of the mixed oxides. The result of O2-TPD experiment indicates that the formation of solid solution has elevation the stabilization and thermal stability of the mixed oxides.

Syntheses of Coordination Compounds of (±)-2-Amino-3-(4-Hydroxyphenyl)Propionic Acid, Mixed Ligand Complexes and Their Biological Activities

Coordination compounds of (±)-2-amino-3-(4-hydroxyphenyl) propionic acid and their mixed ligand complexes with 1,10-phenantroline were synthesized, characterized using electronic and infrared spectral analyses and magnetic susceptibility. The compounds were evaluated for antimicrobial and antioxidant activities. Four different assays were applied for evaluating antioxidant capacity of the compounds. The results obtained indicated a diametric square planar geometry for both cobalt (±)-2-amino-3-(4-hydroxyphenyl) propionic acid complex and its mixed ligand complex. It was suggested that for the binary cobalt(II) complex, the phenolic substituent coordinated with neighbouring central metal ions. However, for the ternary cobalt(II) complex it was suggested it was deprotonated. Octahedral geometry was proposed for both copper complexes. Square planar geometry was indicated for the nickel?(±)-2-amino-3-(4-hydroxyphenyl) propionic acid complex and a mixture of square planar and octahedral geometry for the nickel mixed ligand complex. The cobalt mixed ligand complex elicited the highest activity for all the antioxidant assays. In most cases the binary complexes exhibited better antimicrobial activities relative to their ternary counterparts.

Nonconforming <i>H</i>¹-Galerkin Mixed Finite Element Method for Pseudo-Hyperbolic Equations

Based on H1-Galerkin mixed finite element method with nonconforming quasi-Wilson element, a numerical approximate scheme is established for pseudo-hyperbolic equations under arbitrary quadrilateral meshes. The corresponding optimal order error estimate is derived by the interpolation technique instead of the generalized elliptic projection which is necessary for classical error estimates of finite element analysis.

A mixed-cation lead iodide MA_(1-x)EA_xPbI_3 absorber for perovskite solar cells

The mixed-cation lead halide perovskites have emerged as a new class of promising light harvesting materials for solar cells. The formamidinium（FA）, methylammonium（MA） and Cs cations are widely studied in the field of mixed-cation perovskites. Here, we have investigated ethylammonium（EA） as an alternative cation to fabricate a mixed-cation perovskite of MA_（1-x）EA_xPbI_3. We have characterized the materials using the X-ray diffraction（XRD）, scanning electron microscope（SEM）, and UV–vis spectrum. Our results have confirmed the successful incorporation of EA cations into MAPbI_3. Interestingly, the optimal amount of EA to achieve the best performance is quite low. This is different from the FA–MA mixed-cation perovskites although EA and FA have similar radii. In short, the EA–MA mixed-cation perovskite has some material and device properties highly distinguishable from the FA–MA one.

Syntheses, Characterization and Biological Activity of Coordination Compounds of 3-Hydroxy-2-methyl-4<i>H</i>-pyran-4-one and Its Mixed Ligand Complexes with 1,2-Diaminocyclohexane

Coordination compounds of 3-hydroxy-2-methyl-4H-pyran-4-one with iron(III), cobat(III) and chromium(III) were synthesized with M:L (1:2). Mixed ligand coordination compounds of 3-hydroxy-2-methyl-4H-pyran-4-one and 1,2-diaminocyclohexane using the same metal ions were also synthesized M:L1:L2 (1:1:1) where L1 is 3-hydroxy-2-methyl-4H-pyran-4-one and L2 is 1,2-diaminocyclohexane. The coordination compounds obtained were characterized using electronic and infrared spectral analyses, magnetic susceptibility and percentage metal analysis. They were also evaluated for their cytotoxic and antioxidant activities. The result obtained suggested that octahedral geometry was obtained for all the compounds, as a result of additional two molecules of the solvent coordinated to the metal ions. Both the primary and secondary ligands coordinated in a bidentate fashion. The synthesized compounds exhibited moderate cytotoxicity, although none was as active as the standard. The cobalt(III) mixed ligand complex elicited the highest activity. The synthesized compounds all exhibited good to moderate antioxidant activity.

A SISO mixed H2／l1 optimal control problem and its solution

Study of the SISO mixed H2/l1 problem for discrete time systems showed that there exists a unique optimal solution which can be approximated within any prescribed missing error bound in l2 norm with solvable suboptimal solutions and solvable superoptimal solutions.

Effects of the Water in Mixed Solvent on the Epoxidation Reaction of Propylene with TS-1 Catalyst

The epoxidation reaction of propylene and hydrogen peroxide with zeolite catalyst containing titaniumsilicalite (TS-1)has been studied, and the reaction in the mixed solvent of water/methanol has been discussed. It is shown that the selective of epoxidation propylene decreases while the selective of propylene glycol increases, when the water content increases in the mixed solvent of methanol/water.

RIP1、MLKL蛋白在未分化甲状腺癌中的表达及临床意义

目的探讨受体相互作用蛋白激酶1(RIP1)、混合系激酶区域样蛋白(MLKL)在未分化甲状腺癌(ATC)中的表达及其临床意义。方法选取48例ATC患者为研究对象,检测手术标本组织中RIP1、MLKL的表达,收集患者临床病理参数并随访,统计分析RIP1、MLKL在ATC组织标本中的表达模式及对患者预后的影响。培养人未分化型甲状腺癌THJ-11T、THJ-16T、THJ-21T、ASH-3、BHT101细胞系、分化型甲状腺癌细胞系CAL-62、PDTC-1、正常人甲状腺细胞系Nthy-ori 3-1、HTORI-3,利用Western blot法及RT-PCR检测细胞系中RIP1、MLKL的蛋白mRNA的表达水平。结果(1)RT-PCR及Western blot检测显示,与正常人甲状腺细胞系及分化型甲状腺癌细胞系相比,未分化甲状腺癌细胞系中RIP1、MLKL蛋白和mRNA相对表达水平明显更高。(2)48例ATC患者中,14例起源于乳头状甲状腺癌(PTC),34例起源于滤泡状甲状腺癌(FTC)。肿瘤细胞表现出明显的多形性。形态学特征包括梭形细胞为主的肉瘤样及鳞状细胞样。(3)免疫组化染色显示,RIP1表达主要定位于ATC细胞膜。48例ATCs中有24例(50.0%)RIP1染色阳性。组织中含有混合岛状或低分化癌成分。MLKL阳性细胞核表达清晰,48例ATC患者中有29例(60.4%)患者MLKL染色阳性。(4)Kaplan-Meier生存分析显示,RIP1和MLKL过度表达会缩短ATC患者的无病生存期(DFS)(P<0.05),但对患者的总体生存率(OS)无明显影响(P>0.05)。Cox多因素分析显示,RIP1高表达、MLKL高表达、N分期、M分期均是影响ATC患者DFS的独立性危险因素(P<0.05)。结论RIP1、MLKL高表达与ATC的发生及DFS密切相关,或可作为ATC潜在的治疗靶点及预后预测的生物学标记物。