Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.     

Complete Moment Convergence for the Dependent Linear Processes with Random Coefficients

In this paper, we investigate the complete moment convergence for dependent linear processes with random coefficients to form     

差异化需求下考虑患者预约行为的医疗服务供需匹配方法

如何根据患者的差异化需求,撮合医生与患者双方形成合理有效的医疗服务供需匹配,是医疗服务运作管理中重要的研究问题。本文针对医疗服务中医生与患者的实际需求,提出了一种考虑患者预约行为的匹配决策方法。在该方法中,首先依据患者的预约行为及特征分类;然后,通过计算不同情形下医患双方的差异度,获得了医患双方的满意度矩阵;在此基础上,提出了匹配预约患者与医生的E-HR算法,并进一步构建了匹配剩余患者和医生的多目标优化模型,通过模型求解得到最优匹配结果;最后,通过算例说明了本文提出方法的可行性和实用性。     

Hybrid systems for oral delivery of a therapeutic neuropeptide

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Adsorption of Eu(III) on titanate nanotubes studied by a combination of batch and EXAFS technique

The effects of pH,contact time and natural organic ligands on radionuclide Eu(Ⅲ) adsorption and mechanism on titanate nanotubes(TNTs) are studied by a combination of batch and extended X-ray absorption fine structure(EXAFS) techniques.Macroscopic measurements show that the adsorption is ionic strength dependent at pH < 6.0,but ionic strength independent at pH > 6.0.The presence of humic acid(HA) /fulvic acid(FA) increases Eu(Ⅲ) adsorption on TNTs at low pH,but reduces Eu(Ⅲ) adsorption at high pH.The results of EXAFS analysis indicate that Eu(Ⅲ) adsorption on TNTs is dominated by outer-sphere surface complexation at pH < 6.0,whereas by inner-sphere surface complexation at pH > 6.0.At pH < 6.0,Eu(Ⅲ) consists of ～ 9 O atoms at REu?O ≈ 2.40  in the first coordination sphere,and a decrease in NEu-O with increasing pH indicates the introduction of more asymmetry in the first sphere of adsorbed Eu(Ⅲ).At long contact time or high pH values,the Eu(Ⅲ) consists of ～2 Eu at REu-Eu ≈ 3.60  and ～ 1 Ti at REu-Ti ≈ 4.40 ,indicating the formation of inner-sphere surface complexation,surface precipitation or surface polymers.Surface adsorbed HA/FA on TNTs modifies the species of adsorbed Eu(Ⅲ) as well as the local atomic structures of adsorbed Eu(Ⅲ) on HA/FA-TNT hybrids.Adsorbed Eu(Ⅲ) on HA/FA-TNT hybrids forms both ligand-bridging ternary surface complexes(Eu-HA/FA-TNTs) as well as surface complexes in which Eu(Ⅲ) remains directly bound to TNT surface hydroxyl groups(i.e.,binary Eu-TNTs or Eu-bridging ternary surface complexes(HA/FA-Eu-TNTs)).The findings in this work are important to describe Eu(Ⅲ) interaction with nanomaterials at molecular level and will help to improve the understanding of Eu(Ⅲ) physicochemical behavior in the natural environment.     

Encapsulation and Enhanced Luminescence Properties of IrIII Complexes within a Hexameric Self‐Assembled Capsule

Encapsulation and luminescence studies of [Ir(ppy)₂(bpy)]Cl (ppy=2‐phenylpyridinate, bpy=2,2′‐bipyridine) within a hexameric resorcinarene capsule are reported. One Ir^III complex cation was encapsulated within the capsule, as demonstrated by NMR and dynamic light scattering (DLS) studies. The emission color of the Ir^III complex was drastically changed from orange to yellow by encapsulation, in contrast with the lack of significant changes in the absorption spectrum. The hexameric capsule effectively hampers the non‐radiative pathway to increase both the luminescence quantum yield and the exited state lifetime. The luminescent properties of the encapsulated Ir^III complex depend on the ratio of Ir^III complex to the resorcinarene monomer as well as the concentration of resorcinarene monomer owing to the reversible process of self‐assembly of the hexameric capsule. Quenching experiments revealed that the Ir^III complex in the capsule was effectively separated from quenchers.     

Rate and Product Studies in the Solvolyses of Two Cyclic Phosphorochloridate Esters

Kinetic and product studies of the solvolyses of acyclic phosphorochloridates are extended to two cyclic diesters, 2-chloro-1,3,2-dioxaphospholane-2-oxide (1) and 2-chloro-5,5-dimethyl-1,3,2-dioxaphosphorinane-2-oxide (2). Slightly faster solvolyses are observed for 1 than for the acyclic dimethyl phosphorochloridate (3), and 2 solvolyzes somewhat slower than 3. An extended Grunwald–Winstein equation treatment shows similar sensitivities to changes in solvent nucleophilicity and solvent ionizing power for 1, 2, and 3, and a concerted S_N2 attack is proposed in each case. Product studies for the solvolyses of 2 in aqueous alcohols are presented.

     

AB CROSSLINKED POLYURETHANES THROUGH IONIC CROSSLINKING: INFLUENCE OF CROSSLINKING NETWORKS ON PHYSICO CHEMICAL PROPERTIES

Isocyanate-terminated prepolymers were synthesized using poly(tetramethylene oxide)glycol of molecular weight 1000 (PTMG₁₀₀₀) with tolylene-2,4-diisocyanate (TDI). The prepolymers were chain extended with N-methyldiethanolamine (N-MDEA) to form polyurethanes containing tertiary nitrogen. These polyurethanes were crosslinked with bromine terminated polyurethane, poly(urethane-imide), and poly(urethane-siloxane) through the formation of cationomers at tertiary nitrogen sites across the backbone polyurethanes.

The crosslinked cationomeric polyurethanes were characterized by Fourier Transform Infrared Spectroscopy (FTIR), Thermogravimetric Analysis (TGA), mechanical analyses, (static and dynamic), and static contact angles measurements. FTIR spectral studies confirms the formation of bromine terminated poly(urethane-imide) and poly(urethane-siloxane), as well as quaternization of the tertiary nitrogen which leads to crosslinking. A comparison of thermal stabilities of crosslinked polymers with respect to the chemical nature of bromine terminated prepolymers (BTP) indicates improved thermal stability for poly(urethane-imide) based ABCP. Stress-strain analysis shows high elongation values for poly(urethane-siloxane) and poly(urethane-imide) based ABCPs. Dynamic mechanical analysis reveals better damping for poly(urethane- siloxane) based AB crosslinked polymers.     

Calorimetric Estimation Employing the Unscented Kalman Filter for a Batch Emulsion Polymerization Reactor

Reaction calorimetry is a very useful tool to monitor exothermic polymerization reactions as it is based on the estimation of the heat generated by the reaction. The objective of this work is to analyze the performance of an unscented Kalman filter (UKF) for online monitoring of batch vinyl acetate emulsion polymerization reactions. Reactions are performed in isoperibolic and isothermal conditions. The UKF is compared to an extended Kalman filter that has a very poor performance. The results show that the UKF is able to provide good estimates for the conversion, for the reactor and jacket temperatures, for the overall heat transfer coefficient between the reaction medium and the jacket, and for the heat loss from the jacket to the surroundings.